Solving type-2 fuzzy relation equations via semi-tensor product of matrices
Yongyi YAN; Zengqiang CHEN; Zhongxin LIU
2014-01-01
The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices;an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations;the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.
Cause and effect analysis by fuzzy relational equations and a genetic algorithm
Rotshtein, Alexander P. [Industrial Engineering and Management Department, Jerusalem College of Technology-Machon Lev, Havaad Haleumi St., 21, 91160, Jerusalem (Israel)]. E-mail: rot@jct.ac.il; Posner, Morton [Industrial Engineering and Management Department, Jerusalem College of Technology-Machon Lev, Havaad Haleumi St., 21, 91160, Jerusalem (Israel); Rakytyanska, Hanna B. [Department of Applied Mathematics, Vinnitsa State Technical University, Khmelnitske Sh., 95, 21021, Vinnitsa (Ukraine)]. E-mail: h_rakit@hotmail.com
2006-09-15
This paper proposes using a genetic algorithm as a tool to solve the fault diagnosis problem. The fault diagnosis problem is based on a cause and effect analysis which is formally described by fuzzy relations. Fuzzy relations are formed on the basis of expert assessments. Application of expert fuzzy relations to restore and identify the causes through the observed effects requires the solution to a system of fuzzy relational equations. In this study this search for a solution amounts to solving a corresponding optimization problem. An optimization algorithm is based on the application of genetic operations of crossover, mutation and selection. The genetic algorithm suggested here represents an application in expert systems of fault diagnosis and quality control.
Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD
郭书祥; 吕震宙; 冯立富
2002-01-01
The key component of finite element analysis of structures with fuzzy parameters,which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic.According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers.It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.
A Divide-and-Conquer Approach for Solving Fuzzy Max-Archimedean t-Norm Relational Equations
Jun-Lin Lin
2014-01-01
Full Text Available A system of fuzzy relational equations with the max-Archimedean t-norm composition was considered. The relevant literature indicated that this problem can be reduced to the problem of finding all the irredundant coverings of a binary matrix. A divide-and-conquer approach is proposed to solve this problem and, subsequently, to solve the original problem. This approach was used to analyze the binary matrix and then decompose the matrix into several submatrices such that the irredundant coverings of the original matrix could be constructed using the irredundant coverings of each of these submatrices. This step was performed recursively for each of these submatrices to obtain the irredundant coverings. Finally, once all the irredundant coverings of the original matrix were found, they were easily converted into the minimal solutions of the fuzzy relational equations. Experiments on binary matrices, with the number of irredundant coverings ranging from 24 to 9680, were also performed. The results indicated that, for test matrices that could initially be partitioned into more than one submatrix, this approach reduced the execution time by more than three orders of magnitude. For the other test matrices, this approach was still useful because certain submatrices could be partitioned into more than one submatrix.
Fuzzy differential equations in various approaches
Gomes, Luciana Takata; Bede, Barnabas
2015-01-01
This book may be used as reference for graduate students interested in fuzzy differential equations and researchers working in fuzzy sets and systems, dynamical systems, uncertainty analysis, and applications of uncertain dynamical systems. Beginning with a historical overview and introduction to fundamental notions of fuzzy sets, including different possibilities of fuzzy differentiation and metric spaces, this book moves on to an overview of fuzzy calculus thorough exposition and comparison of different approaches. Innovative theories of fuzzy calculus and fuzzy differential equations using fuzzy bunches of functions are introduced and explored. Launching with a brief review of essential theories, this book investigates both well-known and novel approaches in this field; such as the Hukuhara differentiability and its generalizations as well as differential inclusions and Zadeh’s extension. Through a unique analysis, results of all these theories are examined and compared.
Numerical method for solving fuzzy wave equation
Kermani, M. Afshar
2013-10-01
In this study a numerical method for solving "fuzzy partial differential equation" (FPDE) is considered. We present difference method to solve the FPDEs such as fuzzy hyperbolic equation, then see if stability of this method exist, and conditions for stability are given.
Weakly linear systems of fuzzy relation inequalities: The heterogeneous case
Ignjatović, Jelena; Damljanović, Nada; Jančić, Ivana
2011-01-01
New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatovi\\'c, M. \\'Ciri\\'c, S. Bogdanovi\\'c, On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081--3113.]. The mentioned paper dealt with homogeneous weakly linear systems, composed of fuzzy relations on a single set, and a method for computing their greatest solutions has been provided. This method is based on the computing of the greatest post-fixed point, contained in a given fuzzy relation, of an isotone function on the lattice of fuzzy relations. Here we adapt this method for computing the greatest solutions of heterogeneous weakly linear systems, where the unknown fuzzy relation relates two possibly different sets. We also introduce and study quotient fuzzy relational systems and establish relationships between solutions to heterogeneous and homogeneous weakly linear systems. Besides, we point out ...
On Fuzzy Improper Integral and Its Application for Fuzzy Partial Differential Equations
ElHassan ElJaoui; Said Melliani
2016-01-01
We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.
On Fuzzy Improper Integral and Its Application for Fuzzy Partial Differential Equations
ElHassan ElJaoui
2016-01-01
Full Text Available We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.
On new solutions of fuzzy differential equations
Chalco-Cano, Y. [Departamento de Matematica, Universidad de Tarapaca, Casilla 7D, Arica (Chile)], E-mail: ychalco@uta.cl; Roman-Flores, H. [Instituto de Investigacion, Universidad de Tarapaca, Casilla 7D, Arica (Chile)
2008-10-15
We study fuzzy differential equations (FDE) using the concept of generalized H-differentiability. This concept is based in the enlargement of the class of differentiable fuzzy mappings and, for this, we consider the lateral Hukuhara derivatives. We will see that both derivatives are different and they lead us to different solutions from a FDE. Also, some illustrative examples are given and some comparisons with other methods for solving FDE are made.
Bounded solutions for fuzzy differential and integral equations
Nieto, Juan J. [Departamento de Analisis Matematico Facultad de Matematicas Universidad de Santiago de Compostela, 15782 (Spain)] e-mail: amnieto@usc.es; Rodriguez-Lopez, Rosana [Departamento de Analisis Matematico Facultad de Matematicas Universidad de Santiago de Compostela, 15782 (Spain)] e-mail: amrosana@usc.es
2006-03-01
We find sufficient conditions for the boundness of every solution of first-order fuzzy differential equations as well as certain fuzzy integral equations. Our results are based on several theorems concerning crisp differential and integral inequalities.
Adomian Method for Solving Fuzzy Fredholm-Volterra Integral Equations
M. Barkhordari Ahmadi
2013-09-01
Full Text Available In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.
Functional Equations in Fuzzy Banach Spaces
M. Eshaghi Gordji
2012-01-01
generalized Hyers-Ulam stability of the following additive-quadratic functional equation f(x+ky+f(x−ky=f(x+y+f(x−y+(2(k+1/kf(ky−2(k+1f(y for fixed integers k with k≠0,±1 in fuzzy Banach spaces.
COMPATIBLE EXTENSIONS OF FUZZY RELATIONS
Irina GEORGESCU
2003-01-01
In 1930 Szpilrajn proved that any strict partial order can be embedded in a strict linear order.This theorem was later refined by Dushnik and Miller (1941), Hansson (1968), Suzumura (1976),Donaldson and Weymark (1998), Bossert (1999). Particularly Suzumura introduced the important concept of compatible extension of a (crisp) relation. These extension theorems have an important role in welfare economics. In particular Szpilrajn theorem is the main tool for proving a known theorem of Richter that establishes the equivalence between rational and congruous consumers. In 1999 Duggan proved a general extension theorem that contains all these results. In this paper we introduce the notion of compatible extension of a fuzzy relation and we prove an extension theorem for fuzzy relations. Our result generalizes to fuzzy set theory the main part of Duggan's theorem. As applications we obtain fuzzy versions of the theorems of Szpilrajn, Hansson and Suzumura. We also prove that an asymmetric and transitive fuzzy relation has a compatible extension that is total, asymmetric and transitive.Our results can be useful in the theory of fuzzy consumers. We can prove that any rational fuzzyconsumer is congruous, extending to a fuzzy context a part of Richter's theorem. To prove that acongruous fuzzy consumer is rational remains an open problem. A proof of this result can somehowuse a fuzzy version of Szpilrajn theorem.
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Minimal solution of linear formed fuzzy matrix equations
Maryam Mosleh
2012-10-01
Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.
A neuro approach to solve fuzzy Riccati differential equations
Shahrir, Mohammad Shazri; Kumaresan, N.; Kamali, M. Z. M.; Ratnavelu, Kurunathan
2015-10-01
There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.
A neuro approach to solve fuzzy Riccati differential equations
Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)
2015-10-22
There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.
Ullah, Saif; Farooq, Muhammad; Ahmad, Latif; Abdullah, Saleem
2014-01-01
Fuzzy partial integro-differential equations have a major role in the fields of science and engineering. In this paper, we propose the solution of fuzzy partial Volterra integro-differential equation with convolution type kernel using fuzzy Laplace transform method (FLTM) under Hukuhara differentiability. It is shown that FLTM is a simple and reliable approach for solving such equations analytically. Finally, the method is illustrated with few examples to show the ability of the proposed method.
Norazrizal Aswad Abdul Rahman
2015-07-01
Full Text Available In this paper, we study the classical Sumudu transform in fuzzy environment, referred to as the fuzzy Sumudu transform (FST. We also propose some results on the properties of the FST, such as linearity, preserving, fuzzy derivative, shifting and convolution theorem. In order to show the capability of the FST, we provide a detailed procedure to solve fuzzy differential equations (FDEs. A numerical example is provided to illustrate the usage of the FST.
Nth-order Fuzzy Differential Equations Under Generalized Differentiability
Soheil Salahshour
2011-11-01
Full Text Available In this paper, the multiple solutions of Nth-order fuzzy differential equations by the equivalent integral forms are considered. Also, an Existence and uniqueness theorem of solution of Nth-order fuzzy differential equations is proved under Nth-order generalized differentiability in Banach space.
Stochastic fuzzy differential equations of a nonincreasing type
Malinowski, Marek T.
2016-04-01
Stochastic fuzzy differential equations constitute an apparatus in modeling dynamic systems operating in fuzzy environment and governed by stochastic noises. In this paper we introduce a new kind of such the equations. Namely, the stochastic fuzzy differential of nonincreasing type are considered. The fuzzy stochastic processes which are solutions to these equations have trajectories with nonincreasing fuzziness in their values. In our previous papers, as a first natural extension of crisp stochastic differential equations, stochastic fuzzy differential equations of nondecreasing type were studied. In this paper we show that under suitable conditions each of the equations has a unique solution which possesses property of continuous dependence on data of the equation. To prove existence of the solutions we use sequences of successive approximate solutions. An estimation of an error of the approximate solution is established as well. Some examples of equations are solved and their solutions are simulated to illustrate the theory of stochastic fuzzy differential equations. All the achieved results apply to stochastic set-valued differential equations.
A. Karimi Dizicheh
2016-03-01
Full Text Available In this paper, we firstly introduce system of first order fuzzy differential equations. Then, we convert the problem to two crisp systems of first order differential equations. For numerical aspects, we apply exponentially fitted Runge Kutta method to solve the fuzzy problems. We solve some well-known examples in order to demonstrate the applicability and accuracy of results.
Rough Fuzzy Relation on Two Universal Sets
Xuan Thao Nguyen
2014-03-01
Full Text Available Fuzzy set theory was introduced by L.A. Zadeh in 1965. Immediately, it has many applications in practice and in building databases, one of which is the construction of a fuzzy relational database based on similar relationship. The study of cases of fuzzy relations in different environments will help us understand its applications. In this paper, the rough fuzzy relation on Cartesian product of two universe sets is defined, and then the algebraic properties of them, such as the max, min, and composition of two rough fuzzy relations are examined. Finally, reflexive, α-reflexive, symmetric and transitive rough fuzzy relations on two universe sets are also defined.
A proposed method for solving fuzzy system of linear equations.
Kargar, Reza; Allahviranloo, Tofigh; Rostami-Malkhalifeh, Mohsen; Jahanshaloo, Gholam Reza
2014-01-01
This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m × n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.
Fuzzy relational calculus theory, applications and software
Peeva, Ketty
2004-01-01
This book examines fuzzy relational calculus theory with applications in various engineering subjects. The scope of the text covers unified and exact methods with algorithms for direct and inverse problem resolution in fuzzy relational calculus. Extensive engineering applications of fuzzy relation compositions and fuzzy linear systems (linear, relational and intuitionistic) are discussed. Some examples of such applications include solutions of equivalence, reduction and minimization problems in fuzzy machines, pattern recognition in fuzzy languages, optimization and inference engines in textile and chemical engineering, etc. A comprehensive overview of the authors' original work in fuzzy relational calculus is also provided in each chapter. The attached CD-Rom contains a toolbox with many functions for fuzzy calculations, together with an original algorithm for inverse problem resolution in MATLAB. This book is also suitable for use as a textbook in related courses at advanced undergraduate and graduate level...
