Using fuzzy arithmetic in containment event trees
Rivera, S.S.; Baron, Jorge H.
2000-01-01
The use of fuzzy arithmetic is proposed for the evaluation of containment event trees. Concepts such as improbable, very improbable, and so on, which are subjective by nature, are represented by fuzzy numbers. The quantitative evaluation of containment event trees is based on the extension principle, by which operations on real numbers are extended to operations on fuzzy numbers. Expert knowledge is considered as state of the base variable with a normal distribution, which is considered to represent the membership function. Finally, this paper presents results of an example calculation of a containment event tree for the CAREM-25 nuclear power plant, presently under detailed design stage at Argentina. (author)
Fuzzy Logic and Arithmetical Hierarchy III
Hájek, Petr
2001-01-01
Roč. 68, č. 1 (2001), s. 129-142 ISSN 0039-3215 R&D Projects: GA AV ČR IAA1030004 Institutional research plan: AV0Z1030915 Keywords : fuzzy logic * basic fuzzy logic * Lukasiewicz logic * Godel logic * product logic * arithmetical hierarchy Subject RIV: BA - General Mathematics
Assessing flood forecast uncertainty with fuzzy arithmetic
de Bruyn Bertrand
2016-01-01
Full Text Available Providing forecasts for flow rates and water levels during floods have to be associated with uncertainty estimates. The forecast sources of uncertainty are plural. For hydrological forecasts (rainfall-runoff performed using a deterministic hydrological model with basic physics, two main sources can be identified. The first obvious source is the forcing data: rainfall forecast data are supplied in real time by meteorological forecasting services to the Flood Forecasting Service within a range between a lowest and a highest predicted discharge. These two values define an uncertainty interval for the rainfall variable provided on a given watershed. The second source of uncertainty is related to the complexity of the modeled system (the catchment impacted by the hydro-meteorological phenomenon, the number of variables that may describe the problem and their spatial and time variability. The model simplifies the system by reducing the number of variables to a few parameters. Thus it contains an intrinsic uncertainty. This model uncertainty is assessed by comparing simulated and observed rates for a large number of hydro-meteorological events. We propose a method based on fuzzy arithmetic to estimate the possible range of flow rates (and levels of water making a forecast based on possible rainfalls provided by forcing and uncertainty model. The model uncertainty is here expressed as a range of possible values. Both rainfall and model uncertainties are combined with fuzzy arithmetic. This method allows to evaluate the prediction uncertainty range. The Flood Forecasting Service of Oise and Aisne rivers, in particular, monitors the upstream watershed of the Oise at Hirson. This watershed’s area is 310 km2. Its response time is about 10 hours. Several hydrological models are calibrated for flood forecasting in this watershed and use the rainfall forecast. This method presents the advantage to be easily implemented. Moreover, it permits to be carried out
Modelling arithmetic operations
Shabanov-kushnarenk, Yu P
1981-01-01
The possibility of modelling finite alphabetic operators using formal intelligence theory, is explored, with the setting up of models of a 3-digit adder and a multidigit subtractor, as examples. 2 references.
Lucimar M.F. de Carvalho
2008-06-01
Full Text Available OBJECTIVE: To investigate different fuzzy arithmetical operations to support in the diagnostic of epileptic events and non epileptic events. METHOD: A neuro-fuzzy system was developed using the NEFCLASS (NEuro Fuzzy CLASSIfication architecture and an artificial neural network with backpropagation learning algorithm (ANNB. RESULTS: The study was composed by 244 patients with a bigger frequency of the feminine sex. The number of right decisions at the test phase, obtained by the NEFCLASS and ANNB was 83.60% and 90.16%, respectively. The best sensibility result was attained by NEFCLASS (84.90%; the best specificity result were attained by ANNB with 95.65%. CONCLUSION: The proposed neuro-fuzzy system combined the artificial neural network capabilities in the pattern classifications together with the fuzzy logic qualitative approach, leading to a bigger rate of system success.OBJETIVO: Investigar diferentes operações aritméticas difusas para auxíliar no diagnóstico de eventos epilépticos e eventos não-epilépticos. MÉTODO: Um sistema neuro-difuso foi desenvolvido utilizando a arquitetura NEFCLASS (NEuro Fuzzy CLASSIfication e uma rede neural artificial com o algoritmo de aprendizagem backpropagation (RNAB. RESULTADOS: A amostra estudada foi de 244 pacientes com maior freqüência no sexo feminino. O número de decisões corretas na fase de teste, obtidas através do NEFCLASS e RNAB foi de 83,60% e 90,16%, respectivamente. O melhor resultado de sensibilidade foi obtido com o NEFCLASS (84,90%; o melhor resultado de especificidade foi obtido com a RNAB (95,65%. CONCLUSÃO: O sistema neuro-difuso proposto combinou a capacidade das redes neurais artificiais na classificação de padrões juntamente com a abordagem qualitativa da logica difusa, levando a maior taxa de acertos do sistema.
Operator Arithmetic-Harmonic Mean Inequality on Krein Spaces
M. Dehghani
2014-03-01
Full Text Available We prove an operator arithmetic-harmonic mean type inequality in Krein space setting, by using some block matrix techniques of indefinite type. We also give an example which shows that the operator arithmetic-geometric-harmonic mean inequality for two invertible selfadjoint operators on Krein spaces is not valid, in general.
T. Pathinathan
2015-01-01
Full Text Available In this paper we define diamond fuzzy number with the help of triangular fuzzy number. We include basic arithmetic operations like addition, subtraction of diamond fuzzy numbers with examples. We define diamond fuzzy matrix with some matrix properties. We have defined Nested diamond fuzzy number and Linked diamond fuzzy number. We have further classified Right Linked Diamond Fuzzy number and Left Linked Diamond Fuzzy number. Finally we have verified the arithmetic operations for the above mentioned types of Diamond Fuzzy Numbers.
On Arithmetic in the Cantor-Lukasiewicz Fuzzy Set Theory
Hájek, Petr
2005-01-01
Roč. 44, č. 6 (2005), s. 763-782 ISSN 1432-0665 R&D Projects: GA AV ČR IAA1030004 Institutional research plan: CEZ:AV0Z10300504 Keywords : Lukasiewicz logic * fuzzy set theory * contradiction Subject RIV: BA - General Mathematics Impact factor: 0.490, year: 2005
Uncertainty analysis for dynamic properties of MEMS resonator supported by fuzzy arithmetics
A Martowicz
2016-04-01
Full Text Available In the paper the application of uncertainty analysis performed formicroelectromechanical resonator is presented. Main objective ofundertaken analysis is to assess the propagation of considered uncertaintiesin the variation of chosen dynamic characteristics of Finite Element model ofmicroresonator. Many different model parameters have been assumed tobe uncertain: geometry and material properties. Apart from total uncertaintypropagation, sensitivity analysis has been carried out to study separateinfluences of all input uncertain characteristics. Uncertainty analysis has beenperformed by means of fuzzy arithmetics in which alpha-cut strategy hasbeen applied to assemble output fuzzy number. Monte Carlo Simulation andGenetic Algorithms have been employed to calculate intervals connectedwith each alpha-cut of searched fuzzy number. Elaborated model ofmicroresonator has taken into account in a simplified way the presence ofsurrounding air and constant electrostatic field.
Denise Margareth Kazue Nishimura Kunitaki
2008-01-01
Full Text Available The “torpedo” pile is a foundation system that has been recently considered to anchor mooring lines and risers of floating production systems for offshore oil exploitation. The pile is installed in a free fall operation from a vessel. However, the soil parameters involved in the penetration model of the torpedo pile contain uncertainties that can affect the precision of analysis methods to evaluate its final penetration depth. Therefore, this paper deals with methodologies for the assessment of the sensitivity of the response to the variation of the uncertain parameters and mainly to incorporate into the analysis method techniques for the formal treatment of the uncertainties. Probabilistic and “possibilistic” approaches are considered, involving, respectively, the Monte Carlo method (MC and concepts of fuzzy arithmetic (FA. The results and performance of both approaches are compared, stressing the ability of the latter approach to efficiently deal with the uncertainties of the model, with outstanding computational efficiency, and therefore, to comprise an effective design tool.
Frechet differentiation of nonlinear operators between fuzzy normed spaces
Yilmaz, Yilmaz
2009-01-01
By the rapid advances in linear theory of fuzzy normed spaces and fuzzy bounded linear operators it is natural idea to set and improve its nonlinear peer. We aimed in this work to realize this idea by introducing fuzzy Frechet derivative based on the fuzzy norm definition in Bag and Samanta [Bag T, Samanta SK. Finite dimensional fuzzy normed linear spaces. J Fuzzy Math 2003;11(3):687-705]. The definition is divided into two part as strong and weak fuzzy Frechet derivative so that it is compatible with strong and weak fuzzy continuity of operators. Also we restate fuzzy compact operator definition of Lael and Nouroizi [Lael F, Nouroizi K. Fuzzy compact linear operators. Chaos, Solitons and Fractals 2007;34(5):1584-89] as strongly and weakly fuzzy compact by taking into account the compatibility. We prove also that weak Frechet derivative of a nonlinear weakly fuzzy compact operator is also weakly fuzzy compact.
Relative aggregation operator in database fuzzy querying
Luminita DUMITRIU
2005-12-01
Full Text Available Fuzzy selection criteria querying relational databases include vague terms; they usually refer linguistic values form the attribute linguistic domains, defined as fuzzy sets. Generally, when a vague query is processed, the definitions of vague terms must already exist in a knowledge base. But there are also cases when vague terms must be dynamically defined, when a particular operation is used to aggregate simple criteria in a complex selection. The paper presents a new aggregation operator and the corresponding algorithm to evaluate the fuzzy query.
Fehr, Thorsten; Code, Chris; Herrmann, Manfred
2007-10-03
The issue of how and where arithmetic operations are represented in the brain has been addressed in numerous studies. Lesion studies suggest that a network of different brain areas are involved in mental calculation. Neuroimaging studies have reported inferior parietal and lateral frontal activations during mental arithmetic using tasks of different complexities and using different operators (addition, subtraction, etc.). Indeed, it has been difficult to compare brain activation across studies because of the variety of different operators and different presentation modalities used. The present experiment examined fMRI-BOLD activity in participants during calculation tasks entailing different arithmetic operations -- addition, subtraction, multiplication and division -- of different complexities. Functional imaging data revealed a common activation pattern comprising right precuneus, left and right middle and superior frontal regions during all arithmetic operations. All other regional activations were operation specific and distributed in prominently frontal, parietal and central regions when contrasting complex and simple calculation tasks. The present results largely confirm former studies suggesting that activation patterns due to mental arithmetic appear to reflect a basic anatomical substrate of working memory, numerical knowledge and processing based on finger counting, and derived from a network originally related to finger movement. We emphasize that in mental arithmetic research different arithmetic operations should always be examined and discussed independently of each other in order to avoid invalid generalizations on arithmetics and involved brain areas.
Fuzzy Logic vs. Neutrosophic Logic: Operations Logic
Salah Bouzina
2016-12-01
Full Text Available The goal of this research is first to show how different, thorough, widespread and effective are the operations logic of the neutrosophic logic compared to the fuzzy logic’s operations logical. The second aim is to observe how a fully new logic, the neutrosophic logic, is established starting by changing the previous logical perspective fuzzy logic, and by changing that, we mean changing changing the truth values from the truth and falsity degrees membership in fuzzy logic, to the truth, falsity and indeterminacy degrees membership in neutrosophic logic; and thirdly, to observe that there is no limit to the logical discoveries - we only change the principle, then the system changes completely.
Operational budgeting using fuzzy goal programming
Saeed Mohammadi
2013-10-01
Full Text Available Having an efficient budget normally has different advantages such as measuring the performance of various organizations, setting appropriate targets and promoting managers based on their achievements. However, any budgeting planning requires prediction of different cost components. There are various methods for budgeting planning such as incremental budgeting, program budgeting, zero based budgeting and performance budgeting. In this paper, we present a fuzzy goal programming to estimate operational budget. The proposed model uses fuzzy triangular as well as interval number to estimate budgeting expenses. The proposed study of this paper is implemented for a real-world case study in province of Qom, Iran and the results are analyzed.
The Dirac operator on the Fuzzy sphere
Grosse, H.
1994-01-01
We introduce the Fuzzy analog of spinor bundles over the sphere on which the non-commutative analog of the Dirac operator acts. We construct the complete set of eigenstates including zero modes. In the commutative limit we recover known results. (authors)
Wong, Terry Tin-Yau
2017-12-01
The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.
Operational budgeting using fuzzy goal programming
Saeed Mohammadi; Kamran Feizi; Ali Khatami Firouz Abadi
2013-01-01
Having an efficient budget normally has different advantages such as measuring the performance of various organizations, setting appropriate targets and promoting managers based on their achievements. However, any budgeting planning requires prediction of different cost components. There are various methods for budgeting planning such as incremental budgeting, program budgeting, zero based budgeting and performance budgeting. In this paper, we present a fuzzy goal programming to estimate oper...
Mohsen Omidvar
2015-12-01
Full Text Available Background & objective: Due to the features such as intuitive graphical appearance, ease of perception and straightforward applicability, risk matrix has become as one of the most used risk assessment tools. On the other hand, features such as the lack of precision in the classification of risk index, as well as subjective computational process, has limited its use. In order to solve this problem, in the current study we used fuzzy logic inference systems and mathematical operators (interval numbers and mapping operator. Methods: In this study, first 10 risk scenarios in the excavation and piping process were selected, then the outcome of the risk assessment were studied using four types of matrix including traditional (ORM, displaced cells (RCM , extended (ERM and fuzzy (FRM risk matrixes. Results: The results showed that the use of FRM and ERM matrix have prority, due to the high level of " Risk Tie Density" (RTD and "Risk Level Density" (RLD in the ORM and RCM matrix, as well as more accurate results presented in FRM and ERM, in risk assessment. While, FRM matrix provides more reliable results due to the application of fuzzy membership functions. Conclusion: Using new mathematical issues such as fuzzy sets and arithmetic and mapping operators for risk assessment could improve the accuracy of risk matrix and increase the reliability of the risk assessment results, when the accurate data are not available, or its data are avaliable in a limit range.
Numeral words and arithmetic operations in the Alor-Pantar languages
Schapper, Antoinette; Holton, Gary; Klamer, Marian; Kratochvíl, František; Robinson, Laura; Klamer, Marian
2014-01-01
The indigenous numerals of the AP languages, as well as the indigenous structures for arithmetic operations are currently under pressure from Indonesian, and will inevitably be replaced with Indonesian forms and structures. This chapter presents a documentary record of the forms and patterns
Alternative proposal of arithmetic and image operations in optical parallel computation
Ghosh, Partha; Das, Partha P.; Mukhopadhay, Sourangshu
2001-10-01
Here, we refer our new proposal of applying multi-valued logic (particularly tristate logic) to develop logic gates and systems for arithmetic operation. Space-variant approach is used here to implement the functioning. Also triple input image detection is done here.
Fuzzy Genetic Algorithm Based on Principal Operation and Inequity Degree
Li, Fachao; Jin, Chenxia
In this paper, starting from the structure of fuzzy information, by distinguishing principal indexes and assistant indexes, give comparison of fuzzy information on synthesizing effect and operation of fuzzy optimization on principal indexes transformation, further, propose axiom system of fuzzy inequity degree from essence of constraint, and give an instructive metric method; Then, combining genetic algorithm, give fuzzy optimization methods based on principal operation and inequity degree (denoted by BPO&ID-FGA, for short); Finally, consider its convergence using Markov chain theory and analyze its performance through an example. All these indicate, BPO&ID-FGA can not only effectively merge decision consciousness into the optimization process, but possess better global convergence, so it can be applied to many fuzzy optimization problems.
Laleh Hooshangian
2014-07-01
Full Text Available In this paper, fuzzy nth-order derivative for n in N is introduced. To do this, nth-order derivation under generalized Hukuhara derivative here in discussed. Calculations on the fuzzy nth-order derivative on fuzzy functions and their relationships, in general, are introduced. Then, the fuzzy nth-order differential equations is solved, for n in N.
Useless brackets in arithmetic expressions with mixed operations
Gunnarsson, Robert; Hernell, Bernt; Sönnerhed, Wang Wei
2012-01-01
There can be different intentions with brackets in mathematical expressions. It has previously been suggested that mathematically useless brackets can be educationally useful when learning the order of operations in expressions with mixed operations. This paper reports how students (12-13 years) deal with the implicit mental conflict between brackets as a necessary part of the order of operations and brackets to emphasize precedence. The students taking part in this quasi-experimental study w...
Application of fuzzy logic operation and control to BWRs
Junichi Tanji; Mitsuo Kinoshita; Takaharu Fukuzaki; Yasuhiro Kobayashi
1993-01-01
Fuzzy logic control schemes employing linguistic decision rules for flexible operator control strategies have undergone application tests in dynamic systems. The advantages claimed for fuzzy logic control are its abilities: (a) to facilitate direct use of skillful operator know-how for automatic operation and control of the systems and (b) to provide robust multivariable control for complex plants. The authors have also studied applications of fuzzy logic control to automatic startup operations and load-following control in boiling water reactors, pursuing these same advantages
FFLP problem with symmetric trapezoidal fuzzy numbers
Reza Daneshrad
2015-04-01
Full Text Available The most popular approach for solving fully fuzzy linear programming (FFLP problems is to convert them into the corresponding deterministic linear programs. Khan et al. (2013 [Khan, I. U., Ahmad, T., & Maan, N. (2013. A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2, 536-546.] claimed that there had been no method in the literature to find the fuzzy optimal solution of a FFLP problem without converting it into crisp linear programming problem, and proposed a technique for the same. Others showed that the fuzzy arithmetic operation used by Khan et al. (2013 had some problems in subtraction and division operations, which could lead to misleading results. Recently, Ezzati et al. (2014 [Ezzati, R., Khorram, E., & Enayati, R. (2014. A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions. Journal of Intelligent and Fuzzy Systems, 26(5, 2333-2358.] defined a new operation on symmetric trapezoidal fuzzy numbers and proposed a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multi-objective linear programming problem by using new fuzzy arithmetic operations, but their model was not fully fuzzy optimization. In this paper, a new method, by using Ezzati et al. (2014’s fuzzy arithmetic operation and a fuzzy version of simplex algorithm, is proposed for solving FFLP problem whose parameters are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method, the fuzzy optimal solution of FFLP problem can be easily obtained. A numerical example is provided to illustrate the proposed method.
Mathieu, Romain; Epinat-Duclos, Justine; Sigovan, Monica; Breton, Audrey; Cheylus, Anne; Fayol, Michel; Thevenot, Catherine; Prado, Jérôme
2018-05-01
Do mathematical symbols evoke spatial representations? Although behavioral studies have long demonstrated interactions between space and the processing of Arabic digits, how to interpret these results remains controversial. Here, we tested whether activity in regions supporting spatial processing contributes to the processing of symbols conveying fundamental arithmetic concepts-such as operation signs-even in the absence of associated digits. Using functional magnetic resonance imaging, we show that merely perceiving a "+" sign triggers activity in brain regions that support the orienting of spatial attention in adults. Activity in these regions was greater for "+" than for "×" signs, indicating that it is modulated by whether an operator reflects an operation that evokes numerical manipulation (rather than rote memorization). Finally, the degree to which subjects activated a spatial region in response to a "+" sign was correlated with the degree to which subjects benefited from being briefly presented with that sign before having to calculate a single-digit addition problem, an effect termed operator-priming. Therefore, not only are some arithmetic operators linked to spatial intuitions, but such intuitions might also have an important role during arithmetic calculation. More generally, our findings support the view that mathematical symbols inherently evoke spatial representations.
Fuzzy rule-based model for hydropower reservoirs operation
Moeini, R.; Afshar, A.; Afshar, M.H. [School of Civil Engineering, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)
2011-02-15
Real-time hydropower reservoir operation is a continuous decision-making process of determining the water level of a reservoir or the volume of water released from it. The hydropower operation is usually based on operating policies and rules defined and decided upon in strategic planning. This paper presents a fuzzy rule-based model for the operation of hydropower reservoirs. The proposed fuzzy rule-based model presents a set of suitable operating rules for release from the reservoir based on ideal or target storage levels. The model operates on an 'if-then' principle, in which the 'if' is a vector of fuzzy premises and the 'then' is a vector of fuzzy consequences. In this paper, reservoir storage, inflow, and period are used as premises and the release as the consequence. The steps involved in the development of the model include, construction of membership functions for the inflow, storage and the release, formulation of fuzzy rules, implication, aggregation and defuzzification. The required knowledge bases for the formulation of the fuzzy rules is obtained form a stochastic dynamic programming (SDP) model with a steady state policy. The proposed model is applied to the hydropower operation of ''Dez'' reservoir in Iran and the results are presented and compared with those of the SDP model. The results indicate the ability of the method to solve hydropower reservoir operation problems. (author)
Fuzzy expert systems models for operations research and management science
Turksen, I. B.
1993-12-01
Fuzzy expert systems can be developed for the effective use of management within the domains of concern associated with Operations Research and Management Science. These models are designed with: (1) expressive powers of representation embedded in linguistic variables and their linguistic values in natural language expressions, and (2) improved methods of interference based on fuzzy logic which is a generalization of multi-valued logic with fuzzy quantifiers. The results of these fuzzy expert system models are either (1) approximately good in comparison with their classical counterparts, or (2) much better than their counterparts. Moreover, for fuzzy expert systems models, it is only necessary to obtain ordinal scale data. Whereas for their classical counterparts, it is generally required that data be at least on ratio and absolute scale in order to guarantee the additivity and multiplicativity assumptions.
Feizizadeh, Bakhtiar; Blaschke, Thomas; Tiede, Dirk; Moghaddam, Mohammad Hossein Rezaei
2017-09-01
This article presents a method of object-based image analysis (OBIA) for landslide delineation and landslide-related change detection from multi-temporal satellite images. It uses both spatial and spectral information on landslides, through spectral analysis, shape analysis, textural measurements using a gray-level co-occurrence matrix (GLCM), and fuzzy logic membership functionality. Following an initial segmentation step, particular combinations of various information layers were investigated to generate objects. This was achieved by applying multi-resolution segmentation to IRS-1D, SPOT-5, and ALOS satellite imagery in sequential steps of feature selection and object classification, and using slope and flow direction derivatives from a digital elevation model together with topographically-oriented gray level co-occurrence matrices. Fuzzy membership values were calculated for 11 different membership functions using 20 landslide objects from a landslide training data. Six fuzzy operators were used for the final classification and the accuracies of the resulting landslide maps were compared. A Fuzzy Synthetic Evaluation (FSE) approach was adapted for validation of the results and for an accuracy assessment using the landslide inventory database. The FSE approach revealed that the AND operator performed best with an accuracy of 93.87% for 2005 and 94.74% for 2011, closely followed by the MEAN Arithmetic operator, while the OR and AND (*) operators yielded relatively low accuracies. An object-based change detection was then applied to monitor landslide-related changes that occurred in northern Iran between 2005 and 2011. Knowledge rules to detect possible landslide-related changes were developed by evaluating all possible landslide-related objects for both time steps.
Aggregation Operator Based Fuzzy Pattern Classifier Design
Mönks, Uwe; Larsen, Henrik Legind; Lohweg, Volker
2009-01-01
This paper presents a novel modular fuzzy pattern classifier design framework for intelligent automation systems, developed on the base of the established Modified Fuzzy Pattern Classifier (MFPC) and allows designing novel classifier models which are hardware-efficiently implementable....... The performances of novel classifiers using substitutes of MFPC's geometric mean aggregator are benchmarked in the scope of an image processing application against the MFPC to reveal classification improvement potentials for obtaining higher classification rates....
Bergstra, J.A.; Middelburg, C.A.
2009-01-01
An inversive meadow is a commutative ring with identity equipped with a multiplicative inverse operation made total by choosing 0 as its value at 0. Previously, inversive meadows were shortly called meadows. A divisive meadow is an inversive meadows with the multiplicative inverse operation replaced by a division operation. In the spirit of Peacock's arithmetical algebra, we introduce variants of inversive and divisive meadows without an additive identity element and an additive inverse opera...
Nuclear Power Plant Operator Reliability Research Based on Fuzzy Math
Fang Xiang
2011-01-01
Full Text Available This paper makes use of the concept and theory of fuzzy number in fuzzy mathematics, to research for the response time of operator in accident of Chinese nuclear power plant. Through the quantitative analysis for the performance shape factors (PSFs which influence the response time of operators, the formula of the operator response time is obtained based on the possibilistic fuzzy linear regression model which is used for the first time in this kind of research. The research result shows that the correct research method can be achieved through the analysis of the information from a small sample. This method breaks through the traditional research method and can be used not only for the reference to the safe operation of nuclear power plant, but also in other areas.
Fuzzy multiobjective models for optimal operation of a hydropower system
Teegavarapu, Ramesh S. V.; Ferreira, André R.; Simonovic, Slobodan P.
2013-06-01
Optimal operation models for a hydropower system using new fuzzy multiobjective mathematical programming models are developed and evaluated in this study. The models use (i) mixed integer nonlinear programming (MINLP) with binary variables and (ii) integrate a new turbine unit commitment formulation along with water quality constraints used for evaluation of reservoir downstream impairment. Reardon method used in solution of genetic algorithm optimization problems forms the basis for development of a new fuzzy multiobjective hydropower system optimization model with creation of Reardon type fuzzy membership functions. The models are applied to a real-life hydropower reservoir system in Brazil. Genetic Algorithms (GAs) are used to (i) solve the optimization formulations to avoid computational intractability and combinatorial problems associated with binary variables in unit commitment, (ii) efficiently address Reardon method formulations, and (iii) deal with local optimal solutions obtained from the use of traditional gradient-based solvers. Decision maker's preferences are incorporated within fuzzy mathematical programming formulations to obtain compromise operating rules for a multiobjective reservoir operation problem dominated by conflicting goals of energy production, water quality and conservation releases. Results provide insight into compromise operation rules obtained using the new Reardon fuzzy multiobjective optimization framework and confirm its applicability to a variety of multiobjective water resources problems.
Magnetic operations: a little fuzzy mechanics?
Mielnik, B; RamIrez, A
2011-01-01
We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric centre of the particle trajectory is elucidated. In the quantum case, it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry that enters into the traditional control problems. We show that its application extends beyond the usually considered time-independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields cause the stability maps to differ from the traditional Strutt diagram. The elementary mathematical results help explain the structure of the obtained solutions.
Approximate Solution of LR Fuzzy Sylvester Matrix Equations
Xiaobin Guo
2013-01-01
Full Text Available The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.
Designing reversible arithmetic, logic circuit to implement micro-operation in quantum computation
Kalita, Gunajit; Saikia, Navajit
2016-01-01
The futuristic computing is desired to be more power full with low-power consumption. That is why quantum computing has been a key area of research for quite some time and is getting more and more attention. Quantum logic being reversible, a significant amount of contributions has been reported on reversible logic in recent times. Reversible circuits are essential parts of quantum computers, and hence their designs are of great importance. In this paper, designs of reversible circuits are proposed using a recently proposed reversible gate for arithmetic and logic operations to implement various micro-operations (simple add and subtract, add with carry, subtract with borrow, transfer, incrementing, decrementing etc., and logic operations like XOR, XNOR, complementing etc.) in a reversible computer like quantum computer. The two new reversible designs proposed here for half adder and full adders are also used in the presented reversible circuits to implement various microoperations. The quantum costs of these designs are comparable. Many of the implemented micro-operations are not seen in previous literatures. The performances of the proposed circuits are compared with existing designs wherever available. (paper)
Raveh, Ira; Koichu, Boris; Peled, Irit; Zaslavsky, Orit
2016-01-01
In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic…
Fuzzy operation and real time surveillance of a nuclear reactor
Si-Fodil, M.; Guely, F.; Siarry, P.; Tyran, J.L.
1997-01-01
The operating power of nuclear power plants needs to be modulated according to the thin evolutions of electric power demand. Two parameters are concerned by load following operations: the power axial disequilibrium and the position of control rods. This paper deals with the automation of the control of power axial disequilibrium using boration-dilution. An automatic system based on fuzzy logic is proposed which can be substituted to the expert operator who is in charge of this fastidious manual task. The management of water and boron flow rates are studied in details. A Graphic interface was designed for the real-time surveillance of the reactor. (J.S.)
Tschentscher, Nadja; Hauk, Olaf
2014-05-15
A number of previous studies have interpreted differences in brain activation between arithmetic operation types (e.g. addition and multiplication) as evidence in favor of distinct cortical representations, processes or neural systems. It is still not clear how differences in general task complexity contribute to these neural differences. Here, we used a mental arithmetic paradigm to disentangle brain areas related to general problem solving from those involved in operation type specific processes (addition versus multiplication). We orthogonally varied operation type and complexity. Importantly, complexity was defined not only based on surface criteria (for example number size), but also on the basis of individual participants' strategy ratings, which were validated in a detailed behavioral analysis. We replicated previously reported operation type effects in our analyses based on surface criteria. However, these effects vanished when controlling for individual strategies. Instead, procedural strategies contrasted with memory retrieval reliably activated fronto-parietal and motor regions, while retrieval strategies activated parietal cortices. This challenges views that operation types rely on partially different neural systems, and suggests that previously reported differences between operation types may have emerged due to invalid measures of complexity. We conclude that mental arithmetic is a powerful paradigm to study brain networks of abstract problem solving, as long as individual participants' strategies are taken into account. Copyright © 2014 Elsevier Inc. All rights reserved.
Solving Fully Fuzzy Linear System of Equations in General Form
A. Yousefzadeh
2012-06-01
Full Text Available In this work, we propose an approach for computing the positive solution of a fully fuzzy linear system where the coefficient matrix is a fuzzy $nimes n$ matrix. To do this, we use arithmetic operations on fuzzy numbers that introduced by Kaffman in and convert the fully fuzzy linear system into two $nimes n$ and $2nimes 2n$ crisp linear systems. If the solutions of these linear systems don't satisfy in positive fuzzy solution condition, we introduce the constrained least squares problem to obtain optimal fuzzy vector solution by applying the ranking function in given fully fuzzy linear system. Using our proposed method, the fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.
Stochastic reservoir operation under drought with fuzzy objectives
Parent, E.; Duckstein, L.
1993-01-01
Biojective reservoir operation under drought conditions is investigated using stochastic dynamic programming. As both objectives (irrigation water supply, water quality) can only be defined imprecisely, a fuzzy set approach is used to encode the decision maker (DM)'s preferences. The nature driven components are modeled by means of classical stage-state system analysis. The state is three dimensional (inflow memory, drought irrigation index, reservoir level); the decision vector elements are release and irrigation allocation. Stochasticity stems from the random nature of inflows and irrigation demands. The transition function includes a lag one inflow Markov model and mass balance equations. The human driven component is designed as a confluence of fuzzy objectives and constraints after Bellman and Zadeh. Fuzzy numbers are assessed to represent the DM's objectives by two different techniques, the direct one and indirect pairwise comparison. The real case study of the Neste river system in southwestern France is used to illustrate the approach; the result are compared to a classical sequential decision theoretical model derived earlier from the viewpoints of ease of modeling, computational efforts, plausibility and robustness of results
A Method Based on Intuitionistic Fuzzy Dependent Aggregation Operators for Supplier Selection
Fen Wang
2013-01-01
Full Text Available Recently, resolving the decision making problem of evaluation and ranking the potential suppliers have become as a key strategic factor for business firms. In this paper, two new intuitionistic fuzzy aggregation operators are developed: dependent intuitionistic fuzzy ordered weighed averaging (DIFOWA operator and dependent intuitionistic fuzzy hybrid weighed aggregation (DIFHWA operator. Some of their main properties are studied. A method based on the DIFHWA operator for intuitionistic fuzzy multiple attribute decision making is presented. Finally, an illustrative example concerning supplier selection is given.
Talebi-Daryani, R. [Fachhochschule Koeln (Germany). Lehrgebiet und Lab. fuer Regelungs- und Gebaeudeleittechnik; Luther, C. [JCI Regelungstechnik GmbH, Koeln (Germany)
1998-05-01
The optimization potentials for the operation of chilling systems within the building supervisory control systems are limited to abilities of PLC functions with their binary logic. The aim of this project is to replace inefficient PLC-solutions for the operation of chilling system by a Fuzzy control system. Optimal operation means: reducing operation time and operation costs of the system, reducing cooling energy generation- and consumption costs. Analysis of the thermal behaviour of the building and the chilling system is necessary, in order to find the current efficient cooling potentials and cooling methods during the operation. Three different Fuzzy controller have been developed with a total rule number of just 70. This realized Fuzzy control system is able to forecast the maximum cooling power of the building, but also to determine the cooling potential of the out door air. This new Fuzzy control system has been successfully commissioned, and remarkable improvement of the system behaviour is reached. Comparison of the system behaviour before and after the implementation of Fuzzy control system proved the benefits of the Fuzzy logic based operation system realized here. The system described here is a joint project between the University of applied sciences Cologne, and Johnson Controls International Cologne. The Fuzzy software tool used here (SUCO soft Fuzzy TECH 4.0), was provided by Kloeckner Moeller Bonn. (orig.) [Deutsch] Die Betriebsoptimierung von Kaelteanlagen innerhalb von Gebaeudeleitsystemen ist auf die Faehigkeiten von logischen Steuerverknuepfungen der Digitaltechnik begrenzt. In diesem Zusammenhang kann nur ein geringer Anteil der Information ueber das thermische Speicherverhalten des jeweiligen Gebaeudes herangezogen werden. Ziel des vorliegenden Projektes war es, die unzureichenden logischen Steuerverknuepfungen durch ein Fuzzy-Control-System zu ersetzen, um die Arbeitsweise der Kaelteanlage zu optimieren. Die Optimierungskriterien dieses
Fuzzy inference system for evaluating and improving nuclear power plant operating performance
Guimaraes, Antonio Cesar F.; Lapa, Celso Marcelo Franklin
2003-01-01
This paper presents a fuzzy inference system (FIS) as an approach to estimate Nuclear Power Plant (NPP) performance indicators. The performance indicators for this study are the energy availability factor (EAF) and the planned (PUF) and unplanned unavailability factor (UUF). These indicators are obtained from a non analytical combination among the same operational parameters. Such parameters are, for example, environment impacts, industrial safety, radiological protection, safety indicators, scram rate, thermal efficiency, and fuel reliability. This approach uses the concept of a pure fuzzy logic system where the fuzzy rule base consists of a collection of fuzzy IF-THEN rules. The fuzzy inference engine uses these fuzzy IF-THEN rules to determine a mapping from fuzzy sets in the input universe of discourse to fuzzy sets in the output universe of discourse based on fuzzy logic principles. The results demonstrated the potential of the fuzzy inference to generate a knowledge basis that correlate operations occurrences and NPP performance. The inference system became possible the development of the sensitivity studies, future operational condition previsions and may support the eventual corrections on operation of the plant
Reversible arithmetic logic unit for quantum arithmetic
Thomsen, Michael Kirkedal; Glück, Robert; Axelsen, Holger Bock
2010-01-01
This communication presents the complete design of a reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The presented ALU is garbage free and uses reversible updates to combine the standard reversible arithmetic...... and logical operations in one unit. Combined with a suitable control unit, the ALU permits the construction of an r-Turing complete computing device. The garbage-free ALU developed in this communication requires only 6n elementary reversible gates for five basic arithmetic-logical operations on two n......-bit operands and does not use ancillae. This remarkable low resource consumption was achieved by generalizing the V-shape design first introduced for quantum ripple-carry adders and nesting multiple V-shapes in a novel integrated design. This communication shows that the realization of an efficient reversible...
Construction of Fuzzy Sets and Applying Aggregation Operators for Fuzzy Queries
Hudec, Miroslav; Sudzina, Frantisek
Flexible query conditions could use linguistic terms described by fuzzy sets. The question is how to properly construct fuzzy sets for each linguistic term and apply an adequate aggregation function. For construction of fuzzy sets, the lowest value, the highest value of attribute...... and the distribution of data inside its domain are used. The logarithmic transformation of domains appears to be suitable. This way leads to a balanced distribution of tuples over fuzzy sets. In addition, users’ opinions about linguistic terms as well as current content in database are merged. The second investigated...
Characterizations of intuitionistic fuzzy ideals and filters based on lattice operations
Soheyb Milles
2017-11-01
Full Text Available In a recent paper, Thomas and Nair have introduced the notions of intuitionistic fuzzy ideal and intuitionistic fuzzy filter on a lattice and some basic properties were proved. In this paper, we characterize these notions in terms of the lattice operations and in terms of their associated crisp sets. We introduce the notions of prime intuitionistic fuzzy ideal and filter as interesting kinds, and then we investigate their various characterizations and different properties.
Implementing fuzzy polynomial interpolation (FPI and fuzzy linear regression (LFR
Maria Cristina Floreno
1996-05-01
Full Text Available This paper presents some preliminary results arising within a general framework concerning the development of software tools for fuzzy arithmetic. The program is in a preliminary stage. What has been already implemented consists of a set of routines for elementary operations, optimized functions evaluation, interpolation and regression. Some of these have been applied to real problems.This paper describes a prototype of a library in C++ for polynomial interpolation of fuzzifying functions, a set of routines in FORTRAN for fuzzy linear regression and a program with graphical user interface allowing the use of such routines.
Modelling of Reservoir Operations using Fuzzy Logic and ANNs
Van De Giesen, N.; Coerver, B.; Rutten, M.
2015-12-01
Today, almost 40.000 large reservoirs, containing approximately 6.000 km3 of water and inundating an area of almost 400.000 km2, can be found on earth. Since these reservoirs have a storage capacity of almost one-sixth of the global annual river discharge they have a large impact on the timing, volume and peaks of river discharges. Global Hydrological Models (GHM) are thus significantly influenced by these anthropogenic changes in river flows. We developed a parametrically parsimonious method to extract operational rules based on historical reservoir storage and inflow time-series. Managing a reservoir is an imprecise and vague undertaking. Operators always face uncertainties about inflows, evaporation, seepage losses and various water demands to be met. They often base their decisions on experience and on available information, like reservoir storage and the previous periods inflow. We modeled this decision-making process through a combination of fuzzy logic and artificial neural networks in an Adaptive-Network-based Fuzzy Inference System (ANFIS). In a sensitivity analysis, we compared results for reservoirs in Vietnam, Central Asia and the USA. ANFIS can indeed capture reservoirs operations adequately when fed with a historical monthly time-series of inflows and storage. It was shown that using ANFIS, operational rules of existing reservoirs can be derived without much prior knowledge about the reservoirs. Their validity was tested by comparing actual and simulated releases with each other. For the eleven reservoirs modelled, the normalised outflow, , was predicted with a MSE of 0.002 to 0.044. The rules can be incorporated into GHMs. After a network for a specific reservoir has been trained, the inflow calculated by the hydrological model can be combined with the release and initial storage to calculate the storage for the next time-step using a mass balance. Subsequently, the release can be predicted one time-step ahead using the inflow and storage.
Solving fully fuzzy transportation problem using pentagonal fuzzy numbers
Maheswari, P. Uma; Ganesan, K.
2018-04-01
In this paper, we propose a simple approach for the solution of fuzzy transportation problem under fuzzy environment in which the transportation costs, supplies at sources and demands at destinations are represented by pentagonal fuzzy numbers. The fuzzy transportation problem is solved without converting to its equivalent crisp form using a robust ranking technique and a new fuzzy arithmetic on pentagonal fuzzy numbers. To illustrate the proposed approach a numerical example is provided.
Dual hesitant pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making
Wei Guiwu
2017-09-01
Full Text Available In this paper, we investigate the multiple attribute decision making (MADM problem based on the Hamacher aggregation operators with dual Pythagorean hesitant fuzzy information. Then, motivated by the ideal of Hamacher operation, we have developed some Hamacher aggregation operators for aggregating dual hesitant Pythagorean fuzzy information. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the dual hesitant Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example for supplier selection in supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Relational Demonic Fuzzy Refinement
Fairouz Tchier
2014-01-01
Full Text Available We use relational algebra to define a refinement fuzzy order called demonic fuzzy refinement and also the associated fuzzy operators which are fuzzy demonic join (⊔fuz, fuzzy demonic meet (⊓fuz, and fuzzy demonic composition (□fuz. Our definitions and properties are illustrated by some examples using mathematica software (fuzzy logic.