Bipartite Fuzzy Stochastic Differential Equations with Global Lipschitz Condition
Marek T. Malinowski
2016-01-01
Full Text Available We introduce and analyze a new type of fuzzy stochastic differential equations. We consider equations with drift and diffusion terms occurring at both sides of equations. Therefore we call them the bipartite fuzzy stochastic differential equations. Under the Lipschitz and boundedness conditions imposed on drifts and diffusions coefficients we prove existence of a unique solution. Then, insensitivity of the solution under small changes of data of equation is examined. Finally, we mention that all results can be repeated for solutions to bipartite set-valued stochastic differential equations.
Fuzzy MCDM Based on Fuzzy Relational Degree Analysis
无
2002-01-01
This paper presents a new fuzzy multiple criteria (both qualitative and quantitative) decision-making (MCDM) method based on fuzzy relational degree analysis. The concepts of fuzzy set theory are used to construct a weighted suitability decision matrix to evaluate the weighted suitability of different alternatives versus various criteria. The positive ideal solution and negative ideal solution are then obtained by using a method of ranking fuzzy numbers, and the fuzzy relational degrees of different alternatives versus positive ideal solution and negative ideal solution are calculated by using the proposed arithmetic. Finally, the relative relational degrees of various alternatives versus positive ideal solution are ranked to determine the best alternative. A numerical example is provided to illustrate the proposed method at the end of this paper.
Fractional differential equation with the fuzzy initial condition
Sadia Arshad
2011-02-01
Full Text Available In this paper we study the existence and uniqueness of the solution for a class of fractional differential equation with fuzzy initial value. The fractional derivatives are considered in the Riemann-Liouville sense.
Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
S. Narayanamoorthy
2015-01-01
Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.
Diptiranjan Behera; S Chakraverty
2015-02-01
This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied for the first time in this paper for the present analysis. Using single parametric form, the $n \\times n$ fully fuzzy system of linear equations have been converted to a $2n \\times 2n$ crisp system of linear equations. On the other hand, double parametric form of fuzzy numbers converts the n×n fully fuzzy system of linear equations to a crisp system of same order. Triangular and trapezoidal convex normalized fuzzy sets are used for the present analysis. Known example problems are solved to illustrate the efficacy and reliability of the proposed methods.
Consistent linguistic fuzzy preference relations method with ranking fuzzy numbers
Ridzuan, Siti Amnah Mohd; Mohamad, Daud; Kamis, Nor Hanimah
2014-12-01
Multi-Criteria Decision Making (MCDM) methods have been developed to help decision makers in selecting the best criteria or alternatives from the options given. One of the well known methods in MCDM is the Consistent Fuzzy Preference Relation (CFPR) method, essentially utilizes a pairwise comparison approach. This method was later improved to cater subjectivity in the data by using fuzzy set, known as the Consistent Linguistic Fuzzy Preference Relations (CLFPR). The CLFPR method uses the additive transitivity property in the evaluation of pairwise comparison matrices. However, the calculation involved is lengthy and cumbersome. To overcome this problem, a method of defuzzification was introduced by researchers. Nevertheless, the defuzzification process has a major setback where some information may lose due to the simplification process. In this paper, we propose a method of CLFPR that preserves the fuzzy numbers form throughout the process. In obtaining the desired ordering result, a method of ranking fuzzy numbers is utilized in the procedure. This improved procedure for CLFPR is implemented to a case study to verify its effectiveness. This method is useful for solving decision making problems and can be applied to many areas of applications.
Component reuse in iterative solvers for the solution of fuzzy partial differential equations
Corveleyn, Samuel; Vandewalle, Stefan
2009-01-01
We consider elliptic partial differential equations with an uncertain diffusion parameter, where the uncertainty is modelled by fuzzy numbers or a fuzzy field. Our aim is to efficiently compute the fuzzy characteristics of the solution to the fuzzy equation. Using the so-called alpha-cut approach, it is possible to reformulate the fuzzy problems as a long sequence of global optimization problems. Function and gradient evaluations within these optimization problems, differ from each other thro...
Fuzzy stability of a mixed type functional equation
Jin Sun
2011-01-01
Full Text Available Abstract In this paper, we investigate a fuzzy version of stability for the functional equation f ( x + y + z - f ( x + y - f ( y + z - f ( x + z + f ( x + f ( y + f ( z = 0 in the sense of Mirmostafaee and Moslehian. 1991 Mathematics Subject Classification. Primary 46S40; Secondary 39B52.
Adams Predictor-Corrector Systems for Solving Fuzzy Differential Equations
Dequan Shang
2013-01-01
Full Text Available A predictor-corrector algorithm and an improved predictor-corrector (IPC algorithm based on Adams method are proposed to solve first-order differential equations with fuzzy initial condition. These algorithms are generated by updating the Adams predictor-corrector method and their convergence is also analyzed. Finally, the proposed methods are illustrated by solving an example.
Özlem Türkşen
2013-01-01
Full Text Available The solution set of a multi-response experiment is characterized by Pareto solution set. In this paper, the multi-response experiment is dealed in a fuzzy framework. The responses and model parameters are considered as triangular fuzzy numbers which indicate the uncertainty of the data set. Fuzzy least square approach and fuzzy modified NSGA-II (FNSGA-II are used for modeling and optimization, respectively. The obtained fuzzy Pareto solution set is grouped by using fuzzy relational clustering approach. Therefore, it could be easier to choose the alternative solutions to make better decision. A fuzzy response valued real data set is used as an application.
侯世旺; 朱慧明
2012-01-01
为合理描述制造过程不确定质量异常与异常原因之间的模糊关系，通过设计一种基于最小距离的目标函数，将模糊关系方程转化为最优化问题的求解，并提出了相应的遗传算法，用来求解模糊关系方程的区间解，实现异常原因对不确定质量异常贡献程度的量化。结合精密轴加工过程不确定质量异常的诊断实例，介绍了方案的应用过程。应用结果可以为异因定位提供决策依据。%Fuzzy relation equation can reasonably describe the fuzzy relation between the uncertain quality abnormity and the assignable causes of manufacturing process, but the constraints of its application was formed by solving complexity. By designing an objective function with minimum distance, the fuzzy relation equation was transformed into an optimization problem, A genetic algorithm was proposed to obtain the interval solution. The contribution de gree of assignable causes to given uncertain quality abnormity was located based on the interval solution. Uncertain quality abnormity diagnosis of precision-axis machining was taken as an example to introduce the application process of proposed approach in detail, and the result could provide support for assignable causes' location.
Numerical Solution of Uncertain Beam Equations Using Double Parametric Form of Fuzzy Numbers
Smita Tapaswini
2013-01-01
Full Text Available Present paper proposes a new technique to solve uncertain beam equation using double parametric form of fuzzy numbers. Uncertainties appearing in the initial conditions are taken in terms of triangular fuzzy number. Using the single parametric form, the fuzzy beam equation is converted first to an interval-based fuzzy differential equation. Next, this differential equation is transformed to crisp form by applying double parametric form of fuzzy number. Finally, the same is solved by homotopy perturbation method (HPM to obtain the uncertain responses subject to unit step and impulse loads. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the methodology.
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.
Supplier Segmentation using Fuzzy Linguistic Preference Relations and Fuzzy Clustering
Pegah Sagheb Haghighi
2014-04-01
Full Text Available In an environment characterized by its competitiveness, managing and monitoring relationships with suppliers are of the essence. Supplier management includes supplier segmentation. Existing literature demonstrates that suppliers are mostly segmented by computing their aggregated scores, without taking each supplier’s criterion value into account. The principle aim of this paper is to propose a supplier segmentation method that compares each supplier’s criterion value with exactly the same criterion of other suppliers. The Fuzzy Linguistic Preference Relations (LinPreRa based Analytic Hierarchy Process (AHP is first used to find the weight of each criterion. Then, Fuzzy c-means algorithm is employed to cluster suppliers based on their membership degrees. The obtained results show that the proposed method enhances the quality of the previous findings.
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.
Jiménez-Losada, Andrés
2017-01-01
This book offers a comprehensive introduction to cooperative game theory and a practice-oriented reference guide to new models and tools for studying bilateral fuzzy relations among several agents or players. It introduces the reader to several fuzzy models, each of which is first analyzed in the context of classical games (crisp games) and subsequently in the context of fuzzy games. Special emphasis is given to the value of Shapley, which is presented for the first time in the context of fuzzy games. Students and researchers will find here a self-contained reference guide to cooperative fuzzy games, characterized by a wealth of examples, descriptions of a wide range of possible situations, step-by-step explanations of the basic mathematical concepts involved, and easy-to-follow information on axioms and properties.
Combinational reasoning of quantitative fuzzy topological relations for simple fuzzy regions.
Liu, Bo; Li, Dajun; Xia, Yuanping; Ruan, Jian; Xu, Lili; Wu, Huanyi
2015-01-01
In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models.
Combinational reasoning of quantitative fuzzy topological relations for simple fuzzy regions.
Bo Liu
Full Text Available In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS and Artificial Intelligence (AI. Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1 23 different topological relations between a simple crisp region and a simple fuzzy region; (2 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models.
A Novel Approach to Modeling of Hydrogeologic Systems Using Fuzzy Differential Equations
Faybishenko, B. A.
2003-12-01
The many simultaneously occurring processes in unsaturated-saturated heterogeneous soils and fractured rocks can cause field observations to become imprecise and incomplete. Consequently, the results of predictions using deterministic and stochastic mathematical models are often uncertain, vague or "fuzzy." One of the alternative approaches to modeling hydrogeologic systems is the application of a fuzzy-systems approach, which is already widely used in such fields as engineering, physics, chemistry, and biology. After presenting a hydrogeologic system as a fuzzy system, the author presents a fuzzy form of Darcy's equation. Based on this equation, second-order fuzzy partial differential equations of the elliptic type (analogous to the Laplace equation) and the parabolic type (analogous to the Richards equation) are derived. These equations are then approximated as fuzzy-difference equations and solved using the basic principles of fuzzy arithmetic. The solutions for the fuzzy-difference equations take the form of fuzzy membership functions for each observation point (node). The author gives examples of the solutions of these equations for flow in unsaturated and saturated media and then compares them with those obtained using deterministic and stochastic methods.
Fuzzy Boundary and Fuzzy Semiboundary
Athar, M.; Ahmad, B.
2008-01-01
We present several properties of fuzzy boundary and fuzzy semiboundary which have been supported by examples. Properties of fuzzy semi-interior, fuzzy semiclosure, fuzzy boundary, and fuzzy semiboundary have been obtained in product-related spaces. We give necessary conditions for fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions. Moreover, fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions have been characterized via fuzzy-derived (resp., fuzz...
The extension of Buckley-Feuring solutions for non-polynomial fuzzy partial differential equations
Galvez, David; Pino, Jose Luis
2008-01-01
This paper presents the natural extension of Buckley-Feuring method proposed in \\cite{BuckleyFeuring99} for solving fuzzy partial differential equations (FPDE) in a non-polynomial relation, such as the operator $\\varphi(D_{x_1}, D_{x_2})$, which maps to the quotient between both partials. The new assumptions and conditions proceedings from this consideration are given in this document.
A Fixed Point Approach to the Fuzzy Stability of a Mixed Typ e Functional Equation
Cheng Li-hua; Zhang Jun-min
2016-01-01
Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.
Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method
T. Jayakumar
2015-01-01
Full Text Available In this paper we study the numerical methods for Fuzzy Differential equations by an application of the Runge-Kutta Verner method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.
Farshid Mirzaee; Mohammad Komak Yari
2016-01-01
In this paper, we introduce three-dimensional fuzzy differential transform method and we utilize it to solve fuzzy partial differential equations. This technique is a successful method because of reducing such problems to solve a system of algebraic equations; so, the problem can be solved directly. A considerable advantage of this method is to obtain the analytical solutions if the equation has an exact solution that is a polynomial function. Numerical examples are included to demonstrate th...
Solution of second order linear fuzzy difference equation by Lagrange's multiplier method
Sankar Prasad Mondal
2016-06-01
Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.
Component Reuse in Iterative Solvers for the Solution of Fuzzy Partial Differential Equations
Corveleyn, Samuel; Vandewalle, Stefan
2009-09-01
We consider elliptic partial differential equations with an uncertain diffusion parameter, where the uncertainty is modeled by fuzzy numbers or a fuzzy field. Our aim is to efficiently compute the fuzzy characteristics of the solution to the fuzzy equation. Using the so-called α-cut approach, it is possible to reformulate the fuzzy problem as a long sequence of global optimisation problems. Function and gradient evaluations within these optimisation problems, differ from each other through a possibly small change in one or more of the partial differential equation parameters. In order to reduce the computational complexity of the optimisation problems we consider component reuse in iterative solvers. We concentrate in particular on the reuse of the setup phase in an algebraic multigrid strategy and on reuse of initial approximations.
D. Vivek
2016-11-01
Full Text Available In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE of order $q \\in (0, 1 $ under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor's formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.
Shadan Sadigh Behzadi
2011-12-01
Full Text Available In this paper, Adomian decomposition method (ADM and homotopy analysis method (HAM are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind$(FVFIE-2$. we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy Volterra-Fredholm integral equation. Also, the existence and uniqueness of the solution and convergence of the proposed methods are proved. Examples is given and the results reveal that homotopy analysis method is very effective and simple compared with the Adomian decomposition method.
Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces
Kang Jung Im
2011-01-01
Full Text Available Abstract Lex X be a normed space and Y be a Banach fuzzy space. Let D = {(x, y ∈ X × X : ||x|| + ||y|| ≥ d} where d > 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on D and taking values in Y. We consider also the Pexiderized Cauchy functional equation. 2000 Mathematics Subject Classification: 39B22; 39B82; 46S10.
Stability of Various Functional Equations in Non-Archimedean Intuitionistic Fuzzy Normed Spaces
Syed Abdul Mohiuddine
2012-01-01
Full Text Available We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea of t-norm and t-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framework of non-Archimedean IFN spaces.
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
Behavior of the positive solutions of fuzzy max-difference equations
Stefanidou G; Papaschinopoulos G
2005-01-01
We extend some results obtained in 1998 and 1999 by studying the periodicity of the solutions of the fuzzy difference equations xn+1 = max{A/xn, A/xn-1,...,A/xn-k}, xn+1 = max{A0/xn, A1/xn-1}, where k is a positive integer, A, Ai, i = 0,1, are positive fuzzy numbers, and the initial values xi, i = -k, -k + 1,...,0 (resp., i = -1,0) of the first (resp., second) equation are positive fuzzy numbers.
Fuzzy Relational Databases: Representational Issues and Reduction Using Similarity Measures.
Prade, Henri; Testemale, Claudette
1987-01-01
Compares and expands upon two approaches to dealing with fuzzy relational databases. The proposed similarity measure is based on a fuzzy Hausdorff distance and estimates the mismatch between two possibility distributions using a reduction process. The consequences of the reduction process on query evaluation are studied. (Author/EM)
Uncertain Fuzzy Preference Relations and Their Applications
Gong, Zaiwu; Yao, Tianxiang
2013-01-01
On the basis of fuzzy sets and some of their relevant generalizations, this book systematically presents the fundamental principles and applications of group decision making under different scenarios of preference relations. By using intuitionistic knowledge as the field of discourse, this work investigates by utilizing innovative research means the fundamental principles and methods of group decision making with various different intuitionistic preferences: Mathematical reasoning is employed to study the consistency of group decision making; Methods of fusing information are applied to look at the aggregation of multiple preferences; Techniques of soft computing and optimization are utilized to search for satisfactory decision alternatives. Each chapter follows the following structurally clear format of presentation: literature review, development of basic theory, verification and reasoning of principles , construction of models and computational schemes, and numerical examples, which ...
Farshid Mirzaee
2016-06-01
Full Text Available In this paper, we introduce three-dimensional fuzzy differential transform method and we utilize it to solve fuzzy partial differential equations. This technique is a successful method because of reducing such problems to solve a system of algebraic equations; so, the problem can be solved directly. A considerable advantage of this method is to obtain the analytical solutions if the equation has an exact solution that is a polynomial function. Numerical examples are included to demonstrate the validity and applicability of the method.
Semi analytical solution of second order fuzzy Riccati equation by homotopy perturbation method
Jameel, A. F.; Ismail, Ahmad Izani Md
2014-07-01
In this work, the Homotopy Perturbation Method (HPM) is formulated to find a semi-analytical solution of the Fuzzy Initial Value Problem (FIVP) involving nonlinear second order Riccati equation. This method is based upon homotopy perturbation theory. This method allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily calculated. The effectiveness of the algorithm is demonstrated by solving nonlinear second order fuzzy Riccati equation. The results indicate that the method is very effective and simple to apply.
On the solution of a class of fuzzy system of linear equations
Davod Khojasteh Salkuyeh
2015-04-01
In this paper, we consider the system of linear equations $A\\widetilde{x}=\\widetilde{b}$, where $A \\in \\mathbb{R}^{n \\times n}$ is a crisp H-matrix and \\widetilde{b} is a fuzzy -vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices. Finally, some numerical examples are given to illustrate the presented theoretical results.
Corveleyn, Samuel; Vandewalle, Stefan
2011-01-01
Mathematical models in science and engineering often contain parameters that are uncertain. These parameters are usually represented by random numbers, fields or processes. However, when the stochastic characteristics of these parameters are not precisely known, an interval representation, or, more generally, a fuzzy representation may be more appropriate. This leads to so-called fuzzy differential equations. Unfortunately, there is no real consensus in the literature on how to define and int...
Corveleyn, Samuel; Vandewalle, Stefan
2011-01-01
Uncertain parameters in mathematical models of physical phenomena are typically modeled by means of random numbers, random fields or random processes. If these uncertainties are of the epistemic kind, calculations with random parameters can lead to very unexpected and unreliable results. Fuzzy set theory was introduced as an alternative to probability theory for a better modeling of epistemic uncertainty. We consider the solution of elliptic partial differential equations with a fuzzy diffus...
Sankar Prasad Mondal
Full Text Available In this paper the First Order Linear Ordinary Differential Equations (FOLODE are described in fuzzy environment. Here coefficients and /or initial condition of FOLODE are taken as Generalized Triangular Fuzzy Numbers (GTFNs.The solution procedure of the FOLODE is developed by Laplace transform. It is illustrated by numerical examples. Finally imprecise bank account problem and concentration of drug in blood problem are described.
Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule
Luo, Yousong; Eberhard, Andrew
2005-07-01
A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the "fuzzy sum rule" of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,=u,=2u)=0 is under consideration.
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
De-Gang Wang
2012-01-01
Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
Fuzzy functions: a fuzzy extension of the category SET and some related categories
Ulrich Höhle
2000-10-01
Full Text Available In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex to an L-valued set (Y,Ey. We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.
冯玉瑚; 朱凡昌
2004-01-01
Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets. The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions. The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to now.
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.
Ambiguous representations as fuzzy relations between sets
Nykyforchyn, Oleh; 10.1016/j.fss.2011.02.007
2011-01-01
Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous representations is a lattice and a compact Hausdorff Lawson upper semilattice. The categories of ambiguous and $L$-ambiguous representations are defined and investigated.
Fuzzy approximation relations, modal structures and possibilistic logic
Esteva Massaguer, Francesc; Garcia, Pere; Godo Lacasa, Lluís; Rodríguez, Ricardo Óscar
1998-01-01
The paper introduces a general axiomatic notion of approximation mapping, a mapping that associates to each crisp proposition p a fuzzy set representing "approximately p". It is shown how it can be obtained through fuzzy relations, which are at least reflexive. We study the corresponding multi-modal systems depending on the properties satisfied by the approximate relation. Finally, we show some equivalences between possibilistic logical consequences and global/local logical consequences in...
Indeterminate direction relation model based on fuzzy description framework
2008-01-01
The indetermination of direction relation is a hot topic for fuzzy GIS researchers. The existing models only study the effects of indetermination of spatial objects,but ignore the uncertainty of direction reference framework. In this paper,first a for-malized representation model of indeterminate spatial objects is designed based on quadruple (x,y,A,μ),then a fuzzy direction reference framework is constructed by revising the cone method,in which the partitions of direction tiles are smooth and continuous,and two neighboring sections are overlapped in the transitional zones with fuzzy method. Grounded on these,a fuzzy description model for indeterminate direction relation is proposed in which the uncertainty of all three parts (source object,reference object and reference frame) is taken into account simultaneously. In the end,case studies are implemented to test the rationality and validity of the model.
Towards the Formalization of Fuzzy Relational Database Queries
Aleksandar Perović
2009-03-01
Full Text Available The aim of this paper is to give guidelines on how to formalize fuzzy relationaldatabase queries using 1LΠ 2 fuzzy logic. After the short introduction, we give anoverview of the1LΠ 2 logic. In the continuation we give a brief overview of the FRDBqueries and query-database similarity relation. We conclude the paper with the descriptionof FRDB query formalization using presented definitions.
Bhavana Deshpande
2014-01-01
Full Text Available We establish a common coupled fixed point theorem for weakly compatible mappings on modified intuitionistic fuzzy metric spaces. As an application of our result, we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to demonstrate our result.
An Implicit Method for Solving Fuzzy Partial Differential Equation with Nonlocal Boundary Conditions
B. Orouji
2015-06-01
Full Text Available In this paper we introduce a numerical solution for the fuzzy heat equation with nonlocal boundary conditions. The main purpose is finding a difference scheme for the one dimensional heat equation with nonlocal boundary conditions. In these types of problems, an integral equation is appeared in the boundary conditions. We first express the necessary materials and definitions, and then consider our difference scheme and next the integrals in the boundary equations are approximated by the composite trapezoid rule. In the final part, we present an example for checking the numerical results. In this example we obtain the Hausdorff distance between exact solution and approximate solution.
S. M. Sadatrasoul
2014-01-01
Full Text Available We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2, and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.
Improving the performance of water balance equation using fuzzy logic approach
Khazaei, Bahram; Hosseini, Seyed Mahmood
2015-05-01
It is a common practice to conduct the water budget or water balance analysis in a given area within a specified time in order to investigate the balance between the inputs and outputs of the water system. Such an analysis can be used for water management and water allocation in a designated study area. Due to appearance of an error in water balance equation because of difficulty in accurate estimation of its individual components, the main objective of the current paper was to apply a set of fuzzy coefficients to the components of the water balance equation in order to reduce this error. The fuzzy coefficients reflect the uncertainty and imprecision in evaluating each component, and minimize the overall error of the water balance equation. These coefficients are adjusted by an error minimization procedure, based on fuzzy regression concepts and using available recorded data for a given study area within a specified time scale. The adjusted coefficients can effectively estimate the water balance components in the future. In this study, four different models, representing different types of fuzzy coefficients, were considered and used for annual water balance of Azghand catchment in Khorasan Razavi Province, Iran as a case study. Analysis of results showed that all models were effective in reducing water balance error in Azghand catchment. The best model reduced the error up to 79% in terms of mean absolute error compared with error in water balance equation when conventional (with no correction coefficients) water balance analysis was conducted. Moreover, the results indicated that the performance of the proposed fuzzy models was not significantly sensitive to selection of confidence level in data (h) and improved slightly as h increased.
Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition
Malinowski Marek T.
2015-01-01
Full Text Available We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors. The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect to data of the equation is also presented. We consider equations driven by semimartingale Z and equations driven by processes A;M from decomposition of Z, where A is a process of finite variation and M is a local martingale. These equations are not equivalent. Finally, we show that the analysis of the set-valued stochastic integral equations can be extended to a case of fuzzy stochastic integral equations driven by semimartingales under Osgood type condition. To obtain our results we use the set-valued and fuzzy Maruyama type approximations and Bihari’s inequality.
Fault detection thermal storage system by expert system using fuzzy abduction
Yamada, Koichi [Yamatake-Honeywell Co., Ltd, Yokohama (Japan). Advanced Technology Center; Kamimura, Kazuyuki [Yamatake-Honeywell Co., Ltd., Tokyo (Japan). Building Systems Div.
1996-12-31
Fuzzy abduction is a procedure for deriving fuzzy sets of hypotheses which explain a given fuzzy set of events using a set of rules with a truth value. The derived fuzzy sets of hypotheses are called fuzzy explanations. This presentation starts with discussion about diagnosis using conventional expert systems and that using fuzzy relational equations. Then, it proposes a new approach using a fuzzy abduction, and applies the technique to fault detection of a thermal storage system. (orig.)
Situation resolution with context-sensitive fuzzy relations
Jakobson, Gabriel; Buford, John; Lewis, Lundy
2009-05-01
Context plays a significant role in situation resolution by intelligent agents (human or machine) by affecting how the situations are recognized, interpreted, acted upon or predicted. Many definitions and formalisms for the notion of context have emerged in various research fields including psychology, economics and computer science (computational linguistics, data management, control theory, artificial intelligence and others). In this paper we examine the role of context in situation management, particularly how to resolve situations that are described by using fuzzy (inexact) relations among their components. We propose a language for describing context sensitive inexact constraints and an algorithm for interpreting relations using inexact (fuzzy) computations.
Ruofeng Rao; Zhilin Pu; Shouming Zhong; Jialin Huang
2013-01-01
By the way of Lyapunov-Krasovskii functional approach and some variational methods in the Sobolev space ${W}_{0}^{1,p}\\left(Ω\\right)$ , a global asymptotical stability criterion for p-Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinear p-Laplace diffusion item plays its role in the...
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
A Multiagent Transfer Function Neuroapproach to Solve Fuzzy Riccati Differential Equations
Mohammad Shazri Shahrir
2014-01-01
Full Text Available A numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach for neural networks (NN. This proposed new approach provides different degrees of polynomial subspaces for each of the transfer function. This multitude of transfer functions creates unique “agents” in the structure of the NN. Hence it is named as multiagent neuroapproach (multiagent NN. Previous works have shown that results using Runge-Kutta 4th order (RK4 are reliable. The results can be achieved by solving the 1st order nonlinear differential equation (ODE that is found commonly in Riccati differential equation. Multiagent NN shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al. (2013, RK-4, and the existing neuromethod (NM. Numerical examples are discussed to illustrate the proposed method.
Construction project selection with the use of fuzzy preference relation
Ibadov, Nabi
2016-06-01
In the article, author describes the problem of the construction project variant selection during pre-investment phase. As a solution, the algorithm basing on fuzzy preference relation is presented. The article provides an example of the algorithm used for selection of the best variant for construction project. The choice is made basing on criteria such as: net present value (NPV), level of technological difficulty, financing possibilities, and level of organizational difficulty.