Jianghong Zhu
2018-06-01
Full Text Available As a generalization of the intuitionistic fuzzy set (IFS, a Pythagorean fuzzy set has more flexibility than IFS in expressing uncertainty and fuzziness in the process of multiple criteria group decision-making (MCGDM. Meanwhile, the prominent advantage of the Muirhead mean (MM operator is that it can reflect the relationships among the various input arguments through changing a parameter vector. Motivated by these primary characters, in this study, we introduced the MM operator into the Pythagorean fuzzy context to expand its applied fields. To do so, we presented the Pythagorean fuzzy MM (PFMM operators and Pythagorean fuzzy dual MM (PFDMM operator to fuse the Pythagorean fuzzy information. Then, we investigated their some properties and gave some special cases related to the parameter vector. In addition, based on the developed operators, two MCGDM methods under the Pythagorean fuzzy environment are proposed. An example is given to verify the validity and feasibility of our proposed methods, and a comparative analysis is provided to show their advantages.
Conceptual Knowledge of Fraction Arithmetic
Siegler, Robert S.; Lortie-Forgues, Hugues
2015-01-01
Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…
Ibrahim, Wael Refaat Anis
The present research involves the development of several fuzzy expert systems for power quality analysis and diagnosis. Intelligent systems for the prediction of abnormal system operation were also developed. The performance of all intelligent modules developed was either enhanced or completely produced through adaptive fuzzy learning techniques. Neuro-fuzzy learning is the main adaptive technique utilized. The work presents a novel approach to the interpretation of power quality from the perspective of the continuous operation of a single system. The research includes an extensive literature review pertaining to the applications of intelligent systems to power quality analysis. Basic definitions and signature events related to power quality are introduced. In addition, detailed discussions of various artificial intelligence paradigms as well as wavelet theory are included. A fuzzy-based intelligent system capable of identifying normal from abnormal operation for a given system was developed. Adaptive neuro-fuzzy learning was applied to enhance its performance. A group of fuzzy expert systems that could perform full operational diagnosis were also developed successfully. The developed systems were applied to the operational diagnosis of 3-phase induction motors and rectifier bridges. A novel approach for learning power quality waveforms and trends was developed. The technique, which is adaptive neuro fuzzy-based, learned, compressed, and stored the waveform data. The new technique was successfully tested using a wide variety of power quality signature waveforms, and using real site data. The trend-learning technique was incorporated into a fuzzy expert system that was designed to predict abnormal operation of a monitored system. The intelligent system learns and stores, in compressed format, trends leading to abnormal operation. The system then compares incoming data to the retained trends continuously. If the incoming data matches any of the learned trends, an
Reza Ezzati
2014-08-01
Full Text Available In this paper, we propose the least square method for computing the positive solution of a non-square fully fuzzy linear system. To this end, we use Kaffman' arithmetic operations on fuzzy numbers \\cite{17}. Here, considered existence of exact solution using pseudoinverse, if they are not satisfy in positive solution condition, we will compute fuzzy vector core and then we will obtain right and left spreads of positive fuzzy vector by introducing constrained least squares problem. Using our proposed method, non-square fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.
Solution of the fully fuzzy linear systems using iterative techniques
Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi
2007-01-01
This paper mainly intends to discuss the iterative solution of fully fuzzy linear systems which we call FFLS. We employ Dubois and Prade's approximate arithmetic operators on LR fuzzy numbers for finding a positive fuzzy vector x-tilde which satisfies A-tildex-tilde=b, where A-tilde and b-tilde are a fuzzy matrix and a fuzzy vector, respectively. Please note that the positivity assumption is not so restrictive in applied problems. We transform FFLS and propose iterative techniques such as Richardson, Jacobi, Jacobi overrelaxation (JOR), Gauss-Seidel, successive overrelaxation (SOR), accelerated overrelaxation (AOR), symmetric and unsymmetric SOR (SSOR and USSOR) and extrapolated modified Aitken (EMA) for solving FFLS. In addition, the methods of Newton, quasi-Newton and conjugate gradient are proposed from nonlinear programming for solving a fully fuzzy linear system. Various numerical examples are also given to show the efficiency of the proposed schemes
Arithmetic circuits for DSP applications
Stouraitis, Thanos
2017-01-01
Arithmetic Circuits for DSP Applications is a complete resource on arithmetic circuits for digital signal processing (DSP). It covers the key concepts, designs and developments of different types of arithmetic circuits, which can be used for improving the efficiency of implementation of a multitude of DSP applications. Each chapter includes various applications of the respective class of arithmetic circuits along with information on the future scope of research. Written for students, engineers, and researchers in electrical and computer engineering, this comprehensive text offers a clear understanding of different types of arithmetic circuits used for digital signal processing applications. The text includes contributions from noted researchers on a wide range of topics, including a review o circuits used in implementing basic operations like additions and multiplications; distributed arithmetic as a technique for the multiplier-less implementation of inner products for DSP applications; discussions on look ...
Designing an Energy Storage System Fuzzy PID Controller for Microgrid Islanded Operation
Jin-Hong Jeon
2011-09-01
Full Text Available Recently, interest in microgrids, which are composed of distributed generation (DG, distributed storage (DS, and loads, has been growing as a potentially effective clean energy system to mitigate against climate change. The microgrid is operated in the grid-connected mode and the islanded mode according to the conditions of the upstream power grid. The role of the energy storage system (ESS is especially important to maintain constant the frequency and voltage of an islanded microgrid. For this reason, various approaches for ESS control have been put forth. In this paper, a fuzzy PID controller is proposed to improve the frequency control performance of the ESS. This fuzzy PID controller consists of a fuzzy logic controller and a conventional PI controller, connected in series. The fuzzy logic controller has two input signals, and then the output signal of the fuzzy logic controller is the input signal of the conventional PI controller. For comparison of control performance, gains of each PI controller and fuzzy PID controller are tuned by the particle swam optimization (PSO algorithm. In the simulation study, the control performance of the fuzzy PID was also tested under various operating conditions using the PSCAD/EMTDC simulation platform.
Conceptual Knowledge of Decimal Arithmetic
Lortie-Forgues, Hugues; Siegler, Robert S.
2017-01-01
In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…
Averkin, A.A.
1994-01-01
A new type of fuzzy expert system for assisting the operator's decisions in nuclear power plant system in non-standard situations is proposed. This expert system is based on new approaches to fuzzy logics acquisition and to fuzzy logics testing. Fuzzy logics can be generated by a T-norms axiomatic system to choose the most suitable to operator's way of thinking. Then the chosen fuzzy logic is tested by simulation of inference process in expert system. The designed logic is the input of inference module of expert system
River Stream-Flow and Zayanderoud Reservoir Operation Modeling Using the Fuzzy Inference System
Saeed Jamali
2007-12-01
Full Text Available The Zayanderoud basin is located in the central plateau of Iran. As a result of population increase and agricultural and industrial developments, water demand on this basin has increased extensively. Given the importance of reservoir operation in water resource and management studies, the performance of fuzzy inference system (FIS for Zayanderoud reservoir operation is investigated in this paper. The model of operation consists of two parts. In the first part, the seasonal river stream-flow is forecasted using the fuzzy rule-based system. The southern oscillated index, rain, snow, and discharge are inputs of the model and the seasonal river stream-flow its output. In the second part, the operation model is constructed. The amount of releases is first optimized by a nonlinear optimization model and then the rule curves are extracted using the fuzzy inference system. This model operates on an "if-then" principle, where the "if" is a vector of fuzzy permits and "then" is the fuzzy result. The reservoir storage capacity, inflow, demand, and year condition factor are used as permits. Monthly release is taken as the consequence. The Zayanderoud basin is investigated as a case study. Different performance indices such as reliability, resiliency, and vulnerability are calculated. According to results, FIS works more effectively than the traditional reservoir operation methods such as standard operation policy (SOP or linear regression.
Wang, Chunyong; Li, Qingguo; Zhou, Xiaoqiang; Yang, Tian
2014-01-01
We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.
Operational optimisation of water supply networks using a fuzzy ...
This paper presents a fuzzy system to control the pressure in a water distribution network, by using valves and controlling the rotor speed of the pumping systems. The variable frequency drive tracks the minimum head of the pumping system, while the control valves have the function of eliminating the excess pressure at ...
Arruda, Tiago Jose; Silva Gonzalez, Rodrigo; Sangaletti Tercariol, Cesar Augusto; Souto Martinez, Alexandre
2008-01-01
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on several values of a variable are obtained here. Applications of the above formalism are considered
Risk Assessment for Bridges Safety Management during Operation Based on Fuzzy Clustering Algorithm
Xia Hanyu
2016-01-01
Full Text Available In recent years, large span and large sea-crossing bridges are built, bridges accidents caused by improper operational management occur frequently. In order to explore the better methods for risk assessment of the bridges operation departments, the method based on fuzzy clustering algorithm is selected. Then, the implementation steps of fuzzy clustering algorithm are described, the risk evaluation system is built, and Taizhou Bridge is selected as an example, the quantitation of risk factors is described. After that, the clustering algorithm based on fuzzy equivalence is calculated on MATLAB 2010a. In the last, Taizhou Bridge operation management departments are classified and sorted according to the degree of risk, and the safety situation of operation departments is analyzed.
Wu, Jia-ting; Wang, Jian-qiang; Wang, Jing; Zhang, Hong-yu; Chen, Xiao-hong
2014-01-01
Based on linguistic term sets and hesitant fuzzy sets, the concept of hesitant fuzzy linguistic sets was introduced. The focus of this paper is the multicriteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). A new approach to solving these problems is proposed, which is based on the generalized prioritized aggregation operator of HFLNs. Firstly, the new operations and comparison method for HFLNs are provided and some linguistic scale functions are applied. Subsequently, two prioritized aggregation operators and a generalized prioritized aggregation operator of HFLNs are developed and applied to MCDM problems. Finally, an illustrative example is given to illustrate the effectiveness and feasibility of the proposed method, which are then compared to the existing approach.
Practical considerations for the implantation of a fuzzy control algorithm in a DSP
Perez C, B.; Benitez R, J.S.; Pacheco S, J.O.
2003-01-01
The development of a digital system based on a DSP to implant a Mamdani type algorithm of fuzzy control whose objective is to regulate the neutron power in a nuclear research reactor Type TRIGA Mark III is presented. Its are simultaneously carried out the aggregation des fuzzy stages discreeting the universe of the output variable. The format MPF for the handling of the floating point in the arithmetic operations is used. (Author)
Shi, Yu-Fang; Ma, Yi-Yi; Song, Ping-Ping
2018-03-01
System Reliability Theory is a research hotspot of management science and system engineering in recent years, and construction reliability is useful for quantitative evaluation of project management level. According to reliability theory and target system of engineering project management, the defination of construction reliability appears. Based on fuzzy mathematics theory and language operator, value space of construction reliability is divided into seven fuzzy subsets and correspondingly, seven membership function and fuzzy evaluation intervals are got with the operation of language operator, which provides the basis of corresponding method and parameter for the evaluation of construction reliability. This method is proved to be scientific and reasonable for construction condition and an useful attempt for theory and method research of engineering project system reliability.
Yin, Kedong; Yang, Benshuo; Li, Xuemei
2018-01-24
In this paper, we investigate multiple attribute group decision making (MAGDM) problems where decision makers represent their evaluation of alternatives by trapezoidal fuzzy two-dimensional uncertain linguistic variable. To begin with, we introduce the definition, properties, expectation, operational laws of trapezoidal fuzzy two-dimensional linguistic information. Then, to improve the accuracy of decision making in some case where there are a sort of interrelationship among the attributes, we analyze partition Bonferroni mean (PBM) operator in trapezoidal fuzzy two-dimensional variable environment and develop two operators: trapezoidal fuzzy two-dimensional linguistic partitioned Bonferroni mean (TF2DLPBM) aggregation operator and trapezoidal fuzzy two-dimensional linguistic weighted partitioned Bonferroni mean (TF2DLWPBM) aggregation operator. Furthermore, we develop a novel method to solve MAGDM problems based on TF2DLWPBM aggregation operator. Finally, a practical example is presented to illustrate the effectiveness of this method and analyses the impact of different parameters on the results of decision-making.
Optimal operation planning of radioactive waste processing system by fuzzy theory
Yang, Jin Yeong; Lee, Kun Jai
2000-01-01
This study is concerned with the applications of linear goal programming and fuzzy theory to the analysis of management and operational problems in the radioactive processing system (RWPS). The developed model is validated and verified using actual data obtained from the RWPS at Kyoto University in Japan. The solution by goal programming and fuzzy theory would show the optimal operation point which is to maximize the total treatable radioactive waste volume and minimize the released radioactivity of liquid waste even under the restricted resources. (orig.)
Guofang Zhang
2018-06-01
Full Text Available Hamacher operation is a generalization of the algebraic and Einstein operation and expresses a family of binary operation in the unit interval [0,1]. Heronian mean can deal with correlations of different criteria or input arguments and does not bring out repeated calculation. The normal intuitionistic fuzzy numbers (NIFNs can depict normal distribution information in practical decision making. A decision-making problem was researched under the NIFN environment in this study, and a new multi-criteria group decision-making (MCGDM approach is herein introduced on the basis of Hamacher operation. Firstly, according to Hamacher operation, some operational laws of NIFNs are presented. Secondly, it is noted that Heronian mean not only takes into account mutuality between the attribute values once, but also considers the correlation between input argument and itself. Therefore, in order to aggregate NIFN information, we developed some operators and studied their properties. These operators include Hamacher Heronian mean (NIFHHM, Hamacher weighted Heronian mean (NIFHWHM, Hamacher geometric Heronian mean (NIFHGHM, and Hamacher weighted geometric Heronian mean (NIFHWGHM. Furthermore, we applied the proposed operators to the MCGDM problem and developed a new MCGDM approach. The characteristics of this new approach are that: (1 it is suitable for making a decision under the NIFN environment and it is more reasonable for aggregating the normal distribution data; (2 it utilizes Hamacher operation to provide an effective and powerful MCGDM algorithm and to make more reliable and more flexible decisions under the NIFN circumstance; (3 it uses the Heronian mean operator to deal with interrelations between the attributes or input arguments, and it does not bring about repeated calculation. Therefore, the proposed method can describe the interaction of the different criteria or input arguments and offer some reasonable and reliable MCGDM aggregation operators
Arithmetic the foundation of mathematics
2015-01-01
Arithmetic factors into our lives on a daily basis, so it's hard to imagine a world without the six basic operations: addition, subtraction, multiplication, division, raising to powers, and finding roots. Readers will get a solid overview of arithmetic, while offering useful examples of how they are used in routine activities, such as social media applications. It reinforces Common Core math standards, including understanding basic math concepts and how they apply to students' daily lives and challenges. A history of arithmetic helps provide a contextual framework for the course of its develop
Liu, Peide; Qin, Xiyou
2017-11-01
Linguistic intuitionistic fuzzy number (LIFN) is a special intuitionistic fuzzy number which can more easily describe the vagueness existing in the real decision-making. Maclaurin symmetric mean (MSM) operator has the characteristic of considering the interrelationships among any number of input parameters. In this paper, we extended the MSM operator to the LIFNs and some extended MSM operators for LIFNs were proposed, some new decision-making methods were developed. Firstly, we introduced the definition, score function, properties and operational rules of the LIFNs. Then, we proposed some linguistic intuitionistic fuzzy MSM operators, such as linguistic intuitionistic fuzzy Maclaurin symmetric mean operator, weighted linguistic intuitionistic fuzzy Maclaurin symmetric mean (WLIFMSM) operator, linguistic intuitionistic fuzzy dual Maclaurin symmetric mean operator, weighted linguistic intuitionistic fuzzy dual Maclaurin symmetric mean (WLIFDMSM) operator. In the meantime, we studied some important properties of these operators, and developed some methods based on WLIFMSM operator and WLIFDMSM operator for multi-attribute decision-making. Finally, we use an example to demonstrate the effectiveness of the proposed methods.
Neuro-fuzzy models for systems identification applied to the operation of nuclear power plants
Alves, Antonio Carlos Pinto Dias
2000-09-01
A nuclear power plant has a myriad of complex system and sub-systems that, working cooperatively, make the control of the whole plant. Nevertheless their operation be automatic most of the time, the integral understanding of their internal- logic can be away of the comprehension of even experienced operators because of the poor interpretability those controls offer. This difficulty does not happens only in nuclear power plants but in almost every a little more complex control system. Neuro-fuzzy models have been used for the last years in a attempt of suppress these difficulties because of their ability of modelling in linguist form even a system which behavior is extremely complex. This is a very intuitive human form of interpretation and neuro-fuzzy model are gathering increasing acceptance. Unfortunately, neuro-fuzzy models can grow up to become of hard interpretation because of the complexity of the systems under modelling. In general, that growing occurs in function of redundant rules or rules that cover a very little domain of the problem. This work presents an identification method for neuro-fuzzy models that not only allows models grow in function of the existent complexity but that beforehand they try to self-adapt to avoid the inclusion of new rules. This form of construction allowed to arrive to highly interpretative neuro-fuzzy models even of very complex systems. The use of this kind of technique in modelling the control of the pressurizer of a PWR nuclear power plant allowed verify its validity and how neuro-fuzzy models so built can be useful in understanding the automatic operation of a nuclear power plant. (author)
Gagandeep Kaur
2018-01-01
Full Text Available Cubic intuitionistic fuzzy (CIF set is the hybrid set which can contain much more information to express an interval-valued intuitionistic fuzzy set and an intuitionistic fuzzy set simultaneously for handling the uncertainties in the data. Unfortunately, there has been no research on the aggregation operators on CIF sets so far. Since an aggregation operator is an important mathematical tool in decision-making problems, the present paper proposes some new Bonferroni mean and weighted Bonferroni mean averaging operators between the cubic intuitionistic fuzzy numbers for aggregating the different preferences of the decision-maker. Then, we develop a decision-making method based on the proposed operators under the cubic intuitionistic fuzzy environment and illustrated with a numerical example. Finally, a comparison analysis between the proposed and the existing approaches have been performed to illustrate the applicability and feasibility of the developed decision-making method.
Smets, P
1995-01-01
We start by describing the nature of imperfect data, and giving an overview of the various models that have been proposed. Fuzzy sets theory is shown to be an extension of classical set theory, and as such has a proeminent role or modelling imperfect data. The mathematic of fuzzy sets theory is detailled, in particular the role of the triangular norms. The use of fuzzy sets theory in fuzzy logic and possibility theory,the nature of the generalized modus ponens and of the implication operator for approximate reasoning are analysed. The use of fuzzy logic is detailled for application oriented towards process control and database problems.
On the use of fuzzy logics in the operator support system of an experimental facility
Mozhaev, A.A.
1988-01-01
Problems of consrtuction of the computerized operator support system of the experimental device are considered on the basis of the imitation decision-making model which uses the fuzzy logic apparatus for a formal description of the decision-making process. 22 refs.; 4 figs.; 2 tabs
Jiang, Wen; Wei, Boya
2018-02-01
The theory of intuitionistic fuzzy sets (IFS) is widely used for dealing with vagueness and the Dempster-Shafer (D-S) evidence theory has a widespread use in multiple criteria decision-making problems under uncertain situation. However, there are many methods to aggregate intuitionistic fuzzy numbers (IFNs), but the aggregation operator to fuse basic probability assignment (BPA) is rare. Power average (P-A) operator, as a powerful operator, is useful and important in information fusion. Motivated by the idea of P-A power, in this paper, a new operator based on the IFS and D-S evidence theory is proposed, which is named as intuitionistic fuzzy evidential power average (IFEPA) aggregation operator. First, an IFN is converted into a BPA, and the uncertainty is measured in D-S evidence theory. Second, the difference between BPAs is measured by Jousselme distance and a satisfying support function is proposed to get the support degree between each other effectively. Then the IFEPA operator is used for aggregating the original IFN and make a more reasonable decision. The proposed method is objective and reasonable because it is completely driven by data once some parameters are required. At the same time, it is novel and interesting. Finally, an application of developed models to the 'One Belt, One road' investment decision-making problems is presented to illustrate the effectiveness and feasibility of the proposed operator.
Peide Liu
2017-11-01
Full Text Available A hesitant intuitionistic fuzzy linguistic set (HIFLS that integrates both qualitative and quantitative evaluations is an extension of the linguistic set, intuitionistic fuzzy set (IFS, hesitant fuzzy set (HFS and hesitant intuitionistic fuzzy set (HIFS. It can describe the qualitative evaluation information given by the decision-makers (DMs and reflect their uncertainty. In this article, we defined some new operational laws and comparative method for HIFLSs. Then, based on these operations, we propose two prioritized aggregation (PA operators for HIFLSs: prioritized weighted averaging operator for HIFLSs (HIFLPWA and prioritized weighted geometric operator for HIFLSs (HIFLPWG. Based on these aggregation operators, an approach for multi-attribute decision-making (MADM is developed under the environment of HIFLSs. Finally, a practical example is given to show the practicality and effectiveness of the developed approach by comparing with the other representative methods.
Digital Arithmetic: Division Algorithms
Montuschi, Paolo; Nannarelli, Alberto
2017-01-01
Division is one of the basic arithmetic operations supported by every computer system. The operation can be performed and implemented by either hardware or software, or by a combination of the two. Although division is not as frequent as addition and multiplication, nowadays, most processors impl...... significant hardware resources and is more suitable for software implementation on the existing multiply units. The purpose of this entry is to provide an introductory survey using a presentation style suitable for the interested non-specialist readers as well....
Relational Demonic Fuzzy Refinement
Tchier, Fairouz
2014-01-01
We use relational algebra to define a refinement fuzzy order called demonic fuzzy refinement and also the associated fuzzy operators which are fuzzy demonic join $({\\bigsqcup }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ , fuzzy demonic meet $({\\sqcap }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ , and fuzzy demonic composition $({\\square }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ . Our definitions and properties are illustrated by some examples using ma...
Baby Arithmetic: One Object Plus One Tone
Kobayashi, Tessei; Hiraki, Kazuo; Mugitani, Ryoko; Hasegawa, Toshikazu
2004-01-01
Recent studies using a violation-of-expectation task suggest that preverbal infants are capable of recognizing basic arithmetical operations involving visual objects. There is still debate, however, over whether their performance is based on any expectation of the arithmetical operations, or on a general perceptual tendency to prefer visually…
Jun Liu
2017-01-01
Full Text Available Under the interval-valued hesitant fuzzy information environment, we investigate a multiattribute group decision making (MAGDM method with continuous entropy weights and improved Hamacher information aggregation operators. Firstly, we introduce the axiomatic definition of entropy for interval-valued hesitant fuzzy elements (IVHFEs and construct a continuous entropy formula on the basis of the continuous ordered weighted averaging (COWA operator. Then, based on the Hamacher t-norm and t-conorm, the adjusted operational laws for IVHFEs are defined. In order to aggregate interval-valued hesitant fuzzy information, some new improved interval-valued hesitant fuzzy Hamacher aggregation operators are investigated, including the improved interval-valued hesitant fuzzy Hamacher ordered weighted averaging (I-IVHFHOWA operator and the improved interval-valued hesitant fuzzy Hamacher ordered weighted geometric (I-IVHFHOWG operator, the desirable properties of which are discussed. In addition, the relationship among these proposed operators is analyzed in detail. Applying the continuous entropy and the proposed operators, an approach to MAGDM is developed. Finally, a numerical example for emergency operating center (EOC selection is provided, and comparative analyses with existing methods are performed to demonstrate that the proposed approach is both valid and practical to deal with group decision making problems.
Fuzzy Rough Ring and Its Prop erties
REN Bi-jun; FU Yan-ling
2013-01-01
This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binary operation of ring was discussed.
Ikonomopoulos, A.; Tsoukalas, L.H.
1993-01-01
A novel approach is described for measuring variables with operational significance in a complex system such as a nuclear reactor. The methodology is based on the integration of artificial neural networks with fuzzy reasoning. Neural networks are used to map dynamic time series to a set of user-defined linguistic labels called fuzzy values. The process takes place in a manner analogous to that of measurement. Hence, the entire procedure is referred to as virtual measurement and its software implementation as a virtual measuring device. An optimization algorithm based on information criteria and fuzzy algebra augments the process and assists in the identification of different states of the monitored parameter. The proposed technique is applied for monitoring parameters such as performance, valve position, transient type, and reactivity. The results obtained from the application of the neural network-fuzzy reasoning integration in a high power research reactor clearly demonstrate the excellent tolerance of the virtual measuring device to faulty signals as well as its ability to accommodate noisy inputs
Solution of a System of Linear Equations with Fuzzy Numbers
Horčík, Rostislav
2008-01-01
Roč. 159, č. 14 (2008), s. 1788-1810 ISSN 0165-0114 R&D Projects: GA AV ČR KJB100300502 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy number * fuzzy interval * interval analysis * fuzzy arithmetic * fuzzy class theory * united solution set Subject RIV: BA - General Mathematics Impact factor: 1.833, year: 2008
Murakami, Hiroki; Seki, Hirokazu; Minakata, Hideaki; Tadakuma, Susumu
This paper describes a novel operationality improvement control for electric power assisted wheelchairs. “Electric power assisted wheelchair” which assists the driving force by electric motors is expected to be widely used as a mobility support system for elderly people and disabled people, however, the performance of the straight and circular road driving must be further improved because the two wheels drive independently. This paper proposes a novel operationality improvement control by fuzzy algorithm to realize the stable driving on straight and circular roads. The suitable assisted torque of the right and left wheels is determined by fuzzy algorithm based on the posture angular velocity, the posture angle of the wheelchair, the human input torque proportion and the total human torque of the right and left wheels. Some experiments on the practical roads show the effectiveness of the proposed control system.
Trace formulae for arithmetical systems
Bogomolny, E.B.; Georgeot, B.; Giannoni, M.J.; Schmit, C.
1992-09-01
For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs
New technological design of arithmetics
Hanitriarivo, R.
2008-01-01
There are illogical and irrational rules in numbers writing and pronunciation in almost of languages. A part of the aim is to show the electronic applications possibility of logical and systematic rules which are proposed by Raoelina Andriambololona to write and pronounce numbers; we had studied and created the arithmetic operations representation corresponding in binary basis and in hexadecimal basis. The brand new found concept corresponds as well as the method which uses the matrix product calculation, in according with the writing and the pronunciation of numbers. It was shown how to concept the arithmetic operators in digital electronics; and we proposed and assumed to make headway and to do amelioration for technical conception of calculator and arithmetic unite those are at the basic function of all computers and almost domestic sophisticated machine. The left hand side- right hand side and increasing order writing of number is exploited to build a new computer programming for a scientific calculator. [fr
Perez C, B.; Benitez R, J.S.; Pacheco S, J.O. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)
2003-07-01
The development of a digital system based on a DSP to implant a Mamdani type algorithm of fuzzy control whose objective is to regulate the neutron power in a nuclear research reactor Type TRIGA Mark III is presented. Its are simultaneously carried out the aggregation des fuzzy stages discreeting the universe of the output variable. The format MPF for the handling of the floating point in the arithmetic operations is used. (Author)
[Acquisition of arithmetic knowledge].
Fayol, Michel
2008-01-01
The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3).
ASIC For Complex Fixed-Point Arithmetic
Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.
1995-01-01
Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.
Auto-control of pumping operations in sewerage systems by rule-based fuzzy neural networks
Y.-M. Chiang
2011-01-01
Full Text Available Pumping stations play an important role in flood mitigation in metropolitan areas. The existing sewerage systems, however, are facing a great challenge of fast rising peak flow resulting from urbanization and climate change. It is imperative to construct an efficient and accurate operating prediction model for pumping stations to simulate the drainage mechanism for discharging the rainwater in advance. In this study, we propose two rule-based fuzzy neural networks, adaptive neuro-fuzzy inference system (ANFIS and counterpropagation fuzzy neural network for on-line predicting of the number of open and closed pumps of a pivotal pumping station in Taipei city up to a lead time of 20 min. The performance of ANFIS outperforms that of CFNN in terms of model efficiency, accuracy, and correctness. Furthermore, the results not only show the predictive water levels do contribute to the successfully operating pumping stations but also demonstrate the applicability and reliability of ANFIS in automatically controlling the urban sewerage systems.
Adelic divisors on arithmetic varieties
Moriwaki, Atsushi
2016-01-01
In this article, the author generalizes several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors, Zariski decompositions for arithmetic divisors on arithmetic surfaces and a special case of Dirichlet's unit theorem on arithmetic varieties, to the case of the adelic arithmetic divisors.
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
Ozoemena, P.C.; Onwumechili, C.A.
1988-11-01
Some new theorems have been propounded for the numbers (M-1), as they relate to other numerals, through the basic arithmetical operations, at different bases M. For some reason, we give the proof of the theorems for the case M=10 using mathematical induction, and by Peano's fifth axiom make our generalizations. Comments are made in respect of the numbers (M-1), (in this case 9). Apart from our theorems facilitating mathematical operations, evidences have also been given, from different sources of the interesting properties of this class of numbers, represented in our own case by the numeral 9. The theorems neither violate the divisibility rule for 9 nor are they a consequence of it. From symmetry, a suggestion is made in respect of the possible origin of the numeration in base 10, and the case of a ten dimensional Universe reconsidered. (author). 18 refs, 1 fig., 4 tabs
Zhang, Jian-Hua; Peng, Xiao-Di; Liu, Hua; Raisch, Jörg; Wang, Ru-Bin
2013-12-01
The human operator's ability to perform their tasks can fluctuate over time. Because the cognitive demands of the task can also vary it is possible that the capabilities of the operator are not sufficient to satisfy the job demands. This can lead to serious errors when the operator is overwhelmed by the task demands. Psychophysiological measures, such as heart rate and brain activity, can be used to monitor operator cognitive workload. In this paper, the most influential psychophysiological measures are extracted to characterize Operator Functional State (OFS) in automated tasks under a complex form of human-automation interaction. The fuzzy c-mean (FCM) algorithm is used and tested for its OFS classification performance. The results obtained have shown the feasibility and effectiveness of the FCM algorithm as well as the utility of the selected input features for OFS classification. Besides being able to cope with nonlinearity and fuzzy uncertainty in the psychophysiological data it can provide information about the relative importance of the input features as well as the confidence estimate of the classification results. The OFS pattern classification method developed can be incorporated into an adaptive aiding system in order to enhance the overall performance of a large class of safety-critical human-machine cooperative systems.
Lee, Seung Jun; Seong, Poong Hyun
2002-01-01
In this work, AuTomated Operating Procedure System (ATOPS) is developed. ATOPS is an automation system for operation of a nuclear power plant (NPP) which can monitor signals, diagnose statuses, and generate control actions according to corresponding operating procedures, without any human operator's help. Main functions of ATOPS are anomaly detection function and procedure execution function, but only the procedure execution function is implemented because this work is just the first step. In the procedure execution function, operating procedures of NPP are analyzed and modeled using Fuzzy Colored Petri Nets (FCPN), and executed depending on decision making of the inference engine. In this work, an ATOPS prototype is developed in order to demonstrate its feasibility and it is also validated using FISA-2/WS simulator. The validation is performed for the cases of a loss of coolant accident (LOCA) and a steam generator tube rupture (SGTR). The simulation results show that ATOPS works correctly in the emergency situations
Butt, Muhammad Arif; Akram, Muhammad
2016-01-01
We present a new intuitionistic fuzzy rule-based decision-making system based on intuitionistic fuzzy sets for a process scheduler of a batch operating system. Our proposed intuitionistic fuzzy scheduling algorithm, inputs the nice value and burst time of all available processes in the ready queue, intuitionistically fuzzify the input values, triggers appropriate rules of our intuitionistic fuzzy inference engine and finally calculates the dynamic priority (dp) of all the processes in the ready queue. Once the dp of every process is calculated the ready queue is sorted in decreasing order of dp of every process. The process with maximum dp value is sent to the central processing unit for execution. Finally, we show complete working of our algorithm on two different data sets and give comparisons with some standard non-preemptive process schedulers.
Prioritizing operation strategies of companies using fuzzy AHP and importance-performance matrix
Mohamad Amin Kaviani
2014-06-01
Full Text Available One of the most important steps to build an appropriate business unit is to setup a suitable long-term strategy. A good strategy helps organization take better advantage of the existing resources and improve the performance of the firm. This paper presents a hybrid method consists of importance-performance analysis combined with fuzzy analytical hierarchy process to determine different operating strategies to increase the performance of a cement industry in Iran. The results indicate that being competitive is number one priority followed by fast delivery, quality product, dependability, cost of production and flexibility.
The Interval-Valued Triangular Fuzzy Soft Set and Its Method of Dynamic Decision Making
Xiaoguo Chen; Hong Du; Yue Yang
2014-01-01
A concept of interval-valued triangular fuzzy soft set is presented, and some operations of “AND,” “OR,” intersection, union and complement, and so forth are defined. Then some relative properties are discussed and several conclusions are drawn. A dynamic decision making model is built based on the definition of interval-valued triangular fuzzy soft set, in which period weight is determined by the exponential decay method. The arithmetic weighted average operator of interval-valued triangular...
A Non-Arithmetical Gödel Logic
Hájek, Petr
2005-01-01
Roč. 13, č. 4 (2005), s. 435-441 ISSN 1367-0751 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy logic * Gödel logic * arithmetical hierarchy Subject RIV: BA - General Mathematics Impact factor: 0.382, year: 2005
Development of arithmetical abilities
Tatjana Levstek
2014-02-01
Full Text Available Arithmetic (from the word 'arithmos' which means 'numbers' is an elementary branch of mathematics. Numeracy is essential for understanding mathematics, so the development of arithmetic abilities has been an area of scientific research for a long time. Recent research has shown that the development of arithmetic abilities is not based only on gaining experience and learning. Some arithmetic abilities, especially the sense of quantity, are innate. Even babies are able to distinguish between groups with different number of elements and they perceive numeracy amodally. Six-month-olds distinguish between two groups with the numeracy ratio of 1 : 2. With age this ratio improves rapidly. Five-year-old children already distinguish between groups with the number ratio 7 : 8. The ability to compare two quantities begins to develop after 15 months of age and children learn how to count spontaneously, together with the acquisition of language. Speech enables children to understand number in its abstract, symbolic sense, thus opening the way to symbolic arithmetic. During the preschool period children use intuition when doing calculations, but in school the arithmetic is based on the knowledge of arithmetical algorithms. So, in order to acquire mathematical knowledge, it is necessary to incorporate memory and automate arithmetical processes, without the use of intuition. However, research has shown that intuition is very important and is even a predictive factor for the development of mathematical abilities throughout the schooling process.
Curiosities of arithmetic gases
Bakas, I.; Bowick, M.J.
1991-01-01
Statistical mechanical systems with an exponential density of states are considered. The arithmetic analog of parafermions of arbitrary order is constructed and a formula for boson-parafermion equivalence is obtained using properties of the Riemann zeta function. Interactions (nontrivial mixing) among arithmetic gases using the concept of twisted convolutions are also introduced. Examples of exactly solvable models are discussed in detail
Theory and applications of ordered fuzzy numbers a tribute to professor Witold Kosiński
Czerniak, Jacek; Mikołajewski, Dariusz; Apiecionek, Łukasz; Ślȩzak, Dominik
2017-01-01
This book is open access under a CC BY 4.0 license. This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike.
Xu, Zeshui
2014-01-01
This book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. It presents the most recent research results and advanced methods in the field. These includes: hesitant fuzzy aggregation techniques, hesitant fuzzy preference relations, hesitant fuzzy measures, hesitant fuzzy clustering algorithms and hesitant fuzzy multi-attribute decision making methods. Since its introduction by Torra and Narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a wide range of applications, from decision-making problems to cluster analysis, from medical diagnosis to personnel appraisal and information retrieval. This book offers a comprehensive report on the state-of-the-art in hesitant fuzzy sets theory and applications, aiming at becoming a reference guide for both researchers and practitioners in the area of fuzzy mathematics and other applied research fields (e.g. operations research, information science, management science and engineering) chara...
Darunee Hunwisai
2017-01-01
Full Text Available In this work, we considered two-person zero-sum games with fuzzy payoffs and matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs. The concepts of TrIFNs and their arithmetic operations were used. The cut-set based method for matrix game with payoffs of TrIFNs was also considered. Compute the interval-type value of any alfa-constrategies by simplex method for linear programming. The proposed method is illustrated with a numerical example.
An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations
Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan
2017-11-01
Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.
How to be Brilliant at Mental Arithmetic
Webber, Beryl
2010-01-01
How to be Brilliant at Mental Arithmetic addresses the twin pillars of mental arithmetic - mental recall and mental agility. Mental recall depends on familiarity with number bonds and plenty of opportunity to practise. Mental agility depends more on confidence with the number system and the four operations. Using the worksheets in this book, students will learn about: tens and units; addition, subtraction, multiplication and division; addition shortcuts; product squares; quick recall; number se
FUZZY RINGS AND ITS PROPERTIES
Karyati Karyati
2017-01-01
One of algebraic structure that involves a binary operation is a group that is defined an un empty set (classical with an associative binary operation, it has identity elements and each element has an inverse. In the structure of the group known as the term subgroup, normal subgroup, subgroup and factor group homomorphism and its properties. Classical algebraic structure is developed to algebraic structure fuzzy by the researchers as an example semi group fuzzy and fuzzy group after fuzzy sets is introduced by L. A. Zadeh at 1965. It is inspired of writing about semi group fuzzy and group of fuzzy, a research on the algebraic structure of the ring is held with reviewing ring fuzzy, ideal ring fuzzy, homomorphism ring fuzzy and quotient ring fuzzy with its properties. The results of this study are obtained fuzzy properties of the ring, ring ideal properties fuzzy, properties of fuzzy ring homomorphism and properties of fuzzy quotient ring by utilizing a subset of a subset level and strong level as well as image and pre-image homomorphism fuzzy ring. Keywords: fuzzy ring, subset level, homomorphism fuzzy ring, fuzzy quotient ring
Lee, Seung Jun; Seong, Poong Hyun
2004-01-01
In this work, AuTomated Operating Procedure System (ATOPS) is developed. ATOPS is an automation system for emergency operation of a nuclear power plant (NPP) and it can monitor signals, diagnose statuses, and generate control actions according to corresponding operating procedures without any human operator's help. Main functions of ATOPS are an anomaly detection function and a procedure execution function but only the procedure execution function is implemented in this work because this work is just the first step. In the procedure execution function, operating procedures of NPPs are analyzed and modeled using Fuzzy Colored Petri Nets (FCPN) and executed depending on decision making of the inference engine. In this work, ATOPS prototype is developed to demonstrate its feasibility and it is also validated using the FISA-2/WS simulator. The validation is performed for the cases of a loss of coolant accident (LOCA) and a steam generator tube rupture (SGTR). The simulation results show that ATOPS works correctly in the emergency situations
Pavlichin, Dmitri S.; Mabuchi, Hideo
2014-06-01
Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a weighted" readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.
Compound Option Pricing under Fuzzy Environment
Xiandong Wang
2014-01-01
Full Text Available Considering the uncertainty of a financial market includes two aspects: risk and vagueness; in this paper, fuzzy sets theory is applied to model the imprecise input parameters (interest rate and volatility. We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske’s compound option pricing formula. For each α, the α-level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy-valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. Finally, we present a numerical analysis to illustrate the compound option pricing under fuzzy environment.