Nadernejad, Ehsan; Nikpour, Mohsen
2012-01-01
In this paper, we have proposed two extensions to pixon-based image modeling. The first one is using bicubic interpolation instead of bilinear interpolation and the second one is using fuzzy filtering method, aiming to improve the quality of the pixonal image. Finally, partial differential...... equations (PDEs) are applied on the pixonal image for noise removing. The proposed algorithm has been examined on variety of standard images and their performance compared with the existing algorithms. Experimental results show that in comparison with the other existing methods, the proposed algorithm has...... a better performance in denoising and preserving image edges....
L-Fuzzy集上的L-Fuzzy相容关系%The L-Fuzzy compatible relations on L-Fuzzy set
赵立军
2012-01-01
给出了L-Fuzzy集上的L-Fuzzy相容关系的概念，并给出了L-Fuzzy集上的L-Fuzzy关系是L-Fuzzy相客关系的一个充要条件．%In this paper, the L-Fuzzy compatible relations on L-Fuzzy set are presented,the sufficient and necessary conditions of judging L-Fuzzy compatible relations on L-Fuzzy set are given.
On the Relation Redundancy in Fuzzy Databases
TANG Xiao-hui; CHEN Guo-qing
2006-01-01
This paper concentrates on the problem of data redundancy under the extended-possibility-based model. Based on the information gain in data classification, a measure -relation redundancy - is proposed to evaluate the degree of a given relation being redundant in whole. The properties of relation redundancy are also investigated. This new measure is useful in dealing with data redundancy.
Nguyen, Hung T
2005-01-01
THE CONCEPT OF FUZZINESS Examples Mathematical modeling Some operations on fuzzy sets Fuzziness as uncertainty Exercises SOME ALGEBRA OF FUZZY SETS Boolean algebras and lattices Equivalence relations and partitions Composing mappings Isomorphisms and homomorphisms Alpha-cuts Images of alpha-level sets Exercises FUZZY QUANTITIES Fuzzy quantities Fuzzy numbers Fuzzy intervals Exercises LOGICAL ASPECTS OF FUZZY SETS Classical two-valued logic A three-valued logic Fuzzy logic Fuzzy and Lukasiewi
Monomial geometric programming with an arbitrary fuzzy relational inequality
E. Shivanian
2015-11-01
Full Text Available In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with an arbitrary function. The feasible solution set is determined and compared with some common results in the literature. A necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem. In general a lower bound is always attainable for the optimal objective value by removing the components having no effect on the solution process. By separating problem to non-decreasing and non-increasing function to prove the optimal solution, we simplify operations to accelerate the resolution of the problem.
Evaluation of fuzzy relation method for medical decision support.
Wagholikar, Kavishwar; Mangrulkar, Sanjeev; Deshpande, Ashok; Sundararajan, Vijayraghavan
2012-02-01
The potential of computer based tools to assist physicians in medical decision making, was envisaged five decades ago. Apart from factors like usability, integration with work-flow and natural language processing, lack of decision accuracy of the tools has hindered their utility. Hence, research to develop accurate algorithms for medical decision support tools, is required. Pioneering research in last two decades, has demonstrated the utility of fuzzy set theory for medical domain. Recently, Wagholikar and Deshpande proposed a fuzzy relation based method (FR) for medical diagnosis. In their case studies for heart and infectious diseases, the FR method was found to be better than naive bayes (NB). However, the datasets in their studies were small and included only categorical symptoms. Hence, more evaluative studies are required for drawing general conclusions. In the present paper, we compare the classification performance of FR with NB, for a variety of medical datasets. Our results indicate that the FR method is useful for classification problems in the medical domain, and that FR is marginally better than NB. However, the performance of FR is significantly better for datasets having high proportion of unknown attribute values. Such datasets occur in problems involving linguistic information, where FR can be particularly useful. Our empirical study will benefit medical researchers in the choice of algorithms for decision support tools.
Dynamic properties of fuzzy Petri net model and related analysis
周恺卿; Azlan Mohd Zain; 莫礼平
2015-01-01
Fuzzy Petri net (FPN) has been extensively applied in industrial fields for knowledge-based systems or systems with uncertainty. Although the applications of FPN are known to be successful, the theoretical research of FPN is still at an initial stage. To pave a way for further study, this work explores related dynamic properties of FPN including reachability, boundedness, safeness, liveness and fairness. The whole methodology is divided into two phases. In the first phase, a comparison between elementary net system (EN_system) and FPN is established to prove that the FPN is an extensive formalism of Petri nets using a backwards-compatible extension method. Next, current research results of dynamic properties are utilized to analyze FPN model. The results illustrate that FPN model is bounded, safe, weak live and fair, and can support theoretical evidences for designing related decomposition algorithm.
Ruofeng Rao
2013-01-01
Full Text Available By the way of Lyapunov-Krasovskii functional approach and some variational methods in the Sobolev space W01,p(Ω, a global asymptotical stability criterion for p-Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinear p-Laplace diffusion item plays its role in the new criterion though the nonlinear p-Laplace presents great difficulties. Moreover, numerical examples illustrate that our new stability criterion can judge what the previous criteria cannot do.
Fuzzy Cores and Fuzzy Balancedness
van Gulick, G.; Norde, H.W.
2011-01-01
We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that a
Fuzzy Cores and Fuzzy Balancedness
van Gulick, G.; Norde, H.W.
2011-01-01
We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that
On Conservation Equation Combinations and Closure Relations
William G. Gray
2014-07-01
Full Text Available Fundamental conservation equations for mass, momentum and energy of chemical species can be combined with thermodynamic relations to obtain secondary forms, such as conservation equations for phases, an internal energy balance and a mechanical energy balance. In fact, the forms of secondary equations are infinite and depend on the criteria used in determining which species-based equations to employ and how to combine them. If one uses these secondary forms in developing an entropy inequality to be used in formulating closure relations, care must be employed to ensure that the appropriate equations are used, or problematic results can develop for multispecies systems. We show here that the use of the fundamental forms minimizes the chance of an erroneous formulation in terms of secondary forms and also provides guidance as to which secondary forms should be used if one uses them as a starting point.
AN APPROACH TO GROUP DECISION MAKING BASED ON INTERVAL FUZZY PREFERENCE RELATIONS
Yunliang JIANG
2007-01-01
In this paper,we investigate group decision making problems where the decision information given by decision makers takes the form of interval fuzzy preference relations.We first give an index to measure the similarity degree of two interval fuzzy preference relations,and utilize the similarity index to check the consistency degree of group opinion.Furthermore,we use the error-propagation principle to determine the priority vector of the aggregated matrix,and then develop an approach to group decision making based on interval fuzzy preference relations.Finally,we give an example to illustrate the developed approach.
Equation of State for a Quark Gluon Plasma in the Fuzzy Bag Model
Jacobsen, R. B.; Vasconcellos, C. A. Z.; Bodmann, Bardo E. J.; Dillig, Manfred
2004-12-01
We study two distinct phases of nuclear matter, a baryon-meson phase and a quark-gluon phase (QGP). For the baryon-meson phase we develop an equation of state (EoS) using a quark-meson formulation based on a new version of the fuzzy bag model with scalar-isoscalar, vector-isoscalar and vector-isovector meson-quark couplings and leptonic degrees of freedom as well as the constraints of chemical equilibrium, baryon number and electric charge conservation. For the QGP phase we model an EoS for asymptotically free massless quarks and gluons using the MIT approach and a temperature and baryon chemical potential dependent bag constant, B(T,μ), which allows an isentropic equilibrium phase transition from a QGP to a hadron gas. Our main results indicate the EoS and static global properties of neutron stars and protoneutron stars at low and moderate values of temperature are slightly modified in comparison to the predictions based on the MIT bag model with a constant B.
Kwun, Y C; Hwang, J S; Park, J S; Park, J H [Department of Mathematics, Dong-A University, Pusan 604-714 (Korea, Republic of); Department of Math. Education, Chinju National Universuty of Education, Chinju 660-756 (Korea, Republic of); Division of Math. Sci., Pukyong National University, Pusan 608-737 (Korea, Republic of)], E-mail: jihpark@pknu.ac.kr
2008-02-15
In this paper. we study the controllability for the impulsive semilinear fuzzy integrodifferential control system with nonlocal conditions in E{sub N} by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E{sub N}.
Joint graph cut and relative fuzzy connectedness image segmentation algorithm.
Ciesielski, Krzysztof Chris; Miranda, Paulo A V; Falcão, Alexandre X; Udupa, Jayaram K
2013-12-01
We introduce an image segmentation algorithm, called GC(sum)(max), which combines, in novel manner, the strengths of two popular algorithms: Relative Fuzzy Connectedness (RFC) and (standard) Graph Cut (GC). We show, both theoretically and experimentally, that GC(sum)(max) preserves robustness of RFC with respect to the seed choice (thus, avoiding "shrinking problem" of GC), while keeping GC's stronger control over the problem of "leaking though poorly defined boundary segments." The analysis of GC(sum)(max) is greatly facilitated by our recent theoretical results that RFC can be described within the framework of Generalized GC (GGC) segmentation algorithms. In our implementation of GC(sum)(max) we use, as a subroutine, a version of RFC algorithm (based on Image Forest Transform) that runs (provably) in linear time with respect to the image size. This results in GC(sum)(max) running in a time close to linear. Experimental comparison of GC(sum)(max) to GC, an iterative version of RFC (IRFC), and power watershed (PW), based on a variety medical and non-medical images, indicates superior accuracy performance of GC(sum)(max) over these other methods, resulting in a rank ordering of GC(sum)(max)>PW∼IRFC>GC.
Yamada, K. [Nagaoka Technical Coll., Niigata (Japan)] Mukaidono, M. [Meiji Univ., Tokyo (Japan)
1998-09-30
Abduction is a procedure to derive a set of hypotheses which explains a set of observed events under given knowledge. The obtained set of hypotheses is called explanation. Previously, the authors proposed fuzzy abduction that was an extension of the abduction with the fuzzy theory and showed the way to derive fuzzy explanation. In this theory, observed events and hypotheses are expressed and the given knowledge is expressed by a set of implications with a truth value between zero and one. However, there is no guarantee that fuzzy explanations always exist. This paper clarifies the necessary and sufficient conditions of the existence of fuzzy explanations and proposes a method to obtain approximate solutions when fuzzy explanations do not exist. Fuzzy abduction is a procedure similar to the inverse operation of fuzzy relational equations, however, the proposed method does not require iterative calculation whose number of times cannot be obtain beforehand. 10 refs., 1 fig.
An Analysis of Technology Acceptance in Turkey using Fuzzy Logic and Structural Equation Modelling
Bilgin Şenel
2011-12-01
Full Text Available Technology is in a constant progress in the way of satisfying increasing human needs. This fact will hold true for the years to come. However, the level of adaptation to technological advancements varies greatly across countries. The pace of adjustment is directly proportional to the importance attached to and the funds allocated for this purpose. Despite the abundance of technological investments in Turkey in recent years, there are only a few studies analyzing the current level of individual interest in technology. This study therefore aims to determine the technology acceptance of Turkish people by using the Technology Acceptance Model (TAM developed by Davis (1989 and to demonstrate the reasons to accept or not accept technology departing from the links between dimensions. While accomplishing this aim, Structural Equation Model (SEM that is a highly strong multivariable analysis technique that makes possible the evaluation of latent structures like psychosocial needs, and the Fuzzy Logic Theorem that provides strong and significant instruments for the measurement of ambiguities and provides the opportunity to meaningfully represent ambiguous concepts expressed in the natural language were used. According to the findings of this study, it was determined that the perceived ease of use is more influential in people’s acceptance of technology than the perceived usefulness is. It was also found that technology acceptance does not differ significantly at the statistical significance level of 0.05 with respect to the participants’ demographic characteristics (age, gender, education level, hometown etc.. In addition, analyses performed to define the relationships between the dimensions of the TAM yielded results that highly supported the TAM. In other words, the dimensions affect technology acceptance to positive and significant degrees
Huang, Wei; Oh, Sung-Kwun; Pedrycz, Witold
2017-08-11
This paper presents a hybrid fuzzy wavelet neural network (HFWNN) realized with the aid of polynomial neural networks (PNNs) and fuzzy inference-based wavelet neurons (FIWNs). Two types of FIWNs including fuzzy set inference-based wavelet neurons (FSIWNs) and fuzzy relation inference-based wavelet neurons (FRIWNs) are proposed. In particular, a FIWN without any fuzzy set component (viz., a premise part of fuzzy rule) becomes a wavelet neuron (WN). To alleviate the limitations of the conventional wavelet neural networks or fuzzy wavelet neural networks whose parameters are determined based on a purely random basis, the parameters of wavelet functions standing in FIWNs or WNs are initialized by using the C-Means clustering method. The overall architecture of the HFWNN is similar to the one of the typical PNNs. The main strategies in the design of HFWNN are developed as follows. First, the first layer of the network consists of FIWNs (e.g., FSIWN or FRIWN) that are used to reflect the uncertainty of data, while the second and higher layers consist of WNs, which exhibit a high level of flexibility and realize a linear combination of wavelet functions. Second, the parameters used in the design of the HFWNN are adjusted through genetic optimization. To evaluate the performance of the proposed HFWNN, several publicly available data are considered. Furthermore a thorough comparative analysis is covered.
Reza Ezzati
2013-02-01
Full Text Available In this paper, we prove a general form of a fixed point theorem with contractive-like mapping defined by altering function. We also present its application on study of existence and uniqueness of solution of fuzzy initial value problems in fuzzy partial metric spaces. In order to do this, we recall some fixed point theorems in partial metric spaces either crisp or fuzzy and use these theorems to prove ours.
Reza Ezzati; Maryam Bagherian
2013-01-01
In this paper, we prove a general form of a fixed point theorem with contractive-like mapping defined by altering function. We also present its application on study of existence and uniqueness of solution of fuzzy initial value problems in fuzzy partial metric spaces. In order to do this, we recall some fixed point theorems in partial metric spaces either crisp or fuzzy and use these theorems to prove ours.
Exploring the use of fuzzy logic models to describe the relation between SBP and RR values.
Gouveia, Sónia; Brás, Susana
2012-01-01
In this work, fuzzy logic based models are used to describe the relation between systolic blood pressure (SBP) and tachogram (RR) values as a function of the SBP level. The applicability of these methods is tested using real data in Lying (L) and Standing (S) conditions and generated surrogate data. The results indicate that fuzzy models exhibit a similar performance in both conditions, and their performance is significantly higher with real data than with surrogate data. These results point out the potential of a fuzzy logic approach to model properly the relation between SBP and RR values. As a future work, it remains to assess the clinical impact of these findings and inherent repercussion on the estimation of time domain baroreflex sensitivity indices.
New Results in Fuzzy Clustering Based on the Concept of Indistinguishability Relation
1984-01-01
NEW RESULTS IN Fuzzy CLUSTERING BASED ON THE CONCEPT OF INDISTINGUISHABILITY RELATION KEYWORDS R . Lopez de Mantaras Facultat d ’Informatica...Universitat Politecnica de Barcelona Dulcet, 12. Barcelona-34. Spain. L. Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de... r -cluster that extend Ruspini’s definition (Ruspini, 1982). Our definition is based on the new concept of indis- tinguishability relation (Trillas
Partial Differential Equations in General Relativity
Choquet-Bruhat, Yvonne
2008-09-07
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
Expert system training and control based on the fuzzy relation matrix
Ren, Jie; Sheridan, T. B.
1991-01-01
Fuzzy knowledge, that for which the terms of reference are not crisp but overlapped, seems to characterize human expertise. This can be shown from the fact that an experienced human operator can control some complex plants better than a computer can. Proposed here is fuzzy theory to build a fuzzy expert relation matrix (FERM) from given rules or/and examples, either in linguistic terms or in numerical values to mimic human processes of perception and decision making. The knowledge base is codified in terms of many implicit fuzzy rules. Fuzzy knowledge thus codified may also be compared with explicit rules specified by a human expert. It can also provide a basis for modeling the human operator and allow comparison of what a human operator says to what he does in practice. Two experiments were performed. In the first, control of liquid in a tank, demonstrates how the FERM knowledge base is elicited and trained. The other shows how to use a FERM, build up from linguistic rules, and to control an inverted pendulum without a dynamic model.
Sankar Prasad Mondal
2016-01-01
Full Text Available The numerical algorithm for solving “first-order linear differential equation in fuzzy environment” is discussed. A scheme, namely, “Runge-Kutta-Fehlberg method,” is described in detail for solving the said differential equation. The numerical solutions are compared with (i-gH and (ii-gH differential (exact solutions concepts system. The method is also followed by complete error analysis. The method is illustrated by solving an example and an application.
On generalized fuzzy strongly semiclosed sets in fuzzy topological spaces
Oya Bedre Ozbakir
2002-01-01
semiclosed, generalized fuzzy almost-strongly semiclosed, generalized fuzzy strongly closed, and generalized fuzzy almost-strongly closed sets. In the light of these definitions, we also define some generalizations of fuzzy continuous functions and discuss the relations between these new classes of functions and other fuzzy continuous functions.
Developments in functional equations and related topics
Ciepliński, Krzysztof; Rassias, Themistocles
2017-01-01
This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.
Special functions in Fuzzy Analysis
Angel Garrido
2006-01-01
Full Text Available In the treatment of Fuzzy Logic an useful tool appears: the membership function, with the information about the degree of completion of a condition which defines the respective Fuzzy Set or Fuzzy Relation. With their introduction, it is possible to prove some results on the foundations of Fuzzy Logic and open new ways in Fuzzy Analysis.
Fuzzy Sets and Mathematical Education.
Alsina, C.; Trillas, E.
1991-01-01
Presents the concept of "Fuzzy Sets" and gives some ideas for its potential interest in mathematics education. Defines what a Fuzzy Set is, describes why we need to teach fuzziness, gives some examples of fuzzy questions, and offers some examples of activities related to fuzzy sets. (MDH)
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.
Wuyong Qian
2016-09-01
Full Text Available Although medical waste usually accounts for a small fraction of urban municipal waste, its proper disposal has been a challenging issue as it often contains infectious, radioactive, or hazardous waste. This article proposes a two-level hierarchical multicriteria decision model to address medical waste disposal method selection (MWDMS, where disposal methods are assessed against different criteria as intuitionistic fuzzy preference relations and criteria weights are furnished as real values. This paper first introduces new operations for a special class of intuitionistic fuzzy values, whose membership and non-membership information is cross ratio based ]0, 1[-values. New score and accuracy functions are defined in order to develop a comparison approach for ]0, 1[-valued intuitionistic fuzzy numbers. A weighted geometric operator is then put forward to aggregate a collection of ]0, 1[-valued intuitionistic fuzzy values. Similar to Saaty’s 1–9 scale, this paper proposes a cross-ratio-based bipolar 0.1–0.9 scale to characterize pairwise comparison results. Subsequently, a two-level hierarchical structure is formulated to handle multicriteria decision problems with intuitionistic preference relations. Finally, the proposed decision framework is applied to MWDMS to illustrate its feasibility and effectiveness.
Qian, Wuyong; Wang, Zhou-Jing; Li, Kevin W
2016-09-09
Although medical waste usually accounts for a small fraction of urban municipal waste, its proper disposal has been a challenging issue as it often contains infectious, radioactive, or hazardous waste. This article proposes a two-level hierarchical multicriteria decision model to address medical waste disposal method selection (MWDMS), where disposal methods are assessed against different criteria as intuitionistic fuzzy preference relations and criteria weights are furnished as real values. This paper first introduces new operations for a special class of intuitionistic fuzzy values, whose membership and non-membership information is cross ratio based ]0, 1[-values. New score and accuracy functions are defined in order to develop a comparison approach for ]0, 1[-valued intuitionistic fuzzy numbers. A weighted geometric operator is then put forward to aggregate a collection of ]0, 1[-valued intuitionistic fuzzy values. Similar to Saaty's 1-9 scale, this paper proposes a cross-ratio-based bipolar 0.1-0.9 scale to characterize pairwise comparison results. Subsequently, a two-level hierarchical structure is formulated to handle multicriteria decision problems with intuitionistic preference relations. Finally, the proposed decision framework is applied to MWDMS to illustrate its feasibility and effectiveness.
Kinetic Boltzmann, Vlasov and Related Equations
Sinitsyn, Alexander; Vedenyapin, Victor
2011-01-01
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in
Fuzzy Dot Structure of BG-algebras
Tapan Senapati
2014-09-01
Full Text Available In this paper, the notions of fuzzy dot subalgebras is introduced together with fuzzy normal dot subalgebras and fuzzy dot ideals of BG-algebras. The homomorphic image and inverse image are investigated in fuzzy dot subalgebras and fuzzy dot ideals of BG-algebras. Also, the notion of fuzzy relations on the family of fuzzy dot subalgebras and fuzzy dot ideals of BG-algebras are introduced with some related properties.
广义模糊熵与包含度的相互诱导关系%General Fuzzy Entropy and Inclusion Measure with Their Mutual Induced Relations
张旭慧; 辛小龙
2011-01-01
模糊熵是度量模糊集的非常重要的指标,而广义模糊熵是模糊熵在广义模糊补意义下的推广.本文首先介绍了模糊集的广义模糊熵和包含度的定义,重点研究了包含度的性质,给出了广义模糊熵与包含度之间的相互诱导关系.%Fuzzy entropy is a basic concept in fuzzy set theory. General fuzzy entropy is a generalization of fuzzy entropy under general fuzzy complement. The axiomatization definition of general fuzzy entropy and inclusion measure are given in this paper. We discuss some relative properties of inclusion measure. Moreover we study the mutual induced relations between general fuzzy entropy and inclusion measure of fuzzy sets.
Lossless Join Decomposition for Extended Possibility-Based Fuzzy Relational Databases
Liu, Julie Yu-Chih
2014-01-01
.... However, the problem of achieving lossless join decomposition occurs when employing the fuzzy functional dependencies to database normalization in an extended possibility-based fuzzy data models...
Transformations of Heun's equation and its integral relations
El-Jaick, Léa Jaccoud
2010-01-01
For each variable transformation which preserves the form of Heun's equation we find a transformation which leaves invariant the form of the equation for the kernels of integral relations among solutions of the former equation. This enables us to generate new kernels for the Heun equation, given by single hypergeometric functions (Lambe-Ward-type kernels) and by products of two hypergeometric functions (Erd\\'elyi-type). Such kernels, by a limiting process, afford new kernels for the confluent Heun equation as well.
Structural Holes in Directed Fuzzy Social Networks
Renjie Hu; Guangyu Zhang
2014-01-01
The structural holes have been a key issue in fuzzy social network analysis. For undirected fuzzy social networks where edges are just present or absent undirected fuzzy relation and have no more information attached, many structural holes measures have been presented, such as key fuzzy structural holes, general fuzzy structural holes, strong fuzzy structural holes, and weak fuzzy structural holes. There has been a growing need to design structural holes measures for directed fuzzy social net...
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.
Convergence acceleration algorithm via an equation related to the lattice Boussinesq equation
He, Yi; Sun, Jian-Qing; Weniger, Ernst Joachim
2011-01-01
The molecule solution of an equation related to the lattice Boussinesq equation is derived with the help of determinantal identities. It is shown that this equation can for certain sequences be used as a numerical convergence acceleration algorithm. Numerical examples with applications of this algorithm are presented.
Kurzynski, Marek; Wolczowski, Andrzej
2009-01-01
The paper presents a concept of bio-prosthesis control via recognition of user intent on the basis of myopotentials acquired of his body. We assume that in the control process each prosthesis operation consists of specific sequence of elementary actions. The contextual (sequential) recognition is considered in which the fuzzy relation approach is applied to the construction of a classifying algorithm. Experimental investigations of the proposed algorithm for real data are performed and results are discussed.
Generation of fuzzy mathematical morphologies
2001-01-01
Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implic...
Mezey, Paul G
2014-09-16
Conspectus Just as complete molecules have no boundaries and have "fuzzy" electron density clouds approaching zero density exponentially at large distances from the nearest nucleus, a physically justified choice for electron density fragments exhibits similar behavior. Whereas fuzzy electron densities, just as any fuzzy object, such as a thicker cloud on a foggy day, do not lend themselves to easy visualization, one may partially overcome this by using isocontours. Whereas a faithful representation of the complete fuzzy density would need infinitely many such isocontours, nevertheless, by choosing a selected few, one can still obtain a limited pictorial representation. Clearly, such images are of limited value, and one better relies on more complete mathematical representations, using, for example, density matrices of fuzzy fragment densities. A fuzzy density fragmentation can be obtained in an exactly additive way, using the output from any of the common quantum chemical computational techniques, such as Hartree-Fock, MP2, and various density functional approaches. Such "fuzzy" electron density fragments properly represented have proven to be useful in a rather wide range of applications, for example, (a) using them as additive building blocks leading to efficient linear scaling macromolecular quantum chemistry computational techniques, (b) the study of quantum chemical functional groups, (c) using approximate fuzzy fragment information as allowed by the holographic electron density theorem, (d) the study of correlations between local shape and activity, including through-bond and through-space components of interactions between parts of molecules and relations between local molecular shape and substituent effects, (e) using them as tools of density matrix extrapolation in conformational changes, (f) physically valid averaging and statistical distribution of several local electron densities of common stoichiometry, useful in electron density databank mining, for
Stochastic partial differential equations in turbulence related problems
Chow, P.-L.
1978-01-01
The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.
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...
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...
K.SAROJINI,
2010-06-01
Full Text Available Feature subset selection is an essential task in data mining. This paper presents a new method for dealing with supervised feature subset selection based on Modified Fuzzy Relative Information Measure (MFRIM. First, Discretization algorithm is applied to discretize numeric features to construct the membership functions of each fuzzy sets of a feature. Then the proposed MFRIM is applied to select the feature subset focusing on boundary samples. The proposed method can select feature subset with minimum number of features, which are relevant to get higher average classification accuracy for datasets. The experimental results with UCI datasets show that the proposed algorithm is effective and efficient in selecting subset with minimum number of features getting higher average classification accuracy than the consistency based feature subset selection method.
On Fourier series of fuzzy-valued functions.
Kadak, Uğur; Başar, Feyzi
2014-01-01
Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We derive uniform convergence of a fuzzy-valued function sequences and series with level sets. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, Fourier series of periodic fuzzy-valued functions is defined and its complex form is given via sine and cosine fuzzy coefficients with an illustrative example. Finally, by using the Dirichlet kernel and its properties, we especially examine the convergence of Fourier series of fuzzy-valued functions at each point of discontinuity, where one-sided limits exist.