Macian-Sorribes, Hector; Pulido-Velazquez, Manuel
2016-04-01
This contribution presents a methodology for defining optimal seasonal operating rules in multireservoir systems coupling expert criteria and stochastic optimization. Both sources of information are combined using fuzzy logic. The structure of the operating rules is defined based on expert criteria, via a joint expert-technician framework consisting in a series of meetings, workshops and surveys carried out between reservoir managers and modelers. As a result, the decision-making process used by managers can be assessed and expressed using fuzzy logic: fuzzy rule-based systems are employed to represent the operating rules and fuzzy regression procedures are used for forecasting future inflows. Once done that, a stochastic optimization algorithm can be used to define optimal decisions and transform them into fuzzy rules. Finally, the optimal fuzzy rules and the inflow prediction scheme are combined into a Decision Support System for making seasonal forecasts and simulate the effect of different alternatives in response to the initial system state and the foreseen inflows. The approach presented has been applied to the Jucar River Basin (Spain). Reservoir managers explained how the system is operated, taking into account the reservoirs' states at the beginning of the irrigation season and the inflows previewed during that season. According to the information given by them, the Jucar River Basin operating policies were expressed via two fuzzy rule-based (FRB) systems that estimate the amount of water to be allocated to the users and how the reservoir storages should be balanced to guarantee those deliveries. A stochastic optimization model using Stochastic Dual Dynamic Programming (SDDP) was developed to define optimal decisions, which are transformed into optimal operating rules embedding them into the two FRBs previously created. As a benchmark, historical records are used to develop alternative operating rules. A fuzzy linear regression procedure was employed to
Liudong Zhang
2014-01-01
Full Text Available An uncertain monthly reservoirs operation and multicrop deficit irrigation model was proposed under conjunctive use of underground and surface water for water resources optimization management. The objective is to maximize the total crop yield of the entire irrigation districts. Meanwhile, ecological water remained for the downstream demand. Because of the shortage of water resources, the monthly crop water production function was adopted for multiperiod deficit irrigation management. The model reflects the characteristics of water resources repetitive transformation in typical inland rivers irrigation system. The model was used as an example for water resources optimization management in Shiyang River Basin, China. Uncertainties in reservoir management shown as fuzzy probability were treated through chance-constraint parameter for decision makers. Necessity of dominance (ND was used to analyse the advantages of the method. The optimization results including reservoirs real-time operation policy, deficit irrigation management, and the available water resource allocation could be used to provide decision support for local irrigation management. Besides, the strategies obtained could help with the risk analysis of reservoirs operation stochastically.
Multi-valued and Fuzzy Logic Realization using TaOx Memristive Devices.
Bhattacharjee, Debjyoti; Kim, Wonjoo; Chattopadhyay, Anupam; Waser, Rainer; Rana, Vikas
2018-01-08
Among emerging non-volatile storage technologies, redox-based resistive switching Random Access Memory (ReRAM) is a prominent one. The realization of Boolean logic functionalities using ReRAM adds an extra edge to this technology. Recently, 7-state ReRAM devices were used to realize ternary arithmetic circuits, which opens up the computing space beyond traditional binary values. In this manuscript, we report realization of multi-valued and fuzzy logic operators with a representative application using ReRAM devices. Multi-valued logic (MVL), such as Łukasiewicz logic generalizes Boolean logic by allowing more than two truth values. MVL also permits operations on fuzzy sets, where, in contrast to standard crisp logic, an element is permitted to have a degree of membership to a given set. Fuzzy operations generally model human reasoning better than Boolean logic operations, which is predominant in current computing technologies. When the available information for the modelling of a system is imprecise and incomplete, fuzzy logic provides an excellent framework for the system design. Practical applications of fuzzy logic include, industrial control systems, robotics, and in general, design of expert systems through knowledge-based reasoning. Our experimental results show, for the first time, that it is possible to model fuzzy logic natively using multi-state memristive devices.
Efficient solution of a multi objective fuzzy transportation problem
Vidhya, V.; Ganesan, K.
2018-04-01
In this paper we present a methodology for the solution of multi-objective fuzzy transportation problem when all the cost and time coefficients are trapezoidal fuzzy numbers and the supply and demand are crisp numbers. Using a new fuzzy arithmetic on parametric form of trapezoidal fuzzy numbers and a new ranking method all efficient solutions are obtained. The proposed method is illustrated with an example.
Nihal ERGİNEL
2010-12-01
Full Text Available Mobile number portability systems is a system that can allow portability of GSM (Global System for Mobile Communications number from another operator without changing GSM number. There are several criteria to select the GSM operators by customer after this system is legal in Turkey. The main purpose of this study is to determine the market sharing in the future of GSM operators by expressing the weighting grades of selection criteria and the relationship between criteria and alternatives that include uncertainty as fuzzy triangular numbers. In this study, the selection criteria of GSM operators are defined form literature and views of customer and weighted with linguistic variables by working group. Avea, Turkcell and Vodafone that active in Turkey are graded with linguistic variables to each criterion. Analyzing linguistic variables as qualitative variables and using graded linguistic variables in a specified interval are required fuzzy multi-criteria decision making methods. Expected market sharing of GSM operators is determined by using fuzzy TOPSIS method.
NPP operator support in decision making - diagnostics of the operation failures using fuzzy logic
Petruzela, I.
2000-01-01
In large complex systems such as nuclear power plants (NPP) and chemical industry plants, various subsystems fulfil the needs of process control and safety. Continued operation of these systems has both economic and safety implications. Electric utilities seek continuously to improve the operation of power generating stations. The improvement in the NPP Dukovany (4 x 440 MW) is related to the introduction of the plant to frequency control, meaning that the plant is operated not only in the base load operational mode but in the load follow mode as well. To achieve the improvement of plant operation, it was necessary to provide modifications to the plant control system, plant information system and diagnostics. This chapter deals with utilisation of artificial intelligence (AI) methods in implementation of these plant modifications. (orig.)
Jiahang Yuan
2017-01-01
Full Text Available In consideration of the interaction among attributes and the influence of decision makers’ risk attitude, this paper proposes an intuitionistic trapezoidal fuzzy aggregation operator based on Choquet integral and prospect theory. With respect to a multiattribute group decision-making problem, the prospect value functions of intuitionistic trapezoidal fuzzy numbers are aggregated by the proposed operator; then a grey relation-projection pursuit dynamic cluster method is developed to obtain the ranking of alternatives; the firefly algorithm is used to optimize the objective function of projection for obtaining the best projection direction of grey correlation projection values, and the grey correlation projection values are evaluated, which are applied to classify, rank, and prefer the alternatives. Finally, an illustrative example is taken in the present study to make the proposed method comprehensible.
Yi Cao
2013-06-01
Full Text Available A novel intelligent fault diagnosis method for motor roller bearings which operate under unsteady rotating speed and load is proposed in this paper. The pseudo Wigner-Ville distribution (PWVD and the relative crossing information (RCI methods are used for extracting the feature spectra from the non-stationary vibration signal measured for condition diagnosis. The RCI is used to automatically extract the feature spectrum from the time-frequency distribution of the vibration signal. The extracted feature spectrum is instantaneous, and not correlated with the rotation speed and load. By using the ant colony optimization (ACO clustering algorithm, the synthesizing symptom parameters (SSP for condition diagnosis are obtained. The experimental results shows that the diagnostic sensitivity of the SSP is higher than original symptom parameter (SP, and the SSP can sensitively reflect the characteristics of the feature spectrum for precise condition diagnosis. Finally, a fuzzy diagnosis method based on sequential inference and possibility theory is also proposed, by which the conditions of the machine can be identified sequentially as well.
Y. N. Petrenko
2011-01-01
Full Text Available The purpose of a crane control system is to provide load transfer with minimum swinging. The paper presents a developed three-dimensional simulation model of a bridge crane with fuzzy logic controller designed with application of genetic algorithms. Comparative indices of oscillation while load transferring are given in the paper. The indices have been obtained at various parameters of the fuzzy logic controller.
Andrew John
2014-06-01
Full Text Available The selection of an appropriate resilience investment strategy to optimize the operational efficiency of a seaport is a challenging task given that many criteria need to be considered and modelled under an uncertain environment. The design of such a complex decision system consists of many subjective and imprecise parameters contained in different quantitative and qualitative forms. This paper proposes a fuzzy multi-attribute decision making methodology for the selection of an appropriate resilience investment strategy in a succinct and straightforward manner. The decision support model allows for a collaborative modelling of the system by multiple analysts in a group decision making process. Fuzzy analytical hierarchy process (FAHP was utilized to analyse the complex structure of the system to obtain the weights of all the criteria while fuzzy technique for order of preference by similarity to ideal solution (TOPSIS was employed to facilitate the ranking process of the resilience strategies. Given that it is often financially difficult to invest in all the resilience strategies, it is envisaged that the proposed approach could provide decision makers with a flexible and transparent tool for selecting appropriate resilience strategies aimed at increasing the resilience of seaport operations.
Zhao, Ximei; Ren, Chengyi; Liu, Hao; Li, Haogyi
2014-12-01
Robotic catheter minimally invasive operation requires that the driver control system has the advantages of quick response, strong anti-jamming and real-time tracking of target trajectory. Since the catheter parameters of itself and movement environment and other factors continuously change, when the driver is controlled using traditional proportional-integral-derivative (PID), the controller gain becomes fixed once the PID parameters are set. It can not change with the change of the parameters of the object and environmental disturbance so that its change affects the position tracking accuracy, and may bring a large overshoot endangering patients' vessel. Therefore, this paper adopts fuzzy PID control method to adjust PID gain parameters in the tracking process in order to improve the system anti-interference ability, dynamic performance and tracking accuracy. The simulation results showed that the fuzzy PID control method had a fast tracking performance and a strong robustness. Compared with those of traditional PID control, the feasibility and practicability of fuzzy PID control are verified in a robotic catheter minimally invasive operation.
Lei, Qian
2017-01-01
This book offers a comprehensive and systematic review of the latest research findings in the area of intuitionistic fuzzy calculus. After introducing the intuitionistic fuzzy numbers’ operational laws and their geometrical and algebraic properties, the book defines the concept of intuitionistic fuzzy functions and presents the research on the derivative, differential, indefinite integral and definite integral of intuitionistic fuzzy functions. It also discusses some of the methods that have been successfully used to deal with continuous intuitionistic fuzzy information or data, which are different from the previous aggregation operators focusing on discrete information or data. Mainly intended for engineers and researchers in the fields of fuzzy mathematics, operations research, information science and management science, this book is also a valuable textbook for postgraduate and advanced undergraduate students alike.
A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers
Jiang-Xia Nan
2010-09-01
Full Text Available The intuitionistic fuzzy set (IF-set has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs. Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example.
Quantum arithmetic with the Quantum Fourier Transform
Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos
2014-01-01
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.
Algebraic Aspects of Families of Fuzzy Languages
Asveld, P.R.J.; Heylen, Dirk K.J.; Nijholt, Antinus; Scollo, Giuseppe
2000-01-01
We study operations on fuzzy languages such as union, concatenation,Kleene $\\star$, intersection with regular fuzzy languages, and several kinds of (iterated) fuzzy substitution. Then we consider families of fuzzy languages, closed under a fixed collection of these operations, which results in the
Mukhanov, O.A.; Rylov, S.V.; Semenov, V.K.; Vyshenskii, S.V.
1989-01-01
Several ways of local timing of the Josephson-junction RSFQ (Rapid Single Flux Quantum) logic elements are proposed, and their peculiarities are discussed. Several examples of serial and parallel pipelined arithmetic blocks using various types of timing are suggested and their possible performance is discussed. Serial devices enable one to perform n-bit functions relatively slowly but using integrated circuits of a moderate integration scale, while parallel pipelined devices are more hardware-wasteful but promise extremely high productivity
Arithmetic of Complex Manifolds
Lange, Herbert
1989-01-01
It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms. In recent years such problems, which are simultaneously of arithmetic and geometric interest, have become increasingly important. This proceedings volume contains 12 original research papers. Its main topics are theta functions, modular forms, abelian varieties and algebraic three-folds.
Memory updating and mental arithmetic
Cheng-Ching eHan
2016-02-01
Full Text Available Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults.
Alves, Antonio Carlos Pinto Dias
2000-09-01
A nuclear power plant has a myriad of complex system and sub-systems that, working cooperatively, make the control of the whole plant. Nevertheless their operation be automatic most of the time, the integral understanding of their internal- logic can be away of the comprehension of even experienced operators because of the poor interpretability those controls offer. This difficulty does not happens only in nuclear power plants but in almost every a little more complex control system. Neuro-fuzzy models have been used for the last years in a attempt of suppress these difficulties because of their ability of modelling in linguist form even a system which behavior is extremely complex. This is a very intuitive human form of interpretation and neuro-fuzzy model are gathering increasing acceptance. Unfortunately, neuro-fuzzy models can grow up to become of hard interpretation because of the complexity of the systems under modelling. In general, that growing occurs in function of redundant rules or rules that cover a very little domain of the problem. This work presents an identification method for neuro-fuzzy models that not only allows models grow in function of the existent complexity but that beforehand they try to self-adapt to avoid the inclusion of new rules. This form of construction allowed to arrive to highly interpretative neuro-fuzzy models even of very complex systems. The use of this kind of technique in modelling the control of the pressurizer of a PWR nuclear power plant allowed verify its validity and how neuro-fuzzy models so built can be useful in understanding the automatic operation of a nuclear power plant. (author)
Towards an arithmetical logic the arithmetical foundations of logic
Gauthier, Yvon
2015-01-01
This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of l...
Toward the Use of Fuzzy Relations in the Definition of Mathematical Morphology Operators
Nicolás Madrid
2016-03-01
Full Text Available In this paper we present a definition of erosions and dilations in terms of fuzzy relations and adjoint triples. We firstly show that we can represent any algebraic erosion and dilation in such a terms and secondly, we present a set of approaches that can be covered by our definition of relational erosions and dilations.
Effect of co-operative fuzzy c-means clustering on estimates of three ...
infinite isotropic elastic media in concise matrix ... hydrate and free gas accumulation. 2. AVA method ... wave propagation across the boundaries of hori- zontally .... Flow chart showing the sequence of steps in the present scheme of fuzzy c-mean clustering adapted for AVA ... porosity 0.38, OIL API 28.5, brine salinity 0.07, ...
T Atanassov, Krassimir
2017-01-01
The book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author’s research and others’ findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike.
Sets with Prescribed Arithmetic Densities
Luca, F.; Pomerance, C.; Porubský, Štefan
2008-01-01
Roč. 3, č. 2 (2008), s. 67-80 ISSN 1336-913X R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : generalized arithmetic density * generalized asymptotic density * generalized logarithmic density * arithmetical semigroup * weighted arithmetic mean * ratio set * R-dense set * Axiom A * delta-regularly varying function Subject RIV: BA - General Mathematics
Arithmetic functions in torus and tree networks
Bhanot, Gyan; Blumrich, Matthias A.; Chen, Dong; Gara, Alan G.; Giampapa, Mark E.; Heidelberger, Philip; Steinmacher-Burow, Burkhard D.; Vranas, Pavlos M.
2007-12-25
Methods and systems for performing arithmetic functions. In accordance with a first aspect of the invention, methods and apparatus are provided, working in conjunction of software algorithms and hardware implementation of class network routing, to achieve a very significant reduction in the time required for global arithmetic operation on the torus. Therefore, it leads to greater scalability of applications running on large parallel machines. The invention involves three steps in improving the efficiency and accuracy of global operations: (1) Ensuring, when necessary, that all the nodes do the global operation on the data in the same order and so obtain a unique answer, independent of roundoff error; (2) Using the topology of the torus to minimize the number of hops and the bidirectional capabilities of the network to reduce the number of time steps in the data transfer operation to an absolute minimum; and (3) Using class function routing to reduce latency in the data transfer. With the method of this invention, every single element is injected into the network only once and it will be stored and forwarded without any further software overhead. In accordance with a second aspect of the invention, methods and systems are provided to efficiently implement global arithmetic operations on a network that supports the global combining operations. The latency of doing such global operations are greatly reduced by using these methods.
Introduction to cardinal arithmetic
Holz, M; Weitz, E
1999-01-01
This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the 1970s led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open in the 1970s.Reviews:'The authors aim their text at beginners in set theory. They start
The arithmetic of supersymmetric vacua
Bourget, Antoine; Troost, Jan [Laboratoire de Physique Théorique de l’École Normale Supérieure, CNRS, PSL Research University, Sorbonne Universités,75005 Paris (France)
2016-07-07
We provide explicit formulas for the number of vacua of four-dimensional pure N=1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. The formula for the (SU(N)/ℤ{sub m}){sub n} theory is a key ingredient in the semi-classical calculation of the number of massive vacua of N=1{sup ∗} gauge theories with gauge algebra su(n), compactified on a circle. Using arithmetic, we express that number in an SL(2,ℤ) duality invariant manner. We confirm our tally of massive vacua of the N=1{sup ∗} theories by a count of inequivalent extrema of the exact superpotential.
The Duality Principle in Teaching Arithmetic and Geometric Series
Yeshurun, Shraga
1978-01-01
The author discusses the use of the duality principle in combination with the hierarchy of algebraic operations in helping students to retain and use definitions and rules for arithmetic and geometric sequences and series. (MN)
Shawkat Alkhazaleh
2011-01-01
Full Text Available We introduce the concept of possibility fuzzy soft set and its operation and study some of its properties. We give applications of this theory in solving a decision-making problem. We also introduce a similarity measure of two possibility fuzzy soft sets and discuss their application in a medical diagnosis problem.
A neuro-fuzzy controller for xenon spatial oscillations in load-following operation
Na, Man Gyun [Chosun University, Kwangju (Korea, Republic of); Upadhyaya, Belle R. [The University of Tennessee, Knoxville (United States)
1997-12-31
A neuro-fuzzy control algorithm is applied for xenon spatial oscillations in a pressurized water reactor. The consequent and antecedent parameters of the fuzzy rules are tuned by the gradient descent method. The reactor model used for computer simulations is a two-point xenon oscillation model. The reactor core is axially divided into two regions and each region has one input and one output and is coupled with the other region. The interaction between the regions of the reactor core is treated by a decoupling scheme. This proposed control method exhibits very responses to a step or a ramp change of target axial offest without any residual flux oscillations. 9 refs., 5 figs. (Author)
A neuro-fuzzy controller for xenon spatial oscillations in load-following operation
Na, Man Gyun [Chosun University, Kwangju (Korea, Republic of); Upadhyaya, Belle R [The University of Tennessee, Knoxville (United States)
1998-12-31
A neuro-fuzzy control algorithm is applied for xenon spatial oscillations in a pressurized water reactor. The consequent and antecedent parameters of the fuzzy rules are tuned by the gradient descent method. The reactor model used for computer simulations is a two-point xenon oscillation model. The reactor core is axially divided into two regions and each region has one input and one output and is coupled with the other region. The interaction between the regions of the reactor core is treated by a decoupling scheme. This proposed control method exhibits very responses to a step or a ramp change of target axial offest without any residual flux oscillations. 9 refs., 5 figs. (Author)
The Interval-Valued Triangular Fuzzy Soft Set and Its Method of Dynamic Decision Making
Xiaoguo Chen
2014-01-01
Full Text Available A concept of interval-valued triangular fuzzy soft set is presented, and some operations of “AND,” “OR,” intersection, union and complement, and so forth are defined. Then some relative properties are discussed and several conclusions are drawn. A dynamic decision making model is built based on the definition of interval-valued triangular fuzzy soft set, in which period weight is determined by the exponential decay method. The arithmetic weighted average operator of interval-valued triangular fuzzy soft set is given by the aggregating thought, thereby aggregating interval-valued triangular fuzzy soft sets of different time-series into a collective interval-valued triangular fuzzy soft set. The formulas of selection and decision values of different objects are given; therefore the optimal decision making is achieved according to the decision values. Finally, the steps of this method are concluded, and one example is given to explain the application of the method.
Fuzzy commutative algebra and its application in mechanical engineering
Han, J.; Song, H.
1996-01-01
Based on literature data, this paper discusses the whole mathematical structure about point-fuzzy number set F(R). By introducing some new operations about addition, subtraction, multiplication, division and scalar multiplication, we prove that F(R) can form fuzzy linear space, fuzzy commutative ring, fuzzy commutative algebra in order. Furthermore, we get that A is fuzzy commutative algebra for any fuzzy subset. At last, we give an application of point-fuzzy number to mechanical engineering
Baron, Jorge H.; Rivera, S.S.
2000-01-01
The so-called vulnerability matrix is used in the evaluation part of the probabilistic safety assessment for a nuclear power plant, during the containment event trees calculations. This matrix is established from what is knows as Numerical Categories for Engineering Judgement. This matrix is usually established with numerical values obtained with traditional arithmetic using the set theory. The representation of this matrix with fuzzy numbers is much more adequate, due to the fact that the Numerical Categories for Engineering Judgement are better represented with linguistic variables, such as 'highly probable', 'probable', 'impossible', etc. In the present paper a methodology to obtain a Fuzzy Vulnerability Matrix is presented, starting from the recommendations on the Numerical Categories for Engineering Judgement. (author)
Arithmetic soft-core accelerators
Calderon Rocabado, D.R.H.
2007-01-01
In this dissertation, we address the design of multi-functional arithmetic units working with the most common fixed-point number representations, namely: unsigned, sign-magnitude, fractional, ten's and two's complement notations. The main design goal is to collapse multiple complex arithmetic
Coherent states, pseudodifferential analysis and arithmetic
Unterberger, André
2012-06-01
Basic questions regarding families of coherent states include describing some constructions of such and the way they can be applied to operator theory or partial differential equations. In both questions, pseudodifferential analysis is important. Recent developments indicate that they can contribute to methods in arithmetic, especially modular form theory. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
JuanM. Medina
2012-08-01
Full Text Available This paper proposes a parameterized definition for fuzzy comparators on complex fuzzy datatypes like fuzzy collections with conjunctive semantics and fuzzy objects. This definition and its implementation on a Fuzzy Object-Relational Database Management System (FORDBMS provides the designer with a powerful tool to adapt the behavior of these operators to the semantics of the considered application.
Akhtar Hussain
2017-02-01
Full Text Available The resiliency of power systems can be enhanced during emergency situations by using microgrids, due to their capability to supply local loads. However, precise prediction of disturbance events is very difficult rather the occurrence probability can be expressed as, high, medium, or low, etc. Therefore, a fuzzy logic-based battery energy storage system (BESS operation controller is proposed in this study. In addition to BESS state-of-charge and market price signals, event occurrence probability is taken as crisp input for the BESS operation controller. After assessing the membership levels of all the three inputs, BESS operation controller decides the operation mode (subservient or resilient of BESS units. In subservient mode, BESS is fully controlled by an energy management system (EMS while in the case of resilient mode, the EMS follows the commands of the BESS operation controller for scheduling BESS units. Therefore, the proposed hybrid microgrid model can operate in normal, resilient, and emergency modes with the respective objective functions and scheduling horizons. Due to the consideration of resilient mode, load curtailment can be reduced during emergency operation periods. Numerical simulations have demonstrated the effectiveness of the proposed strategy for enhancing the resiliency of hybrid microgrids.
Komal
2018-05-01
Nowadays power consumption is increasing day-by-day. To fulfill failure free power requirement, planning and implementation of an effective and reliable power management system is essential. Phasor measurement unit(PMU) is one of the key device in wide area measurement and control systems. The reliable performance of PMU assures failure free power supply for any power system. So, the purpose of the present study is to analyse the reliability of a PMU used for controllability and observability of power systems utilizing available uncertain data. In this paper, a generalized fuzzy lambda-tau (GFLT) technique has been proposed for this purpose. In GFLT, system components' uncertain failure and repair rates are fuzzified using fuzzy numbers having different shapes such as triangular, normal, cauchy, sharp gamma and trapezoidal. To select a suitable fuzzy number for quantifying data uncertainty, system experts' opinion have been considered. The GFLT technique applies fault tree, lambda-tau method, fuzzified data using different membership functions, alpha-cut based fuzzy arithmetic operations to compute some important reliability indices. Furthermore, in this study ranking of critical components of the system using RAM-Index and sensitivity analysis have also been performed. The developed technique may be helpful to improve system performance significantly and can be applied to analyse fuzzy reliability of other engineering systems. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
Application of fuzzy logic to social choice theory
Mordeson, John N; Clark, Terry D
2015-01-01
Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the ""union"" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow's
Pulido-Velazquez, Manuel; Macian-Sorribes, Hector; María Benlliure-Moreno, Jose; Fullana-Montoro, Juan
2015-04-01
Water resources systems in areas with a strong tradition in water use are complex to manage by the high amount of constraints that overlap in time and space, creating a complicated framework in which past, present and future collide between them. In addition, it is usual to find "hidden constraints" in system operations, which condition operation decisions being unnoticed by anyone but the river managers and users. Being aware of those hidden constraints requires usually years of experience and a degree of involvement in that system's management operations normally beyond the possibilities of technicians. However, their impact in the management decisions is strongly imprinted in the historical data records available. The purpose of this contribution is to present a methodology capable of assessing operating rules in complex water resources systems combining historical records and expert criteria. Both sources are coupled using fuzzy logic. The procedure stages are: 1) organize expert-technicians preliminary meetings to let the first explain how they manage the system; 2) set up a fuzzy rule-based system (FRB) structure according to the way the system is managed; 3) use the historical records available to estimate the inputs' fuzzy numbers, to assign preliminary output values to the FRB rules and to train and validate these rules; 4) organize expert-technician meetings to discuss the rule structure and the input's quantification, returning if required to the second stage; 5) once the FRB structure is accepted, its output values must be refined and completed with the aid of the experts by using meetings, workshops or surveys; 6) combine the FRB with a Decision Support System (DSS) to simulate the effect of those management decisions; 7) compare its results with the ones offered by the historical records and/or simulation or optimization models; and 8) discuss with the stakeholders the model performance returning, if it's required, to the fifth or the second stage
Alaoui Youssef Lamrani
2017-12-01
Full Text Available Managing operational risk efficiently is a critical factor of microfinance institutions (MFIs to get a financial and social return. The purpose of this paper is to identify, assess and prioritize the root causes of failure within the microfinance lending process (MLP especially in Moroccan microfinance institutions. Considering the limitation of traditional failure mode and effect analysis (FMEA method in assessing and classifying risks, the methodology adopted in this study focuses on developing a fuzzy logic inference system (FLIS based on (FMEA. This approach can take into account the subjectivity of risk indicators and the insufficiency of statistical data. The results show that the Moroccan MFIs need to focus more on customer relationship management and give more importance to their staff training, to clients screening as well as to their business analysis.
Hybrid content addressable memory MSD arithmetic
Li, Yao; Kim, Dai Hyun; Kostrzewski, Andrew A.; Eichmann, George
1990-07-01
The modified signed-digit (MSD) number system, because of its inherent weak interdigit dependance, has been suggested as a useful means for a fast and parallel digital arithmetic. To maintain a fast processing speed, a single-stage holographic optical content-addressable memory (CAM) based MSD algorithm was suggested. In this paper, a novel non-holographic opto-electronic CAM based fast MSD addition processing architecture is proposed. The proposed concept has been verified with our first-order proof-of-principle experiments. A figure of merit comparison of this and other existing approaches is also presented. Based on this key opto-electronic CAM element, implementation of more sophisticated I'VISD arithmetic, such as optical MSD subtraction and multiplication operations, are proposed.
Petr Hájek on mathematical fuzzy logic
Montagna, Franco
2014-01-01
This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vague
Some studies on arithmetical chaos in classical and quantum mechanics
Bolte, J.
1993-04-01
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furthermore, the arithmetical systems are distinguished by a structure that appears as a generalization of geometric symmetries. These pseudosymmetries occur in the quantization of the classical arithmetic systems as Hecke operators, which form an infinite algebra of self-adjoint operators commuting with the Hamiltonian. The statistical properties of quantum energies in the arithmetical systems have previously been identified as exceptional. They do not fit into the general scheme of random matrix theory. It is shown with the help of a simplified model for the spectral form factor how the spectral statistics in arithmetical quantum chaos can be understood by the properties of the corresponding classical geodesic length spectra. A decisive role is played by the exponentially increasing multiplicities of lengths. The model developed for the level spacings distribution and for the number variance is compared to the corresponding quantities obtained from quantum energies for a specific arithmetical system. Finally, the convergence properties of a representation for the Selberg zeta function as a Dirichlet series are studied. It turns out that the exceptional classical and quantum mechanical properties shared by the arithmetical systems prohibit a convergence of this important function in the physically interesting domain. (orig.)
Grey Language Hesitant Fuzzy Group Decision Making Method Based on Kernel and Grey Scale.
Li, Qingsheng; Diao, Yuzhu; Gong, Zaiwu; Hu, Aqin
2018-03-02
Based on grey language multi-attribute group decision making, a kernel and grey scale scoring function is put forward according to the definition of grey language and the meaning of the kernel and grey scale. The function introduces grey scale into the decision-making method to avoid information distortion. This method is applied to the grey language hesitant fuzzy group decision making, and the grey correlation degree is used to sort the schemes. The effectiveness and practicability of the decision-making method are further verified by the industry chain sustainable development ability evaluation example of a circular economy. Moreover, its simplicity and feasibility are verified by comparing it with the traditional grey language decision-making method and the grey language hesitant fuzzy weighted arithmetic averaging (GLHWAA) operator integration method after determining the index weight based on the grey correlation.
If Gravity is Geometry, is Dark Energy just Arithmetic?
Czachor, Marek
2017-04-01
Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, R+4 and (- L/2, L/2)4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms of the corresponding calculus. However, when one switches to the `natural' Diophantine arithmetic and calculus, the Minkowskian character of the space is lost and what one effectively obtains is a Lorentzian manifold. I discuss in more detail the problem of electromagnetic fields produced by a pointlike charge. The solution has the standard form when expressed in terms of the non-Diophantine formalism. When the `natural' formalsm is used, the same solution looks as if the fields were created by a charge located in an expanding universe, with nontrivially accelerating expansion. The effect is clearly visible also in solutions of the Friedman equation with vanishing cosmological constant. All of this suggests that phenomena attributed to dark energy may be a manifestation of a miss-match between the arithmetic employed in mathematical modeling, and the one occurring at the level of natural laws. Arithmetic is as physical as geometry.
Rahonis, George
The theory of fuzzy recognizable languages over bounded distributive lattices is presented as a paradigm of recognizable formal power series. Due to the idempotency properties of bounded distributive lattices, the equality of fuzzy recognizable languages is decidable, the determinization of multi-valued automata is effective, and a pumping lemma exists. Fuzzy recognizable languages over finite and infinite words are expressively equivalent to sentences of the multi-valued monadic second-order logic. Fuzzy recognizability over bounded ℓ-monoids and residuated lattices is briefly reported. The chapter concludes with two applications of fuzzy recognizable languages to real world problems in medicine.
Intuitionistic fuzzy aggregation and clustering
Xu, Zeshui
2012-01-01
This book offers a systematic introduction to the clustering algorithms for intuitionistic fuzzy values, the latest research results in intuitionistic fuzzy aggregation techniques, the extended results in interval-valued intuitionistic fuzzy environments, and their applications in multi-attribute decision making, such as supply chain management, military system performance evaluation, project management, venture capital, information system selection, building materials classification, and operational plan assessment, etc.
A study on generalized hesitant intuitionistic Fuzzy soft sets
Nazra, A.; Syafruddin; Wicaksono, G. C.; Syafwan, M.
2018-03-01
By combining the concept of hesitant intuitionistic fuzzy sets, fuzzy soft sets and fuzzy sets, we extend hesitant intuitionistic fuzzy soft sets to a generalized hesitant intuitionistic fuzzy soft sets. Some operations on generalized hesitant intuitionistic fuzzy soft sets, such as union, complement, operations “AND” and “OR”, and intersection are defined. From such operations the authors obtain related properties such as commutative, associative and De Morgan's laws. The authors also get an algebraic structure of the collection of all generalized hesitant intuitionistic fuzzy soft sets over a set.
Arithmetic learning in advanced age.
Zamarian, Laura; Scherfler, Christoph; Kremser, Christian; Pertl, Marie-Theres; Gizewski, Elke; Benke, Thomas; Delazer, Margarete
2018-01-01
Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger
Face Recognition using Approximate Arithmetic
Marso, Karol
Face recognition is image processing technique which aims to identify human faces and found its use in various diﬀerent ﬁelds for example in security. Throughout the years this ﬁeld evolved and there are many approaches and many diﬀerent algorithms which aim to make the face recognition as eﬀective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....
А. М. Невиніцин
2000-12-01
Full Text Available The paper deals with the problem of definition of optimal and ultimate-acceptable interruptions in training for operations in emergency cases of flight. The theory of fuzzy sets is applied for this purpose and built are belonging functions of a linguistic variable "professional preparation level". For the 1st, 2nd and 3rd classes of air traffic controllers the optimal and ultimate-acceptable interruptions in learning are determined depending on the type of emergency case of flight
Solutions to Arithmetic Convolution Equations
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2007-01-01
Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007
Some arithmetically symmetrical bandpass filters
Paranasi, P.; Roy, S. C. D.
1981-01-01
A combination of the conventional and Matthaei lowpass-bandpass transformations is shown to result in some bandpass filters having very good arithmetic symmetry. The technique presented is applicable to the Butterworth and inverse Chebyshev types of magnitude approximations and the Bessel type of delay approximations. It is not valid, however, for the Chebyshev and elliptic varieties of filters.
Equations for arithmetic pointed tori
Sijsling, J.R.
2010-01-01
In 1983, Kisao Takeuchi enumerated all 71 arithmetic (1;e)-groups. This is a special set of discrete subgroups of SL(2,R) of finite covolume and signature (1;e). The corresponding quotients of the upper half plane (called (1;e)-curves) have genus equal to 1 and a single elliptic point of order e.
Groups and fields in arithmetic
Kosters, Michiel F.
2014-01-01
This thesis consists of 8 chapters in which we discuss various aspects of arithmetic. In the first chapter, we give an introduction to the algebraic theory of valued fields. In the second chapter, we give an introduction to the theory of normal projective curves. In particular, we study curves over
Rewrite systems for integer arithmetic
H.R. Walters (Pum); H. Zantema (Hans)
1995-01-01
textabstractWe present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground confluent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by
Rewrite systems for integer arithmetic
Walters, H.R.; Zantema, H.
1994-01-01
We present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground con uent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by successor and
Kang, Ki Sig
1995-02-01
The on - line Operator Aid SYStem (OASYS) has been developed to support operator's decision making process and to ensure the safety of nuclear power plants (NPPs) by timely providing operators with proper guidelines according to the plant operation mode. The OASYS consists of four systems such as the signal validation and management system (SVMS), the plant monitoring system (PMS), the alarm filtering and diagnostic system (AFDS), and the dynamic emergency procedure tracking system (DEPTS). The SVMS and the PMS help operators to maintain a plant as a normal operation condition. The AFDS covers the abnormal events until they result in exceeding the limit range of reactor trip signals, while after a reactor trip, the DEPTS aids operators with proper guidelines so as to shutdown safely. The OASYS uses a rule based expert system and a fuzzy logic. The rule based expert system is used to classify the pre-defined events and track the emergency operating procedures (EOPs) through data processing. The fuzzy logic is used to generate the conceptual high level alarms for the prognostic diagnosis and to evaluate the qualitative fuzzy criteria used in EOPs. Performance assessment of the OASYS demonstrates that it is capable of diagnosing plant abnormal conditions and providing operators appropriate guidelines with fast response time and consistency. The developed technology for OASYS will be used to design the Integrated Advanced Control Room in which a plant can be operated by one operator during normal operation. The advanced EOP for emergency operation has been developed by focusing attention on the importance of the operators' role in emergency conditions. To overcome the complexity of current EOPs and maintain the consistency of operators' action according to plant emergency conditions, operator's tasks were allocated according to their duties in the advanced EOP and the computerized operator aid system (COAS) has been developed as an alternative to reduce operator
A Qualitative Simulation Framework in Smalltalk Based on Fuzzy Arithmetic
Richard L. Olson; Daniel L. Schmoldt; David L. Peterson
1996-01-01
For many systems, it is not practical to collect and correlate empirical data necessary to formulate a mathematical model. However, it is often sufficient to predict qualitative dynamics effects (as opposed to system quantities), especially for research purposes. In this effort, an object-oriented application framework (AF) was developed for the qualitative modeling of...
Vamvakoussi, Xenia; Van Dooren, Wim; Verschaffel, Lieven
2013-01-01
This study tested the hypothesis that intuitions about the effect of operations, e.g., "addition makes bigger" and "division makes smaller", are still present in educated adults, even after years of instruction. To establish the intuitive character, we applied a reaction time methodology, grounded in dual process theories of reasoning. Educated…
C. S. Rajan
2006-11-11
Nov 11, 2006 ... In other words, knowing the sounds that emanate from the drum can you figure out the shape of the drum? ... other words it is the lift of the metric to a natural second order differential operator. self-adjoint. ... It is expected in some fundamental sense that these spaces are universal for the class of algebraic ...
Reading instead of reasoning? Predictors of arithmetic skills in children with cochlear implants.
Huber, Maria; Kipman, Ulrike; Pletzer, Belinda
2014-07-01
The aim of the present study was to evaluate whether the arithmetic achievement of children with cochlear implants (CI) was lower or comparable to that of their normal hearing peers and to identify predictors of arithmetic achievement in children with CI. In particular we related the arithmetic achievement of children with CI to nonverbal IQ, reading skills and hearing variables. 23 children with CI (onset of hearing loss in the first 24 months, cochlear implantation in the first 60 months of life, atleast 3 years of hearing experience with the first CI) and 23 normal hearing peers matched by age, gender, and social background participated in this case control study. All attended grades two to four in primary schools. To assess their arithmetic achievement, all children completed the "Arithmetic Operations" part of the "Heidelberger Rechentest" (HRT), a German arithmetic test. To assess reading skills and nonverbal intelligence as potential predictors of arithmetic achievement, all children completed the "Salzburger Lesetest" (SLS), a German reading screening, and the Culture Fair Intelligence Test (CFIT), a nonverbal intelligence test. Children with CI did not differ significantly from hearing children in their arithmetic achievement. Correlation and regression analyses revealed that in children with CI, arithmetic achievement was significantly (positively) related to reading skills, but not to nonverbal IQ. Reading skills and nonverbal IQ were not related to each other. In normal hearing children, arithmetic achievement was significantly (positively) related to nonverbal IQ, but not to reading skills. Reading skills and nonverbal IQ were positively correlated. Hearing variables were not related to arithmetic achievement. Children with CI do not show lower performance in non-verbal arithmetic tasks, compared to normal hearing peers. Copyright © 2014. Published by Elsevier Ireland Ltd.
Perceiving fingers in single-digit arithmetic problems
Ilaria eBerteletti
2015-03-01
Full Text Available In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.
Perceiving fingers in single-digit arithmetic problems.
Berteletti, Ilaria; Booth, James R
2015-01-01
In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.
Analysis of additive generators of fuzzy operations represented by rational functions
Ledeneva, T. M.
2018-03-01
This article presents an approach for determining additive generators of commutative and associative operations. Its applicability for finding generators of triangular norms and conorms is shown. Conditions for the parameters of increasing generators that generate triangular conorms in the class of rational functions are determined.
Trinary signed-digit arithmetic using an efficient encoding scheme
Salim, W. Y.; Alam, M. S.; Fyath, R. S.; Ali, S. A.
2000-09-01
The trinary signed-digit (TSD) number system is of interest for ultrafast optoelectronic computing systems since it permits parallel carry-free addition and borrow-free subtraction of two arbitrary length numbers in constant time. In this paper, a simple coding scheme is proposed to encode the decimal number directly into the TSD form. The coding scheme enables one to perform parallel one-step TSD arithmetic operation. The proposed coding scheme uses only a 5-combination coding table instead of the 625-combination table reported recently for recoded TSD arithmetic technique.
Computer arithmetic and validity theory, implementation, and applications
Kulisch, Ulrich
2013-01-01
This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic capability of the computer can be enhanced. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties
Designing an Energy Storage System Fuzzy PID Controller for Microgrid Islanded Operation
Jong-Yul Kim; Hak-Man Kim; Seul-Ki Kim; Jin-Hong Jeon; Heung-Kwan Choi
2011-01-01
Recently, interest in microgrids, which are composed of distributed generation (DG), distributed storage (DS), and loads, has been growing as a potentially effective clean energy system to mitigate against climate change. The microgrid is operated in the grid-connected mode and the islanded mode according to the conditions of the upstream power grid. The role of the energy storage system (ESS) is especially important to maintain constant the frequency and voltage of an islanded microgrid. For...
Adebanjo, Dotun; Laosirihongthong, Tritos; Samaranayake, Premaratne
2016-01-01
The objective of this study is to investigate the perceptions of practitioners/experts about the prioritisation of healthcare performance measures and their relationship with lean supply chain management (LSCM) practices. The study will also prioritise the drivers and resources required to implement LSCM in a healthcare operations context. The prioritisation is based on the relative weights of various initiatives on a range of performance measures. Twenty-four LSCM initiatives were identified...
Numerical calculation of economic uncertainty by intervals and fuzzy numbers
Schjær-Jacobsen, Hans
2010-01-01
This paper emphasizes that numerically correct calculation of economic uncertainty with intervals and fuzzy numbers requires implementation of global optimization techniques in contrast to straightforward application of interval arithmetic. This is demonstrated by both a simple case from managerial...... World Academic Press, UK. All rights reserved....
Abdul Hameed Q. A. Al-Tai
2011-01-01
Full Text Available The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed (every real number r is replaced by a fuzzy number r¯ (either triangular fuzzy number or singleton fuzzy set (fuzzy point. And then, we will consider that some results respect effect of the upper sequence on the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence.
Juels, Ari
The purpose of this chapter is to introduce fuzzy commitment, one of the earliest and simplest constructions geared toward cryptography over noisy data. The chapter also explores applications of fuzzy commitment to two problems in data security: (1) secure management of biometrics, with a focus on iriscodes, and (2) use of knowledge-based authentication (i.e., personal questions) for password recovery.
Macian-Sorribes, Hector; Pulido-Velazquez, Manuel
2013-04-01
Water resources systems are operated, mostly, using a set of pre-defined rules not regarding, usually, to an optimal allocation in terms of water use or economic benefits, but to historical and institutional reasons. These operating policies are reproduced, commonly, as hedging rules, pack rules or zone-based operations, and simulation models can be used to test their performance under a wide range of hydrological and/or socio-economic hypothesis. Despite the high degree of acceptation and testing that these models have achieved, the actual operation of water resources systems hardly follows all the time the pre-defined rules with the consequent uncertainty on the system performance. Real-world reservoir operation is very complex, affected by input uncertainty (imprecision in forecast inflow, seepage and evaporation losses, etc.), filtered by the reservoir operator's experience and natural risk-aversion, while considering the different physical and legal/institutional constraints in order to meet the different demands and system requirements. The aim of this work is to expose a fuzzy logic approach to derive and assess the historical operation of a system. This framework uses a fuzzy rule-based system to reproduce pre-defined rules and also to match as close as possible the actual decisions made by managers. After built up, the fuzzy rule-based system can be integrated in a water resources management model, making possible to assess the system performance at the basin scale. The case study of the Mijares basin (eastern Spain) is used to illustrate the method. A reservoir operating curve regulates the two main reservoir releases (operated in a conjunctive way) with the purpose of guaranteeing a high realiability of supply to the traditional irrigation districts with higher priority (more senior demands that funded the reservoir construction). A fuzzy rule-based system has been created to reproduce the operating curve's performance, defining the system state (total
Fuzzy logic controller using different inference methods
Liu, Z.; De Keyser, R.
1994-01-01
In this paper the design of fuzzy controllers by using different inference methods is introduced. Configuration of the fuzzy controllers includes a general rule-base which is a collection of fuzzy PI or PD rules, the triangular fuzzy data model and a centre of gravity defuzzification algorithm. The generalized modus ponens (GMP) is used with the minimum operator of the triangular norm. Under the sup-min inference rule, six fuzzy implication operators are employed to calculate the fuzzy look-up tables for each rule base. The performance is tested in simulated systems with MATLAB/SIMULINK. Results show the effects of using the fuzzy controllers with different inference methods and applied to different test processes
On Intuitionistic Fuzzy Context-Free Languages
Jianhua Jin
2013-01-01
automata theory. Additionally, we introduce the concepts of Chomsky normal form grammar (IFCNF and Greibach normal form grammar (IFGNF based on intuitionistic fuzzy sets. The results of our study indicate that intuitionistic fuzzy context-free languages generated by IFCFGs are equivalent to those generated by IFGNFs and IFCNFs, respectively, and they are also equivalent to intuitionistic fuzzy recognizable step functions. Then some operations on the family of intuitionistic fuzzy context-free languages are discussed. Finally, pumping lemma for intuitionistic fuzzy context-free languages is investigated.
Operator’s Fuzzy Norm and Some Properties
Bag, T.; Samanta, S.K.
2015-01-01
In this paper, a concept of operator’s fuzzy norm is introduced for the first time in general t-norm setting. Ideas of fuzzy continuous operators, fuzzy bounded linear operators are given with some properties of such operators studied in this general setting.
Design of interpretable fuzzy systems
Cpałka, Krzysztof
2017-01-01
This book shows that the term “interpretability” goes far beyond the concept of readability of a fuzzy set and fuzzy rules. It focuses on novel and precise operators of aggregation, inference, and defuzzification leading to flexible Mamdani-type and logical-type systems that can achieve the required accuracy using a less complex rule base. The individual chapters describe various aspects of interpretability, including appropriate selection of the structure of a fuzzy system, focusing on improving the interpretability of fuzzy systems designed using both gradient-learning and evolutionary algorithms. It also demonstrates how to eliminate various system components, such as inputs, rules and fuzzy sets, whose reduction does not adversely affect system accuracy. It illustrates the performance of the developed algorithms and methods with commonly used benchmarks. The book provides valuable tools for possible applications in many fields including expert systems, automatic control and robotics.
Anker, Thomas Boysen; Kappel, Klemens; Eadie, Douglas
2012-01-01
as narrative material to communicate self-identity. Finally, (c) we propose that brands deliver fuzzy experiential promises through effectively motivating consumers to adopt and play a social role implicitly suggested and facilitated by the brand. A promise is an inherently ethical concept and the article...... concludes with an in-depth discussion of fuzzy brand promises as two-way ethical commitments that put requirements on both brands and consumers....
A Unified Formal Description of Arithmetic and Set Theoretical Data Types
Tarau, Paul
2010-01-01
We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type classes with examples of instances converging to an efficient implementation in terms of arbitrary length integers and bit operations. As an instance, we derive algorithms to perform arithmetic operations efficiently directly with hereditarily finite sets. The s...
Arithmetic of quantum entropy function
Sen, Ashoke
2009-01-01
Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.
赵晓冬; 臧誉琪; 孙微
2017-01-01
针对属性值为区间犹豫模糊元且属性间存在相互关联的多属性决策问题,提出一种基于区间犹豫模糊Heronian平均算子的多属性决策方法.首先,给出了区间犹豫模糊元的定义及运算法则;然后,提出了区间犹豫模糊Heronian平均算子和区间犹豫模糊几何Heronian平均算子,并探讨了它们的特性;在此基础上,考虑到各属性的不同重要性,定义了区间犹豫模糊加权Heronian平均算子和区间犹豫模糊加权几何Heronian平均算子;最后,将区间犹豫模糊加权Heronian平均算子应用于多属性决策问题中,验证了所提算子的有效性和可行性.%With respect to the multiple attribute decision making problems in which the a ttribute values are in the form of interval-valued hesitant fuzzy information and attributes are associated with each other,in this paper proposed a multiple attribute decision making method based on the intervalvalued hesitant fuzzy Heronian mean operator.Firstly,the definition of the interval-valued hesitant fuzzy set is given,some basic operation laws of it are discussed;Then,the interval-valued hesitant fuzzy Heronian mean operator and the interval-valued hesitant fuzzy geometric Heronian mean operator are proposed,some desirable properties are studied in detail;Furthermore,considering the attributes with different importance,the interval-valued hesitant fuzzy weighted Heronian mean operator and the interval-valued hesitant fuzzy weighted geometric Heronian mean operator are defined.Finally,the interval-valued hesitant fuzzy weighted Heronian mean operator is applied to the multiple attribute decision making problem,in order to illustrate the effectiveness and feasibility of the proposed operators.
Numerical Magnitude Representations Influence Arithmetic Learning
Booth, Julie L.; Siegler, Robert S.
2008-01-01
This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be…
A Computational Model of Fraction Arithmetic
Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.
2017-01-01
Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…
Fuzzy logic control for camera tracking system
Lea, Robert N.; Fritz, R. H.; Giarratano, J.; Jani, Yashvant
1992-01-01
A concept utilizing fuzzy theory has been developed for a camera tracking system to provide support for proximity operations and traffic management around the Space Station Freedom. Fuzzy sets and fuzzy logic based reasoning are used in a control system which utilizes images from a camera and generates required pan and tilt commands to track and maintain a moving target in the camera's field of view. This control system can be implemented on a fuzzy chip to provide an intelligent sensor for autonomous operations. Capabilities of the control system can be expanded to include approach, handover to other sensors, caution and warning messages.
Application of fuzzy logic control in industry
Van der Wal, A.J.
1994-01-01
An overview is given of the various ways fuzzy logic can be used to improve industrial control. The application of fuzzy logic in control is illustrated by two case studies. The first example shows how fuzzy logic, incorporated in the hardware of an industrial controller, helps to finetune a PID controller, without the operator having any a priori knowledge of the system to be controlled. The second example is from process industry. Here, fuzzy logic supervisory control is implemented in software and enhances the operation of a sintering oven through a subtle combination of priority management and deviation-controlled timing
Zhixiong Zhong
2013-01-01
Full Text Available The stability analysis and stabilization of Takagi-Sugeno (T-S fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.
Berks, G.; Keyserlingk, Diedrich Graf von; Jantzen, Jan
2000-01-01
A symptom is a condition indicating the presence of a disease, especially, when regarded as an aid in diagnosis.Symptoms are the smallest units indicating the existence of a disease. A syndrome on the other hand is an aggregate, set or cluster of concurrent symptoms which together indicate...... and clustering are the basic concerns in medicine. Classification depends on definitions of the classes and their required degree of participant of the elements in the cases' symptoms. In medicine imprecise conditions are the rule and therefore fuzzy methods are much more suitable than crisp ones. Fuzzy c......-mean clustering is an easy and well improved tool, which has been applied in many medical fields. We used c-mean fuzzy clustering after feature extraction from an aphasia database. Factor analysis was applied on a correlation matrix of 26 symptoms of language disorders and led to five factors. The factors...
On a Fuzzy Algebra for Querying Graph Databases
Pivert , Olivier; Thion , Virginie; Jaudoin , Hélène; Smits , Grégory
2014-01-01
International audience; This paper proposes a notion of fuzzy graph database and describes a fuzzy query algebra that makes it possible to handle such database, which may be fuzzy or not, in a flexible way. The algebra, based on fuzzy set theory and the concept of a fuzzy graph, is composed of a set of operators that can be used to express preference queries on fuzzy graph databases. The preferences concern i) the content of the vertices of the graph and ii) the structure of the graph. In a s...
Integrating Fuzzy AHP and Fuzzy ARAS for evaluating financial performance
Abdolhamid Safaei Ghadikolaei
2014-09-01
Full Text Available Multi Criteria Decision Making (MCDM is an advanced field of Operation Research; recently MCDM methods are efficient and common tools for performance evaluation in many areas such as finance and economy. The aim of this study is to show one of applications of mathematics in real word. This study with considering value based measures and accounting based measures simultaneously, provided a hybrid approach of MCDM methods in fuzzy environment for financial performance evaluation of automotive and parts manufacturing industry of Tehran stock exchange (TSE.for this purpose Fuzzy analytic hierarchy process (FAHP is applied to determine the relative important of each criterion, then The companies are ranked according their financial performance by using fuzzy additive ratio assessment (Fuzzy ARAS method. The finding of this study showed effective of this approach in evaluating financial performance.
Children learn spurious associations in their math textbooks: Examples from fraction arithmetic.
Braithwaite, David W; Siegler, Robert S
2018-04-26
Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge-rather than understanding of mathematical concepts and procedures-to guide choices of solution strategies. They further proposed that this associative knowledge reflects distributional characteristics of the fraction arithmetic problems children encounter. To test these hypotheses, we examined textbooks and middle school children in the United States (Experiments 1 and 2) and China (Experiment 3). We asked the children to predict which arithmetic operation would accompany a specified pair of operands, to generate operands to accompany a specified arithmetic operation, and to match operands and operations. In both countries, children's responses indicated that they associated operand pairs having equal denominators with addition and subtraction, and operand pairs having a whole number and a fraction with multiplication and division. The children's associations paralleled the textbook input in both countries, which was consistent with the hypothesis that children learned the associations from the practice problems. Differences in the effects of such associative knowledge on U.S. and Chinese children's fraction arithmetic performance are discussed, as are implications of these differences for educational practice. (PsycINFO Database Record (c) 2018 APA, all rights reserved).
Christensen, Line Hjorth
"Fuzzy stuff". Exploring the displacement of the design sketch. What kind of knowledge can historical sketches reveal when they have outplayed their primary instrumental function in the design process and are moved into a museum collection? What are the rational benefits of ‘archival displacement...
Fuzzy logic control and optimization system
Lou, Xinsheng [West Hartford, CT
2012-04-17
A control system (300) for optimizing a power plant includes a chemical loop having an input for receiving an input signal (369) and an output for outputting an output signal (367), and a hierarchical fuzzy control system (400) operably connected to the chemical loop. The hierarchical fuzzy control system (400) includes a plurality of fuzzy controllers (330). The hierarchical fuzzy control system (400) receives the output signal (367), optimizes the input signal (369) based on the received output signal (367), and outputs an optimized input signal (369) to the input of the chemical loop to control a process of the chemical loop in an optimized manner.
Fuzzy set theoretic approach to fault tree analysis | Tyagi ...
This approach can be widely used to improve the reliability and to reduce the operating cost of a system. The proposed techniques are discussed and illustrated by taking an example of a nuclear power plant. Keywords: Fault tree, Triangular and Trapezoidal fuzzy number, Fuzzy importance, Ranking of fuzzy numbers ...
Relational thinking: The bridge between arithmetic and algebra
Ayhan Kızıltoprak
2017-09-01
Full Text Available The purpose of this study is to investigate the development of relational thinking skill, which is an important component of the transition from arithmetic to algebra, of 5th grade students. In the study, the qualitative research method of teaching experiment was used. The research data were collected from six secondary school 5th grade students by means of clinical interviews and teaching episodes. For observing the development of relational thinking, pre and post clinical interviews were also conducted before and after the eight-session teaching experiment. Qualitative analysis of the research data revealed that the relational thinking skills of all the students developed. It was also found that there was an interaction between the development of fundamental arithmetic concepts and relational thinking; that the students developed concepts related to arithmetical operations such as addend and sum; minuend, subtrahend and difference; multiplicator and product; and dividend, divisor and quotient. Moreover, students were able to use these concepts effectivelyalthough they failed to provide formal explanations about the relations between them. In addition, the students perceived the equal sign not only finding a result but also as a symbol used to establish a relation between operations and expressions.
Fuzzy model-based control of a nuclear reactor
Van Den Durpel, L.; Ruan, D.
1994-01-01
The fuzzy model-based control of a nuclear power reactor is an emerging research topic world-wide. SCK-CEN is dealing with this research in a preliminary stage, including two aspects, namely fuzzy control and fuzzy modelling. The aim is to combine both methodologies in contrast to conventional model-based PID control techniques, and to state advantages of including fuzzy parameters as safety and operator feedback. This paper summarizes the general scheme of this new research project
Foundations of arithmetic differential geometry
Buium, Alexandru
2017-01-01
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Handbook of floating-point arithmetic
Muller, Jean-Michel; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge
2018-01-01
This handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-point numbers, and understanding their various implementations will allow readers to develop programs specifically tailored for the standard’s technical features. Algorithms for floating-point arithmetic are presented throughout the book and illustrated where possible by example programs which show how these techniques appear in actual coding and design. The volume itself breaks its core topic into four parts: the basic concepts and history of floating-point arithmetic; methods of analyzing floating-point algorithms and optimizing them; implementations of IEEE 754-2008 in hardware and software; and useful extensions to the standard floating-point system, such as interval arithmetic, double- and triple-word arithm...
Specificity and Overlap in Skills Underpinning Reading and Arithmetical Fluency
van Daal, Victor; van der Leij, Aryan; Ader, Herman
2013-01-01
The aim of this study was to examine unique and common causes of problems in reading and arithmetic fluency. 13- to 14-year-old students were placed into one of five groups: reading disabled (RD, n = 16), arithmetic disabled (AD, n = 34), reading and arithmetic disabled (RAD, n = 17), reading, arithmetic, and listening comprehension disabled…
Quality of Arithmetic Education for Children with Cerebral Palsy
Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest C. D. M.; Withagen, Floortje
2010-01-01
The aim of this exploratory study was to investigate the quality of arithmetic education for children with cerebral palsy. The use of individual educational plans, amount of arithmetic instruction time, arithmetic instructional grouping, and type of arithmetic teaching method were explored in three groups: children with cerebral palsy (CP) in…
Studi Kompresi Data dengan Metode Arithmetic Coding
Santoso, Petrus
2001-01-01
In Bahasa Indonesia : Ada banyak sekali metode kompresi data yang ada saat ini. Sebagian besar metode tersebut bisa dikelompokkan ke dalam salah satu dari dua kelompok besar, statistical based dan dictionary based. Contoh dari dictionary based coding adalah Lempel Ziv Welch dan contoh dari statistical based coding adalah Huffman Coding dan Arithmetic Coding yang merupakan algoritma terbaru. Makalah ini mengulas prinsip-prinsip dari Arithmetic Coding serta keuntungan-keuntungannya dibandi...
Hoell, Simon; Omenzetter, Piotr
2016-04-01
Fueled by increasing demand for carbon neutral energy, erections of ever larger wind turbines (WTs), with WT blades (WTBs) with higher flexibilities and lower buckling capacities lead to increasing operation and maintenance costs. This can be counteracted with efficient structural health monitoring (SHM), which allows scheduling maintenance actions according to the structural state and preventing dramatic failures. The present study proposes a novel multi-step approach for vibration-based structural damage localization and severity estimation for application in operating WTs. First, partial autocorrelation coefficients (PACCs) are estimated from vibrational responses. Second, principal component analysis is applied to PACCs from the healthy structure in order to calculate scores. Then, the scores are ranked with respect to their ability to differentiate different damage scenarios. This ranking information is used for constructing hierarchical adaptive neuro-fuzzy inference systems (HANFISs), where cross-validation is used to identify optimal numbers of hierarchy levels. Different HANFISs are created for the purposes of structural damage localization and severity estimation. For demonstrating the applicability of the approach, experimental data are superimposed with signals from numerical simulations to account for characteristics of operational noise. For the physical experiments, a small scale WTB is excited with a domestic fan and damage scenarios are introduced non-destructively by attaching small masses. Numerical simulations are also performed for a representative fully functional small WT operating in turbulent wind. The obtained results are promising for future applications of vibration-based SHM to facilitate improved safety and reliability of WTs at lower costs.
Valenca, Mauricio Mendonca
1993-05-01
The power system static operation planning has a main objective the determination of performance strategies which satisfy operational criteria. A fuzzy set decision model which takes the load attainment and the compromise between optimality and critical operational constraints into account is presented. The prime characteristic of this methodology is the incorporation of the planner`s preferences structure in a decision process modeled by fuzzy sets. A routine of optimal power flow calculation is used as a computational tool for solving the nonlinear model of the electric power system and for defining the universe of discourse of the decision-making problem. tests were carried on a 30-bus IEEE system in order to find a compromise solution of electric operational goal versus reactive power generation limits. Results and conclusions are presented. (author) 28 refs., 32 figs.
Mathieu, Romain; Epinat-Duclos, Justine; Léone, Jessica; Fayol, Michel; Thevenot, Catherine; Prado, Jérôme
2017-06-13
Understanding the meaning of abstract mathematical symbols is a cornerstone of arithmetic learning in children. Studies have long focused on the role of spatial intuitions in the processing of numerals. However, it has been argued that such intuitions may also underlie symbols that convey fundamental arithmetic concepts, such as arithmetic operators. In the present cross-sectional study, we used fMRI to investigate how and when associations between arithmetic operators and brain regions processing spatial information emerge in children from 3 rd to 10 th grade. We found that the mere perception of a '+' sign elicited grade-related increases of spatial activity in the right hippocampus. That is, merely perceiving '+' signs - without any operands - elicited enhanced hippocampal activity after around 7 th grade (12-13 years old). In these children, hippocampal activity in response to a '+' sign was further correlated with the degree to which calculation performance was facilitated by the preview of that sign before an addition problem, an effect termed operator-priming. Grade-related increases of hippocampal spatial activity were operation-specific because they were not observed with '×' signs, which might evoke rote retrieval rather than numerical manipulation. Our study raises the possibility that hippocampal spatial mechanisms help build associations between some arithmetic operators and space throughout age and/or education. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.
Quantile arithmetic methodology for uncertainty propagation in fault trees
Abdelhai, M.; Ragheb, M.
1986-01-01
A methodology based on quantile arithmetic, the probabilistic analog to interval analysis, is proposed for the computation of uncertainties propagation in fault tree analysis. The basic events' continuous probability density functions (pdf's) are represented by equivalent discrete distributions by dividing them into a number of quantiles N. Quantile arithmetic is then used to performthe binary arithmetical operations corresponding to the logical gates in the Boolean expression of the top event expression of a given fault tree. The computational advantage of the present methodology as compared with the widely used Monte Carlo method was demonstrated for the cases of summation of M normal variables through the efficiency ratio defined as the product of the labor and error ratios. The efficiency ratio values obtained by the suggested methodology for M = 2 were 2279 for N = 5, 445 for N = 25, and 66 for N = 45 when compared with the results for 19,200 Monte Carlo samples at the 40th percentile point. Another advantage of the approach is that the exact analytical value of the median is always obtained for the top event
An Asynchronous IEEE Floating-Point Arithmetic Unit
Joel R. Noche
2007-12-01
Full Text Available An asynchronous floating-point arithmetic unit is designed and tested at the transistor level usingCadence software. It uses CMOS (complementary metal oxide semiconductor and DCVS (differentialcascode voltage switch logic in a 0.35 µm process using a 3.3 V supply voltage, with dual-rail data andsingle-rail control signals using four-phase handshaking.Using 17,085 transistors, the unit handles single-precision (32-bit addition/subtraction, multiplication,division, and remainder using the IEEE 754-1985 Standard for Binary Floating-Point Arithmetic, withrounding and other operations to be handled by separate hardware or software. Division and remainderare done using a restoring subtractive algorithm; multiplication uses an additive algorithm. Exceptionsare noted by flags (and not trap handlers and the output is in single-precision.Previous work on asynchronous floating-point arithmetic units have mostly focused on single operationssuch as division. This is the first work to the authors' knowledge that can perform floating-point addition,multiplication, division, and remainder using a common datapath.
Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos
2016-01-01
This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…
Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.; Powell, Sarah R.; Seethaler, Pamela M.; Capizzi, Andrea M.; Schatschneider, Christopher; Fletcher, Jack M.
2006-01-01
The purpose of this study was to examine the cognitive correlates of RD-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Third graders (N = 312) were measured on language, nonverbal problem solving, concept formation, processing speed, long-term memory, working memory, phonological decoding, and sight word…
Research and Implementation of Automatic Fuzzy Garage Parking System Based on FPGA
Wang Kaiyu
2016-01-01
Full Text Available Because of many common scenes of reverse parking in real life, this paper presents a fuzzy controller which accommodates front and back adjustment of vehicle’s body attitude, and based on chaotic-genetic arithmetic to optimize the membership function of this controller, and get a vertical parking fuzzy controller whose simulation result is good .The paper makes the hardware-software embedded design for system based on Field-Programmable Gate Array (FPGA, and set up a 1:10 verification platform of smart car to verify the fuzzy garage parking system with real car. Verification results show that, the system can complete the parking task very well.
On Witnessed Models in Fuzzy Logic III - Witnessed Gödel Logics
Hájek, Petr
2010-01-01
Roč. 56, č. 2 (2010), s. 171-174 ISSN 0942-5616 R&D Projects: GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : mathematical fuzzy logic * Gödel logic * witnessed models * arithmetical complexity Subject RIV: BA - General Mathematics Impact factor: 0.361, year: 2010
Ahmadianfar, Iman; Adib, Arash; Taghian, Mehrdad
2017-10-01
The reservoir hedging rule curves are used to avoid severe water shortage during drought periods. In this method reservoir storage is divided into several zones, wherein the rationing factors are changed immediately when water storage level moves from one zone to another. In the present study, a hedging rule with fuzzy rationing factors was applied for creating a transition zone in up and down each rule curve, and then the rationing factor will be changed in this zone gradually. For this propose, a monthly simulation model was developed and linked to the non-dominated sorting genetic algorithm for calculation of the modified shortage index of two objective functions involving water supply of minimum flow and agriculture demands in a long-term simulation period. Zohre multi-reservoir system in south Iran has been considered as a case study. The results of the proposed hedging rule have improved the long-term system performance from 10 till 27 percent in comparison with the simple hedging rule, where these results demonstrate that the fuzzification of hedging factors increase the applicability and the efficiency of the new hedging rule in comparison to the conventional rule curve for mitigating the water shortage problem.
Using fuzzy fractal features of digital images for the material surface analisys
Privezentsev, D. G.; Zhiznyakov, A. L.; Astafiev, A. V.; Pugin, E. V.
2018-01-01
Edge detection is an important task in image processing. There are a lot of approaches in this area: Sobel, Canny operators and others. One of the perspective techniques in image processing is the use of fuzzy logic and fuzzy sets theory. They allow us to increase processing quality by representing information in its fuzzy form. Most of the existing fuzzy image processing methods switch to fuzzy sets on very late stages, so this leads to some useful information loss. In this paper, a novel method of edge detection based on fuzzy image representation and fuzzy pixels is proposed. With this approach, we convert the image to fuzzy form on the first step. Different approaches to this conversion are described. Several membership functions for fuzzy pixel description and requirements for their form and view are given. A novel approach to edge detection based on Sobel operator and fuzzy image representation is proposed. Experimental testing of developed method was performed on remote sensing images.
Chen, Guanrong
2005-01-01
Introduction to Fuzzy Systems provides students with a self-contained introduction that requires no preliminary knowledge of fuzzy mathematics and fuzzy control systems theory. Simplified and readily accessible, it encourages both classroom and self-directed learners to build a solid foundation in fuzzy systems. After introducing the subject, the authors move directly into presenting real-world applications of fuzzy logic, revealing its practical flavor. This practicality is then followed by basic fuzzy systems theory. The book also offers a tutorial on fuzzy control theory, based mainly on th
Enric Trillas a passion for fuzzy sets : a collection of recent works on fuzzy logic
Verdegay, Jose; Esteva, Francesc
2015-01-01
This book presents a comprehensive collection of the latest and most significant research advances and applications in the field of fuzzy logic. It covers fuzzy structures, rules, operations and mathematical formalisms, as well as important applications of fuzzy logic in a number of fields, like decision-making, environmental prediction and prevention, communication, controls and many others. Dedicated to Enric Trillas in recognition of his pioneering research in the field, the book also includes a foreword by Lotfi A. Zadeh and an outlook on the future of fuzzy logic.
Shah, Mazlina Muzafar; Wahab, Abdul Fatah
2017-08-01
Epilepsy disease occurs because of there is a temporary electrical disturbance in a group of brain cells (nurons). The recording of electrical signals come from the human brain which can be collected from the scalp of the head is called Electroencephalography (EEG). EEG then considered in digital format and in fuzzy form makes it a fuzzy digital space data form. The purpose of research is to identify the area (curve and surface) in fuzzy digital space affected by inside epilepsy seizure in epileptic patient's brain. The main focus for this research is to generalize fuzzy topological digital space, definition and basic operation also the properties by using digital fuzzy set and the operations. By using fuzzy digital space, the theory of digital fuzzy spline can be introduced to replace grid data that has been use previously to get better result. As a result, the flat of EEG can be fuzzy topological digital space and this type of data can be use to interpolate the digital fuzzy spline.
Arithmetic geometry over global function fields
Longhi, Ignazio; Trihan, Fabien
2014-01-01
This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009–2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the con...
Relating arithmetical techniques of proportion to geometry
Wijayanti, Dyana
2015-01-01
The purpose of this study is to investigate how textbooks introduce and treat the theme of proportion in geometry (similarity) and arithmetic (ratio and proportion), and how these themes are linked to each other in the books. To pursue this aim, we use the anthropological theory of the didactic....... Considering 6 common Indonesian textbooks in use, we describe how proportion is explained and appears in examples and exercises, using an explicit reference model of the mathematical organizations of both themes. We also identify how the proportion themes of the geometry and arithmetic domains are linked. Our...
Grabner, Roland H; Rütsche, Bruno; Ruff, Christian C; Hauser, Tobias U
2015-07-01
The successful acquisition of arithmetic skills is an essential step in the development of mathematical competencies and has been associated with neural activity in the left posterior parietal cortex (PPC). It is unclear, however, whether this brain region plays a causal role in arithmetic skill acquisition and whether arithmetic learning can be modulated by means of non-invasive brain stimulation of this key region. In the present study we addressed these questions by applying transcranial direct current stimulation (tDCS) over the left PPC during a short-term training that simulates the typical path of arithmetic skill acquisition (specifically the transition from effortful procedural to memory-based problem-solving strategies). Sixty participants received either anodal, cathodal or sham tDCS while practising complex multiplication and subtraction problems. The stability of the stimulation-induced learning effects was assessed in a follow-up test 24 h after the training. Learning progress was modulated by tDCS. Cathodal tDCS (compared with sham) decreased learning rates during training and resulted in poorer performance which lasted over 24 h after stimulation. Anodal tDCS showed an operation-specific improvement for subtraction learning. Our findings extend previous studies by demonstrating that the left PPC is causally involved in arithmetic learning (and not only in arithmetic performance) and that even a short-term tDCS application can modulate the success of arithmetic knowledge acquisition. Moreover, our finding of operation-specific anodal stimulation effects suggests that the enhancing effects of tDCS on learning can selectively affect just one of several cognitive processes mediated by the stimulated area. © 2015 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.
A consensus model for group decision making under interval type-2 fuzzy environment
Xiao-xiong ZHANG; Bing-feng GE; Yue-jin TAN
2016-01-01
We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situa-tions. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute com-parable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.
Advances in type-2 fuzzy sets and systems theory and applications
Mendel, Jerry; Tahayori, Hooman
2013-01-01
This book explores recent developments in the theoretical foundations and novel applications of general and interval type-2 fuzzy sets and systems, including: algebraic properties of type-2 fuzzy sets, geometric-based definition of type-2 fuzzy set operators, generalizations of the continuous KM algorithm, adaptiveness and novelty of interval type-2 fuzzy logic controllers, relations between conceptual spaces and type-2 fuzzy sets, type-2 fuzzy logic systems versus perceptual computers; modeling human perception of real world concepts with type-2 fuzzy sets, different methods for generating membership functions of interval and general type-2 fuzzy sets, and applications of interval type-2 fuzzy sets to control, machine tooling, image processing and diet. The applications demonstrate the appropriateness of using type-2 fuzzy sets and systems in real world problems that are characterized by different degrees of uncertainty.
Fuzzy logic of Aristotelian forms
Perlovsky, L.I. [Nichols Research Corp., Lexington, MA (United States)
1996-12-31
Model-based approaches to pattern recognition and machine vision have been proposed to overcome the exorbitant training requirements of earlier computational paradigms. However, uncertainties in data were found to lead to a combinatorial explosion of the computational complexity. This issue is related here to the roles of a priori knowledge vs. adaptive learning. What is the a-priori knowledge representation that supports learning? I introduce Modeling Field Theory (MFT), a model-based neural network whose adaptive learning is based on a priori models. These models combine deterministic, fuzzy, and statistical aspects to account for a priori knowledge, its fuzzy nature, and data uncertainties. In the process of learning, a priori fuzzy concepts converge to crisp or probabilistic concepts. The MFT is a convergent dynamical system of only linear computational complexity. Fuzzy logic turns out to be essential for reducing the combinatorial complexity to linear one. I will discuss the relationship of the new computational paradigm to two theories due to Aristotle: theory of Forms and logic. While theory of Forms argued that the mind cannot be based on ready-made a priori concepts, Aristotelian logic operated with just such concepts. I discuss an interpretation of MFT suggesting that its fuzzy logic, combining a-priority and adaptivity, implements Aristotelian theory of Forms (theory of mind). Thus, 2300 years after Aristotle, a logic is developed suitable for his theory of mind.
Intuitionistic supra fuzzy topological spaces
Abbas, S.E.
2004-01-01
In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space
Fuzzy Arden Syntax: A fuzzy programming language for medicine.
Vetterlein, Thomas; Mandl, Harald; Adlassnig, Klaus-Peter
2010-05-01
The programming language Arden Syntax has been optimised for use in clinical decision support systems. We describe an extension of this language named Fuzzy Arden Syntax, whose original version was introduced in S. Tiffe's dissertation on "Fuzzy Arden Syntax: Representation and Interpretation of Vague Medical Knowledge by Fuzzified Arden Syntax" (Vienna University of Technology, 2003). The primary aim is to provide an easy means of processing vague or uncertain data, which frequently appears in medicine. For both propositional and number data types, fuzzy equivalents have been added to Arden Syntax. The Boolean data type was generalised to represent any truth degree between the two extremes 0 (falsity) and 1 (truth); fuzzy data types were introduced to represent fuzzy sets. The operations on truth values and real numbers were generalised accordingly. As the conditions to decide whether a certain programme unit is executed or not may be indeterminate, a Fuzzy Arden Syntax programme may split. The data in the different branches may be optionally aggregated subsequently. Fuzzy Arden Syntax offers the possibility to formulate conveniently Medical Logic Modules (MLMs) based on the principle of a continuously graded applicability of statements. Furthermore, ad hoc decisions about sharp value boundaries can be avoided. As an illustrative example shows, an MLM making use of the features of Fuzzy Arden Syntax is not significantly more complex than its Arden Syntax equivalent; in the ideal case, a programme handling crisp data remains practically unchanged when compared to its fuzzified version. In the latter case, the output data, which can be a set of weighted alternatives, typically depends continuously from the input data. In typical applications an Arden Syntax MLM can produce a different output after only slight changes of the input; discontinuities are in fact unavoidable when the input varies continuously but the output is taken from a discrete set of possibilities
Design of supply chain in fuzzy environment
Rao, Kandukuri Narayana; Subbaiah, Kambagowni Venkata; Singh, Ganja Veera Pratap
2013-05-01
Nowadays, customer expectations are increasing and organizations are prone to operate in an uncertain environment. Under this uncertain environment, the ultimate success of the firm depends on its ability to integrate business processes among supply chain partners. Supply chain management emphasizes cross-functional links to improve the competitive strategy of organizations. Now, companies are moving from decoupled decision processes towards more integrated design and control of their components to achieve the strategic fit. In this paper, a new approach is developed to design a multi-echelon, multi-facility, and multi-product supply chain in fuzzy environment. In fuzzy environment, mixed integer programming problem is formulated through fuzzy goal programming in strategic level with supply chain cost and volume flexibility as fuzzy goals. These fuzzy goals are aggregated using minimum operator. In tactical level, continuous review policy for controlling raw material inventories in supplier echelon and controlling finished product inventories in plant as well as distribution center echelon is considered as fuzzy goals. A non-linear programming model is formulated through fuzzy goal programming using minimum operator in the tactical level. The proposed approach is illustrated with a numerical example.
Carlsson, Christer; Fullér, Robert
2004-01-01
Fuzzy Logic in Management demonstrates that difficult problems and changes in the management environment can be more easily handled by bringing fuzzy logic into the practice of management. This explicit theme is developed through the book as follows: Chapter 1, "Management and Intelligent Support Technologies", is a short survey of management leadership and what can be gained from support technologies. Chapter 2, "Fuzzy Sets and Fuzzy Logic", provides a short introduction to fuzzy sets, fuzzy relations, the extension principle, fuzzy implications and linguistic variables. Chapter 3, "Group Decision Support Systems", deals with group decision making, and discusses methods for supporting the consensus reaching processes. Chapter 4, "Fuzzy Real Options for Strategic Planning", summarizes research where the fuzzy real options theory was implemented as a series of models. These models were thoroughly tested on a number of real life investments, and validated in 2001. Chapter 5, "Soft Computing Methods for Reducing...
Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept.
Mazandarani, Mehran; Pariz, Naser
2018-05-01
This paper deals with sub-optimal control of a fuzzy linear dynamical system. The aim is to keep the state variables of the fuzzy linear dynamical system close to zero in an optimal manner. In the fuzzy dynamical system, the fuzzy derivative is considered as the granular derivative; and all the coefficients and initial conditions can be uncertain. The criterion for assessing the optimality is regarded as a granular integral whose integrand is a quadratic function of the state variables and control inputs. Using the relative-distance-measure (RDM) fuzzy interval arithmetic and calculus of variations, the optimal control law is presented as the fuzzy state variables feedback. Since the optimal feedback gains are obtained as fuzzy functions, they need to be defuzzified. This will result in the sub-optimal control law. This paper also sheds light on the restrictions imposed by the approaches which are based on fuzzy standard interval arithmetic (FSIA), and use strongly generalized Hukuhara and generalized Hukuhara differentiability concepts for obtaining the optimal control law. The granular eigenvalues notion is also defined. Using an RLC circuit mathematical model, it is shown that, due to their unnatural behavior in the modeling phenomenon, the FSIA-based approaches may obtain some eigenvalues sets that might be different from the inherent eigenvalues set of the fuzzy dynamical system. This is, however, not the case with the approach proposed in this study. The notions of granular controllability and granular stabilizability of the fuzzy linear dynamical system are also presented in this paper. Moreover, a sub-optimal control for regulating a Boeing 747 in longitudinal direction with uncertain initial conditions and parameters is gained. In addition, an uncertain suspension system of one of the four wheels of a bus is regulated using the sub-optimal control introduced in this paper. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
Schildt, G.H.
1997-01-01
A fuzzy controller for safety related process control is presented for applications in the field of NPPs. The size of necessary rules is relatively small. Thus, there exists a real chance for verification and validation of software due to the fact that the whole software can be structured into standard fuzzy software (like fuzzyfication, inference algorithms, and defuzzyfication), real-time operating system software, and the contents of the rule base. Furthermore, there is an excellent advantage fuel to real-time behaviour, because program execution time is much more predictable than for conventional PID-controller software. Additionally, up to now special know-how does exist to prove stability of fuzzy controller. Hardware design has been done due to fundamental principles of safety technique like watch dog function, dynamization principles, and quiescent current principle. (author). 3 refs, 5 figs
Schildt, G.H.
1996-01-01
After an introduction into safety terms a fuzzy controller for safety related process control will be presented, especially for applications in the field of NPPs. One can show that the size of necessary rules is relatively small. Thus, there exists a real chance for verification and validation of software due to the fact that the whole software can be structured into standard fuzzy software (like fuzzyfication, inference algorithms, and defuzzyfication), real-time operating system software, and the contents of the rule base. Furthermore, there is an excellent advantage due to real-time behaviour, because program execution time can be much more planned than for conventional PID-controller software. Additionally, up to now special know-how does exist to prove stability of fuzzy controller. Hardware design has been done due to fundamental principles of safety technique like watch dog function, dynamization principle, and quiescent current principle
Schildt, G H [Technische Univ., Vienna (Austria)
1997-07-01
A fuzzy controller for safety related process control is presented for applications in the field of NPPs. The size of necessary rules is relatively small. Thus, there exists a real chance for verification and validation of software due to the fact that the whole software can be structured into standard fuzzy software (like fuzzyfication, inference algorithms, and defuzzyfication), real-time operating system software, and the contents of the rule base. Furthermore, there is an excellent advantage fuel to real-time behaviour, because program execution time is much more predictable than for conventional PID-controller software. Additionally, up to now special know-how does exist to prove stability of fuzzy controller. Hardware design has been done due to fundamental principles of safety technique like watch dog function, dynamization principles, and quiescent current principle. (author). 3 refs, 5 figs.
Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic
Kim, Wonjoo; Chattopadhyay, Anupam; Siemon, Anne; Linn, Eike; Waser, Rainer; Rana, Vikas
2016-11-01
Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement Boolean logic functionality gained wide interest. Here, we report on seven-states Tantalum Oxide Devices, which enable the realization of an intrinsic modular arithmetic using a ternary number system. Modular arithmetic, a fundamental system for operating on numbers within the limit of a modulus, is known to mathematicians since the days of Euclid and finds applications in diverse areas ranging from e-commerce to musical notations. We demonstrate that multistate devices not only reduce the storage area consumption drastically, but also enable novel in-memory operations, such as computing using high-radix number systems, which could not be implemented using two-state devices. The use of high radix number system reduces the computational complexity by reducing the number of needed digits. Thus the number of calculation operations in an addition and the number of logic devices can be reduced.
Self-reference in Arithmetic I
Halbach, Volker; Visser, Albert|info:eu-repo/dai/nl/068579985
2014-01-01
A Gödel sentence is often described as a sentence saying about itself that it is not provable, and a Henkin sentence as a sentence stating its own provability. We discuss what it could mean for a sentence of arithmetic to ascribe to itself a property such as provability or unprovability. The
A functional interpretation for nonstandard arithmetic
van den Berg, B.; Briseid, E.; Safarik, P.
2012-01-01
We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Gödel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones. These functional interpretations show in particular that our
Secret Codes, Remainder Arithmetic, and Matrices.
Peck, Lyman C.
This pamphlet is designed for use as enrichment material for able junior and senior high school students who are interested in mathematics. No more than a clear understanding of basic arithmetic is expected. Students are introduced to ideas from number theory and modern algebra by learning mathematical ways of coding and decoding secret messages.…
PandA : pairings and arithmetic
Chuengsatiansup, C.; Naehrig, M.; Ribarski, P.; Schwabe, P.; Cao, Z.; Zhang, F.
2014-01-01
This paper introduces PandA, a software framework for Pairings and Arithmetic. It is designed to bring together advances in the efficient computation of cryptographic pairings and the development and implementation of pairing-based protocols. The intention behind the PandA framework is to give
Lattice for FPGAs using logarithmic arithmetic
Kadlec, Jiří; Matoušek, Rudolf; Heřmánek, Antonín; Líčko, Miroslav; Tichý, Milan
2002-01-01
Roč. 74, č. 906 (2002), s. 53-56 ISSN 0013-4902 Grant - others: ESPRIT (XE) 33544 Institutional research plan: CEZ:AV0Z1075907 Keywords : lattice Rls algorithm * FPGA * logarithmic arithmetic Subject RIV: JC - Computer Hardware ; Software Impact factor: 0.039, year: 2002
Circuit lower bounds in bounded arithmetics
Pich, Ján
2015-01-01
Roč. 166, č. 1 (2015), s. 29-45 ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Keywords : bounded arithmetic * circuit lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.582, year: 2015 http://www.sciencedirect.com/science/article/pii/S0168007214000888
Non-commutative arithmetic circuits with division
Hrubeš, Pavel; Wigderson, A.
2015-01-01
Roč. 11, Article 14 (2015), s. 357-393 ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/
Model Theory in Algebra, Analysis and Arithmetic
Dries, Lou; Macpherson, H Dugald; Pillay, Anand; Toffalori, Carlo; Wilkie, Alex J
2014-01-01
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Design of a self-adaptive fuzzy PID controller for piezoelectric ceramics micro-displacement system
Zhang, Shuang; Zhong, Yuning; Xu, Zhongbao
2008-12-01
In order to improve control precision of the piezoelectric ceramics (PZT) micro-displacement system, a self-adaptive fuzzy Proportional Integration Differential (PID) controller is designed based on the traditional digital PID controller combining with fuzzy control. The arithmetic gives a fuzzy control rule table with the fuzzy control rule and fuzzy reasoning, through this table, the PID parameters can be adjusted online in real time control. Furthermore, the automatic selective control is achieved according to the change of the error. The controller combines the good dynamic capability of the fuzzy control and the high stable precision of the PID control, adopts the method of using fuzzy control and PID control in different segments of time. In the initial and middle stage of the transition process of system, that is, when the error is larger than the value, fuzzy control is used to adjust control variable. It makes full use of the fast response of the fuzzy control. And when the error is smaller than the value, the system is about to be in the steady state, PID control is adopted to eliminate static error. The problems of PZT existing in the field of precise positioning are overcome. The results of the experiments prove that the project is correct and practicable.
A version of Stone-Weierstrass theorem in Fuzzy Analysis
Font, J.J.; Sanchis, D.; Sanchis, M.
2017-07-01
Fuzzy numbers provide formalized tools to deal with non-precise quantities. They are indeed fuzzy sets in the real line and were introduced in 1978 by Dubois and Prade , who also defined their basic operations. Since then, Fuzzy Analysis has developed based on the notion of fuzzy number just as much as classical Real Analysis did based on the concept of real number. Such development was eased by a characterization of fuzzy numbers provided in 1986 by Goetschel and Voxman leaning on their level sets. As in the classical setting, continuous fuzzy-valued functions (fuzzy functions) are the central core of the theory. The principal difference with regard to real-valued continuous functions is the fact that the fuzzy numbers do not form a vectorial space, which determines all the results, and, especially, the proofs. The study of fuzzy functions has developed, principally, about two lines of investigation: - Differential fuzzy equations, which have turned out to be the natural way of modelling physical and engineering problems in contexts where the parameters are vague or incomplete. - The problem of approximation of fuzzy functions, basically using the approximation capability of fuzzy neural networks. We will focus on this second line of investigation, though our approach will be more general and based on an adaptation of the famous Stone-Weierstrass Theorem to the fuzzy context. This way so, we introduce the concept of “multiplier” of a set of fuzzy functions and use it to give a constructive proof of a Stone-Weiestrass type theorem for fuzzy functions. (Author)
Why fuzzy controllers should be fuzzy
Nowe, A.
1996-01-01
Fuzzy controllers are usually looked at as crisp valued mappings especially when artificial intelligence learning techniques are used to build up the controller. By doing so the semantics of a fuzzy conclusion being a fuzzy restriction on the viable control actions is non-existing. In this paper the authors criticise from an approximation point of view using a fuzzy controller to express a crisp mapping does not seem the right way to go. Secondly it is illustrated that interesting information is contained in a fuzzy conclusion when indeed this conclusion is considered as a fuzzy restriction. This information turns out to be very valuable when viability problems are concerned, i.e. problems where the objective is to keep a system within predefined boundaries
Personal Experience and Arithmetic Meaning in Semantic Dementia
Julien, Camille L.; Neary, David; Snowden, Julie S.
2010-01-01
Arithmetic skills are generally claimed to be preserved in semantic dementia (SD), suggesting functional independence of arithmetic knowledge from other aspects of semantic memory. However, in a recent case series analysis we showed that arithmetic performance in SD is not entirely normal. The finding of a direct association between severity of…
Specificity and overlap in skills underpinning reading and arithmetical fluency
van Daal, V.; van der Leij, A.; Adèr, H.
2013-01-01
The aim of this study was to examine unique and common causes of problems in reading and arithmetic fluency. 13- to 14-year-old students were placed into one of five groups: reading disabled (RD, n = 16), arithmetic disabled (AD, n = 34), reading and arithmetic disabled (RAD, n = 17), reading,
Learning, Realizability and Games in Classical Arithmetic
Aschieri, Federico
2010-12-01
In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel modified realizability to a classical fragment of first order Arithmetic, Heyting Arithmetic plus EM1 (Excluded middle axiom restricted to Sigma^0_1 formulas). We introduce a new realizability semantics we call "Interactive Learning-Based Realizability". Our realizers are self-correcting programs, which learn from their errors and evolve through time. Secondly, we extend the class of learning based realizers to a classical version PCFclass of PCF and, then, compare the resulting notion of realizability with Coquand game semantics and prove a full soundness and completeness result. In particular, we show there is a one-to-one correspondence between realizers and recursive winning strategies in the 1-Backtracking version of Tarski games. Third, we provide a complete and fully detailed constructive analysis of learning as it arises in learning based realizability for HA+EM1, Avigad's update procedures and epsilon substitution method for Peano Arithmetic PA. We present new constructive techniques to bound the length of learning processes and we apply them to reprove - by means of our theory - the classic result of Godel that provably total functions of PA can be represented in Godel's system T. Last, we give an axiomatization of the kind of learning that is needed to computationally interpret Predicative classical second order Arithmetic. Our work is an extension of Avigad's and generalizes the concept of update procedure to the transfinite case. Transfinite update procedures have to learn values of transfinite sequences of non computable functions in order to extract witnesses from classical proofs.
Castro, Antonio Orestes de Salvo [PETROBRAS, Rio de Janeiro, RJ (Brazil); Ferreira Filho, Virgilio Jose Martins [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil)
2004-07-01
The hydraulic fracture operation is wide used to increase the oil wells production and to reduce formation damage. Reservoir studies and engineer analysis are made to select the wells for this kind of operation. As the reservoir parameters have some diffuses characteristics, Fuzzy Inference Systems (SIF) have been tested for this selection processes in the last few years. This paper compares the performance of a neuro fuzzy system and a genetic fuzzy system used for hydraulic Fracture well selection, with knowledge acquisition from an operational data base to set the SIF membership functions. The training data and the validation data used were the same for both systems. We concluded that, in despite of the genetic fuzzy system would be a younger process, it got better results than the neuro fuzzy system. Another conclusion was that, as the genetic fuzzy system can work with constraints, the membership functions setting kept the consistency of variables linguistic values. (author)
Fuzzy Neuroidal Nets and Recurrent Fuzzy Computations
Wiedermann, Jiří
2001-01-01
Roč. 11, č. 6 (2001), s. 675-686 ISSN 1210-0552. [SOFSEM 2001 Workshop on Soft Computing. Piešťany, 29.11.2001-30.11.2001] R&D Projects: GA ČR GA201/00/1489; GA AV ČR KSK1019101 Institutional research plan: AV0Z1030915 Keywords : fuzzy computing * fuzzy neural nets * fuzzy Turing machines * non-uniform computational complexity Subject RIV: BA - General Mathematics
Hesitant fuzzy soft sets with application in multicriteria group decision making problems.
Wang, Jian-qiang; Li, Xin-E; Chen, Xiao-hong
2015-01-01
Soft sets have been regarded as a useful mathematical tool to deal with uncertainty. In recent years, many scholars have shown an intense interest in soft sets and extended standard soft sets to intuitionistic fuzzy soft sets, interval-valued fuzzy soft sets, and generalized fuzzy soft sets. In this paper, hesitant fuzzy soft sets are defined by combining fuzzy soft sets with hesitant fuzzy sets. And some operations on hesitant fuzzy soft sets based on Archimedean t-norm and Archimedean t-conorm are defined. Besides, four aggregation operations, such as the HFSWA, HFSWG, GHFSWA, and GHFSWG operators, are given. Based on these operators, a multicriteria group decision making approach with hesitant fuzzy soft sets is also proposed. To demonstrate its accuracy and applicability, this approach is finally employed to calculate a numerical example.
interval type-2 fuzzy gain-adaptive controller of a doubly fed
Loukal K and Benalia L
2016-05-01
May 1, 2016 ... machine a converter PWM (Pulse Width Modulation) between the machine ... operations on fuzzy sets increases with the increasing type of the fuzzy set. ...... Several simulations have been run using the Matlab and Simulink® ...
Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion
Didier Kumwimba Seya
2015-11-01
Full Text Available In this paper we take into account the fuzzy stochastic integral driven by fuzzy Brownian motion. To define the metric between two fuzzy numbers and to take into account the limit of a sequence of fuzzy numbers, we invoke the Hausdorff metric. First this fuzzy stochastic integral is constructed for fuzzy simple stochastic functions, then the construction is done for fuzzy stochastic integrable functions.
Zhang, Xiao; Räsänen, Pekka; Koponen, Tuire; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik
2017-01-01
The longitudinal relations of domain-general and numerical skills at ages 6-7 years to 3 cognitive domains of arithmetic learning, namely knowing (written computation), applying (arithmetic word problems), and reasoning (arithmetic reasoning) at age 11, were examined for a representative sample of 378 Finnish children. The results showed that…
GDI based full adders for energy efficient arithmetic applications
Mohan Shoba
2016-03-01
Full Text Available Addition is a vital arithmetic operation and acts as a building block for synthesizing all other operations. A high-performance adder is one of the key components in the design of application specific integrated circuits. In this paper, three low power full adders are designed with full swing AND, OR and XOR gates to alleviate threshold voltage problem which is commonly encountered in Gate Diffusion Input (GDI logic. This problem usually does not allow the full adder circuits to operate without additional inverters. However, the three full adders are successfully realized using full swing gates with the significant improvement in their performance. The performance of the proposed designs is compared with the other full adder designs, namely CMOS, CPL, hybrid and GDI through SPICE simulations using 45 nm technology models. Simulation results reveal that proposed designs have lower energy consumption among all the conventional designs taken for comparison.
Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.
Chen, Yalin; Yanke, Jill; Campbell, Jamie I D
2016-04-01
The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.
Properties of Fuzzy Entropy Based on the Shape Change of Membership Function
无
2007-01-01
Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers (TFNs), the entropies of any two TFNs which can not be always the same type, also,have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets (TFSs) with same sizes of support intervals and different heights, the relationship of their entropies lies on their height.Finally, we point it out a mistake that Chen's assertion that the entropy of resultant fuzzy set of elevation operation is directly proportional to that of the original one while elevation factor just acts as a proportional factor. These results should contribute to the analysis and design of a fuzzy system.
Group Evidential Reasoning Approach for MADA under Fuzziness and Uncertainties
Mi Zhou
2013-05-01
Full Text Available Multiple attribute decision analysis (MADA problems often include both qualitative and quantitative attributes which may be either precise or inaccurate. The evidential reasoning (ER approach is one of reliable and rational methods for dealing with MADA problems and can generate aggregated assessments from a variety of attributes. In many real world decision situations, accurate assessments are difficult to provide such as in group decision situations. Extensive research in dealing with imprecise or uncertain belief structures has been conducted on the basis of the ER approach, such as interval belief degrees, interval weights and interval uncertainty. In this paper, the weights of attributes and utilities of evaluation grades are considered to be fuzzy numbers for the ER approach. Fuzzy analytic hierarchy process (FAHP is used for generating triangular fuzzy weights for attributes from a triangular fuzzy judgment matrix provided by an expert. The weighted arithmetic mean method is proposed to aggregate the triangular fuzzy weights of attributes from a group of experts. -cut is then used to transform the combined triangular fuzzy weights to interval weights for the purpose of dealing with the fuzzy type of weight and utility in a consistent way. Several pairs of group evidential reasoning based nonlinear programming models are then designed to calculate the global fuzzy belief degrees and the overall expected interval utilities of each alternative with interval weights and interval utilities as constraints. A case study is conducted to show the validity and effectiveness of the proposed approach and sensitivity analysis is also conducted on interval weights generated by different -cuts.
reactor power control using fuzzy logic
Ahmed, A.E.E.
2001-01-01
power stabilization is a critical issue in nuclear reactors. convention pd- controller is currently used in egypt second testing research reactor (ETRR-2). two fuzzy controllers are proposed to control the reactor power of ETRR-2 reactor. the design of the first one is based on a set of linguistic rules that were adopted from the human operators experience. after off-line fuzzy computations, the controller is a lookup table, and thus, real time controller is achieved. comparing this f lc response with the pd-controller response, which already exists in the system, through studying the expected transients during the normal operation of ETRR-2 reactor, the simulation results show that, fl s has the better response, the second controller is adaptive fuzzy controller, which is proposed to deal with system non-linearity . The simulation results show that the proposed adaptive fuzzy controller gives a better integral square error (i se) index than the existing conventional od controller
One-step trinary signed-digit arithmetic using an efficient encoding scheme
Salim, W. Y.; Fyath, R. S.; Ali, S. A.; Alam, Mohammad S.
2000-11-01
The trinary signed-digit (TSD) number system is of interest for ultra fast optoelectronic computing systems since it permits parallel carry-free addition and borrow-free subtraction of two arbitrary length numbers in constant time. In this paper, a simple coding scheme is proposed to encode the decimal number directly into the TSD form. The coding scheme enables one to perform parallel one-step TSD arithmetic operation. The proposed coding scheme uses only a 5-combination coding table instead of the 625-combination table reported recently for recoded TSD arithmetic technique.
Competing Biases in Mental Arithmetic: When Division Is More and Multiplication Is Less.
Shaki, Samuel; Fischer, Martin H
2017-01-01
Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such "operational momentum" (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic.
Rodríguez, J. Tinguaro; Franco de los Ríos, Camilo; Gómez, Daniel
2015-01-01
In this paper we want to stress the relevance of paired fuzzy sets, as already proposed in previous works of the authors, as a family of fuzzy sets that offers a unifying view for different models based upon the opposition of two fuzzy sets, simply allowing the existence of different types...
Mesiar, Radko
2005-01-01
Roč. 28, č. 156 (2005), s. 365-370 ISSN 0165-0114 R&D Projects: GA ČR(CZ) GA402/04/1026 Institutional research plan: CEZ:AV0Z10750506 Keywords : fuzzy measures * fuzzy integral * regular fuzzy integral Subject RIV: BA - General Mathematics Impact factor: 1.039, year: 2005
Fuzzy Graph Language Recognizability
Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros
2012-01-01
Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.
Rodic, Maja; Zhou, Xinlin; Tikhomirova, Tatiana; Wei, Wei; Malykh, Sergei; Ismatulina, Victoria; Sabirova, Elena; Davidova, Yulia; Tosto, Maria Grazia; Lemelin, Jean-Pascal; Kovas, Yulia
2015-01-01
The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic - operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were small, 13% of the variance in arithmetic skills could be explained by the sample, replicating the pattern, previously found with older children in PISA. Furthermore, the same cognitive skills were related to early arithmetic in these diverse populations. Only understanding of symbolic number explained variation in mathematical performance in all samples. We discuss the results in terms of potential influences of socio-demographic, linguistic and genetic factors on individual differences in mathematics. © 2014 John Wiley & Sons Ltd.
Intuitionistic Fuzzy Subbialgebras and Duality
Wenjuan Chen
2014-01-01
Full Text Available We investigate connections between bialgebras and Atanassov’s intuitionistic fuzzy sets. Firstly we define an intuitionistic fuzzy subbialgebra of a bialgebra with an intuitionistic fuzzy subalgebra structure and also with an intuitionistic fuzzy subcoalgebra structure. Secondly we investigate the related properties of intuitionistic fuzzy subbialgebras. Finally we prove that the dual of an intuitionistic fuzzy strong subbialgebra is an intuitionistic fuzzy strong subbialgebra.
Schoppek, Wolfgang; Tulis, Maria
2010-01-01
The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a…
Leich, A.; Polyntsev, A.D.
1982-01-01
The structure and software of the arithmetical module for the multi-microprocessor intelligent graphics terminal designed for realization of the world coordinate two-dimensional transformation are described. The module performs the operations like coordinate system displacement, scaling and rotation as well as transformations for window/viewport separation
Probabilistic fuzzy systems as additive fuzzy systems
Almeida, R.J.; Verbeek, N.; Kaymak, U.; Costa Sousa, da J.M.; Laurent, A.; Strauss, O.; Bouchon-Meunier, B.; Yager, R.
2014-01-01
Probabilistic fuzzy systems combine a linguistic description of the system behaviour with statistical properties of data. It was originally derived based on Zadeh’s concept of probability of a fuzzy event. Two possible and equivalent additive reasoning schemes were proposed, that lead to the
Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients
Xue-Gang Zhou
2014-01-01
Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.
Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space
Apu Kumar Saha
2015-06-01
Full Text Available This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.
Dictionary of algebra, arithmetic, and trigonometry
Krantz, Steven G
2000-01-01
Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Algebra, Arithmetic, and Trigonometry- the second published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,800 detailed definitions, written in a clear, readable style, complete with alternative meanings, and related references.From Abelian cohomology to zero ring and from the very basic to the highly advanced, this unique lexicon includes terms associated with arithmetic, algebra, and trigonometry, with natural overlap into geom...
Nonverbal arithmetic in humans: light from noise.
Cordes, Sara; Gallistel, C R; Gelman, Rochel; Latham, Peter
2007-10-01
Animal and human data suggest the existence of a cross-species system of analog number representation (e.g., Cordes, Gelman, Gallistel, & Whalen, 2001; Meeck & Church, 1983), which may mediate the computation of statistical regularities in the environment (Gallistel, Gelman, & Cordes, 2006). However, evidence of arithmetic manipulation of these nonverbal magnitude representations is sparse and lacking in depth. This study uses the analysis of variability as a tool for understanding properties of these combinatorial processes. Human subjects participated in tasks requiring responses dependent upon the addition, subtraction, or reproduction of nonverbal counts. Variance analyses revealed that the magnitude of both inputs and answer contributed to the variability in the arithmetic responses, with operand variability dominating. Other contributing factors to the observed variability and implications for logarithmic versus scalar models of magnitude representation are discussed in light of these results.
A sorting network in bounded arithmetic
Jeřábek, Emil
2011-01-01
Roč. 162, č. 4 (2011), s. 341-355 ISSN 0168-0072 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * sorting network * proof complexity * monotone sequent calculus Subject RIV: BA - General Mathematics Impact factor: 0.450, year: 2011 http://www.sciencedirect.com/science/article/pii/S0168007210001272
Boroushaki, M.; Ghofrani, M.B.; Lucas, C.; Yazdanpanah, M.J.
2003-01-01
In the last decade, the intelligent control community has paid great attention to the topic of intelligent control systems for nuclear plants (core, steam generator...). Papers mostly used approximate and simple mathematical SISO (single-input-single-output) model of nuclear plants for testing and/or tuning of the control systems. They also tried to generalize theses models to a real MIMO (multi-input-multi-output) plant, while nuclear plants are typically of complex nonlinear and multivariable nature with high interactions between their state variables and therefore, many of these proposed intelligent control systems are not appropriate for real cases. In this paper, we designed an on-line intelligent core controller for load following operations, based on a heuristic control algorithm, using a valid and updatable recurrent neural network (RNN). We have used an accurate 3-dimensional core calculation code to represent the real plant and to train the RNN. The results of simulation show that this intelligent controller can control the reactor core during load following operations, using optimum control rod groups manoeuvre and variable overlapping strategy. This methodology represents a simple and reliable procedure for controlling other complex nonlinear MIMO plants, and may improve the responses, comparing to other control systems
Recurrent fuzzy ranking methods
Hajjari, Tayebeh
2012-11-01
With the increasing development of fuzzy set theory in various scientific fields and the need to compare fuzzy numbers in different areas. Therefore, Ranking of fuzzy numbers plays a very important role in linguistic decision-making, engineering, business and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce non-intuitive results in certain case. In this paper, we reviewed some recent ranking methods, which will be useful for the researchers who are interested in this area.
B Gibilisco, Michael; E Albert, Karen; N Mordeson, John; J Wierman, Mark; D Clark, Terry
2014-01-01
This book offers a comprehensive analysis of the social choice literature and shows, by applying fuzzy sets, how the use of fuzzy preferences, rather than that of strict ones, may affect the social choice theorems. To do this, the book explores the presupposition of rationality within the fuzzy framework and shows that the two conditions for rationality, completeness and transitivity, do exist with fuzzy preferences. Specifically, this book examines: the conditions under which a maximal set exists; the Arrow’s theorem; the Gibbard-Satterthwaite theorem; and the median voter theorem. After showing that a non-empty maximal set does exists for fuzzy preference relations, this book goes on to demonstrating the existence of a fuzzy aggregation rule satisfying all five Arrowian conditions, including non-dictatorship. While the Gibbard-Satterthwaite theorem only considers individual fuzzy preferences, this work shows that both individuals and groups can choose alternatives to various degrees, resulting in a so...
Classified one-step high-radix signed-digit arithmetic units
Cherri, Abdallah K.
1998-08-01
High-radix number systems enable higher information storage density, less complexity, fewer system components, and fewer cascaded gates and operations. A simple one-step fully parallel high-radix signed-digit arithmetic is proposed for parallel optical computing based on new joint spatial encodings. This reduces hardware requirements and improves throughput by reducing the space-bandwidth produce needed. The high-radix signed-digit arithmetic operations are based on classifying the neighboring input digit pairs into various groups to reduce the computation rules. A new joint spatial encoding technique is developed to present both the operands and the computation rules. This technique increases the spatial bandwidth product of the spatial light modulators of the system. An optical implementation of the proposed high-radix signed-digit arithmetic operations is also presented. It is shown that our one-step trinary signed-digit and quaternary signed-digit arithmetic units are much simpler and better than all previously reported high-radix signed-digit techniques.
Fuzzy-based HAZOP study for process industry
Ahn, Junkeon; Chang, Daejun, E-mail: djchang@kaist.edu
2016-11-05
Highlights: • HAZOP is the important technique to evaluate system safety and its risks while process operations. • Fuzzy theory can handle the inherent uncertainties of process systems for the HAZOP. • Fuzzy-based HAZOP considers the aleatory and epistemic uncertainties and provides the risk level with less uncertainty. • Risk acceptance criteria should be considered regarding the transition region for each risk. - Abstract: This study proposed a fuzzy-based HAZOP for analyzing process hazards. Fuzzy theory was used to express uncertain states. This theory was found to be a useful approach to overcome the inherent uncertainty in HAZOP analyses. Fuzzy logic sharply contrasted with classical logic and provided diverse risk values according to its membership degree. Appropriate process parameters and guidewords were selected to describe the frequency and consequence of an accident. Fuzzy modeling calculated risks based on the relationship between the variables of an accident. The modeling was based on the mean expected value, trapezoidal fuzzy number, IF-THEN rules, and the center of gravity method. A cryogenic LNG (liquefied natural gas) testing facility was the objective process for the fuzzy-based and conventional HAZOPs. The most significant index is the frequency to determine risks. The comparison results showed that the fuzzy-based HAZOP provides better sophisticated risks than the conventional HAZOP. The fuzzy risk matrix presents the significance of risks, negligible risks, and necessity of risk reduction.
Integrating Fuzzy AHP and Fuzzy ARAS for evaluating financial performance
Abdolhamid Safaei Ghadikolaei; Saber Khalili Esbouei
2014-01-01
Multi Criteria Decision Making (MCDM) is an advanced field of Operation Research; recently MCDM methods are efficient and common tools for performance evaluation in many areas such as finance and economy. The aim of this study is to show one of applications of mathematics in real word. This study with considering value based measures and accounting based measures simultaneously, provided a hybrid approach of MCDM methods in fuzzy environment for financial performance evaluation of automotive ...
Fuzzy controllers in nuclear material accounting
Zardecki, A.
1994-01-01
Fuzzy controllers are applied to predicting and modeling a time series, with particular emphasis on anomaly detection in nuclear material inventory differences. As compared to neural networks, the fuzzy controllers can operate in real time; their learning process does not require many iterations to converge. For this reason fuzzy controllers are potentially useful in time series forecasting, where the authors want to detect and identify trends in real time. They describe an object-oriented implementation of the algorithm advanced by Wang and Mendel. Numerical results are presented both for inventory data and time series corresponding to chaotic situations, such as encountered in the context of strange attractors. In the latter case, the effects of noise on the predictive power of the fuzzy controller are explored
Shafiqur Rehman
2016-10-01
Full Text Available The emergence of wind energy as a potential alternative to traditional sources of fuel has prompted notable research in recent years. One primary factor contributing to efficient utilization of wind energy from a wind farm is the type of turbines used. However, selection of a specific wind turbine type is a difficult task due to several criteria involved in the selection process. Important criteria include turbine’s power rating, height of tower, energy output, rotor diameter, cut-in wind speed, and rated wind speed. The complexity of this selection process is further amplified by the presence of conflicts between the decision criteria. Therefore, a decision is desired that provides the best balance between all selection criteria. Considering the complexities involved in the decision-making process, this paper proposes a two-level decision turbine selection strategy based on fuzzy logic and multi-criteria decision-making (MCDM approach. More specifically, the fuzzy arithmetic mean operator is used in the decision process. The proposed approach is applied to wind data collected from the site of Qassim, Saudi Arabia. Results indicate that the proposed approach was effective in finding the optimal turbine from a set of 20 turbines of various capacities.
Advanced Concepts in Fuzzy Logic and Systems with Membership Uncertainty
Starczewski, Janusz T
2013-01-01
This book generalizes fuzzy logic systems for different types of uncertainty, including - semantic ambiguity resulting from limited perception or lack of knowledge about exact membership functions - lack of attributes or granularity arising from discretization of real data - imprecise description of membership functions - vagueness perceived as fuzzification of conditional attributes. Consequently, the membership uncertainty can be modeled by combining methods of conventional and type-2 fuzzy logic, rough set theory and possibility theory. In particular, this book provides a number of formulae for implementing the operation extended on fuzzy-valued fuzzy sets and presents some basic structures of generalized uncertain fuzzy logic systems, as well as introduces several of methods to generate fuzzy membership uncertainty. It is desirable as a reference book for under-graduates in higher education, master and doctor graduates in the courses of computer science, computational intelligence, or...
Puskajler, J.
2004-01-01
The paper explains how can computer understand and process inaccurate (indefinite) information. It is processing of terms like e.g. 'around in the middle of month' or 'not too big'. Fuzzy logic, fuzzy sets, operations with them, fuzzy rules and using of linguistics variables are explained. The possibilities of application of fuzzy systems in automation of regulation of small-scale hydro power plants are discussed. (author)
Arithmetic differential equations on $GL_n$, I: differential cocycles
Buium, Alexandru; Dupuy, Taylor
2013-01-01
The theory of differential equations has an arithmetic analogue in which derivatives are replaced by Fermat quotients. One can then ask what is the arithmetic analogue of a linear differential equation. The study of usual linear differential equations is the same as the study of the differential cocycle from $GL_n$ into its Lie algebra given by the logarithmic derivative. However we prove here that there are no such cocycles in the context of arithmetic differential equations. In sequels of t...
Introduction to Fuzzy Set Theory
Kosko, Bart
1990-01-01
An introduction to fuzzy set theory is described. Topics covered include: neural networks and fuzzy systems; the dynamical systems approach to machine intelligence; intelligent behavior as adaptive model-free estimation; fuzziness versus probability; fuzzy sets; the entropy-subsethood theorem; adaptive fuzzy systems for backing up a truck-and-trailer; product-space clustering with differential competitive learning; and adaptive fuzzy system for target tracking.
Research and Implementation of Automatic Fuzzy Garage Parking System Based on FPGA
Wang Kaiyu; Yu Zongmin; Guan Sanghai; Yang Xing; Sheng Menglin; Tang Zhenan
2016-01-01
Because of many common scenes of reverse parking in real life, this paper presents a fuzzy controller which accommodates front and back adjustment of vehicle’s body attitude, and based on chaotic-genetic arithmetic to optimize the membership function of this controller, and get a vertical parking fuzzy controller whose simulation result is good .The paper makes the hardware-software embedded design for system based on Field-Programmable Gate Array (FPGA), and set up a 1:10 verification platfo...
Hierarchical fuzzy control of low-energy building systems
Yu, Zhen; Dexter, Arthur [Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ (United Kingdom)
2010-04-15
A hierarchical fuzzy supervisory controller is described that is capable of optimizing the operation of a low-energy building, which uses solar energy to heat and cool its interior spaces. The highest level fuzzy rules choose the most appropriate set of lower level rules according to the weather and occupancy information; the second level fuzzy rules determine an optimal energy profile and the overall modes of operation of the heating, ventilating and air-conditioning system (HVAC); the third level fuzzy rules select the mode of operation of specific equipment, and assign schedules to the local controllers so that the optimal energy profile can be achieved in the most efficient way. Computer simulation is used to compare the hierarchical fuzzy control scheme with a supervisory control scheme based on expert rules. The performance is evaluated by comparing the energy consumption and thermal comfort. (author)
Arithmetic fundamental groups and moduli of curves
Makoto Matsumoto
2000-01-01
This is a short note on the algebraic (or sometimes called arithmetic) fundamental groups of an algebraic variety, which connects classical fundamental groups with Galois groups of fields. A large part of this note describes the algebraic fundamental groups in a concrete manner. This note gives only a sketch of the fundamental groups of the algebraic stack of moduli of curves. Some application to a purely topological statement, i.e., an obstruction to the subjectivity of Johnson homomorphisms in the mapping class groups, which comes from Galois group of Q, is explained. (author)
Algebra 1 groups, rings, fields and arithmetic
Lal, Ramji
2017-01-01
This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.
The Structure of Models of Peano Arithmetic
Kossak, Roman
2006-01-01
Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants: families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to HaimGaifman, and some of the results are classical but have never been published in a book form before.
Embedded systems design with special arithmetic and number systems
Sousa, Leonel; Chang, Chip-Hong
2017-01-01
This book introduces readers to alternative approaches to designing efficient embedded systems using unconventional number systems. The authors describe various systems that can be used for designing efficient embedded and application-specific processors, such as Residue Number System, Logarithmic Number System, Redundant Binary Number System Double-Base Number System, Decimal Floating Point Number System and Continuous Valued Number System. Readers will learn the strategies and trade-offs of using unconventional number systems in application-specific processors and be able to apply and design appropriate arithmetic operations from these number systems to boost the performance of digital systems. • Serves as a single-source reference to designing embedded systems with unconventional number systems • Covers theory as well as implementation on application-specific processors • Explains mathematical concepts in a manner accessible to readers with diverse backgrounds.
Guest Editors' Introduction: Special Section on Computer Arithmetic
Nannarelli, Alberto; Seidel, Peter-Michael; Tang, Ping Tak Peter
2014-01-01
and their subsequent testing and verification. Many practitioners of the field also focus on the art and science of using computer arithmetic to carry out scientific and engineering computations. Computer arithmetic is therefore an interdisciplinary field that draws upon mathematics, computer science and electrical......The articles in this special issue focus on current trends and developments in the field of computer arithmetic. This is a field that encompasses the definition and standardization of arithmetic system for computers. The field also deals with issues of hardware and software implementations...
A Fuzzy Rule-based Controller For Automotive Vehicle Guidance
Hessburg, Thomas; Tomizuka, Masayoshi
1991-01-01
A fuzzy rule-based controller is applied to lateral guidance of a vehicle for an automated highway system. The fuzzy rules, based on human drivers' experiences, are developed to track the center of a lane in the presence of external disturbances and over a range of vehicle operating conditions.
Decomposition of fuzzy continuity and fuzzy ideal continuity via fuzzy idealization
Zahran, A.M.; Abbas, S.E.; Abd El-baki, S.A.; Saber, Y.M.
2009-01-01
Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy α-I-open and r-fuzzy β-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy α-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal α-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.
Markowski, Adam S.; Mannan, M. Sam
2008-01-01
A risk matrix is a mechanism to characterize and rank process risks that are typically identified through one or more multifunctional reviews (e.g., process hazard analysis, audits, or incident investigation). This paper describes a procedure for developing a fuzzy risk matrix that may be used for emerging fuzzy logic applications in different safety analyses (e.g., LOPA). The fuzzification of frequency and severity of the consequences of the incident scenario are described which are basic inputs for fuzzy risk matrix. Subsequently using different design of risk matrix, fuzzy rules are established enabling the development of fuzzy risk matrices. Three types of fuzzy risk matrix have been developed (low-cost, standard, and high-cost), and using a distillation column case study, the effect of the design on final defuzzified risk index is demonstrated
Jantzen, Jan
The objective of this textbook is to acquire an understanding of the behaviour of fuzzy logic controllers. Under certain conditions a fuzzy controller is equivalent to a proportional-integral-derivative (PID) controller. Using that equivalence as a link, the book applies analysis methods from...... linear and nonlinear control theory. In the linear domain, PID tuning methods and stability analyses are transferred to linear fuzzy controllers. The Nyquist plot shows the robustness of different settings of the fuzzy gain parameters. As a result, a fuzzy controller is guaranteed to perform as well...... as any PID controller. In the nonlinear domain, the stability of four standard control surfaces is analysed by means of describing functions and Nyquist plots. The self-organizing controller (SOC) is shown to be a model reference adaptive controller. There is a possibility that a nonlinear fuzzy PID...
Metamathematics of fuzzy logic
Hájek, Petr
1998-01-01
This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named `fuzzy inference' can be naturally understood as logical deduction.
Dotoli, M.; Jantzen, Jan
1999-01-01
The tutorial concerns automatic control of an inverted pendulum, especially rule based control by means of fuzzy logic. A ball balancer, implemented in a software simulator in Matlab, is used as a practical case study. The objectives of the tutorial are to teach the basics of fuzzy control......, and to show how to apply fuzzy logic in automatic control. The tutorial is distance learning, where students interact one-to-one with the teacher using e-mail....
Fuzzy control and identification
Lilly, John H
2010-01-01
This book gives an introduction to basic fuzzy logic and Mamdani and Takagi-Sugeno fuzzy systems. The text shows how these can be used to control complex nonlinear engineering systems, while also also suggesting several approaches to modeling of complex engineering systems with unknown models. Finally, fuzzy modeling and control methods are combined in the book, to create adaptive fuzzy controllers, ending with an example of an obstacle-avoidance controller for an autonomous vehicle using modus ponendo tollens logic.
Class dependency of fuzzy relational database using relational calculus and conditional probability
Deni Akbar, Mohammad; Mizoguchi, Yoshihiro; Adiwijaya
2018-03-01
In this paper, we propose a design of fuzzy relational database to deal with a conditional probability relation using fuzzy relational calculus. In the previous, there are several researches about equivalence class in fuzzy database using similarity or approximate relation. It is an interesting topic to investigate the fuzzy dependency using equivalence classes. Our goal is to introduce a formulation of a fuzzy relational database model using the relational calculus on the category of fuzzy relations. We also introduce general formulas of the relational calculus for the notion of database operations such as ’projection’, ’selection’, ’injection’ and ’natural join’. Using the fuzzy relational calculus and conditional probabilities, we introduce notions of equivalence class, redundant, and dependency in the theory fuzzy relational database.
Relations Among Some Fuzzy Entropy Formulae
卿铭
2004-01-01
Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.
On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets
Xiaoyan Liu
2014-01-01
Full Text Available Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov’s soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation =L. We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets.
On some nonclassical algebraic properties of interval-valued fuzzy soft sets.
Liu, Xiaoyan; Feng, Feng; Zhang, Hui
2014-01-01
Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation = L . We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets.
On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets
2014-01-01
Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation =L. We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets. PMID:25143964
On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes
Rajesh K. Thumbakara
2013-01-01
Full Text Available Frame theory is the study of topology based on its open set lattice, and it was studied extensively by various authors. In this paper, we study quotients of intuitionistic fuzzy filters of an intuitionistic fuzzy coframe. The quotients of intuitionistic fuzzy filters are shown to be filters of the given intuitionistic fuzzy coframe. It is shown that the collection of all intuitionistic fuzzy filters of a coframe and the collection of all intutionistic fuzzy quotient filters of an intuitionistic fuzzy filter are coframes.
Children's Acquisition of Arithmetic Principles: The Role of Experience
Prather, Richard; Alibali, Martha W.
2011-01-01
The current study investigated how young learners' experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children's acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children…
Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One
We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over C C . Let be a nodal curve of arithmetic genus one defined over R R , with exactly one node, such that does not have any real points apart from the node. We classify all isomorphism ...