Hossien Pourghassem
2011-04-01
Full Text Available Relevance feedback approaches is used to improve the performance of content-based image retrieval systems. In this paper, a novel relevance feedback approach based on similarity measure modification in an X-ray image retrieval system based on fuzzy representation using fuzzy attributed relational graph (FARG is presented. In this approach, optimum weight of each feature in feature vector is calculated using similarity rate between query image and relevant and irrelevant images in user feedback. The calculated weight is used to tune fuzzy graph matching algorithm as a modifier parameter in similarity measure. The standard deviation of the retrieved image features is applied to calculate the optimum weight. The proposed image retrieval system uses a FARG for representation of images, a fuzzy matching graph algorithm as similarity measure and a semantic classifier based on merging scheme for determination of the search space in image database. To evaluate relevance feedback approach in the proposed system, a standard X-ray image database consisting of 10000 images in 57 classes is used. The improvement of the evaluation parameters shows proficiency and efficiency of the proposed system.
Anirut Pipatprapa
2016-03-01
Full Text Available Currently, the environment and sustainability are important topics for every industry. The food industry is particularly complicated in this regard because of the dynamic and complex character of food products and their production. This study uses structural equation modeling (SEM and a fuzzy analytic hierarchy process (FAHP to investigate which factors are suitable for evaluating the environmental performance of Thailand’s food industry. A first-stage questionnaire survey was conducted with 178 managers in the food industry that obtained a certificate from the Department of Industrial Work of Thailand to synthesize the performance measurement model and the significance of the relationship between the indicators. A second-stage questionnaire measured 18 experts’ priorities regarding the criteria and sub-factors involved in the different aspects and assessment items regarding environmental performance. SEM showed that quality management, market orientation, and innovation capability have a significantly positive effect on environmental performance. The FAHP showed that the experts were most concerned about quality management, followed by market orientation and innovation capability; the assessment items for quality policy, quality assurance, and customer orientation were of the most concern. The findings of this study can be referenced and support managerial decision making when monitoring environmental performance.
无
2007-01-01
Considering the disadvantages of selecting evaluation index of supplier based on old purchase relation and in view of transformation of relation between manufacture and supplier under the dynamic, cooperative, competitive and quickly response environment, research on supplier selection evaluation was presented based on enterprise capability, cooperation degree and service level from the perspective of cooperative partnership and coordination, and the evaluation index system was established. A more objective and veracious supplier selection and evaluation method based on fuzzy analysis hierarchy process and grey relational analysis was developed, and then empirical research on electric equipment manufacturer was explored to analyze the supplier selection and evaluation.
Matter Equation of State in General Relativity
Kim, Hyeong-Chan
2016-01-01
We study how a strong gravity affects the equation of state of matters. For this purpose, we employ a canonical ensemble of classical monoatomic ideal gas inside a box in a Rindler spacetime. The total energy decreases monotonically with the increase of the external gravity representing its attractiveness. It is however bounded below, which is different from that of the Newtonian gravity case. As for the entropy, it decreases with the external gravity in the Newtonian regime. However, in the presence of strong gravity or ultra-relativistic high temperature, the entropy increases with the gravity. This result can be a resolution of the negative entropy problem of the ideal gas in the Newtonian gravity. In the presence of strong gravity, the bottom of the box is very close to the event horizon of the Rindler spacetime mimiking a blackhole and the gas behaves as if it is on an effective two dimensional surface located at the bottom of the box. Investigating the equation of state in the strong gravity regime, the...
Symmetries and (Related Recursion Operators of Linear Evolution Equations
Giampaolo Cicogna
2010-02-01
Full Text Available Significant cases of time-evolution equations, the linear Schr¨odinger and the Fokker–Planck equation are considered. It is known that equations of this type can be transformed, in some cases, into a highly simplified form. The properties of these equations in their initial and their simplified form are compared, showing in particular that this transformation partially prevents a clear understanding and a full application of the (physically relevant notion of the so-called step up/down operators. These operators are shown to be recursion operators, related to the Lie point symmetries of the equations, which are also carefully discussed.
王中兴; 唐芝兰; 邵翠丽
2012-01-01
The concept of relative superiority of interval numbers was extended to intuitionistic fuzzy numbers. The fuzzy complementary judgment matrix was given, and then a ranking method of intuitionistic fuzzy numbers was presented.based on the relative superiority matrix for the binary comparison of intuitionistic fuzzy numbers. In the following stage, this method was applied to multi-attribute fuzzy decision-making with intuitionistic fuzzy numbers, and a multi-criteria fuzzy decision-making method with intuitionistic fuzzy sets was given based on relative superiority.%把区间数的相对优势度概念推广到直觉模糊数,再根据直觉模糊数两两比较的相对优势度构建模糊互补判断矩阵,提出一种直觉模糊数的排序方法,并将此排序方法应用到直觉模糊多属性决策中,得到一种基于相对优势度的直觉模糊数多属性决策方法.
General relativity and the Einstein equations
Choquet-Bruhat, Yvonne
2009-01-01
Aimed at researchers in mathematics and physics, this monograph, in which the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field. - ;General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been. proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the. field....
Generalized de Broglie Relations for Dirac Equations in Curved Spacetimes
Arminjon, Mayeul
2011-01-01
One may ask whether the special relativistic relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We do this by applying Whitham's Lagrangian method to derive covariant equations describing wave packet motion which preserve the symmetries of the Dirac Lagrangian, and in particular, conserve the probability current. We show that generalized de Broglie relations emerge from the Whitham equations after transforming each Dirac equation into a canonical form via a local similarity transformation of the type first introduced by Pauli. This gives the de Broglie relations a universal character for spin-half particles in a curved spacetime. We show that COW and Sagnac type terms also appear in the Whitham equations. We further discuss the classical-quantum correspondence in a curved spa...
Contra continuity and almost contra continuity in generalized fuzzy topological spaces
Bhattacharya, Baby; Chakraborty, Jayasree
2015-05-01
In this paper we introduce fuzzy contra continuity and almost contra continuity in generalized fuzzy topological space. Fuzzy almost contra continuity is weaker than fuzzy contra continuity in generalized fuzzy topological space. Then we investigate their characterizations and properties. We also established some equivalent relation on fuzzy contra continuity and fuzzy almost contra continuity in generalized fuzzy topological spaces.
GÜNER, Erdal
2007-01-01
Abstract. In this paper, .rstly some fundamental concepts are included re- lating to fuzzy topological spaces. Secondly, the fuzzy connected set is intro- duced. Finally, de.ning fuzzy contractible space, it is shown that X is a fuzzy contractible space if and only if X is fuzzy homotopic equivalent with a fuzzy single-point space.
Tong, Yubing; Udupa, Jayaram K.; Odhner, Dewey; Wu, Caiyun; Zhao, Yue; McDonough, Joseph M.; Capraro, Anthony; Torigian, Drew A.; Campbell, Robert M.
2017-03-01
Lung delineation via dynamic 4D thoracic magnetic resonance imaging (MRI) is necessary for quantitative image analysis for studying pediatric respiratory diseases such as thoracic insufficiency syndrome (TIS). This task is very challenging because of the often-extreme malformations of the thorax in TIS, lack of signal from bone and connective tissues resulting in inadequate image quality, abnormal thoracic dynamics, and the inability of the patients to cooperate with the protocol needed to get good quality images. We propose an interactive fuzzy connectedness approach as a potential practical solution to this difficult problem. Manual segmentation is too labor intensive especially due to the 4D nature of the data and can lead to low repeatability of the segmentation results. Registration-based approaches are somewhat inefficient and may produce inaccurate results due to accumulated registration errors and inadequate boundary information. The proposed approach works in a manner resembling the Iterative Livewire tool but uses iterative relative fuzzy connectedness (IRFC) as the delineation engine. Seeds needed by IRFC are set manually and are propagated from slice-to-slice, decreasing the needed human labor, and then a fuzzy connectedness map is automatically calculated almost instantaneously. If the segmentation is acceptable, the user selects "next" slice. Otherwise, the seeds are refined and the process continues. Although human interaction is needed, an advantage of the method is the high level of efficient user-control on the process and non-necessity to refine the results. Dynamic MRI sequences from 5 pediatric TIS patients involving 39 3D spatial volumes are used to evaluate the proposed approach. The method is compared to two other IRFC strategies with a higher level of automation. The proposed method yields an overall true positive and false positive volume fraction of 0.91 and 0.03, respectively, and Hausdorff boundary distance of 2 mm.
Wenbo Sun
2016-06-01
Full Text Available Aging alters muscular coordination patterns. This study aimed to investigate aging-related changes in the coordination of agonist and antagonist muscles from two aspects, the activities of individual muscles and the inter-muscular coupling. Eighteen young subjects and 10 elderly subjects were recruited to modulate the agonist muscle activity to track a target during voluntary isometric elbow flexion and extension. Normalized muscle activation and fuzzy entropy (FuzzyEn were applied to depict the activities of biceps and triceps. Mutual information (MI was utilized to measure the inter-muscular coupling between biceps and triceps. The agonist activation decreased and the antagonist activation increased significantly during elbow flexion and extension with aging. FuzzyEn values of agonist electromyogram (EMG were similar between the two age groups. FuzzyEn values of antagonist EMG increased significantly with aging during elbow extension. MI decreased significantly with aging during elbow extension. These results indicated increased antagonist co-activation and decreased inter-muscular coupling with aging during elbow extension, which might result from the reduced reciprocal inhibition and the recruitment of additional cortical-spinal pathways connected to biceps. Based on FuzzyEn and MI, this study provided a comprehensive understanding of the mechanisms underlying the aging-related changes in the coordination of agonist and antagonist muscles.
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...
BOOK REVIEW: Partial Differential Equations in General Relativity
Halburd, Rodney G.
2008-11-01
Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed
Time-dependent closure relations for relativistic collisionless fluid equations.
Bendib-Kalache, K; Bendib, A; El Hadj, K Mohammed
2010-11-01
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space (ω,k), where ω and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter ω/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc²/T , where m is the particle rest mass and T, the plasma temperature in energy units.
Seed robustness of oriented relative fuzzy connectedness: core computation and its applications
Tavares, Anderson C. M.; Bejar, Hans H. C.; Miranda, Paulo A. V.
2017-02-01
In this work, we present a formal definition and an efficient algorithm to compute the cores of Oriented Relative Fuzzy Connectedness (ORFC), a recent seed-based segmentation technique. The core is a region where the seed can be moved without altering the segmentation, an important aspect for robust techniques and reduction of user effort. We show how ORFC cores can be used to build a powerful hybrid image segmentation approach. We also provide some new theoretical relations between ORFC and Oriented Image Foresting Transform (OIFT), as well as their cores. Experimental results among several methods show that the hybrid approach conserves high accuracy, avoids the shrinking problem and provides robustness to seed placement inside the desired object due to the cores properties.
The Fuzzy Grey Relational Analysis of the Factors Influencing Farm Produce Logistics
Yan; LI; Hongmei; SHAN
2014-01-01
The farm produce logistics plays an important role in promoting the agricultural production and prosperity of the rural economy,so grasping the main factors influencing the development of farm produce logistics,is of important significance to accelerating the development of farm produce logistics. The values of identification coefficient in the grey relational analysis are taken based on the experience,so the accuracy of the results is affected. This article uses the improved fuzzy grey relational analysis to analyze the main factors influencing farm produce logistics. The results show that the number of storage companies has a great impact on the development of farm produce logistics,followed by the farm produce processing machinery capacity,rural transport infrastructure,farm produce market conditions and government financial support for agriculture,while the total number of Internet users in rural areas has an limited impact on the development of farm produce logistics.
A Consistent Fuzzy Preference Relations Based ANP Model for R&D Project Selection
Chia-Hua Cheng
2017-08-01
Full Text Available In today’s rapidly changing economy, technology companies have to make decisions on research and development (R&D projects investment on a routine bases with such decisions having a direct impact on that company’s profitability, sustainability and future growth. Companies seeking profitable opportunities for investment and project selection must consider many factors such as resource limitations and differences in assessment, with consideration of both qualitative and quantitative criteria. Often, differences in perception by the various stakeholders hinder the attainment of a consensus of opinion and coordination efforts. Thus, in this study, a hybrid model is developed for the consideration of the complex criteria taking into account the different opinions of the various stakeholders who often come from different departments within the company and have different opinions about which direction to take. The decision-making trial and evaluation laboratory (DEMATEL approach is used to convert the cause and effect relations representing the criteria into a visual network structure. A consistent fuzzy preference relations based analytic network process (CFPR-ANP method is developed to calculate the preference-weights of the criteria based on the derived network structure. The CFPR-ANP is an improvement over the original analytic network process (ANP method in that it reduces the problem of inconsistency as well as the number of pairwise comparisons. The combined complex proportional assessment (COPRAS-G method is applied with fuzzy grey relations to resolve conflicts arising from differences in information and opinions provided by the different stakeholders about the selection of the most suitable R&D projects. This novel combination approach is then used to assist an international brand-name company to prioritize projects and make project decisions that will maximize returns and ensure sustainability for the company.