Arithmetic Training Does Not Improve Approximate Number System Acuity
Marcus Lindskog
2016-10-01
Full Text Available The Approximate Number System (ANS is thought to support non-symbolic representations of numerical magnitudes in humans. Recently much debate has focused on the causal direction for an observed relation between ANS acuity and arithmetic fluency. Here we investigate if arithmetic training can improve ANS acuity. We show with an experimental training study consisting of six 45-minute training sessions that although feedback during arithmetic training improves arithmetic performance substantially, it does not influence ANS acuity. Hence, we find no support for a causal link where symbolic arithmetic training influences the ANS acuity. Further, although short-term number memory is likely involved in arithmetic tasks we did not find that short-term memory capacity for numbers, measured by a digit-span test, was effected by arithmetic training. This suggests that the improvement in arithmetic fluency may have occurred independent of short-term memory efficiency, but rather due to long-term memory processes and/or mental calculation strategy development. The theoretical implications of these findings are discussed.
A novel chaotic encryption scheme based on arithmetic coding
Mi Bo; Liao Xiaofeng; Chen Yong
2008-01-01
In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail
Arithmetic groups and their generalizations what, why, and how
Ji, Lizhen
2010-01-01
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as \\mathbf{Z} or \\mathrm{SL}(n,\\mathbf{Z}). Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics.
Properties of Bipolar Fuzzy Hypergraphs
Akram, M.; Dudek, W. A.; Sarwar, S.
2013-01-01
In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some properties of bipolar fuzzy hypergraphs. We introduce the notion of $A-$ tempered bipolar fuzzy hypergraphs and present some of their properties. We also present application examples of bipolar fuzzy hypergraphs.
A fuzzy expert system based on relations
Hall, L.O.; Kandel, A.
1986-01-01
The Fuzzy Expert System (FESS) is an expert system which makes use of the theory of fuzzy relations to perform inference. Relations are very general and can be used for any application, which only requires different types of relations be implemented and used. The incorporation of fuzzy reasoning techniques enables the expert system to deal with imprecision in a well-founded manner. The knowledge is represented in relational frames. FESS may operate in either a forward chaining or backward chaining manner. It uses primarily implication and factual relations. A unique methodology for combination of evidence has been developed. It makes uses of a blackboard for communication between the various knowledge sources which may operate in parallel. The expert system has been designed in such a manner that it may be used for diverse applications
Resource integrated planning through fuzzy techniques
Haddad, J; Torres, G Lambert [Escola Federal de Engenharia de Itajuba, MG (Brazil); Jannuzzi, G de M. [Universidade Estadual de Campinas, SP (Brazil). Faculdade de Engenharia Mecanica
1994-12-31
A methodology for decision-making in studies involving energy saving by using the Fuzzy Sets Theory is presented. The Fuzzy Sets Theory permits to handle and to operate exact and non-exact propositions, that is, to incorporate both numerical data (exact) and the knowledge of either the expert or the analyst (inexact). The basic concepts of this theory are presented with its main operations and properties. Following, some criteria and technical-economical parameters used in the planning of the generation expansion are shown and, finally, the Theory of the Fuzzy Sets is applied aiming to establish electrical power generation and conservation strategies considering the power demand. (author) 6 refs., 8 tabs.
PaCAL: A Python Package for Arithmetic Computations with Random Variables
Marcin Korze?
2014-05-01
Full Text Available In this paper we present PaCAL, a Python package for arithmetical computations on random variables. The package is capable of performing the four arithmetic operations: addition, subtraction, multiplication and division, as well as computing many standard functions of random variables. Summary statistics, random number generation, plots, and histograms of the resulting distributions can easily be obtained and distribution parameter ?tting is also available. The operations are performed numerically and their results interpolated allowing for arbitrary arithmetic operations on random variables following practically any probability distribution encountered in practice. The package is easy to use, as operations on random variables are performed just as they are on standard Python variables. Independence of random variables is, by default, assumed on each step but some computations on dependent random variables are also possible. We demonstrate on several examples that the results are very accurate, often close to machine precision. Practical applications include statistics, physical measurements or estimation of error distributions in scienti?c computations.
Statistical Methods for Fuzzy Data
Viertl, Reinhard
2011-01-01
Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy m
Quality Improvement of Liver Ultrasound Images Using Fuzzy Techniques.
Bayani, Azadeh; Langarizadeh, Mostafa; Radmard, Amir Reza; Nejad, Ahmadreza Farzaneh
2016-12-01
Liver ultrasound images are so common and are applied so often to diagnose diffuse liver diseases like fatty liver. However, the low quality of such images makes it difficult to analyze them and diagnose diseases. The purpose of this study, therefore, is to improve the contrast and quality of liver ultrasound images. In this study, a number of image contrast enhancement algorithms which are based on fuzzy logic were applied to liver ultrasound images - in which the view of kidney is observable - using Matlab2013b to improve the image contrast and quality which has a fuzzy definition; just like image contrast improvement algorithms using a fuzzy intensification operator, contrast improvement algorithms applying fuzzy image histogram hyperbolization, and contrast improvement algorithms by fuzzy IF-THEN rules. With the measurement of Mean Squared Error and Peak Signal to Noise Ratio obtained from different images, fuzzy methods provided better results, and their implementation - compared with histogram equalization method - led both to the improvement of contrast and visual quality of images and to the improvement of liver segmentation algorithms results in images. Comparison of the four algorithms revealed the power of fuzzy logic in improving image contrast compared with traditional image processing algorithms. Moreover, contrast improvement algorithm based on a fuzzy intensification operator was selected as the strongest algorithm considering the measured indicators. This method can also be used in future studies on other ultrasound images for quality improvement and other image processing and analysis applications.
Tohir, M.; Abidin, Z.; Dafik; Hobri
2018-04-01
Arithmetics is one of the topics in Mathematics, which deals with logic and detailed process upon generalizing formula. Creativity and flexibility are needed in generalizing formula of arithmetics series. This research aimed at analyzing students creative thinking skills in generalizing arithmetic series. The triangulation method and research-based learning was used in this research. The subjects were students of the Master Program of Mathematics Education in Faculty of Teacher Training and Education at Jember University. The data was collected by giving assignments to the students. The data collection was done by giving open problem-solving task and documentation study to the students to arrange generalization pattern based on the dependent function formula i and the function depend on i and j. Then, the students finished the next problem-solving task to construct arithmetic generalization patterns based on the function formula which depends on i and i + n and the sum formula of functions dependent on i and j of the arithmetic compiled. The data analysis techniques operative in this study was Miles and Huberman analysis model. Based on the result of data analysis on task 1, the levels of students creative thinking skill were classified as follows; 22,22% of the students categorized as “not creative” 38.89% of the students categorized as “less creative” category; 22.22% of the students categorized as “sufficiently creative” and 16.67% of the students categorized as “creative”. By contrast, the results of data analysis on task 2 found that the levels of students creative thinking skills were classified as follows; 22.22% of the students categorized as “sufficiently creative”, 44.44% of the students categorized as “creative” and 33.33% of the students categorized as “very creative”. This analysis result can set the basis for teaching references and actualizing a better teaching model in order to increase students creative thinking skills.
The arithmetic basis of special relativity
Greenspan, D.
1976-01-01
Under relatively general particle and rocket frame motions, it is shown that, for special relativity, the basic concepts can be formulated and the basic properties deduced using only arithmetic. Particular attention is directed toward velocity, acceleration, proper time, momentum, energy, and 4-vectors in both space-time and Minkowski space, and to relativistic generalizations of Newton's second law. The resulting mathematical simplification is not only completely compatible with modern computer technology, but it yields dynamical equations that can be solved directly by such computers. Particular applications of the numerical equations, which are either Lorentz invariant or are directly related to Lorentz-invariant formulas, are made to the study of a relativistic harmonic oscillator and to the motion of an electric particle in a magnetic field. (author)
Barrouillet, P; Fayol, M
1998-03-01
A number of theories of mental arithmetic suggest that the ability to solve simple addition and subtraction problems develops from an algorithmic strategy toward a strategy based on the direct retrieval of the result from memory. In the experiment presented here, 2nd and 12th graders were asked to solve two tasks of number and alphabet arithmetic. The subjects transformed series of 1 to 4 numbers or letters (item span) by adding or subtracting an operand varying from 1 to 4 (operation span). Although both the item and operation span were associated with major and identical effects in the case of both numbers and letters at 2nd grade, such effects were clearly observable only in the case of letters for the adult subjects. This suggests the use of an algorithmic strategy for both types of material in the case of the children and for the letters only in the case of the adults, who retrieved numerical results directly from memory.
Construction of fuzzy automata by fuzzy experiments
Mironov, A.
1994-01-01
The solving the problem of canonical realization of partial reaction morphisms (PRM) for automata in toposes and fuzzy automata is addressed. This problem extends the optimal construction problem for finite deterministic automata by experiments. In the present paper the conception of canonical realization of PRM for automata in toposes is introduced and the sufficient conditions for the existence of canonical realizations for PRM in toposes are presented. As a consequence of this result the existence of canonical realizations for PRM in the category of fuzzy sets over arbitrary complete chain is proven
Construction of fuzzy automata by fuzzy experiments
Mironov, A [Moscow Univ. (Russian Federation). Dept. of Mathematics and Computer Science
1994-12-31
The solving the problem of canonical realization of partial reaction morphisms (PRM) for automata in toposes and fuzzy automata is addressed. This problem extends the optimal construction problem for finite deterministic automata by experiments. In the present paper the conception of canonical realization of PRM for automata in toposes is introduced and the sufficient conditions for the existence of canonical realizations for PRM in toposes are presented. As a consequence of this result the existence of canonical realizations for PRM in the category of fuzzy sets over arbitrary complete chain is proven.
Wide-range nuclear reactor temperature control using automatically tuned fuzzy logic controller
Ramaswamy, P.; Edwards, R.M.; Lee, K.Y.
1992-01-01
In this paper, a fuzzy logic controller design for optimal reactor temperature control is presented. Since fuzzy logic controllers rely on an expert's knowledge of the process, they are hard to optimize. An optimal controller is used in this paper as a reference model, and a Kalman filter is used to automatically determine the rules for the fuzzy logic controller. To demonstrate the robustness of this design, a nonlinear six-delayed-neutron-group plant is controlled using a fuzzy logic controller that utilizes estimated reactor temperatures from a one-delayed-neutron-group observer. The fuzzy logic controller displayed good stability and performance robustness characteristics for a wide range of operation
Multi-Model Adaptive Fuzzy Controller for a CSTR Process
Shubham Gogoria
2015-09-01
Full Text Available Continuous Stirred Tank Reactors are intensively used to control exothermic reactions in chemical industries. It is a very complex multi-variable system with non-linear characteristics. This paper deals with linearization of the mathematical model of a CSTR Process. Multi model adaptive fuzzy controller has been designed to control the reactor concentration and temperature of CSTR process. This method combines the output of multiple Fuzzy controllers, which are operated at various operating points. The proposed solution is a straightforward implementation of Fuzzy controller with gain scheduler to control the linearly inseparable parameters of a highly non-linear process.
On Negations and Algebras in Fuzzy Set Theory
1986-03-19
Esteva Departament de Matematiques i Estadistica ~ Universitat Politecnica de Catalunya Diagonal 649 08028 Barcelona !Spain) ABSTRACT Dual... Estadistica Universitat Politecnica de Catalunya Diagonal 649 08028 Barcelona (Spain) In Zadeh’s definition of Fuzzy Sets [1] the operations are defined
Creating Clinical Fuzzy Automata with Fuzzy Arden Syntax.
de Bruin, Jeroen S; Steltzer, Heinz; Rappelsberger, Andrea; Adlassnig, Klaus-Peter
2017-01-01
Formal constructs for fuzzy sets and fuzzy logic are incorporated into Arden Syntax version 2.9 (Fuzzy Arden Syntax). With fuzzy sets, the relationships between measured or observed data and linguistic terms are expressed as degrees of compatibility that model the unsharpness of the boundaries of linguistic terms. Propositional uncertainty due to incomplete knowledge of relationships between clinical linguistic concepts is modeled with fuzzy logic. Fuzzy Arden Syntax also supports the construction of fuzzy state monitors. The latter are defined as monitors that employ fuzzy automata to observe gradual transitions between different stages of disease. As a use case, we re-implemented FuzzyARDS, a previously published clinical monitoring system for patients suffering from acute respiratory distress syndrome (ARDS). Using the re-implementation as an example, we show how key concepts of fuzzy automata, i.e., fuzzy states and parallel fuzzy state transitions, can be implemented in Fuzzy Arden Syntax. The results showed that fuzzy state monitors can be implemented in a straightforward manner.
Application of Fuzzy Theory to Radiological Emergency Preparedness
Han, Moon Hee; Jeong, Hyo Joon; Kim, Eun Han; Suh, Kyung Suk; Hwang, Won Tae
2005-01-01
Emergency preparedness for nuclear facility is considered as an important part for public health and safety. In an emergency, it is not easy to get the information which is needed for the operation of an emergency system. Even though the lack of the information, decision-maker should make an early decision for the public. And the real situation is often not crisp and deterministic. The concept of fuzzy set provides the mathematical formulations which can characterize the uncertain variables in the models related to radiological emergency preparedness. And it provides a method which can describe the characteristics of uncertain variables represented by the fuzzy membership functions, and the effects of distribution can be handled with the fuzzy relation and the fuzzy reasoning. By the application of linguistic variables and fuzzy algorithms, it is possible to provide an approximate and effective tool to describe the system which is too complex or ill defined to use precise mathematical analysis
Model predictive control using fuzzy decision functions
Kaymak, U.; Costa Sousa, da J.M.
2001-01-01
Fuzzy predictive control integrates conventional model predictive control with techniques from fuzzy multicriteria decision making, translating the goals and the constraints to predictive control in a transparent way. The information regarding the (fuzzy) goals and the (fuzzy) constraints of the
Approximations of Fuzzy Systems
Vinai K. Singh
2013-03-01
Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions
Govindarajan, T R; Padmanabhan, Pramod; Shreecharan, T
2010-01-01
We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in R 3 . We find that several surfaces, differing by constants, are described by the Higgs algebra at the fuzzy level. Some of these surfaces have a singularity and we overcome this by quantizing this manifold using coherent states for this nonlinear algebra. This is seen in the measure constructed from these coherent states. We also find the star product for this non-commutative algebra as a first step in constructing field theories on such fuzzy spaces.
Fuzzy Control in the Process Industry
Jantzen, Jan; Verbruggen, Henk; Østergaard, Jens-Jørgen
1999-01-01
Control problems in the process industry are dominated by non-linear and time-varying behaviour, many inner loops, and much interaction between the control loops. Fuzzy controllers have in some cases nevertheless mimicked the control actions of a human operator. Simple fuzzy controllers can...... be designed starting from PID controllers, and in more complex cases these can be used in connection with model-based predictive control. For high level control and supervisory control several simple controllers can be combined in a priority hierarchy such as the one developed in the cement industry...
Fuzzy TU games and their classes
Mareš, Milan
2001-01-01
Roč. 7, č. 13 (2001), s. 83-88 ISSN 1212-074X R&D Projects: GA ČR GA402/99/0032 Institutional research plan: AV0Z1075907 Keywords : fuzzy set * coalitional gam * fuzzification of game Subject RIV: BB - Applied Statistics, Operational Research
Automating Software Development Process using Fuzzy Logic
Marcelloni, Francesco; Aksit, Mehmet; Damiani, Ernesto; Jain, Lakhmi C.; Madravio, Mauro
2004-01-01
In this chapter, we aim to highlight how fuzzy logic can be a valid expressive tool to manage the software development process. We characterize a software development method in terms of two major components: artifact types and methodological rules. Classes, attributes, operations, and inheritance
Frege, Dedekind, and Peano on the foundations of arithmetic
Gillies, Donald
2013-01-01
First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosop
Landscape evaluation of heterogeneous areas using fuzzy sets
Ralf-Uwe Syrbe
1998-02-01
Full Text Available Landscape evaluation is an interesting field for fuzzy approaches, because it happens on the transition line between natural and social systems. Both are very complex. Therefore, transformation of scientific results to politically significant statements on environmental problems demands intelligent support. Particularly landscape planners need methods to gather natural facts of an area and assess them in consideration of its meaning to society as a whole. Since each land unit is heterogeneous, a special methodology is necessary. Such an evaluation technique was developed within a Geographical Information System (ARC/INFO. The methodology combines several known methods with fuzzy approaches to catch the intrinsic fuzziness of ecological systems as well as the heterogeneity of landscape. Additionally, a way will be discussed to vary the fuzzy inference in order to consider spatial relations of various landscape elements. Fuzzy logic is used to process the data uncertainty, to simulate the vagueness of knowledge about ecological functionality, and to model the spatial structure of landscape. Fuzzy sets describe the attributes of thematically defined land units and their assessment results. In this way, the available information will be preserved in their full diversity. The fuzzy operations are executed by AML-programs (ARC/INFO Macro Language. With such a tight coupling, it is possible to use the geographical functions (neighbourhoods, distances, etc. of GIS within the fuzzy system directly.
Fuzzy Multi-objective Linear Programming Approach
Amna Rehmat
2007-07-01
Full Text Available Traveling salesman problem (TSP is one of the challenging real-life problems, attracting researchers of many fields including Artificial Intelligence, Operations Research, and Algorithm Design and Analysis. The problem has been well studied till now under different headings and has been solved with different approaches including genetic algorithms and linear programming. Conventional linear programming is designed to deal with crisp parameters, but information about real life systems is often available in the form of vague descriptions. Fuzzy methods are designed to handle vague terms, and are most suited to finding optimal solutions to problems with vague parameters. Fuzzy multi-objective linear programming, an amalgamation of fuzzy logic and multi-objective linear programming, deals with flexible aspiration levels or goals and fuzzy constraints with acceptable deviations. In this paper, a methodology, for solving a TSP with imprecise parameters, is deployed using fuzzy multi-objective linear programming. An example of TSP with multiple objectives and vague parameters is discussed.
Kurt, Ünal
2014-01-01
The location selection for nuclear power plant (NPP) is a strategic decision, which has significant impact on the economic operation of the plant and sustainable development of the region. This paper proposes fuzzy TOPSIS and generalized Choquet fuzzy integral algorithm for evaluation and selection of optimal locations for NPP in Turkey. Many sub-criteria such as geological, social, touristic, transportation abilities, cooling water capacity and nearest to consumptions markets are taken into account. Among the evaluated locations, according to generalized Choquet fuzzy integral method, Inceburun–Sinop was selected as a study site due to its highest performance and meeting most of the investigated criteria. The Inceburun-Sinop is selected by generalized Choquet fuzzy integral and fuzzy TOPSIS Iğneada–Kırklareli took place in the first turn. The Mersin–Akkuyu is not selected in both methods. (author)
Samir Dey
2015-07-01
Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.
Application of Fuzzy TOPSIS for evaluating machining techniques using sustainability metrics
Digalwar, Abhijeet K.
2018-04-01
Sustainable processes and techniques are getting increased attention over the last few decades due to rising concerns over the environment, improved focus on productivity and stringency in environmental as well as occupational health and safety norms. The present work analyzes the research on sustainable machining techniques and identifies techniques and parameters on which sustainability of a process is evaluated. Based on the analysis these parameters are then adopted as criteria’s to evaluate different sustainable machining techniques such as Cryogenic Machining, Dry Machining, Minimum Quantity Lubrication (MQL) and High Pressure Jet Assisted Machining (HPJAM) using a fuzzy TOPSIS framework. In order to facilitate easy arithmetic, the linguistic variables represented by fuzzy numbers are transformed into crisp numbers based on graded mean representation. Cryogenic machining was found to be the best alternative sustainable technique as per the fuzzy TOPSIS framework adopted. The paper provides a method to deal with multi criteria decision making problems in a complex and linguistic environment.
Use of fuzzy set theory in the aggregation of expert judgments
Moon, Joo Hyun; Kang, Chang Sun
1999-01-01
It is sometimes impossible to make a correct decision in a certain engineering task without the help from professional expert judgments. Even though there are different expert opinions available, however, they should be appropriately aggregated to a useful form for making an acceptable engineering decision. This paper proposes a technique which utilizes the fuzzy set theory in the aggregation of expert judgments. In the technique, two main key concepts are employed: linguistic variables and fuzzy numbers. Linguistic variables first represent the relative importance of evaluation criteria under consideration and the degree of confidence on each expert perceived by the decision maker, and then are replaced by suitable triangular fuzzy numbers for arithmetic manipulation. As a benchmark problem, the pressure increment in the containment of Sequoyah nuclear power plant due to reactor vessel breach was estimated to verify and validate the proposed technique
Fuzzy technology present applications and future challenges
Fedrizzi, Mario; Kacprzyk, Janusz
2016-01-01
This book provides readers with a timely and comprehensive yet concise view on the field of fuzzy logic and its real-world applications. The chapters, written by authoritative scholars in the field, report on promising new models for data analysis, decision making, and systems modeling, with a special emphasis on their applications in management science. The book is a token of appreciation from the fuzzy research community to Professor Christer Carlsson for his long time research and organizational commitment, which have among other things resulted in the foundation and success of the Institute for Advanced Management Systems Research (IAMSR) at Åbo Akademi University, in Åbo (Turku), Finland. The book serves as timely guide for the fuzzy logic and operations research communities alike. .
Intelligent control-III: fuzzy control system
Nagrial, M.H.
2004-01-01
During the last decade or so, fuzzy logic control (FLC) has emerged as one of the most active and fruitful areas of research and development. The applications include industrial process control to medical diagnostic and financial markets. Many consumer products using this technology are available in the market place. FLC is best suited to complex ill-defined processes that can be controlled by a skilled human operator without much knowledge of their underlying dynamics. This lecture will cover the basic architecture and the design methodology of fuzzy logic controllers. FLC will be strongly based on the concepts of fuzzy set theory, introduced in first lecture. Some practical applications will also be discussed and presented. (author)
IMPLEMENTING FUZZY LOGIC IN DETERMINING SELLING PRICE
Danny Prabowo Soetanto
2000-01-01
Full Text Available The determination of the price should meet certain criteria, both from the society and the company itself. The combination of various criteria will result in another problem. Fuzzy Logic covers all influencing factors and displays the membership function graphic. Furthermore, by implementing fuzzy rules and fuzzy operator, the right price can be determined which covers all the factors above. The determination of the rules is based on the raw material cost, direct labor cost, distribution cost and the customers' opinion regarding the appropriate price. Then, the model is designed with the help of Matlab software. The result is finally obtained in the form of a model performed by Matlab software. The model displays the output concerning the selling price of the product for each change in the dominant factors.
Počítání s vágností I - Fuzzy veličiny
Mareš, Milan
2001-01-01
Roč. 44, č. 1 (2001), s. 34-37 ISSN 0005-125X R&D Projects: GA AV ČR IAA1075106; GA ČR GA402/99/0032 Institutional research plan: AV0Z1075907 Keywords : fuzzy numbers * fuzzy sets * fuzzy quantities Subject RIV: BB - Applied Statistics, Operational Research
Pinel, Philippe; Dehaene, Stanislas
2010-01-01
Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall "dominance" of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific…
Habiby, Sarry F.; Collins, Stuart A., Jr.
1987-01-01
The design and implementation of a digital (numerical) optical matrix-vector multiplier are presented. A Hughes liquid crystal light valve, the residue arithmetic representation, and a holographic optical memory are used to construct position coded optical look-up tables. All operations are performed in effectively one light valve response time with a potential for a high information density.
Fleeting footsteps tracing the conception of arithmetic and algebra in ancient China
Yong, Lam Lay
2004-01-01
The Hindu-Arabic numeral system (1, 2, 3,...) is one of mankind''sgreatest achievements and one of its most commonly usedinventions. How did it originate? Those who have written about thenumeral system have hypothesized that it originated in India; however,there is little evidence to support this claim. This book provides considerable evidence to show that theHindu-Arabic numeral system, despite its commonly accepted name,has its origins in the Chinese rod numeral system. This system waswidely used in China from antiquity till the 16th century. It was usedby officials, astronomers, traders and others to perform addition,subtraction, multiplication, division and other arithmetic operations,and also used by mathematicians to develop arithmetic andalgebra. Based on this system, numerous mathematical treatises werewritten.
Simplification of integrity constraints with aggregates and arithmetic built-ins
Martinenghi, Davide
2004-01-01
Both aggregates and arithmetic built-ins are widely used in current database query languages: Aggregates are second-order constructs such as CNT and SUM of SQL; arithmetic built-ins include relational and other mathematical operators that apply to numbers, such as < and +. These features are also...... time, simplified versions of such integrity constraints that can be tested before the execution of any update. In this way, virtually no time is spent for optimization or rollbacks at run time. Both set and bag semantics are considered....... of interest in the context of database integrity constraints: correct and efficient integrity checking is crucial, as, without any guarantee of data consistency, the answers to queries cannot be trusted. In this paper we propose a method of practical relevance that can be used to derive, at database design...
Design of Improved Arithmetic Logic Unit in Quantum-Dot Cellular Automata
Heikalabad, Saeed Rasouli; Gadim, Mahya Rahimpour
2018-06-01
The quantum-dot cellular automata (QCA) can be replaced to overcome the limitation of CMOS technology. An arithmetic logic unit (ALU) is a basic structure of any computer devices. In this paper, design of improved single-bit arithmetic logic unit in quantum dot cellular automata is presented. The proposed structure for ALU has AND, OR, XOR and ADD operations. A unique 2:1 multiplexer, an ultra-efficient two-input XOR and a low complexity full adder are used in the proposed structure. Also, an extended design of this structure is provided for two-bit ALU in this paper. The proposed structure of ALU is simulated by QCADesigner and simulation result is evaluated. Evaluation results show that the proposed design has best performance in terms of area, complexity and delay compared to the previous designs.
Bandemer, Hans
1992-01-01
Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common. In Fuzzy Data Analysis the authors collect their recent results providing the reader with ideas, approaches and methods for processing such data when looking for sub-structures in knowledge bases for an evaluation of functional relationship, e.g. in order to specify diagnostic or control systems. The modelling presented uses ideas from fuzzy set theory and the suggested methods solve problems usually tackled by data analysis if the data are real numbers. Fuzzy Data Analysis is self-contained and is addressed to mathematicians oriented towards applications and to practitioners in any field of application who have some background in mathematics and statistics.
Fuzzy stochastic multiobjective programming
Sakawa, Masatoshi; Katagiri, Hideki
2011-01-01
With a stress on interactive decision-making, this work breaks new ground by covering both the random nature of events related to environments, and the fuzziness of human judgements. The text runs from mathematical preliminaries to future research directions.
Goguen categories a categorical approach to l-fuzzy relations
Winter, Michael; Mundici, Daniele
2007-01-01
Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations. The book then introduces Goguen categories and provides a comprehensive study of these structures including their representation theory, and the definability of norm-based operations. The power of the theory is demonstrated by a comprehensive example. A certain Goguen category is used to specify and to develop a fuzzy controller. Based on its abstract description as well as certain desirable properties and their formal proofs, a verified controller is derived without compromising the - sometimes - intuitive choice of norm-based operations by fuzzy engineers.
Arithmetical aspects of the large sieve inequality
2009-01-01
This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is square...
Conference on Number Theory and Arithmetic Geometry
Silverman, Joseph; Stevens, Glenn; Modular forms and Fermat’s last theorem
1997-01-01
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, ...
Verification of Linear (In)Dependence in Finite Precision Arithmetic
Rohn, Jiří
2014-01-01
Roč. 8, č. 3-4 (2014), s. 323-328 ISSN 1661-8289 Institutional support: RVO:67985807 Keywords : linear dependence * linear independence * pseudoinverse matrix * finite precision arithmetic * verification * MATLAB file Subject RIV: BA - General Mathematics
Arithmetic convergent sequence space defined by modulus function
Taja Yaying
2019-10-01
Full Text Available The aim of this article is to introduce the sequence spaces $AC(f$ and $AS(f$ using arithmetic convergence and modulus function, and study algebraic and topological properties of this space, and certain inclusion results.
Klaus-Dietrich Kramer
2016-05-01
Full Text Available Many degree courses at technical universities include the subject of control systems engineering. As an addition to conventional approaches Fuzzy Control can be used to easily find control solutions for systems, even if they include nonlinearities. To support further educational training, models which represent a technical system to be controlled are required. These models have to represent the system in a transparent and easy cognizable manner. Furthermore, a programming tool is required that supports an easy Fuzzy Control development process, including the option to verify the results and tune the system behavior. In order to support the development process a graphical user interface is needed to display the fuzzy terms under real time conditions, especially with a debug system and trace functionality. The experiences with such a programming tool, the Fuzzy Control Design Tool (FHFCE Tool, and four fuzzy teaching models will be presented in this paper. The methodical and didactical objective in the utilization of these teaching models is to develop solution strategies using Computational Intelligence (CI applications for Fuzzy Controllers in order to analyze different algorithms of inference or defuzzyfication and to verify and tune those systems efficiently.
Investigation of an American Arithmetic Text Book (I)
植村, 憲治; UEMURA, Kenji
2006-01-01
The teaching method of mathematics and/or arithmetic essentially does not depend on language or culture. In this paper we introduce and investigate an American arithmetic text book and teacher's book of kindergarten, named "Mathematics" published by McGraw-Hill Company. And we point out the difference of Japanese teaching methods from those of the U.S. especially from the point of the Problem Solving Method which is still not taught in Japan as a system.
Fuzzy forecasting based on fuzzy-trend logical relationship groups.
Chen, Shyi-Ming; Wang, Nai-Yi
2010-10-01
In this paper, we present a new method to predict the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) based on fuzzy-trend logical relationship groups (FTLRGs). The proposed method divides fuzzy logical relationships into FTLRGs based on the trend of adjacent fuzzy sets appearing in the antecedents of fuzzy logical relationships. First, we apply an automatic clustering algorithm to cluster the historical data into intervals of different lengths. Then, we define fuzzy sets based on these intervals of different lengths. Then, the historical data are fuzzified into fuzzy sets to derive fuzzy logical relationships. Then, we divide the fuzzy logical relationships into FTLRGs for forecasting the TAIEX. Moreover, we also apply the proposed method to forecast the enrollments and the inventory demand, respectively. The experimental results show that the proposed method gets higher average forecasting accuracy rates than the existing methods.
Fuzzy algorithm for an automatic reactor power control in a PWR
Hah, Yung Joon; Song, In Ho; Yu, Sung Sik; Choi, Jung In; Lee, Byong Whi
1994-01-01
A fuzzy algorithm is presented for automatic reactor power control in a pressurized water reactor. Automatic power shape control is complicated by the use of control rods because it is highly coupled with reactivity compensation. Thus, manual shape controls are usually employed even for the limited capability for the load - follow operation including frequency control. In an attempt to achieve automatic power shape control without any design modification of the core, a fuzzy power control algorithm is proposed. For the fuzzy control, the rule base is formulated based on a multi - input multi - output system. The minimum operation rule and the center of area method are implemented for the development of the fuzzy algorithm. The fuzzy power control algorithm has been applied to the Yonggwang Nuclear Unit 3. The simulation results show that the fuzzy control can be adapted as a practical control strategy for automatic reactor power control of the pressurized water reactor during the load - follow operation
Arianti Iman Sari
2016-12-01
Full Text Available The purpose of this research were to describe: (1 the study result of arithmetic addition operation for fourth grade student with mentally retarded in SDLB before playing the Snake and Ladder activity (2 the study result of arithmetic addition operation for fourth grade student with mentally retarded in SDLB after playing the Snake and Ladder activity (3 the effect of Snake and Ladder playing toward the result study of arithmetic addition for fourth grade student with mentally retarded SDLB. This research used SSR (Single Subject Research with A-B-A design. Collecting the data was done by using assessment instrument, tests and observations. The result of this research showed that playing Snake and Ladder affected the study result of arithmetic addition operation for fourth-grade children with mentally retarded student in SDLB. Tujuan penelitian ini adalah mendeskripsikan (1 Hasil belajar penjumlahan siswa kelas 4 SDLB sebelum melakukan kegiatan bermain Ular Tangga (2 Hasil belajar penjumlahan siswa kelas 4 SDLB sesudah melakukan kegiatan bermain Ular Tangga (3 Pengaruh bermain Ular Tangga terhadap hasil belajar penjumlahan siswa kelas 4 SDLB. Penelitian ini menggunakan rancangan penelitian SSR (Single Subject Research dengan desain A-B-A. Pengumpulan data menggunakan instrumen assesmen, tes dan observasi. Hasil penelitian menunjukkan bermain ular tangga berpengaruh terhadap hasil belajar penjumlahan siswa tunagrahita kelas 4 SDLB.
Lossless Authentication Watermarking Based on Adaptive Modular Arithmetic
H. Yang
2010-04-01
Full Text Available Reversible watermarking schemes based on modulo-256 addition may cause annoying salt-and-pepper noise. To avoid the salt-and-pepper noise, a reversible watermarking scheme using human visual perception characteristics and adaptive modular arithmetic is proposed. First, a high-bit residual image is obtained by extracting the most significant bits (MSB of the original image, and a new spatial visual perception model is built according to the high-bit residual image features. Second, the watermark strength and the adaptive divisor of modulo operation for each pixel are determined by the visual perception model. Finally, the watermark is embedded into different least significant bits (LSB of original image with adaptive modulo addition. The original image can be losslessly recovered if the stego-image has not been altered. Extensive experiments show that the proposed algorithm eliminates the salt-and-pepper noise effectively, and the visual quality of the stego-image with the proposed algorithm has been dramatically improved over some existing reversible watermarking algorithms. Especially, the stegoimage of this algorithm has about 9.9864 dB higher PSNR value than that of modulo-256 addition based reversible watermarking scheme.
Interstructure Lattices and Types of Peano Arithmetic
Abdul-Quader, Athar
The collection of elementary substructures of a model of PA forms a lattice, and is referred to as the substructure lattice of the model. In this thesis, we study substructure and interstructure lattices of models of PA. We apply techniques used in studying these lattices to other problems in the model theory of PA. In Chapter 2, we study a problem that had its origin in Simpson ([Sim74]), who used arithmetic forcing to show that every countable model of PA has an expansion to PA* that is pointwise definable. Enayat ([Ena88]) later showed that there are 2N0 models with the property that every expansion to PA* is pointwise definable. In this Chapter, we use techniques involved in representations of lattices to show that there is a model of PA with this property which contains an infinite descending chain of elementary cuts. In Chapter 3, we study the question of when subsets can be coded in elementary end extensions with prescribed interstructure lattices. This problem originated in Gaifman [Gai76], who showed that every model of PA has a conservative, minimal elementary end extension. That is, every model of PA has a minimal elementary end extension which codes only definable sets. Kossak and Paris [KP92] showed that if a model is countable and a subset X can be coded in any elementary end extension, then it can be coded in a minimal extension. Schmerl ([Sch14] and [Sch15]) extended this work by considering which collections of sets can be the sets coded in a minimal elementary end extension. In this Chapter, we extend this work to other lattices. We study two questions: given a countable model M, which sets can be coded in an elementary end extension such that the interstructure lattice is some prescribed finite distributive lattice; and, given an arbitrary model M, which sets can be coded in an elementary end extension whose interstructure lattice is a finite Boolean algebra?
Shapley's value for fuzzy games
Raúl Alvarado Sibaja
2009-02-01
Full Text Available This is the continuation of a previous article titled "Fuzzy Games", where I defined a new type of games based on the Multilinear extensions f, of characteristic functions and most of standard theorems for cooperative games also hold for this new type of games: The fuzzy games. Now we give some other properties and the extension of the definition of Shapley¨s Value for Fuzzy Games Keywords: game theory, fuzzy sets, multiattribute decisions.
Design of a fuzzy logic based controller for neutron power regulation
Velez D, D.
2000-01-01
This work presents a fuzzy logic controller design for neutron power control, from its source to its full power level, applied to a nuclear reactor model. First, we present the basic definitions on fuzzy sets as generalized definitions of the crisp (non fuzzy) set theory. Likewise, we define the basic operations on fuzzy sets (complement, union, and intersection), and the operations on fuzzy relations such as projection and cylindrical extension operations. Furthermore, some concepts of the fuzzy control theory, such as the main modules of the typical fuzzy controller structure and its internal variables, are defined. After the knowledge base is obtained by simulation of the reactor behavior, where the controlled system is modeled by a simple nonlinear reactor model, this model is used to infer a set of fuzzy rules for the reactor response to different insertions of reactivity. The reduction of the response time, using fuzzy rule based controllers on this reactor, is possible by adjusting the output membership functions, by selecting fuzzy rule sets, or by increasing the number of crisp inputs to the fuzzy controller. System characteristics, such as number of rules, response times, and safety parameter values, were considered in the evaluation of each controller merits. Different fuzzy controllers are designed to attain the desired power level, to maintain a constant level for long periods of time, and to keep the reactor away from a shutdown condition. The basic differences among the controllers are the number of crisp inputs and the novel implementation of a crisp power level-based selection of different sets of output membership functions. Simulation results highlight, mainly: (1) A decrease of the response variations at low power level, and (2) a decrease in the time required to attain the desired neutron power. Finally, we present a comparative study of different fuzzy control algorithms applied to a nuclear model. (Author)
Fuzzy multiple objective decision making methods and applications
Lai, Young-Jou
1994-01-01
In the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, control theory, artificial intelligence/expert system, etc. In this volume, methods and applications of crisp, fuzzy and possibilistic multiple objective decision making are first systematically and thoroughly reviewed and classified. This state-of-the-art survey provides readers with a capsule look into the existing methods, and their characteristics and applicability to analysis of fuzzy and possibilistic programming problems. To realize practical fuzzy modelling, it presents solutions for real-world problems including production/manufacturing, location, logistics, environment management, banking/finance, personnel, marketing, accounting, agriculture economics and data analysis. This book is a guided tour through the literature in the rapidly growing fields of operations research and decision making and includes the most up-to-date bibliographical listing of literature on the topi...
Algorithmic solution of arithmetic problems and operands-answer associations in long-term memory.
Thevenot, C; Barrouillet, P; Fayol, M
2001-05-01
Many developmental models of arithmetic problem solving assume that any algorithmic solution of a given problem results in an association of the two operands and the answer in memory (Logan & Klapp, 1991; Siegler, 1996). In this experiment, adults had to perform either an operation or a comparison on the same pairs of two-digit numbers and then a recognition task. It is shown that unlike comparisons, the algorithmic solution of operations impairs the recognition of operands in adults. Thus, the postulate of a necessary and automatic storage of operands-answer associations in memory when young children solve additions by algorithmic strategies needs to be qualified.
CHARACTERIZATIONS OF FUZZY SOFT PRE SEPARATION AXIOMS
El-Latif, Alaa Mohamed Abd
2015-01-01
− The notions of fuzzy pre open soft sets and fuzzy pre closed soft sets were introducedby Abd El-latif et al. [2]. In this paper, we continue the study on fuzzy soft topological spaces andinvestigate the properties of fuzzy pre open soft sets, fuzzy pre closed soft sets and study variousproperties and notions related to these structures. In particular, we study the relationship betweenfuzzy pre soft interior fuzzy pre soft closure. Moreover, we study the properties of fuzzy soft pre regulars...
Individual differences in children's understanding of inversion and arithmetical skill.
Gilmore, Camilla K; Bryant, Peter
2006-06-01
Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6-7 and 8-9 years). Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the 'high ability' and 'low ability' groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem-solving skills.