Classical-Quantum Correspondence and Functional Relations for Painleve Equations
Zabrodin, A
2012-01-01
In the light of the Quantum Painleve-Calogero Correspondence established in our previous papers [1,2], we investigate the inverse problem. We imply that this type of the correspondence (Classical-Quantum Correspondence) holds true and find out what kind of potentials arise from the compatibility conditions of the related linear problems. The latter conditions are written as functional equations for the potentials depending on a choice of a single function - the left-upper element of the Lax connection. The conditions of the Correspondence impose restrictions on this function. In particular, it satisfies the heat equation. It is shown that all natural choices of this function (rational, hyperbolic and elliptic) reproduce exactly the Painleve list of equations. In this sense the Classical-Quantum Correspondence can be regarded as an alternative definition of the Painleve equations.
Fuzzy dot ideals and fuzzy dot H-ideals of BCH-algebras
PENG Jia-yin
2008-01-01
The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are intro duced,several appropriate examples are provided,and their some properties are investigated.The relations among fuzzy ideal,fuzzy H-ideal,fuzzy dot ideal and fuzzy dot H-ideals in BCH algebras are discussed,several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals (fuzzy dot H-ideals) are studied. The relations between a fuzzy dot ideal (fuzzy dot H-ideal) in BCH-algebras and a fuzzy dot ideal (fuzzy dot H-ideal) in the product algebra of BCH-algebras are given.
A Fuzzy Preference Relation Based Method for Face Recognition by Gabor Filters
Soumak Biswas
2012-06-01
Full Text Available In this paper we have applied Gabor filter for fiducial point localization. After obtaining the fiducial points the number of fiducial points are reduced using a distance formula. The distance of each of this fiducial point is then calculated by the distance formula and stored in the database of the system. The same methodology is also applied on the input face which is to be matched with the faces available in the database. Then a fuzzy preference relation matrix is obtained . the largest eigen value of this matrix is then determined by algebraic method or numerical method depending on the order of the matrix. To apply the numerical method which is more easier for large order matrices we have used the C programming of this method . Once the largest eigen value is determined the corresponding priority vector can easily be obtained from which we can easily match the input face with the database.
Fast interactive segmentation algorithm of image sequences based on relative fuzzy connectedness
Tian Chunna; Gao Xinbo
2005-01-01
A fast interactive segmentation algorithm of image-sequences based on relative fuzzy connectedness is presented. In comparison with the original algorithm, the proposed one, with the same accuracy, accelerates the segmentation speed by three times for single image. Meanwhile, this fast segmentation algorithm is extended from single object to multiple objects and from single-image to image-sequences. Thus the segmentation of multiple objects from complex background and batch segmentation of image-sequences can be achieved. In addition, a post-processing scheme is incorporated in this algorithm, which extracts smooth edge with one-pixel-width for each segmented object. The experimental results illustrate that the proposed algorithm can obtain the object regions of interest from medical image or image-sequences as well as man-made images quickly and reliably with only a little interaction.
Differential Forms and Wave Equations for General Relativity
Lau, S R
1996-01-01
Recently, Choquet-Bruhat and York and Abrahams, Anderson, Choquet-Bruhat, and York (AACY) have cast the 3+1 evolution equations of general relativity in gauge-covariant and causal ``first-order symmetric hyperbolic form,'' thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation which governs the light-speed propagation of the extrinsic curvature tensor. Along a similar line, we construct a related wave equation which, as the key equation in a system, describes vacuum general relativity. Whereas the approach of AACY is based on tensor-index methods, the present formulation is written solely in the language of differential forms. Our approach starts with Sparling's tetrad-dependent differential forms, and our wave equation governs the propagation of Sparling's 2-form, which in the ``time-gauge'' is built linearly from the ``extrinsic curvature 1-form.'' The tensor-index version of our wave e...
Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists
Kandasamy, W B Vasantha; Amal, K
2008-01-01
This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational Maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. The authors introduce 13 multi-expert models using the notion of fuzzy supermatrices. These models are described with illustrative examples. This book has three chapters. In the first chaper, the basic concepts about super matrices and fuzzy super matrices are recalled. Chapter two introduces the notion of fuzzy super matrices adn their properties. The final chapter introduces many super fuzzy multi expert models.
Metrics on Noncompact Fuzzy Number Space (E^)n
冯玉瑚
2004-01-01
The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy random variables and fuzzy stochastic processes etc.. But, a large part of this theory heavily depends on the condition that fuzzy number has to have compact support set and so fails to analyze and apply noncompact fuzzy numbers. The purpose of this paper is to introduce three classes of metrics on noncompact fuzzy number space and to discuss their basic properties, completeness and separability in detail.
NHL and RCGA Based Multi-Relational Fuzzy Cognitive Map Modeling for Complex Systems
Zhen Peng
2015-11-01
Full Text Available In order to model multi-dimensions and multi-granularities oriented complex systems, this paper firstly proposes a kind of multi-relational Fuzzy Cognitive Map (FCM to simulate the multi-relational system and its auto construct algorithm integrating Nonlinear Hebbian Learning (NHL and Real Code Genetic Algorithm (RCGA. The multi-relational FCM fits to model the complex system with multi-dimensions and multi-granularities. The auto construct algorithm can learn the multi-relational FCM from multi-relational data resources to eliminate human intervention. The Multi-Relational Data Mining (MRDM algorithm integrates multi-instance oriented NHL and RCGA of FCM. NHL is extended to mine the causal relationships between coarse-granularity concept and its fined-granularity concepts driven by multi-instances in the multi-relational system. RCGA is used to establish high-quality high-level FCM driven by data. The multi-relational FCM and the integrating algorithm have been applied in complex system of Mutagenesis. The experiment demonstrates not only that they get better classification accuracy, but it also shows the causal relationships among the concepts of the system.
Oscillatory Universe, dark energy equation of state and general relativity
Ghosh, Partha Pratim; Usmani, A A; Mukhopadhyay, Utpal
2012-01-01
The concept of oscillatory Universe appears to be realistic and buried in the dynamic dark energy equation of state. We explore its evolutionary history under the frame work of general relativity. We observe that oscillations do not go unnoticed with such an equation of state and that their effects persist later on in cosmic evolution. The `classical' general relativity seems to retain the past history of oscillatory Universe in the form of increasing scale factor as the classical thermodynamics retains this history in the form of increasing cosmological entropy.
Mahdi Karbasian1
2012-02-01
Full Text Available In today’s organizations, performance measurement comes more to the foreground with the advancement in the high technology. Supplier selection is an important issue in supply chain management. In recent years, determining the best supplier in the supply chain has become a key strategic consideration. However, these decisions usually involve several objectives or criteria, and it is often necessary to compromise among possibly conflicting factors. Thus, the multiple criteria decision making (MCDM becomes a useful approach to solve this kind of problem. In order to use the conceptual framework for measuring performance supplier, a methodology that takes into account both quantitative and qualitative factors and the interrelations between them should be utilized. for leveling an integrated approach of analytic hierarchy process AHP and fuzzy TOPSIS method is proposed to obtain final ranking. The interactions among the criteria are also analyzed before arriving at a decision for the selection of supplier from among six alternatives. Linguistic values are used to assess the ratings and weights for criterion. These linguistic ratings can be expressed in triangular fuzzy numbers. Then, a hierarchy multiple criteria decision-making (MCDM model based on fuzzy-sets theory including FAHP and FTOPSIS are applied. There are two approaches for aggregating values including relative importance of evaluation criteria with respect to the overall objective and rating of alternatives with respect to each criterion in fuzzy group TOPSIS: First aggregation and Last aggregation. In first aggregation approach weight of each criterion and rating of alternatives with respect to each criterion gained from decision makers are aggregated at first and TOPSIS method then apply to these aggregate values. In last aggregation approach weight of each criterion and rating of alternatives with respect to each criterion gained from decision makers are used in TOPSIS method
A Novel Weak Fuzzy Solution for Fuzzy Linear System
Soheil Salahshour
2016-03-01
Full Text Available This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.
Kyung Ho Kim
2001-01-01
Full Text Available We consider the semigroup S¯ of the fuzzy points of a semigroup S, and discuss the relation between the fuzzy interior ideals and the subsets of S¯ in an (intra-regular semigroup S.
GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS
无
2007-01-01
The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (∈, ∈∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investigated. In particular, the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.
模糊一次方程求解的实际研究%Practical Considerations on the Solution of First Order Fuzzy Equations
买买提热依木·阿布力孜; Reda; BOUKKEZOLA
2005-01-01
传统的加法,减法,乘法和除法运算都属于自然运算,因此不能用于区间数(interval)的分析中,故需要进一步研究区间数的特殊的运算规律.本文介绍模糊集合理论中的区间数进行加、减、乘、除等特殊的算术运算规律为基础,主要介绍并提出模糊一次方程bx+a=c的求解过程及方法,并给出其模糊方程的解.%Traditional ways such as arithmetic addition, subtraction, multiplication and division are natural operation, so they can't be used to interval number analysis. We need research special operation for interval number. Based on introducing addition, subtraction, multiplication and division operations of interval number in fuzzy theory,this paper presents the formalism associated with the solution of the fuzzy equation bx+a=c, which is fundamental, in the control design methodology.
Jantzen, Jan
1998-01-01
Design of a fuzzy controller requires more design decisions than usual, for example regarding rule base, inference engine, defuzzification, and data pre- and post processing. This tutorial paper identifies and describes the design choices related to single-loop fuzzy control, based...... on an international standard which is underway. The paper contains also a design approach, which uses a PID controller as a starting point. A design engineer can view the paper as an introduction to fuzzy controller design....
Equivalence of modified gravity equation to the Clausius relation
Bamba, Kazuharu; Nojiri, Shin'ichi; Odintsov, Sergei D
2009-01-01
We show that the equations of motion for modified gravity theories are equivalent to the Clausius relation in thermodynamics. For modified gravity theories, we study $F(R)$-gravity, the scalar-Gauss-Bonnet gravity, $F(\\mathcal{G})$-gravity and the non-local gravity. In addition, we discuss the relation between the expression of the entropy and the contribution from the modified gravity as well as the matter to the definition of the energy flux (heat).
Fuzzy正则语言与Fuzzy正则文法的关系%The Relation between Fuzzy Regular Language and Fuzzy Regular Grammar
柏明强; 莫智文
2001-01-01
In this paper, the relationship between fuzzy regular languagesand fuzzy regular grammars is discussed. It is proved that they are equivalent in sence. It is a start of further study of fuzzy languages and fuzzy finite automata.%通过对Fuzzy正则语言与Fuzzy正则文法的关系的讨论，得到了二者的等价关系，这是进一步研究Fuzzy正则语言与Fuzzy有限状态自动机的一个起点.
Fuzzy variable linear programming with fuzzy technical coefficients
Sanwar Uddin Ahmad
2012-11-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. In this paper an approximate but convenient method for solving these problems with fuzzy non-negative technical coefficient and without using the ranking functions, is proposed. With the help of numerical examples, the method is illustrated.
A high performance, ad-hoc, fuzzy query processing system for relational databases
Mansfield, William H., Jr.; Fleischman, Robert M.
1992-01-01
Database queries involving imprecise or fuzzy predicates are currently an evolving area of academic and industrial research. Such queries place severe stress on the indexing and I/O subsystems of conventional database environments since they involve the search of large numbers of records. The Datacycle architecture and research prototype is a database environment that uses filtering technology to perform an efficient, exhaustive search of an entire database. It has recently been modified to include fuzzy predicates in its query processing. The approach obviates the need for complex index structures, provides unlimited query throughput, permits the use of ad-hoc fuzzy membership functions, and provides a deterministic response time largely independent of query complexity and load. This paper describes the Datacycle prototype implementation of fuzzy queries and some recent performance results.
Supply chain management under fuzziness recent developments and techniques
Öztayşi, Başar
2014-01-01
Supply Chain Management Under Fuzziness presents recently developed fuzzy models and techniques for supply chain management. These include: fuzzy PROMETHEE, fuzzy AHP, fuzzy ANP, fuzzy VIKOR, fuzzy DEMATEL, fuzzy clustering, fuzzy linear programming, and fuzzy inference systems. The book covers both practical applications and new developments concerning these methods. This book offers an excellent resource for researchers and practitioners in supply chain management and logistics, and will provide them with new suggestions and directions for future research. Moreover, it will support graduate students in their university courses, such as specialized courses on supply chains and logistics, as well as related courses in the fields of industrial engineering, engineering management and business administration.
Essence of Special Relativity, Reduced Dirac Equation and Antigravity
Ni, Guang-jiong; Lou, Senyue; Xu, Jianjun
2010-01-01
The essence of special relativity is hiding in the equal existence of particle and antiparticle, which can be expressed by two discrete symmetries within one inertial frame --- the invariance under the (newly defined) space-time inversion (${\\bf x}\\to -{\\bf x},t\\to -t$), or equivalently, the invariance under a mass inversion ($m\\to -m$). The problems discussed are: the evolution of the $CPT$ invariance into a basic postulate, an unique solution to the original puzzle in Einstein-Podolsky-Rosen paradox, the reduced Dirac equation for hydrogenlike atoms, and the negative mass paradox leading to the prediction of antigravity between matter and antimatter. {\\bf Keywords}: Special relativity, Reduced Dirac Equation, Antiparticle, Antigravity
Shih-Tong Lu
2013-01-01
Full Text Available This study employs fuzzy linguistic preference relation (Fuzzy LinPreRa approach to assess the relative degree of impact of risk factors in software development project for two expert groups working in technology enterprises and software development companies. For the identified risk dimensions, the results show the same rankings for these two groups. “Organization function risk” is considered the most important dimension influencing the software development project performance, with the others, in order, being “developing technology risk,” “resources integration risk,” “personnel system risk” and “system requirement risk.” The proposed approach not only facilitates the information collecting for making pairwise comparisons, but it also eliminates the inconsistencies in the collected information.