Fuzzy Logic and Intelligent Technologies in Nuclear Science (FLINS)
Da Ruan
2000-01-01
FLINS is the acronym for Fuzzy Logic and Intelligent Technologies in Nuclear Science. In 1994, SCK-CEN launched a programme on FLINS. The first FLINS project dealt with the specific prototyping of fuzzy logic control (FLC) of the BR-1 research reactor. This project focussed on controlling the power level of the BR1 reactor added value of FLC for both safety and economic aspects for a nuclear reactor control operation. Main achievements in 1999 are reported
A neural fuzzy controller learning by fuzzy error propagation
Nauck, Detlef; Kruse, Rudolf
1992-01-01
In this paper, we describe a procedure to integrate techniques for the adaptation of membership functions in a linguistic variable based fuzzy control environment by using neural network learning principles. This is an extension to our work. We solve this problem by defining a fuzzy error that is propagated back through the architecture of our fuzzy controller. According to this fuzzy error and the strength of its antecedent each fuzzy rule determines its amount of error. Depending on the current state of the controlled system and the control action derived from the conclusion, each rule tunes the membership functions of its antecedent and its conclusion. By this we get an unsupervised learning technique that enables a fuzzy controller to adapt to a control task by knowing just about the global state and the fuzzy error.
Towards a Fuzzy Expert System on Toxicological Data Quality Assessment.
Yang, Longzhi; Neagu, Daniel; Cronin, Mark T D; Hewitt, Mark; Enoch, Steven J; Madden, Judith C; Przybylak, Katarzyna
2013-01-01
Quality assessment (QA) requires high levels of domain-specific experience and knowledge. QA tasks for toxicological data are usually performed by human experts manually, although a number of quality evaluation schemes have been proposed in the literature. For instance, the most widely utilised Klimisch scheme1 defines four data quality categories in order to tag data instances with respect to their qualities; ToxRTool2 is an extension of the Klimisch approach aiming to increase the transparency and harmonisation of the approach. Note that the processes of QA in many other areas have been automatised by employing expert systems. Briefly, an expert system is a computer program that uses a knowledge base built upon human expertise, and an inference engine that mimics the reasoning processes of human experts to infer new statements from incoming data. In particular, expert systems have been extended to deal with the uncertainty of information by representing uncertain information (such as linguistic terms) as fuzzy sets under the framework of fuzzy set theory and performing inferences upon fuzzy sets according to fuzzy arithmetic. This paper presents an experimental fuzzy expert system for toxicological data QA which is developed on the basis of the Klimisch approach and the ToxRTool in an effort to illustrate the power of expert systems to toxicologists, and to examine if fuzzy expert systems are a viable solution for QA of toxicological data. Such direction still faces great difficulties due to the well-known common challenge of toxicological data QA that "five toxicologists may have six opinions". In the meantime, this challenge may offer an opportunity for expert systems because the construction and refinement of the knowledge base could be a converging process of different opinions which is of significant importance for regulatory policy making under the regulation of REACH, though a consensus may never be reached. Also, in order to facilitate the implementation
Fuzzy power control algorithm for a pressurized water reactor
Hah, Y.J.; Lee, B.W.
1994-01-01
A fuzzy power control algorithm is presented for automatic reactor power control in a pressurized water reactor (PWR). Automatic power shape control is complicated by the use of control rods with a conventional proportional-integral-differential controller because it is highly coupled with reactivity compensation. Thus, manual shape controls are usually employed even for the limited capability needed for load-following operations including frequency control. In an attempt to achieve automatic power shape control without any design modifications to the core, a fuzzy power control algorithm is proposed. For the fuzzy control, the rule base is formulated based on a multiple-input multiple-output system. The minimum operation rule and the center of area method are implemented for the development of the fuzzy algorithm. The fuzzy power control algorithm has been applied to Yonggwang Nuclear Unit 3. The simulation results show that the fuzzy control can be adapted as a practical control strategy for automatic reactor power control of PWRs during the load-following operations
Edge detection methods based on generalized type-2 fuzzy logic
Gonzalez, Claudia I; Castro, Juan R; Castillo, Oscar
2017-01-01
In this book four new methods are proposed. In the first method the generalized type-2 fuzzy logic is combined with the morphological gra-dient technique. The second method combines the general type-2 fuzzy systems (GT2 FSs) and the Sobel operator; in the third approach the me-thodology based on Sobel operator and GT2 FSs is improved to be applied on color images. In the fourth approach, we proposed a novel edge detec-tion method where, a digital image is converted a generalized type-2 fuzzy image. In this book it is also included a comparative study of type-1, inter-val type-2 and generalized type-2 fuzzy systems as tools to enhance edge detection in digital images when used in conjunction with the morphologi-cal gradient and the Sobel operator. The proposed generalized type-2 fuzzy edge detection methods were tested with benchmark images and synthetic images, in a grayscale and color format. Another contribution in this book is that the generalized type-2 fuzzy edge detector method is applied in the preproc...
The foundations of fuzzy control
Lewis, Harold W
1997-01-01
Harold Lewis applied a cross-disciplinary approach in his highly accessible discussion of fuzzy control concepts. With the aid of fifty-seven illustrations, he thoroughly presents a unique mathematical formalism to explain the workings of the fuzzy inference engine and a novel test plant used in the research. Additionally, the text posits a new viewpoint on why fuzzy control is more popular in some countries than in others. A direct and original view of Japanese thinking on fuzzy control methods, based on the author's personal knowledge of - and association with - Japanese fuzzy research, is also included.
Bajat Branislav
2007-01-01
Full Text Available A period of fifty years has been reached since the introduction of the first applications based upon geographical information systems (GIS. GIS has not only influenced the development of methods, collection techniques, processing, manipulation and visualization of spatial data. It influenced also the expansion of scientific research in geosciences, as well as the technical disciplines that are engaged in spatial analysis. Nowadays, GIS is becoming the tool for verification and practical implementation of models and algorithms that have been developed within the frame of basic scientific disciplines. The meaning of the GIS acronym is becoming more and more related to term of Geographical or Geo Information Sciences. Scientific concepts that are increasingly applied in GIS are more emphasized in that way. GIS computational techniques, required also the development of geographical data models that should effectively support GIS operations. These models represent formal equivalents of conceptual models used by people in observing geographic phenomena. Spatial phenomena used to be mapped as clearly defined points with known coordinates, or as lines which connect the very same points, or as polygons with exactly defined borders. They were mapped previously in analog form and nowadays in digital format. This approach of perceiving a space, data analyses and visualization of spatial quires is limited on the application of basic rules of Boolean algebra and binary logic, with final results presented as classical thematic maps. The need for a mathematical model that would describe uncertainty of spatial data, resulted in the introduction of the theory of fuzzy sets in spatial analysis. Moreover, this model will provide a solution for visualization and grouping up of spatial phenomena in classes which do not have clearly defined borders.
Abbas Parchami
2016-09-01
Full Text Available Such as other statistical problems, we may confront with uncertain and fuzzy concepts in quality control. One particular case in process capability analysis is a situation in which specification limits are two fuzzy sets. In such a uncertain and vague environment, the produced product is not qualified with a two-valued Boolean view, but to some degree depending on the decision-maker strictness and the quality level of the produced product. This matter can be cause to a rational decision-making on the quality of the production line. First, a comprehensive approach is presented in this paper for modeling the fuzzy quality concept. Then, motivations and advantages of applying this flexible approach instead of using classical quality are mentioned.
Training of Attention in Children With Low Arithmetical Achievement
Maria Guarnera
2014-05-01
Full Text Available This study focuses on the role of attentional processes in arithmetical skills and examines if training of basic attentive skills may improve also working memory abilities reducing arithmetic difficulties. In order to study the efficacy of attentional treatment in arithmetic achievement and in enhancing working memory abilities a test-treatment-retest quasi experimental design was adopted. The research involved 14 children, attending fourth and fifth grades, with Arithmetical Learning Disabilities (ALD assigned to experimental and control conditions. The numerical comprehension and calculation processes were assessed using the ABCA battery (Lucangeli, Tressoldi, & Fiore, 1998. Attentional abilities were evaluated using a multitask computerized assessment battery Attenzione e Concentrazione (Di Nuovo, 2000. WM abilities were evaluated by Listening span task, Digit span backward, Making verbal trails and Making colour trails. The results showed that intensive computerized attention training increased basic attentive skills and arithmetical performances with respect to numeric system in children with ALD. No effect on working memory abilities was found. Results are also important from a clinical perspective, since they may suggest strategies for planning individualized training programs.
Patterns of problem-solving in children's literacy and arithmetic.
Farrington-Flint, Lee; Vanuxem-Cotterill, Sophie; Stiller, James
2009-11-01
Patterns of problem-solving among 5-to-7 year-olds' were examined on a range of literacy (reading and spelling) and arithmetic-based (addition and subtraction) problem-solving tasks using verbal self-reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years I and 2 on the arithmetic (addition and subtraction) than literacy-based tasks (reading and spelling). However, across all four tasks, the children showed a tendency to move from less sophisticated procedural-based strategies, which included phonological strategies for reading and spelling and counting-all and finger modellingfor addition and subtraction, to more efficient retrieval methods from Years I to 2. Distinct patterns in children's problem-solving skill were identified on the literacy and arithmetic tasks using two separate cluster analyses. There was a strong association between these two profiles showing that those children with more advanced problem-solving skills on the arithmetic tasks also showed more advanced profiles on the literacy tasks. The results highlight how different-aged children show flexibility in their use of problem-solving strategies across literacy and arithmetical contexts and reinforce the importance of studying variations in children's problem-solving skill across different educational contexts.
Number processing and arithmetic skills in children with cochlear implants
Silvia ePixner
2014-12-01
Full Text Available Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties.
Fu-Gui Shi
2010-01-01
Full Text Available The notion of (L,M-fuzzy σ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzy σ-algebras. In our definition of (L,M-fuzzy σ-algebras, each L-fuzzy subset can be regarded as an L-measurable set to some degree.
The first order fuzzy predicate logic (I)
Sheng, Y.M.
1986-01-01
Some analysis tools of fuzzy measures, Sugeno's integrals, etc. are introduced into the semantic of the first order predicate logic to explain the concept of fuzzy quantifiers. The truth value of a fuzzy quantification proposition is represented by Sugeno's integral. With this framework, several important notions of formation rules, fuzzy valutions and fuzzy validity are discussed
Higher arithmetic an algorithmic introduction to number theory
Edwards, Harold M
2008-01-01
Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to m...
Lossless Image Compression Based on Multiple-Tables Arithmetic Coding
Rung-Ching Chen
2009-01-01
Full Text Available This paper is intended to present a lossless image compression method based on multiple-tables arithmetic coding (MTAC method to encode a gray-level image f. First, the MTAC method employs a median edge detector (MED to reduce the entropy rate of f. The gray levels of two adjacent pixels in an image are usually similar. A base-switching transformation approach is then used to reduce the spatial redundancy of the image. The gray levels of some pixels in an image are more common than those of others. Finally, the arithmetic encoding method is applied to reduce the coding redundancy of the image. To promote high performance of the arithmetic encoding method, the MTAC method first classifies the data and then encodes each cluster of data using a distinct code table. The experimental results show that, in most cases, the MTAC method provides a higher efficiency in use of storage space than the lossless JPEG2000 does.
Optimized 4-bit Quantum Reversible Arithmetic Logic Unit
Ayyoub, Slimani; Achour, Benslama
2017-08-01
Reversible logic has received a great attention in the recent years due to its ability to reduce the power dissipation. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. The arithmetic logic unit (ALU) is an important part of central processing unit (CPU) as the execution unit. This paper presents a complete design of a new reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The proposed ALU based on a reversible low power control unit and small performance parameters full adder named double Peres gates. The presented ALU can produce the largest number (28) of arithmetic and logic functions and have the smallest number of quantum cost and delay compared with existing designs.
Evaluation about the performance of E-government based on interval-valued intuitionistic fuzzy set.
Zhang, Shuai; Yu, Dejian; Wang, Yan; Zhang, Wenyu
2014-01-01
The evaluation is an important approach to promote the development of the E-Government. Since the rapid development of E-Government in the world, the E-Government performance evaluation has become a hot issue in the academia. In this paper, we develop a new evaluation method for the development of the E-Government based on the interval-valued intuitionistic fuzzy set which is a powerful technique in expressing the uncertainty of the real situation. First, we extend the geometric Heronian mean (GHM) operator to interval-valued intuitionistic fuzzy environment and proposed the interval-valued intuitionistic fuzzy GHM (IIFGHM) operator. Then, we investigate the relationships between the IIFGHM operator and some existing ones, such as generalized interval-valued intuitionistic fuzzy HM (GIIFHM) and interval-valued intuitionistic fuzzy weighted Bonferoni mean operator. Furthermore, we validate the effectiveness of the proposed method using a real case about the E-Government evaluation in Hangzhou City, China.
Evaluating supplier quality performance using fuzzy analytical hierarchy process
Ahmad, Nazihah; Kasim, Maznah Mat; Rajoo, Shanmugam Sundram Kalimuthu
2014-12-01
Evaluating supplier quality performance is vital in ensuring continuous supply chain improvement, reducing the operational costs and risks towards meeting customer's expectation. This paper aims to illustrate an application of Fuzzy Analytical Hierarchy Process to prioritize the evaluation criteria in a context of automotive manufacturing in Malaysia. Five main criteria were identified which were quality, cost, delivery, customer serviceand technology support. These criteria had been arranged into hierarchical structure and evaluated by an expert. The relative importance of each criteria was determined by using linguistic variables which were represented as triangular fuzzy numbers. The Center of Gravity defuzzification method was used to convert the fuzzy evaluations into their corresponding crisps values. Such fuzzy evaluation can be used as a systematic tool to overcome the uncertainty evaluation of suppliers' performance which usually associated with human being subjective judgments.
Improved Fuzzy Art Method for Initializing K-means
Sevinc Ilhan
2010-09-01
Full Text Available The K-means algorithm is quite sensitive to the cluster centers selected initially and can perform different clusterings depending on these initialization conditions. Within the scope of this study, a new method based on the Fuzzy ART algorithm which is called Improved Fuzzy ART (IFART is used in the determination of initial cluster centers. By using IFART, better quality clusters are achieved than Fuzzy ART do and also IFART is as good as Fuzzy ART about capable of fast clustering and capability on large scaled data clustering. Consequently, it is observed that, with the proposed method, the clustering operation is completed in fewer steps, that it is performed in a more stable manner by fixing the initialization points and that it is completed with a smaller error margin compared with the conventional K-means.
Application of fuzzy control in cooling systems save energy design
Chen, M.L.; Liang, H.Y. [Chienkuo Technology Univ., Changhua, Taiwan (China). Dept. of Electrical Engineering
2005-07-01
A fuzzy logic programmable logic controller (PLC) was used to control the cooling systems of frigorific equipment. Frigorific equipment is used to move unwanted heat outside of building in order to control indoor temperatures. The aim of the fuzzy logic PLC was to improve the energy efficiency of the cooling system. Control of the cooling pump and cooling tower in the system was based on the water temperature of the condenser during frigorific system operation. A human computer design for the cooling system control was used to set speeds and to automate and adjust the motor according to the fuzzy logic controller. It was concluded that if fuzzy logic controllers are used with all components of frigorific equipment, energy efficiency will be significantly increased. 5 refs., 3 tabs., 9 figs.
Multi-stage fuzzy load frequency control using PSO
Shayeghi, H.; Jalili, A.; Shayanfar, H.A.
2008-01-01
In this paper, a particle swarm optimization (PSO) based multi-stage fuzzy (PSOMSF) controller is proposed for solution of the load frequency control (LFC) problem in a restructured power system that operate under deregulation based on the bilateral policy scheme. In this strategy the control is tuned on line from the knowledge base and fuzzy inference, which request fewer sources and has two rule base sets. In the proposed method, for achieving the desired level of robust performance, exact tuning of membership functions is very important. Thus, to reduce the design effort and find a better fuzzy system control, membership functions are designed automatically by PSO algorithm, that has a strong ability to find the most optimistic results. The motivation for using the PSO technique is to reduce fuzzy system effort and take large parametric uncertainties into account. This newly developed control strategy combines the advantage of PSO and fuzzy system control techniques and leads to a flexible controller with simple stricture that is easy to implement. The proposed PSO based MSF (PSOMSF) controller is tested on a three-area restructured power system under different operating conditions and contract variations. The results of the proposed PSOMSF controller are compared with genetic algorithm based multi-stage fuzzy (GAMSF) control through some performance indices to illustrate its robust performance for a wide range of system parameters and load changes
Multi-stage fuzzy load frequency control using PSO
Shayeghi, H. [Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil (Iran); Jalili, A. [Islamic Azad University, Ardabil Branch, Ardabil (Iran); Shayanfar, H.A. [Center of Excellence for Power Automation and Operation, Electrical Engineering Department, Iran University of Science and Technology, Tehran (Iran)
2008-10-15
In this paper, a particle swarm optimization (PSO) based multi-stage fuzzy (PSOMSF) controller is proposed for solution of the load frequency control (LFC) problem in a restructured power system that operate under deregulation based on the bilateral policy scheme. In this strategy the control is tuned on line from the knowledge base and fuzzy inference, which request fewer sources and has two rule base sets. In the proposed method, for achieving the desired level of robust performance, exact tuning of membership functions is very important. Thus, to reduce the design effort and find a better fuzzy system control, membership functions are designed automatically by PSO algorithm, that has a strong ability to find the most optimistic results. The motivation for using the PSO technique is to reduce fuzzy system effort and take large parametric uncertainties into account. This newly developed control strategy combines the advantage of PSO and fuzzy system control techniques and leads to a flexible controller with simple stricture that is easy to implement. The proposed PSO based MSF (PSOMSF) controller is tested on a three-area restructured power system under different operating conditions and contract variations. The results of the proposed PSOMSF controller are compared with genetic algorithm based multi-stage fuzzy (GAMSF) control through some performance indices to illustrate its robust performance for a wide range of system parameters and load changes. (author)
Should we naturalize mind, or should we arithmetize matter?
Marchal Bruno
2017-12-01
Full Text Available We provide an argument showing that once we assume the mechanist hypothesis in the cognitive science then we have to explain physics from intensional number theory and/or mathematical computer science alone. The proof is constructive. It shows how to derive the physical laws from elementary arithmetic. It makes the computationalist thesis empirically refutable, by comparing the physics extracted from numbers and the inferred physics from observation. The proof shows that if mechanism is true, we cannot naturalize the mind, and we have to arithmetize matter, or beliefs in matter, instead.
Bit-wise arithmetic coding for data compression
Kiely, A. B.
1994-01-01
This article examines the problem of compressing a uniformly quantized independent and identically distributed (IID) source. We present a new compression technique, bit-wise arithmetic coding, that assigns fixed-length codewords to the quantizer output and uses arithmetic coding to compress the codewords, treating the codeword bits as independent. We examine the performance of this method and evaluate the overhead required when used block-adaptively. Simulation results are presented for Gaussian and Laplacian sources. This new technique could be used as the entropy coder in a transform or subband coding system.
File compression and encryption based on LLS and arithmetic coding
Yu, Changzhi; Li, Hengjian; Wang, Xiyu
2018-03-01
e propose a file compression model based on arithmetic coding. Firstly, the original symbols, to be encoded, are input to the encoder one by one, we produce a set of chaotic sequences by using the Logistic and sine chaos system(LLS), and the values of this chaotic sequences are randomly modified the Upper and lower limits of current symbols probability. In order to achieve the purpose of encryption, we modify the upper and lower limits of all character probabilities when encoding each symbols. Experimental results show that the proposed model can achieve the purpose of data encryption while achieving almost the same compression efficiency as the arithmetic coding.
Fuzzy batch controller for granular materials
Zamyatin Nikolaj
2018-01-01
Full Text Available The paper focuses on batch control of granular materials in production of building materials from fluorine anhydrite. Batching equipment is intended for smooth operation and timely feeding of supply hoppers at a required level. Level sensors and a controller of an asynchronous screw drive motor are used to control filling of the hopper with industrial anhydrite binders. The controller generates a required frequency and ensures required productivity of a feed conveyor. Mamdani-type fuzzy inference is proposed for controlling the speed of the screw that feeds mixture components. As related to production of building materials based on fluoride anhydrite, this method is used for the first time. A fuzzy controller is proven to be effective in controlling the filling level of the supply hopper. In addition, the authors determined optimal parameters of the batching process to ensure smooth operation and production of fluorine anhydrite materials of specified properties that can compete with gypsum-based products.
Fuzzy-set based contingency ranking
Hsu, Y.Y.; Kuo, H.C.
1992-01-01
In this paper, a new approach based on fuzzy set theory is developed for contingency ranking of Taiwan power system. To examine whether a power system can remain in a secure and reliable operating state under contingency conditions, those contingency cases that will result in loss-of-load, loss-of generation, or islanding are first identified. Then 1P-1Q iteration of fast decoupled load flow is preformed to estimate post-contingent quantities (line flows, bus voltages) for other contingency cases. Based on system operators' past experience, each post-contingent quantity is assigned a degree of severity according to the potential damage that could be imposed on the power system by the quantity, should the contingency occurs. An approach based on fuzzy set theory is developed to deal with the imprecision of linguistic terms
Fuzzy efficiency without convexity
Hougaard, Jens Leth; Balezentis, Tomas
2014-01-01
approach builds directly upon the definition of Farrell's indexes of technical efficiency used in crisp FDH. Therefore we do not require the use of fuzzy programming techniques but only utilize ranking probabilities of intervals as well as a related definition of dominance between pairs of intervals. We...
Mohana Sundaram Muthuvalu
2015-12-01
Full Text Available High reliability users of microelectronic devices have been derating junction temperature and other critical stress parameters to improve device reliability and extend operating life. The reliability of a semiconductor is determined by junction temperature. This paper gives a useful analysis on mathematical approach which can be implemented to predict temperature of a silicon die. The problem could be modeled as heat conduction equation. In this study, numerical approach based on implicit scheme and Arithmetic Mean (AM iterative method will be applied to solve the governing heat conduction equation. Numerical results are also included in order to assert the effectiveness of the proposed technique.
CMIS arithmetic and multiwire news for QCD on the connection machine
Brickner, R.G.
1991-01-01
Our collaboration has been running Wilson fermion QCD simulations on various Connection Machines for over a year and a half. During this time, we have continually optimized our code for operations found in the fermion matrix inversion. Our current version of the matrix inversion is written almost entirely in CMIS (Connection Machine Instruction Set), and utilizes both high-speed arithmetic and multiwire 'news' (nearest-neighbor communications). We present details of how these and other features of our code are implemented on the CM-2. (orig.)
An automatic tuning method of a fuzzy logic controller for nuclear reactors
Ramaswamy, P.; Lee, K.Y.; Edwards, R.M.
1993-01-01
The design and evaluation by simulation of an automatically tuned fuzzy logic controller is presented. Typically, fuzzy logic controllers are designed based on an expert's knowledge of the process. However, this approach has its limitations in the fact that the controller is hard to optimize or tune to get the desired control action. A method to automate the tuning process using a simplified Kalman filter approach is presented for the fuzzy logic controller to track a suitable reference trajectory. Here, for purposes of illustration an optimal controller's response is used as a reference trajectory to determine automatically the rules for the fuzzy logic controller. To demonstrate the robustness of this design approach, a nonlinear six-delayed neutron group plant is controlled using a fuzzy logic controller that utilizes estimated reactor temperatures from a one-delayed neutron group observer. The fuzzy logic controller displayed good stability and performance robustness characteristics for a wide range of operation
Lei, Meizhen; Wang, Liqiang
2018-01-01
The halbach-type linear oscillatory motor (HT-LOM) is multi-variable, highly coupled, nonlinear and uncertain, and difficult to get a satisfied result by conventional PID control. An incremental adaptive fuzzy controller (IAFC) for stroke tracking was presented, which combined the merits of PID control, the fuzzy inference mechanism and the adaptive algorithm. The integral-operation is added to the conventional fuzzy control algorithm. The fuzzy scale factor can be online tuned according to the load force and stroke command. The simulation results indicate that the proposed control scheme can achieve satisfied stroke tracking performance and is robust with respect to parameter variations and external disturbance.
Fuzzy batch controller for granular materials
Zamyatin Nikolaj; Smirnov Gennadij; Fedorchuk Yuri; Rusina Olga
2018-01-01
The paper focuses on batch control of granular materials in production of building materials from fluorine anhydrite. Batching equipment is intended for smooth operation and timely feeding of supply hoppers at a required level. Level sensors and a controller of an asynchronous screw drive motor are used to control filling of the hopper with industrial anhydrite binders. The controller generates a required frequency and ensures required productivity of a feed conveyor. Mamdani-type fuzzy infer...
Neuro-fuzzy system modeling based on automatic fuzzy clustering
Yuangang TANG; Fuchun SUN; Zengqi SUN
2005-01-01
A neuro-fuzzy system model based on automatic fuzzy clustering is proposed.A hybrid model identification algorithm is also developed to decide the model structure and model parameters.The algorithm mainly includes three parts:1) Automatic fuzzy C-means (AFCM),which is applied to generate fuzzy rules automatically,and then fix on the size of the neuro-fuzzy network,by which the complexity of system design is reducesd greatly at the price of the fitting capability;2) Recursive least square estimation (RLSE).It is used to update the parameters of Takagi-Sugeno model,which is employed to describe the behavior of the system;3) Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network.Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.
Hierarchical type-2 fuzzy aggregation of fuzzy controllers
Cervantes, Leticia
2016-01-01
This book focuses on the fields of fuzzy logic, granular computing and also considering the control area. These areas can work together to solve various control problems, the idea is that this combination of areas would enable even more complex problem solving and better results. In this book we test the proposed method using two benchmark problems: the total flight control and the problem of water level control for a 3 tank system. When fuzzy logic is used it make it easy to performed the simulations, these fuzzy systems help to model the behavior of a real systems, using the fuzzy systems fuzzy rules are generated and with this can generate the behavior of any variable depending on the inputs and linguistic value. For this reason this work considers the proposed architecture using fuzzy systems and with this improve the behavior of the complex control problems.
Arithmetic crystal classes of magnetic symmetries
Angelova, M.N.; Boyle, L.L.
1993-01-01
The symmetries and properties of a broad class of magnetic crystals are described by magnetic space groups which contain both (unitary) spatial symmetry operations and their combinations with the (anti-unitary operation of) time inversion, 0. The spatial symmetry operations form a halving, non-magnetic, space group H of the magnetic group M such that M=H+aH. As an abstract group the magnetic group M is isomorphic to a non-magnetic group G. The anti-unitary operator a is simply the time inversion 0 when M is a grey group but a product of time inversion with some spatial operation belonging to the coset G-H when M is a black-and-white group. (Author)
Word Similarity from Dictionaries: Inferring Fuzzy Measures from Fuzzy Graphs
Vicenc Torra
2008-01-01
Full Text Available WORD SIMILARITY FROM DICTIONARIES: INFERRING FUZZY MEASURES FROM FUZZY GRAPHS The computation of similarities between words is a basic element of information retrieval systems, when retrieval is not solely based on word matching. In this work we consider a measure between words based on dictionaries. This is achieved assuming that a dictionary is formalized as a fuzzy graph. We show that the approach permits to compute measures not only for pairs of words but for sets of them.
Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard
2018-03-01
A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.
Fuzzy control. Fundamentals, stability and design of fuzzy controllers
Michels, K. [Fichtner GmbH und Co. KG, Stuttgart (Germany); Klawonn, F. [Fachhochschule Braunschweig/Wolfenbuettel (Germany). Fachbereich Informatik; Kruse, R. [Magdeburg Univ. (Germany). Fakultaet Informatik, Abt. Wiss.- und Sprachverarbeitung; Nuernberger, A. (eds.) [California Univ., Berkeley, CA (United States). Computer Science Division
2006-07-01
The book provides a critical discussion of fuzzy controllers from the perspective of classical control theory. Special emphases are placed on topics that are of importance for industrial applications, like (self-) tuning of fuzzy controllers, optimisation and stability analysis. The book is written as a textbook for graduate students as well as a comprehensive reference book about fuzzy control for researchers and application engineers. Starting with a detailed introduction to fuzzy systems and control theory the reader is guided to up-to-date research results. (orig.)
Feasibility analysis of fuzzy logic control for ITER Poloidal field (PF) AC/DC converter system
Hassan, Mahmood Ul; Fu, Peng [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); University of Science and Technology of China (China); Song, Zhiquan, E-mail: zhquansong@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Chen, Xiaojiao [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); University of Science and Technology of China (China); Zhang, Xiuqing [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Humayun, Muhammad [Shanghai Jiaotong University (China)
2017-05-15
Highlights: • The implementation of the Fuzzy controller for the ITER PF converter system is presented. • The comparison of the FLC and PI simulation are investigated. • The FLC single and parallel bridge operation are presented. • Fuzzification and Defuzzification algorithms are presented using FLC controller. - Abstract: This paper describes the feasibility analysis of the fuzzy logic control to increase the performance of the ITER poloidal field (PF) converter systems. A fuzzy-logic-based controller is designed for ITER PF converter system, using the traditional PI controller and Fuzzy controller (FC), the dynamic behavior and transient response of the PF converter system are compared under normal operation by analysis and simulation. The analysis results show that the fuzzy logic control can achieve better operation performance than PI control.
FUZZY LOGIC CONTROL OF ELECTRIC MOTORS AND MOTOR DRIVES: FEASIBILITY STUDY
The report gives results of a study (part 1) of fuzzy logic motor control (FLMC). The study included: 1) reviews of existing applications of fuzzy logic, of motor operation, and of motor control; 2) a description of motor control schemes that can utilize FLMC; 3) selection of a m...
Application of fuzzy logic control system for reactor feed-water control
Iijima, T.; Nakajima, Y.
1994-01-01
The successful actual application of a fuzzy logic control system to the a nuclear Fugen nuclear power reactor is described. Fugen is a heavy-water moderated, light-water cooled reactor. The introduction of fuzzy logic control system has enabled operators to control the steam drum water level more effectively in comparison to a conventional proportional-integral (PI) control system
Fuzzy pharmacology: theory and applications.
Sproule, Beth A; Naranjo, Claudio A; Türksen, I Burhan
2002-09-01
Fuzzy pharmacology is a term coined to represent the application of fuzzy logic and fuzzy set theory to pharmacological problems. Fuzzy logic is the science of reasoning, thinking and inference that recognizes and uses the real world phenomenon that everything is a matter of degree. It is an extension of binary logic that is able to deal with complex systems because it does not require crisp definitions and distinctions for the system components. In pharmacology, fuzzy modeling has been used for the mechanical control of drug delivery in surgical settings, and work has begun evaluating its use in other pharmacokinetic and pharmacodynamic applications. Fuzzy pharmacology is an emerging field that, based on these initial explorations, warrants further investigation.
Why Is Learning Fraction and Decimal Arithmetic so Difficult?
Lortie-Forgues, Hugues; Tian, Jing; Siegler, Robert S.
2015-01-01
Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…
Schema Knowledge for Solving Arithmetic Story Problems: Some Affective Components.
Marshall, Sandra P.
This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…
Bit-Wise Arithmetic Coding For Compression Of Data
Kiely, Aaron
1996-01-01
Bit-wise arithmetic coding is data-compression scheme intended especially for use with uniformly quantized data from source with Gaussian, Laplacian, or similar probability distribution function. Code words of fixed length, and bits treated as being independent. Scheme serves as means of progressive transmission or of overcoming buffer-overflow or rate constraint limitations sometimes arising when data compression used.
A wild model of linear arithmetic and discretely ordered modules
Glivický, Petr; Pudlák, Pavel
2017-01-01
Roč. 63, č. 6 (2017), s. 501-508 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : linear arithmetics Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.250, year: 2016
Simple arithmetic: not so simple for highly math anxious individuals.
Chang, Hyesang; Sprute, Lisa; Maloney, Erin A; Beilock, Sian L; Berman, Marc G
2017-12-01
Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low-compared to high-math anxious individuals perform better when they activate this network less-a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently. © The Author (2017). Published by Oxford University Press.
Neuroanthropological Understanding of Complex Cognition – Numerosity and Arithmetics
Zarja Mursic
2013-10-01
Full Text Available Humankind has a long evolutionary history. When we are trying to understand human complex cognition, it is as well important to look back to entire evolution. I will present the thesis that our biological predispositions and culture, together with natural and social environment, are tightly connected. During ontogenetically development we are shaped by various factors, and they enabled humans to develop some aspects of complex cognition, such as mathematics.In the beginning of the article I present the importance of natural and cultural evolution in other animals. In the following part, I briefly examine the field of mathematics – numerosity and arithmetic. Presentation of comparative animal studies, mainly made on primates, provides some interesting examples in animals’ abilities to separate between different quantities. From abilities for numerosity in animals I continue to neuroscientific studies of humans and our ability to solve simple arithmetic tasks. I also mention cross-cultural studies of arithmetic skills. In the final part of the text I present the field neuroanthropology as a possible new pillar of cognitive science. Finally, it is important to connect human evolution and development with animal cognition studies, but as well with cross-cultural studies in shaping of human ability for numerosity and arithmetic.
Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking
Napaphun, Vishnu
2012-01-01
Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…
0011-0030.Data Representation amp Computer Arithmetic6 IEEE ...
Home; public; Volumes; reso; 021; 01; 0011-0030.Data Representation amp Computer Arithmetic6 IEEE Standard Double Precision FormatIn.pdf. 404! error. The page your are looking for can not be found! Please check the link or use the navigation bar at the top. YouTube; Twitter; Facebook; Blog. Academy News.
The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic
Meurant, G.; Strakoš, Zdeněk
2006-01-01
Roč. 15, - (2006), s. 471-542 ISSN 0962-4929 R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : Lanczos method * conjugate gradient method * finite precision arithmetic * numerical stability * iterative methods Subject RIV: BA - General Mathematics
Numbers in action: individual differences and interactivity in mental arithmetic.
Guthrie, Lisa G; Vallée-Tourangeau, Frédéric
2018-02-03
Previous research indicates that interactive arithmetic tasks may alleviate the deleterious impact of maths anxiety on arithmetic performance. Our aim here was to further test the impact of interactivity on maths-anxious individuals and those with poorer numeracy skills. In the experiment reported here participants completed sums in two interactivity contexts. In a low-interactivity condition, sums were completed with hands down. In a second, high-interactivity condition, participants used moveable number tokens. As anticipated, accuracy and efficiency were greater in the high compared to the low-interactivity condition. Correlational analyses indicated that maths anxiety, objective numeracy, measures of maths expertise and working memory were stronger predictors of performance in the low- than in the high-interactivity conditions. Interactivity transformed the deployment of arithmetic skills, improved performance, and reduced the gap between high- and low-ability individuals. These findings suggest that traditional psychometric efforts that identify the cognitive capacities and dispositions involved in mental arithmetic should take into account the degree of interactivity afforded by the task environment.
Partial sums of arithmetical functions with absolutely convergent ...
For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the ∑ n ≤ N f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan's totient functions.
Interactive Realizability and the elimination of Skolem functions in Peano Arithmetic
Federico Aschieri
2012-10-01
Full Text Available We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result – which shows that the Excluded Middle principle can be used to eliminate Skolem functions – has been previously proved by other techniques, among them the epsilon substitution method and forcing. In our proof, we employ Interactive Realizability, a computational semantics for Peano Arithmetic which extends Kreisel's modified realizability to the classical case.
Stochastic Optimal Estimation with Fuzzy Random Variables and Fuzzy Kalman Filtering
FENG Yu-hu
2005-01-01
By constructing a mean-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts: a real-valued non-random recurrence equation and the standard Kalman filtering.
Fuzzy Controllers for a Gantry Crane System with Experimental Verifications
Naif B. Almutairi
2016-01-01
Full Text Available The control problem of gantry cranes has attracted the attention of many researchers because of the various applications of these cranes in the industry. In this paper we propose two fuzzy controllers to control the position of the cart of a gantry crane while suppressing the swing angle of the payload. Firstly, we propose a dual PD fuzzy controller where the parameters of each PD controller change as the cart moves toward its desired position, while maintaining a small swing angle of the payload. This controller uses two fuzzy subsystems. Then, we propose a fuzzy controller which is based on heuristics. The rules of this controller are obtained taking into account the knowledge of an experienced crane operator. This controller is unique in that it uses only one fuzzy system to achieve the control objective. The validity of the designed controllers is tested through extensive MATLAB simulations as well as experimental results on a laboratory gantry crane apparatus. The simulation results as well as the experimental results indicate that the proposed fuzzy controllers work well. Moreover, the simulation and the experimental results demonstrate the robustness of the proposed control schemes against output disturbances as well as against uncertainty in some of the parameters of the crane.
Matrix inequalities for the difference between arithmetic mean and harmonic mean
Liao, Wenshi; Wu, Junliang
2015-01-01
Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established.
Digital speech processing arithmetic and its realization on ADSP-2191 system
Zhang Wansheng; Wang Yonggang
2005-01-01
The paper reports the realization of LPC arithmetic in fixed-point DSP system. First we introduce the theory of LPC arithmetic and describe the chip (ADSP-2191)'s structure and function relating to the LPC arithmetic; emphasized on the realization process of LPC in ADSP-2191 and its result. (authors)
On the mathematics of fuzziness
Chulichkov, A.I.; Chulichkova, N.M.; Pyt`ev, Y. P.; Smolnik, L.
1994-12-31
The problem of the minimax linear interpretation of stochastic measurements with fuzzy conditions on values of the object`s parameters is considered. The result of a measurement interpretation is the fuzzy element (u, h, alpha, mu(.,.,.)), where u is the object`s parameter estimation, h is the estimation accuracy and alpha is the reliability of interpretation, mu is the characteristic function of a fuzzy element. Reliability is the characteristic of the agreement between fuzzy a priori information and measuring data. The information on the values of the parameters of an object under investigation is interactively submitted to the computer.
Systematic methods for the design of a class of fuzzy logic controllers
Yasin, Saad Yaser
2002-09-01
data, and a conversion algorithm, to develop a fuzzy-based control algorithm. Results were similar to those obtained by recently published conventional control based studies. The influence of the fuzzy inference operators and parameters on performance and stability of the fuzzy logic controller was studied Results indicated that, the selections of certain parameters or combinations of parameters, affect greatly the performance and stability of the fuzzy controller. Diagnostic guidelines used to tune or change certain factors or parameters to improve controller performance were developed based on knowledge gained from conventional control methods and knowledge gained from the experimental and the simulation results of this study.
Imprecise Arithmetic for Low Power Image Processing
Albicocco, Pietro; Cardarilli, Gian Carlo; Nannarelli, Alberto
2012-01-01
Sometimes reducing the precision of a numerical processor, by introducing errors, can lead to significant performance (delay, area and power dissipation) improvements without compromising the overall quality of the processing. In this work, we show how to perform the two basic operations, additio...... and multiplication, in an imprecise manner by simplifying the hardware implementation. With the proposed ”sloppy” operations, we obtain a reduction in delay, area and power dissipation, and the error introduced is still acceptable for applications such as image processing.......Sometimes reducing the precision of a numerical processor, by introducing errors, can lead to significant performance (delay, area and power dissipation) improvements without compromising the overall quality of the processing. In this work, we show how to perform the two basic operations, addition...
W-algebra for solving problems with fuzzy parameters
Shevlyakov, A. O.; Matveev, M. G.
2018-03-01
A method of solving the problems with fuzzy parameters by means of a special algebraic structure is proposed. The structure defines its operations through operations on real numbers, which simplifies its use. It avoids deficiencies limiting applicability of the other known structures. Examples for solution of a quadratic equation, a system of linear equations and a network planning problem are given.
Use of fuzzy logic in signal processing and validation
Heger, A.S.; Alang-Rashid, N.K.; Holbert, K.E.
1993-01-01
The advent of fuzzy logic technology has afforded another opportunity to reexamine the signal processing and validation process (SPV). The features offered by fuzzy logic can lend themselves to a more reliable and perhaps fault-tolerant approach to SPV. This is particularly attractive to complex system operations, where optimal control for safe operation depends on reliable input data. The reason for the use of fuzzy logic as the tool for SPV is its ability to transform information from the linguistic domain to a mathematical domain for processing and then transformation of its result back into the linguistic domain for presentation. To ensure the safe and optimal operation of a nuclear plant, for example, reliable and valid data must be available to the human and computer operators. Based on these input data, the operators determine the current state of the power plant and project corrective actions for future states. This determination is based on available data and the conceptual and mathematical models for the plant. A fault-tolerant SPV based on fuzzy logic can help the operators meet the objective of effective, efficient, and safe operation of the nuclear power plant. The ultimate product of this project will be a code that will assist plant operators in making informed decisions under uncertain conditions when conflicting signals may be present
On-line tuning of a fuzzy-logic power system stabilizer
Hossein-Zadeh, N.; Kalam, A.
2002-01-01
A scheme for on-line tuning of a fuzzy-logic power system stabilizer is presented. firstly, a fuzzy-logic power system stabilizer is developed using speed deviation and accelerating power as the controller input variables. The inference mechanism of fuzzy-logic controller is represented by a decision table, constructed of linguistic IF-THEN rules. The Linguistic rules are available from experts and the design procedure is based on these rules. It assumed that an exact model of the plant is not available and it is difficult to extract the exact parameters of the power plant. Thus, the design procedure can not be based on an exact model. This is an advantage of fuzzy logic that makes the design of a controller possible without knowing the exact model of the plant. Secondly, two scaling parameters are introduced to tune the fuzzy-logic power system stabilizer. These scaling parameters are the outputs of another fuzzy-logic system, which gets the operating conditions of power system as inputs. These mechanism of tuning the fuzzy-logic power system stabilizer makes the fuzzy-logic power system stabilizer adaptive to changes in the operating conditions. Therefore, the degradation of the system response, under a wide range of operating conditions, is less compared to the system response with a fixed-parameter fuzzy-logic power system stabilizer and a conventional (linear) power system stabilizer. The tuned stabilizer has been tested by performing nonlinear simulations using a synchronous machine-infinite bus model. The responses are compared with a fixed parameters fuzzy-logic power system stabilizer and a conventional (linear) power system stabilizer. It is shown that the tuned fuzzy-logic power system stabilizer is superior to both of them
Rooijen, M. van; Verhoeven, L.T.W.; Steenbergen, B.
2015-01-01
Children with cerebral palsy (CP) are generally delayed in arithmetic compared to their peers. The development of early numeracy performance in children with CP is not yet evident, nor have the factors associated with change over time been identified. Therefore, we examined the development of
Education Development Center, Inc., Newton, MA.
This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being…
Yashon O. Ouma
2015-01-01
Full Text Available For road pavement maintenance and repairs prioritization, a multiattribute approach that compares fuzzy Analytical Hierarchy Process (AHP and fuzzy Technique for Order Preference by Ideal Situation (TOPSIS is evaluated. The pavement distress data was collected through empirical condition surveys and rating by pavement experts. In comparison to the crisp AHP, the fuzzy AHP and fuzzy TOPSIS pairwise comparison techniques are considered to be more suitable for the subjective analysis of the pavement conditions for automated maintenance prioritization. From the case study results, four pavement maintenance objectives were determined as road safety, pavement surface preservation, road operational status and standards, and road aesthetics, with corresponding depreciating significance weights of W=0.37,0.31,0.22,0.10T. The top three maintenance functions were identified as Thin Hot Mix Asphalt (HMA overlays, resurfacing and slurry seals, which were a result of pavement cracking, potholes, raveling, and patching, while the bottom three were cape seal, micro surfacing, and fog seal. The two methods gave nearly the same prioritization ranking. In general, the fuzzy AHP approach tended to overestimate the maintenance prioritization ranking as compared to the fuzzy TOPSIS.
Personnel Selection Using Fuzzy Axiomatic Design Principles
Anant V. Khandekar
2016-09-01
Full Text Available Overall competency of the working personnel is often observed to ultimately affect the productivity of an organization. The globalised competitive atmosphere coupled with technological improvements demands for efficient and specialized manpower for the industrial operations. A set of typical technological skills and attitudes is thus demanded for every job profile. Most often, these skills and attitudes are expressed imprecisely and hence, necessitating the support of fuzzy sets for their effective understanding and further processing. In this paper, a method based on fuzzy axiomatic design principles is applied for solving the personnel selection problems. Selecting a middle management staff of a service department for a large scale organization is demonstrated here as a real life example. Five shortlisted candidates are assessed with respect to a set of 18 evaluation criteria, and the selection committee with experts from the related fields also realizes the outcome of the adopted approach to be quite appropriate, befitting and in agreement with their expectations.
Optimizing pipeline transportation using a fuzzy controller
Aramaki, Thiago L.; Correa, Joao L. L.; Montalvoa, Antonio F. F. [National Control and Operation Center Tranpetro, Rio de Janeiro, (Brazil)
2010-07-01
The optimization of pipeline transportation is a big concern for the transporter companies. This paper is the third of a series of three articles which investigated the application of a system to simulate the human ability to operate a pipeline in an optimized way. The present paper presents the development of a proportional integral (PI) fuzzy controller, in order to optimize pipeline transportation capacity. The fuzzy adaptive PI controller system was developed and tested with a hydraulic simulator. On-field data were used from the OSBRA pipeline. The preliminary tests showed that the performance of the software simulation was satisfactory. It varied the set-point of the conventional controller within the limits of flow meters. The transport capacity of the pipe was maximize without compromising the integrity of the commodities transported. The system developed proved that it can be easily deployed as a specialist optimizing system to be added to SCADA systems.
Performance measurement with fuzzy data envelopment analysis
Tavana, Madjid
2014-01-01
The intensity of global competition and ever-increasing economic uncertainties has led organizations to search for more efficient and effective ways to manage their business operations. Data envelopment analysis (DEA) has been widely used as a conceptually simple yet powerful tool for evaluating organizational productivity and performance. Fuzzy DEA (FDEA) is a promising extension of the conventional DEA proposed for dealing with imprecise and ambiguous data in performance measurement problems. This book is the first volume in the literature to present the state-of-the-art developments and applications of FDEA. It is designed for students, educators, researchers, consultants and practicing managers in business, industry, and government with a basic understanding of the DEA and fuzzy logic concepts.
Berenstein, David; Dzienkowski, Eric; Lashof-Regas, Robin
2015-01-01
We construct various exact analytical solutions of the SO(3) BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori. These are also solutions of Yang Mills theory compactified on a sphere times time and they are also translationally invariant solutions of the N=1"∗ field theory with a non-trivial charge density. The solutions we construct have a ℤ_N symmetry, where N is the rank of the matrices. After an appropriate ansatz, we reduce the problem to solving a set of polynomial equations in 2N real variables. These equations have a discrete set of solutions for each value of the angular momentum. We study the phase structure of the solutions for various values of N. Also the continuum limit where N→∞, where the problem reduces to finding periodic solutions of a set of coupled differential equations. We also study the topology change transition from the sphere to the torus.
Coufal, David
2017-01-01
Roč. 319, 15 July (2017), s. 1-27 ISSN 0165-0114 R&D Projects: GA MŠk(CZ) LD13002 Institutional support: RVO:67985807 Keywords : fuzzy systems * radial functions * coherence Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 2.718, year: 2016
Non-Archimedean L-functions and arithmetical Siegel modular forms
1991-01-01
This book is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth (which were first introduced by Amice, Velu and Vishik in the elliptic modular case when they come from a good supersingular reduction of ellptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arihmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a rapidly developping domain of algebraic number theory: ...
Wu, Yunna; Geng, Shuai; Xu, Hu; Zhang, Haobo
2014-01-01
Highlights: • Experts’ opinions are expressed by using the intuitionistic fuzzy values. • Fuzzy measure is used to solve the dependence problem of criteria. • The compensatory problem of performance scores is reasonably processed. - Abstract: Project selection plays an important role in the entire life cycle of wind farm project and the multi-criteria decision making (MCDM) methods are very important in the whole wind farm project plan selection process. There are problems in the present MCDM methods decrease evaluation quality of the wind farm project plans: first, the information loss exists in the wind farm project plan evaluation process. Second, it is difficult to satisfy the independent assumption of the multi-criteria decision making methods used in the wind farm project plan evaluation in fact. Third, the compensatory problem of performance scores of the wind farm project plans is processed unreasonably. Hence the innovation points of this paper are as follows: first, the intuitionistic fuzzy numbers are used instead of fuzzy numbers or numerical values to reflect the experts’ intuitive preferences to decrease the probability of information loss; second, the fuzzy measure is used to rate the important degrees of criteria in order to avoid the independent assumption and to increase the reasonability; third, the partial compensatory problem of performance scores is well processed by using intuitionistic fuzzy Choquet (IFC) operator and generalized intuitionistic fuzzy ordered geometric averaging (GIFOGA) operator. These operators can deal with the compensatory performance scores and non-compensatory performance scores respectively. Finally, a case study demonstrates the effectiveness of decision framework
T-S Fuzzy Modelling and H∞ Attitude Control for Hypersonic Gliding Vehicles
Weidong Zhang
2017-01-01
Full Text Available This paper addresses the T-S fuzzy modelling and H∞ attitude control in three channels for hypersonic gliding vehicles (HGVs. First, the control-oriented affine nonlinear model has been established which is transformed from the reentry dynamics. Then, based on Taylor’s expansion approach and the fuzzy linearization approach, the homogeneous T-S local modelling technique for HGVs is proposed. Given the approximation accuracy and controller design complexity, appropriate fuzzy premise variables and operating points of interest are selected to construct the T-S homogeneous submodels. With so-called fuzzy blending, the original plant is transformed into the overall T-S fuzzy model with disturbance. By utilizing Lyapunov functional approach, a state feedback fuzzy controller has been designed based on relaxed linear matrix inequality (LMI conditions to stable the original plants with a prescribed H∞ performance of disturbance. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed H∞ T-S fuzzy controller for the original attitude dynamics; the superiority of the designed T-S fuzzy controller compared with other local controllers based on the constructed fuzzy model is shown as well.
Kreinovich, Vladik YA.; Quintana, Chris; Lea, Robert
1991-01-01
Fuzzy control has been successfully applied in industrial systems. However, there is some caution in using it. The reason is that it is based on quite reasonable ideas, but each of these ideas can be implemented in several different ways, and depending on which of the implementations chosen different results are achieved. Some implementations lead to a high quality control, some of them not. And since there are no theoretical methods for choosing the implementation, the basic way to choose it now is experimental. But if one chooses a method that is good for several examples, there is no guarantee that it will work fine in all of them. Hence the caution. A theoretical basis for choosing the fuzzy control procedures is provided. In order to choose a procedure that transforms a fuzzy knowledge into a control, one needs, first, to choose a membership function for each of the fuzzy terms that the experts use, second, to choose operations of uncertainty values that corresponds to 'and' and 'or', and third, when a membership function for control is obtained, one must defuzzy it, that is, somehow generate a value of the control u that will be actually used. A general approach that will help to make all these choices is described: namely, it is proved that under reasonable assumptions membership functions should be linear or fractionally linear, defuzzification must be described by a centroid rule and describe all possible 'and' and 'or' operations. Thus, a theoretical explanation of the existing semi-heuristic choices is given and the basis for the further research on optimal fuzzy control is formulated.
Fuzzy Clustering Methods and their Application to Fuzzy Modeling
Kroszynski, Uri; Zhou, Jianjun
1999-01-01
Fuzzy modeling techniques based upon the analysis of measured input/output data sets result in a set of rules that allow to predict system outputs from given inputs. Fuzzy clustering methods for system modeling and identification result in relatively small rule-bases, allowing fast, yet accurate....... An illustrative synthetic example is analyzed, and prediction accuracy measures are compared between the different variants...
Distributed Arithmetic for Efficient Base-Band Processing in Real-Time GNSS Software Receivers
Grégoire Waelchli
2010-01-01
Full Text Available The growing market of GNSS capable mobile devices is driving the interest of GNSS software solutions, as they can share many system resources (processor, memory, reducing both the size and the cost of their integration. Indeed, with the increasing performance of modern processors, it becomes now feasible to implement in software a multichannel GNSS receiver operating in real time. However, a major issue with this approach is the large computing resources required for the base-band processing, in particular for the correlation operations. Therefore, new algorithms need to be developed in order to reduce the overall complexity of the receiver architecture. Towards that aim, this paper first introduces the challenges of the software implementation of a GPS receiver, with a main focus given to the base-band processing and correlation operations. It then describes the already existing solutions and, from this, introduces a new algorithm based on distributed arithmetic.
Mack, Harold; Reddi, S. S.
1980-04-01
Supertracker represents a programmable parallel pipeline computer architecture that has been designed to meet the real time image processing requirements of auto-cueing target data processing. The prototype bread-board currently under development will be designed to perform input video preprocessing and processing for 525-line and 875-line TV formats FLIR video, automatic display gain and contrast control, and automatic target cueing, classification, and tracking. The video preprocessor is capable of performing operations full frames of video data in real time, e.g., frame integration, storage, 3 x 3 convolution, and neighborhood processing. The processor architecture is being implemented using bit-slice microprogrammable arithmetic processors, operating in parallel. Each processor is capable of up to 20 million operations per second. Multiple frame memories are used for additional flexibility.
Improvements to Earthquake Location with a Fuzzy Logic Approach
Gökalp, Hüseyin
2018-01-01
In this study, improvements to the earthquake location method were investigated using a fuzzy logic approach proposed by Lin and Sanford (Bull Seismol Soc Am 91:82-93, 2001). The method has certain advantages compared to the inverse methods in terms of eliminating the uncertainties of arrival times and reading errors. In this study, adopting this approach, epicentral locations were determined based on the results of a fuzzy logic space concerning the uncertainties in the velocity models. To map the uncertainties in arrival times into the fuzzy logic space, a trapezoidal membership function was constructed by directly using the travel time difference between the two stations for the P- and S-arrival times instead of the P- and S-wave models to eliminate the need for obtaining information concerning the velocity structure of the study area. The results showed that this method worked most effectively when earthquakes occurred away from a network or when the arrival time data contained phase reading errors. In this study, to resolve the problems related to determining the epicentral locations of the events, a forward modeling method like the grid search technique was used by applying different logical operations (i.e., intersection, union, and their combination) with a fuzzy logic approach. The locations of the events were depended on results of fuzzy logic outputs in fuzzy logic space by searching in a gridded region. The process of location determination with the defuzzification of only the grid points with the membership value of 1 obtained by normalizing all the maximum fuzzy output values of the highest values resulted in more reliable epicentral locations for the earthquakes than the other approaches. In addition, throughout the process, the center-of-gravity method was used as a defuzzification operation.
Fuzzy Neuron: Method and Hardware Realization
Krasowski, Michael J.; Prokop, Norman F.
2014-01-01
This innovation represents a method by which single-to-multi-input, single-to-many-output system transfer functions can be estimated from input/output data sets. This innovation can be run in the background while a system is operating under other means (e.g., through human operator effort), or may be utilized offline using data sets created from observations of the estimated system. It utilizes a set of fuzzy membership functions spanning the input space for each input variable. Linear combiners associated with combinations of input membership functions are used to create the output(s) of the estimator. Coefficients are adjusted online through the use of learning algorithms.
Fuzzy linguistic model for interpolation
Abbasbandy, S.; Adabitabar Firozja, M.
2007-01-01
In this paper, a fuzzy method for interpolating of smooth curves was represented. We present a novel approach to interpolate real data by applying the universal approximation method. In proposed method, fuzzy linguistic model (FLM) applied as universal approximation for any nonlinear continuous function. Finally, we give some numerical examples and compare the proposed method with spline method
Environmental impact assessment procedure: A new approach based on fuzzy logic
Peche, Roberto; Rodriguez, Esther
2009-01-01
The information related to the different environmental impacts produced by the execution of activities and projects is often limited, described by semantic variables and, affected by a high degree of inaccuracy and uncertainty, thereby making fuzzy logic a suitable tool with which to express and treat this information. The present study proposes a new approach based on fuzzy logic to carry out the environmental impact assessment (EIA) of these activities and projects. Firstly, a set of impact properties is stated and two nondimensional parameters - ranging from 0 to 100 -are assigned, (p i ) to assess the value of the property and (v i ) to assess its contribution to each environmental impact. Next, the impact properties are described by means of fuzzy numbers p i - using generalised confidence intervals. Then, a procedure based on fuzzy arithmetic is developed to define the assessment functions v-bar = f(p-bar) - conventional mathematical functions, which incorporate the knowledge of these impact properties and give the fuzzy values v i - corresponding to each p i - . Subsequently, the fuzzy value of each environmental impact V-bar is estimated by aggregation of the values v i - , in order to obtain the total positive and negative environmental impacts V +- and V -- and, later - from them - the total environmental impact of the activity or project TV - . Finally, the defuzzyfication of TV - leads to a punctual impact estimator TV (1) - a conventional EI estimation - and its corresponding uncertainty interval estimator {(δ l (TV - ),δ r (TV - )}, which represent the total value of the environmental impact caused by the execution of the considered activity or project.
Fuzzy Logic in Medicine and Bioinformatics
Angela Torres
2006-01-01
Full Text Available The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions and in bioinformatics (comparison of genomes.
Fuzzy control in environmental engineering
Chmielowski, Wojciech Z
2016-01-01
This book is intended for engineers, technicians and people who plan to use fuzzy control in more or less developed and advanced control systems for manufacturing processes, or directly for executive equipment. Assuming that the reader possesses elementary knowledge regarding fuzzy sets and fuzzy control, by way of a reminder, the first parts of the book contain a reminder of the theoretical foundations as well as a description of the tools to be found in the Matlab/Simulink environment in the form of a toolbox. The major part of the book presents applications for fuzzy controllers in control systems for various manufacturing and engineering processes. It presents seven processes and problems which have been programmed using fuzzy controllers. The issues discussed concern the field of Environmental Engineering. Examples are the control of a flood wave passing through a hypothetical, and then the real Dobczyce reservoir in the Raba River, which is located in the upper Vistula River basin in Southern Poland, th...
On Intuitionistic Fuzzy Sets Theory
Atanassov, Krassimir T
2012-01-01
This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author´s previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author´s most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.
Safety critical application of fuzzy control
Schildt, G.H.
1995-01-01
After an introduction into safety terms a short description of fuzzy logic will be given. Especially, for safety critical applications of fuzzy controllers a possible controller structure will be described. The following items will be discussed: Configuration of fuzzy controllers, design aspects like fuzzfiication, inference strategies, defuzzification and types of membership functions. As an example a typical fuzzy rule set will be presented. Especially, real-time behaviour a fuzzy controllers is mentioned. An example of fuzzy controlling for temperature control purpose within a nuclear reactor together with membership functions and inference strategy of such a fuzzy controller will be presented. (author). 4 refs, 17 figs
Image matching navigation based on fuzzy information
田玉龙; 吴伟仁; 田金文; 柳健
2003-01-01
In conventional image matching methods, the image matching process is mostly based on image statistic information. One aspect neglected by all these methods is that there is much fuzzy information contained in these images. A new fuzzy matching algorithm based on fuzzy similarity for navigation is presented in this paper. Because the fuzzy theory is of the ability of making good description of the fuzzy information contained in images, the image matching method based on fuzzy similarity would look forward to producing good performance results. Experimental results using matching algorithm based on fuzzy information also demonstrate its reliability and practicability.
Radiation protection and fuzzy set theory
Nishiwaki, Y.
1993-01-01
In radiation protection we encounter a variety of sources of uncertainties which are due to fuzziness in our cognition or perception of objects. For systematic treatment of this type of uncertainty, the concepts of fuzzy sets or fuzzy measures could be applied to construct system models, which may take into consideration both subjective or intrinsic fuzziness and objective or extrinsic fuzziness. The theory of fuzzy sets and fuzzy measures is still in a developing stage, but its concept may be applied to various problems of subjective perception of risk, nuclear safety, radiation protection and also to the problems of man-machine interface and human factor engineering or ergonomic
Segment LLL Reduction of Lattice Bases Using Modular Arithmetic
Sanjay Mehrotra
2010-07-01
Full Text Available The algorithm of Lenstra, Lenstra, and Lovász (LLL transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n using modular arithmetic. Koy and Schnorr developed a segment-LLL basis reduction algorithm that generates lattice basis satisfying a weaker condition than the LLL reduced basis with O(n improvement than the LLL algorithm. In this paper we combine Storjohann’s modular arithmetic approach with the segment-LLL approach to further improve the worst case complexity of the segment-LLL algorithms by a factor of n0.5.
An efficient adaptive arithmetic coding image compression technology
Wang Xing-Yuan; Yun Jiao-Jiao; Zhang Yong-Lei
2011-01-01
This paper proposes an efficient lossless image compression scheme for still images based on an adaptive arithmetic coding compression algorithm. The algorithm increases the image coding compression rate and ensures the quality of the decoded image combined with the adaptive probability model and predictive coding. The use of adaptive models for each encoded image block dynamically estimates the probability of the relevant image block. The decoded image block can accurately recover the encoded image according to the code book information. We adopt an adaptive arithmetic coding algorithm for image compression that greatly improves the image compression rate. The results show that it is an effective compression technology. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
A Learning Trajectory for Teaching Social Arithmetic using RME Approach
Fauzan, A.; Armiati, A.; Ceria, C.
2018-04-01
This paper discusses the role of a learning trajectory (LT) in promoting students’ reasoning when they learn social arithmetic using Realistic Mathematics Education (RME) approach. In our LT, we built the intertwining of the concepts such as profit, loss, percentage, discount, and interest rate, so that the students understand the relations among them. The LT was developed through a design research that consisted of a cyclic process of preparing for the experiment, conducting the experiment, and retrospective analysis. The research’s subject was 32 students at grade 7 MTsN Sintoga, Pariaman, Indonesia. Data were collected through observations, interviews, checklist, videotaping, and analyzing the students' works. The results showed that the LT could help the students to reinvent the concepts in social arithmetic. The students had more confidence to use their own strategies in solving contextual problems. The most important thing, we discovered the growth in the students’ mathematical reasoning.
On the arithmetic of fractal dimension using hyperhelices
Toledo-Suarez, Carlos D.
2009-01-01
A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension
Domain-General Factors Influencing Numerical and Arithmetic Processing
André Knops
2017-12-01
Full Text Available This special issue contains 18 articles that address the question how numerical processes interact with domain-general factors. We start the editorial with a discussion of how to define domain-general versus domain-specific factors and then discuss the contributions to this special issue grouped into two core numerical domains that are subject to domain-general influences (see Figure 1. The first group of contributions addresses the question how numbers interact with spatial factors. The second group of contributions is concerned with factors that determine and predict arithmetic understanding, performance and development. This special issue shows that domain-general (Table 1a as well as domain-specific (Table 1b abilities influence numerical and arithmetic performance virtually at all levels and make it clear that for the field of numerical cognition a sole focus on one or several domain-specific factors like the approximate number system or spatial-numerical associations is not sufficient. Vice versa, in most studies that included domain-general and domain-specific variables, domain-specific numerical variables predicted arithmetic performance above and beyond domain-general variables. Therefore, a sole focus on domain-general aspects such as, for example, working memory, to explain, predict and foster arithmetic learning is also not sufficient. Based on the articles in this special issue we conclude that both domain-general and domain-specific factors contribute to numerical cognition. But the how, why and when of their contribution still needs to be better understood. We hope that this special issue may be helpful to readers in constraining future theory and model building about the interplay of domain-specific and domain-general factors.
Alternating minima and maxima, Nash equilibria and bounded arithmetic
Pudlák, Pavel; Thapen, Neil
2012-01-01
Roč. 163, č. 5 (2012), s. 604-614 ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Institutional research plan: CEZ:AV0Z10190503 Keywords : proof complexity * bounded arithmetic * search problems Subject RIV: BA - General Mathematics Impact factor: 0.504, year: 2012 http://www.sciencedirect.com/science/article/pii/S016800721100090X
An algorithm for the arithmetic classification of multilattices.
Indelicato, Giuliana
2013-01-01
A procedure for the construction and the classification of monoatomic multilattices in arbitrary dimension is developed. The algorithm allows one to determine the location of the points of all monoatomic multilattices with a given symmetry, or to determine whether two assigned multilattices are arithmetically equivalent. This approach is based on ideas from integral matrix theory, in particular the reduction to the Smith normal form, and can be coded to provide a classification software package.
General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2009-01-01
Roč. 193, č. 2 (2009), s. 109-129 ISSN 0039-3223 R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic function * Dirichlet convolution * polynomial equation * analytic equation * topological algebra * holomorphic functional calculus * implicit function theorem * Laplace transform * semigroup * complex measure Subject RIV: BA - General Mathematics Impact factor: 0.645, year: 2009 http://arxiv.org/abs/0712.3172
Bi-amalgamations subject to the arithmetical property
Kabbaj, S.; Mahdou, N.; Moutui, M. A. S.
2016-01-01
This paper establishes necessary and sufficient conditions for a bi-amalgamation to inherit the arithmetical property, with applications on the weak global dimension and transfer of the semihereditary property. The new results compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations. All results are backed with new and illustrative examples arising as bi-amalgamations.
Manusov, V.Z.; Zaytseva, N.M.
2017-01-01
The goal of this work is to prove a possibility of determining soil parameters that influence its conductivity being the basis of grounding, step voltage and touch voltage calculation. This in its turn increases the safety level of electric equipment operation. The article is devoted to development of new, no conventional models of soil conductivity using the theory of fuzzy sets and fuzzy logic. The description of the solution includes the following sections: fuzzy models of specific electri...
A CABAC codec of H.264AVC with secure arithmetic coding
Neji, Nihel; Jridi, Maher; Alfalou, Ayman; Masmoudi, Nouri
2013-02-01
This paper presents an optimized H.264/AVC coding system for HDTV displays based on a typical flow with high coding efficiency and statics adaptivity features. For high quality streaming, the codec uses a Binary Arithmetic Encoding/Decoding algorithm with high complexity and a JVCE (Joint Video compression and encryption) scheme. In fact, particular attention is given to simultaneous compression and encryption applications to gain security without compromising the speed of transactions [1]. The proposed design allows us to encrypt the information using a pseudo-random number generator (PRNG). Thus we achieved the two operations (compression and encryption) simultaneously and in a dependent manner which is a novelty in this kind of architecture. Moreover, we investigated the hardware implementation of CABAC (Context-based adaptive Binary Arithmetic Coding) codec. The proposed architecture is based on optimized binarizer/de-binarizer to handle significant pixel rates videos with low cost and high performance for most frequent SEs. This was checked using HD video frames. The obtained synthesis results using an FPGA (Xilinx's ISE) show that our design is relevant to code main profile video stream.
Design and evaluation of online arithmetic for signal processing applications on FPGAs
Galli, Reto; Tenca, Alexandre F.
2001-11-01
This paper shows the design and the evaluation of on-line arithmetic modules for the most common operators used in DSP applications, using FPGAs as the target technology. The designs are highly optimized for the target technology and the common range of precision in DSP. The results are based on experimental data collected using CAD tools. All designs are synthesized for the same type of devices (Xilinx XC4000) for comparison, avoiding rough estimates of the system performance, and generating a more reliable and detailed comparison of on-line signal processing solutions with other state of the art approaches, such as distributed arithmetic. We show that on-line designs have a hard stand for basic DSP applications that use only addition and multiplication. However, we also show that on-line designs are able to overtake other approaches as the applications become more sophisticated, e.g. when data dependencies exist, or when non constant multiplicands restrict the use of other approaches.
Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions
Tsaur, Ruey-Chyn
2015-02-01
In the finance market, a short-term investment strategy is usually applied in portfolio selection in order to reduce investment risk; however, the economy is uncertain and the investment period is short. Further, an investor has incomplete information for selecting a portfolio with crisp proportions for each chosen security. In this paper we present a new method of constructing fuzzy portfolio model for the parameters of fuzzy-input return rates and fuzzy-output proportions, based on possibilistic mean-standard deviation models. Furthermore, we consider both excess or shortage of investment in different economic periods by using fuzzy constraint for the sum of the fuzzy proportions, and we also refer to risks of securities investment and vagueness of incomplete information during the period of depression economics for the portfolio selection. Finally, we present a numerical example of a portfolio selection problem to illustrate the proposed model and a sensitivity analysis is realised based on the results.
Improvement of Fuzzy Image Contrast Enhancement Using Simulated Ergodic Fuzzy Markov Chains
Behrouz Fathi-Vajargah
2014-01-01
Full Text Available This paper presents a novel fuzzy enhancement technique using simulated ergodic fuzzy Markov chains for low contrast brain magnetic resonance imaging (MRI. The fuzzy image contrast enhancement is proposed by weighted fuzzy expected value. The membership values are then modified to enhance the image using ergodic fuzzy Markov chains. The qualitative performance of the proposed method is compared to another method in which ergodic fuzzy Markov chains are not considered. The proposed method produces better quality image.
The World of Combinatorial Fuzzy Problems and the Efficiency of Fuzzy Approximation Algorithms
Yamakami, Tomoyuki
2015-01-01
We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and produce fuzzy values. To solve such problems efficiently, we design fast fuzzy algorithms, which are modeled by polynomial-time deterministic fuzzy Turing machines equipped with read-only auxiliary tapes and write-only output tapes and also modeled by polynomia...
Berg, Derek H.; Hutchinson, Nancy L.
2010-01-01
This study investigated whether processing speed, short-term memory, and working memory accounted for the differential mental addition fluency between children typically achieving in arithmetic (TA) and children at-risk for failure in arithmetic (AR). Further, we drew attention to fluency differences in simple (e.g., 5 + 3) and complex (e.g., 16 +…
A fuzzy behaviorist approach to sensor-based robot control
Pin, F.G.
1996-05-01
Sensor-based operation of autonomous robots in unstructured and/or outdoor environments has revealed to be an extremely challenging problem, mainly because of the difficulties encountered when attempting to represent the many uncertainties which are always present in the real world. These uncertainties are primarily due to sensor imprecisions and unpredictability of the environment, i.e., lack of full knowledge of the environment characteristics and dynamics. An approach. which we have named the {open_quotes}Fuzzy Behaviorist Approach{close_quotes} (FBA) is proposed in an attempt to remedy some of these difficulties. This approach is based on the representation of the system`s uncertainties using Fuzzy Set Theory-based approximations and on the representation of the reasoning and control schemes as sets of elemental behaviors. Using the FBA, a formalism for rule base development and an automated generator of fuzzy rules have been developed. This automated system can automatically construct the set of membership functions corresponding to fuzzy behaviors. Once these have been expressed in qualitative terms by the user. The system also checks for completeness of the rule base and for non-redundancy of the rules (which has traditionally been a major hurdle in rule base development). Two major conceptual features, the suppression and inhibition mechanisms which allow to express a dominance between behaviors are discussed in detail. Some experimental results obtained with the automated fuzzy, rule generator applied to the domain of sensor-based navigation in aprion unknown environments. using one of our autonomous test-bed robots as well as a real car in outdoor environments, are then reviewed and discussed to illustrate the feasibility of large-scale automatic fuzzy rule generation using the {open_quotes}Fuzzy Behaviorist{close_quotes} concepts.
Design of a Tele-Control Electrical Vehicle System Using a Fuzzy Logic Control
M. Boukhnifer
2012-11-01
Full Text Available This paper presents a fuzzy logic design of a tele-control electrical vehicle system. We showed that the application of fuzzy logic control allows the stability of tele-vehicle system in spite of communication delays between the operator and the vehicle. A robust bilateral controller design using fuzzy logic frameworks was proposed. This approach allows a convenient means to trade off robustness and stability for a pre-specified time-delay margin. Both the performance and robustness of the proposed method were demonstrated by simulation results for a constant time delay between the operator and the electrical vehicle system.
Internet and Fuzzy Based Control System for Rotary Kiln in Cement Manufacturing Plant
Hanane Zermane
2017-01-01
Full Text Available This paper develops an Internet-based fuzzy control system for an industrial process plant to ensure the remote and fuzzy control in cement factories in Algeria. The remote process consists of control, diagnosing alarms occurs, maintaining and synchronizing different regulation loops. Fuzzy control of the kiln ensures that the system be operational at all times, with minimal downtime. Internet technology ensures remote control. The system reduces downtimes and can guided by operators in the main control room or via Internet.
a fuzzy logic approach to non-linearity problem of load frequency
user
2016-07-03
Jul 3, 2016 ... reduction in settling time, percent overshoot and steady state error. Keywords: fuzzy logic ... power system to regain a state of operating equilibrium given ... power system depends basically on the active (real) power balance ...
Fuzzy set approach to quality function deployment: An investigation
Masud, Abu S. M.
1992-01-01
The final report of the 1992 NASA/ASEE Summer Faculty Fellowship at the Space Exploration Initiative Office (SEIO) in Langley Research Center is presented. Quality Function Deployment (QFD) is a process, focused on facilitating the integration of the customer's voice in the design and development of a product or service. Various input, in the form of judgements and evaluations, are required during the QFD analyses. All the input variables in these analyses are treated as numeric variables. The purpose of the research was to investigate how QFD analyses can be performed when some or all of the input variables are treated as linguistic variables with values expressed as fuzzy numbers. The reason for this consideration is that human judgement, perception, and cognition are often ambiguous and are better represented as fuzzy numbers. Two approaches for using fuzzy sets in QFD have been proposed. In both cases, all the input variables are considered as linguistic variables with values indicated as linguistic expressions. These expressions are then converted to fuzzy numbers. The difference between the two approaches is due to how the QFD computations are performed with these fuzzy numbers. In Approach 1, the fuzzy numbers are first converted to their equivalent crisp scores and then the QFD computations are performed using these crisp scores. As a result, the output of this approach are crisp numbers, similar to those in traditional QFD. In Approach 2, all the QFD computations are performed with the fuzzy numbers and the output are fuzzy numbers also. Both the approaches have been explained with the help of illustrative examples of QFD application. Approach 2 has also been applied in a QFD application exercise in SEIO, involving a 'mini moon rover' design. The mini moon rover is a proposed tele-operated vehicle that will traverse and perform various tasks, including autonomous operations, on the moon surface. The output of the moon rover application exercise is a
Wei Zhou
2014-01-01
Full Text Available Due to convenience and powerfulness in dealing with vagueness and uncertainty of real situation, hesitant fuzzy set has received more and more attention and has been a hot research topic recently. To differently process and effectively aggregate hesitant fuzzy information and capture their interrelationship, in this paper, we propose the hesitant fuzzy reducible weighted Bonferroni mean (HFRWBM and present its four prominent characteristics, namely, reductibility, monotonicity, boundedness, and idempotency. Then, we further investigate its generalized form, that is, the generalized hesitant fuzzy reducible weighted Bonferroni mean (GHFRWBM. Based on the discussion of model parameters, some special cases of the HFRWBM and GHFRWBM are studied in detail. In addition, to deal with the situation that multicriteria have connections in hesitant fuzzy information aggregation, a three-step aggregation approach has been proposed on the basis of the HFRWBM and GHFRWBM. In the end, we apply the proposed aggregation operators to multicriteria aggregation and give an example to illustrate our results.
Fuzzy logic and information fusion to commemorate the 70th birthday of Professor Gaspar Mayor
Sastre, Joan
2016-01-01
This book offers a timely report on key theories and applications of soft-computing. Written in honour of Professor Gaspar Mayor on his 70th birthday, it primarily focuses on areas related to his research, including fuzzy binary operators, aggregation functions, multi-distances, and fuzzy consensus/decision models. It also discusses a number of interesting applications such as the implementation of fuzzy mathematical morphology based on Mayor-Torrens t-norms. Importantly, the different chapters, authored by leading experts, present novel results and offer new perspectives on different aspects of Mayor’s research. The book also includes an overview of evolutionary fuzzy systems, a topic that is not one of Mayor’s main areas of interest, and a final chapter written by the Spanish pioneer in fuzzy logic, Professor E. Trillas. Computer and decision scientists, knowledge engineers and mathematicians alike will find here an authoritative overview of key soft-computing concepts and techniques.
Xiao Luo
2017-01-01
Full Text Available An intuitionistic fuzzy VIKOR (IF-VIKOR method is proposed based on a new distance measure considering the waver of intuitionistic fuzzy information. The method aggregates all individual decision-makers’ assessment information based on intuitionistic fuzzy weighted averaging operator (IFWA, determines the weights of decision-makers and attributes objectively using intuitionistic fuzzy entropy, calculates the group utility and individual regret by the new distance measure, and then reaches a compromise solution. It can be effectively applied to multiattribute decision-making (MADM problems where the weights of decision-makers and attributes are completely unknown and the attribute values are intuitionistic fuzzy numbers (IFNs. The validity and stability of this method are verified by example analysis and sensitivity analysis, and its superiority is illustrated by the comparison with the existing method.
A Compensatory Approach to Multiobjective Linear Transportation Problem with Fuzzy Cost Coefficients
Hale Gonce Kocken
2011-01-01
Full Text Available This paper deals with the Multiobjective Linear Transportation Problem that has fuzzy cost coefficients. In the solution procedure, many objectives may conflict with each other; therefore decision-making process becomes complicated. And also due to the fuzziness in the costs, this problem has a nonlinear structure. In this paper, fuzziness in the objective functions is handled with a fuzzy programming technique in the sense of multiobjective approach. And then we present a compensatory approach to solve Multiobjective Linear Transportation Problem with fuzzy cost coefficients by using Werner's and operator. Our approach generates compromise solutions which are both compensatory and Pareto optimal. A numerical example has been provided to illustrate the problem.
Hybrid Type II fuzzy system & data mining approach for surface finish
Tzu-Liang (Bill Tseng
2015-07-01
Full Text Available In this study, a new methodology in predicting a system output has been investigated by applying a data mining technique and a hybrid type II fuzzy system in CNC turning operations. The purpose was to generate a supplemental control function under the dynamic machining environment, where unforeseeable changes may occur frequently. Two different types of membership functions were developed for the fuzzy logic systems and also by combining the two types, a hybrid system was generated. Genetic algorithm was used for fuzzy adaptation in the control system. Fuzzy rules are automatically modified in the process of genetic algorithm training. The computational results showed that the hybrid system with a genetic adaptation generated a far better accuracy. The hybrid fuzzy system with genetic algorithm training demonstrated more effective prediction capability and a strong potential for the implementation into existing control functions.
Fuzzy-valued linguistic soft set theory and multi-attribute decision-making application
Aiwu, Zhao; Hongjun, Guan
2016-01-01
In this work, we propose the theory of fuzzy linguistic soft set (FLSS) to represent the uncertainty and multi-angle of view when decision makers evaluate an object during decision-making. FLSS integrates fuzzy set theory, linguistic variable and soft set theory. It allows decision makers to utilize linguistic variables to evaluate an object and utilize fuzzy values to describe the corresponding grade of their support of their decisions. Meanwhile, because of the flexibility of soft set, decision makers can use more than one pair of fuzzy-linguistic evaluations to express their opinions from multiple perspectives directly, if necessary. Therefore, it is more flexible and practical than traditional fuzzy set or 2-dimension uncertainty linguistic variable. We also develop a generalized weighted aggregation operator for FLSSs to solve corresponding decision-making issues. Finally, we give a numerical example to verify the practicality and effectiveness of the proposed method.
Sanchez, Mauricio A; Castro, Juan R
2017-01-01
In this book, a series of granular algorithms are proposed. A nature inspired granular algorithm based on Newtonian gravitational forces is proposed. A series of methods for the formation of higher-type information granules represented by Interval Type-2 Fuzzy Sets are also shown, via multiple approaches, such as Coefficient of Variation, principle of justifiable granularity, uncertainty-based information concept, and numerical evidence based. And a fuzzy granular application comparison is given as to demonstrate the differences in how uncertainty affects the performance of fuzzy information granules.
Fuzzy resource optimization for safeguards
Zardecki, A.; Markin, J.T.
1991-01-01
Authorization, enforcement, and verification -- three key functions of safeguards systems -- form the basis of a hierarchical description of the system risk. When formulated in terms of linguistic rather than numeric attributes, the risk can be computed through an algorithm based on the notion of fuzzy sets. Similarly, this formulation allows one to analyze the optimal resource allocation by maximizing the overall detection probability, regarded as a linguistic variable. After summarizing the necessary elements of the fuzzy sets theory, we outline the basic algorithm. This is followed by a sample computation of the fuzzy optimization. 10 refs., 1 tab