黄义; 张引科
2003-01-01
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot' s equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.
SESAME Equations of State for Stress Cushion and Related Materials
Coe, Joshua Damon [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-12
I examine LANL equations of state (EOS) for stress cushion and related materials, namely S5370, SX358, and Sylgard 184. In the the rst two cases, the SESAME library contains entries for both the inert (unreacted) and decomposition products. I compare inert EOS results with ambient property measurements to the extent possible, then I check the compositions used to build the products tables. I plot the predicted Hugoniots alongside the available shock data, then draw some conclusions.
Full averaging of fuzzy impulsive differential inclusions
Natalia V. Skripnik
2010-09-01
Full Text Available In this paper the substantiation of the method of full averaging for fuzzy impulsive differential inclusions is studied. We extend the similar results for impulsive differential inclusions with Hukuhara derivative (Skripnik, 2007, for fuzzy impulsive differential equations (Plotnikov and Skripnik, 2009, and for fuzzy differential inclusions (Skripnik, 2009.
Some Duality Results for Fuzzy Nonlinear Programming Problem
Sangeeta Jaiswal; Geetanjali Panda
2012-01-01
The concept of duality plays an important role in optimization theory. This paper discusses some relations between primal and dual nonlinear programming problems in fuzzy environment. Here, fuzzy feasible region for a general fuzzy nonlinear programming is formed and the concept of fuzzy feasible solution is defined. First order dual relation for fuzzy nonlinear programming problem is studied.
Modelling on fuzzy control systems
LI; Hongxing(李洪兴); WANG; Jiayin(王加银); MIAO; Zhihong(苗志宏)
2002-01-01
A kind of modelling method for fuzzy control systems is first proposed here, which is calledmodelling method based on fuzzy inference (MMFI). It should be regarded as the third modelling method thatis different from two well-known modelling methods, that is, the first modelling method, mechanism modellingmethod (MMM), and the second modelling method, system identification modelling method (SlMM). Thismethod can, based on the interpolation mechanism on fuzzy logic system, transfer a group of fuzzy inferencerules describing a practice system into a kind of nonlinear differential equation with variable coefficients, calledHX equations, so that the mathematical model of the system can be obtained. This means that we solve thedifficult problem of how to get a model represented as differential equations on a complicated or fuzzy controlsystem.
FUZZY ALGEBRA IN TRIANGULAR NORM SYSTEM
宋晓秋; 潘志
1994-01-01
Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triangular norm, we introduce some concepts such as fuzzy algebra, fuzzy o algebra and fuzzy monotone class, and discuss the relations among them, obtaining the following main conclusions.
Using Fuzzy Relations and GIS Method to Evaluate Debris Flow Hazard
SONG Shujun; ZHANG Baolei; FENG Wenlan; ZHOU Wancun
2006-01-01
The study area,located in the southeast of Tibet along the Sichuan-Tibet highway,is a part of Palongzangbu River basin where mountain hazards take place frequently.On the ground of field surveying,historical data and previous research,a total of 31 debris flow gullies are identified in the study area and 5 factors are chosen as main parameters for evaluating the hazard of debris flows in this study.Spatial analyst functions of geographic information system (GIS) are utilized to produce debris flow inventory and parameter maps.All data are built into a spatial database for evaluating debris flow hazard.Integrated with GIS techniques,the fuzzy relation method is used to calculate the strength of relationship between debris flow inventory and parameters of the database.With this methodology,a hazard map of debris flows is produced.According to this map,6.6% of the study area is classified as very high hazard,7.3% as high hazard,8.4% as moderate hazard,32.1% as low hazard and 45.6% as very low hazard or non-hazard areas.After validating the results,this methodology is ultimately confirmed to be available.
Fuzzy Set Field and Fuzzy Metric
Gebru Gebray; B. Krishna Reddy
2014-01-01
The notation of fuzzy set field is introduced. A fuzzy metric is redefined on fuzzy set field and on arbitrary fuzzy set in a field. The metric redefined is between fuzzy points and constitutes both fuzziness and crisp property of vector. In addition, a fuzzy magnitude of a fuzzy point in a field is defined.
Duality in Dynamic Fuzzy Systems
Yoshida, Yuji
1995-01-01
This paper shows the resolvent equation, the maximum principle and the co-balayage theorem for a dynamic fuzzy system. We define a dual system for the dynamic fuzzy system, and gives a duality for Snell's optimal stopping problem by the dual system.
Jensen, E W; Nebot, A; Caminal, P;
1999-01-01
) methodology. A fuzzy model is able to identify non-linear and linear components of a causal relationship by means of optimization of information content of available data. Nine young female patients undergoing hysterectomy under general anaesthesia were included. Mean arterial pressure (MAP), heart rate (HR......The aim of this study was to identify a possible relationship between haemodynamic variables, auditory evoked potentials (AEP) and inspired fraction of isoflurane (ISOFl). Two different models (isoflurane and mean arterial pressure) were identified using the fuzzy inductive reasoning (FIR...... the depth of anaesthesia index (DAI) normalized to 100 when the patient was awake and descending to an average of 25 during loss of consciousness. The FIR methodology identified those variables among the input variables (MAP, HR, CO2ET, DAI or ISOFl) that had the highest causal relation with the output...
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
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
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.
Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors
Horatiu Nastase
2010-07-01
Full Text Available We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional field theory.
ON FUZZY h-IDEALS OF HEMIRINGS
Xueling MA; Jianming ZHAN
2007-01-01
The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the quasi-coincidence of a fuzzy point in a fuzzy set. By using this new concept, the authors define the notion of interval valued (∈, ∈ Vq)-fuzzy h-ideals of hemirings and study their related properties. In addition, the authors also extend the concept of a fuzzy subgroup with thresholds to the concept of an interval valued fuzzy h-ideal with thresholds in hemirings.
A new fuzzy edge detection algorithm
SunWei; XiaLiangzheng
2003-01-01
Based upon the maximum entropy theorem of information theory, a novel fuzzy approach for edge detection is presented. Firsdy, a definition of fuzzy partition entropy is proposed after introducing the concepts of fuzzy probability and fuzzy partition. The relation of the probability partition and the fuzzy c-partition of the image gradient are used in the algorithm. Secondly, based on the conditional probabilities and the fuzzy partition, the optimal thresholding is searched adaptively through the maximum fuzzy entropy principle, and then the edge image is obtained. Lastly, an edge-enhancing procedure is executed on the edge image. The experimental results show that the proposed approach performs well.
BOOK REVIEW: Partial Differential Equations in General Relativity
Choquet-Bruhat, Yvonne
2008-09-01
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory.
Static gravitational equations of general relativity and "the fifth force"
Das, A.
2015-10-01
Einstein's static field equations are investigated in various coordinate charts. After comparing Newtonian gravitational theory (in a curvilinear coordinate chart) with various charts of Einstein's static gravitational equations, the most appropriate choice of the coordinate chart for Einstein's static field equations is made. As a consequence, Einstein's equations imply the non-linear potential equation instead of the usual Poisson's equation of the Newtonian theory. Investigating the non-linear potential equation above in the spherically symmetric cases, the corresponding potentials yield scenarios comparable to "the fifth force". Next, static gravitational and electric fields generated by an incoherent charged dust are investigated. The corresponding non-linear potential equation is derived. Finally, the static Einstein-Maxwell-Klein-Gordon equations are explored and again, the corresponding non-linear potential equation is obtained. This potential resembles the static Higgs boson field.
Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
Chen, Hua; Sato, Yuki
2016-01-01
The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the ADM formalism of general relativity, and is studied as a discretized model for quantum gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the tensor up to the forth order, and show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation with an appropriate choice of an action. The action contains a scalar field potential of an exponential form, and the system classically respects a dilatational symmetry. We find that the system has a critical dimension, given by six, over which it becomes unstable due to the wrong sign of the scalar kinetic term. In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal s...
HU Hong; LI Su; WANG YunJiu; QI XiangLin; SHI ZhongZhi
2008-01-01
Analytical study of large-scale nonlinear neural circuits is a difficult task. Here we analyze the function of neural systems by probing the fuzzy logical framework of the neural cells' dynamical equations. Al-though there is a close relation between the theories of fuzzy logical systems and neural systems and many papers investigate this subject, most investigations focus on finding new functions of neural systems by hybridizing fuzzy logical and neural system. In this paper, the fuzzy logical framework of neural cells is used to understand the nonlinear dynamic attributes of a common neural system by abstracting the fuzzy logical framework of a neural cell. Our analysis enables the educated design of network models for classes of computation. As an example, a recurrent network model of the primary visual cortex has been built and tested using this approach.
2008-01-01
Analytical study of large-scale nonlinear neural circuits is a difficult task. Here we analyze the function of neural systems by probing the fuzzy logical framework of the neural cells’ dynamical equations. Al- though there is a close relation between the theories of fuzzy logical systems and neural systems and many papers investigate this subject, most investigations focus on finding new functions of neural systems by hybridizing fuzzy logical and neural system. In this paper, the fuzzy logical framework of neural cells is used to understand the nonlinear dynamic attributes of a common neural system by abstracting the fuzzy logical framework of a neural cell. Our analysis enables the educated design of network models for classes of computation. As an example, a recurrent network model of the primary visual cortex has been built and tested using this approach.
Hu, Hong; Li, Su; Wang, YunJiu; Qi, XiangLin; Shi, ZhongZhi
2008-10-01
Analytical study of large-scale nonlinear neural circuits is a difficult task. Here we analyze the function of neural systems by probing the fuzzy logical framework of the neural cells' dynamical equations. Although there is a close relation between the theories of fuzzy logical systems and neural systems and many papers investigate this subject, most investigations focus on finding new functions of neural systems by hybridizing fuzzy logical and neural system. In this paper, the fuzzy logical framework of neural cells is used to understand the nonlinear dynamic attributes of a common neural system by abstracting the fuzzy logical framework of a neural cell. Our analysis enables the educated design of network models for classes of computation. As an example, a recurrent network model of the primary visual cortex has been built and tested using this approach.
2010-05-01
the world of logic than friction in mechanics. — Charles Sanders Peirce 1 Rational deterrence theory rests on the foundation that...4 Kosko, Fuzzy Thinking, 4-17. 5 Daniel McNeill and Paul Freiberger, Fuzzy Logic: The Revolutionary Computer Technology That Is Changing Our...1 McNeill and Freiberger, Fuzzy Logic, 174. 2 Yarger, Little Book on Big Strategy, 16. 3 Mukaidono, Fuzzy Logic for
Relations between nonlinear Riccati equations and other equations in fundamental physics
Schuch, Dieter
2014-10-01
Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.
Composition of processes and related partial differential equations
D'Ovidio, Mirko
2010-01-01
In this paper different types of compositions involving independent fractional Brownian motions $B^j_{H_j}(t)$, $t>0$, $j=1,2$ are examined. The partial differential equations governing the distributions of $I_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|)$, $t>0$ and $J_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|^{1/H_1})$, $t>0$ are derived by different methods and compared with those existing in the literature and with those related to $B^1(|B^2_{H_2}(t)|)$, $t>0$. The process of iterated Brownian motion $I^n_F(t)$, $t>0$ is examined in detail and its moments are calculated. Furthermore for $J^{n-1}_F(t)=B^1_{H}(|B^2_H(...|B^n_H(t)|^{1/H}...)|^{1/H})$, $t>0$ the following factorization is proved $J^{n-1}_F(t)=\\prod_{j=1}^{n} B^j_{\\frac{H}{n}}(t)$, $t>0$. A series of compositions involving Cauchy processes and fractional Brownian motions are also studied and the corresponding non-homogeneous wave equations are derived.
On the Klein-Gordon equation using the dispersion relation of Doubly Special Relativity
Felipe, Yese J.
2017-01-01
The theory of Doubly Special Relativity or Deformed Special Relativity (DSR), proposes that there is a maximum energy scale and a minimum length scale that is invariant for all observers. These maximum energy and minimum length correspond to the Planck energy and the Planck length, respectively. As a consequence, the dispersion relation is modified to be E2 =p2c2 +m2c4 + λE3 + ... Previous work has been done to express Quantum Mechanics using the dispersion relation of DSR. Solutions of the free particle, the harmonic oscillator, and the Hydrogen atom have been obtained from the DSR Schrodinger equation. We explore how the DSR Klein-Gordon equation can be consistently approximated in the non-relativistic limit in order to derive the DSR Schrodinger equation.
On the Superstability Related with the Trigonometric Functional Equation
Kim GwangHui
2009-01-01
Full Text Available Abstract We will investigate the superstability of the (hyperbolic trigonometric functional equation from the following functional equations: , , , , which can be considered the mixed functional equations of the sine function and cosine function, of the hyperbolic sine function and hyperbolic cosine function, and of the exponential functions, respectively.
Relations between Stochastic and Partial Differential Equations in Hilbert Spaces
I. V. Melnikova
2012-01-01
Full Text Available The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces. Connection between solutions to the abstract stochastic differential equation and solutions to the deterministic partial differential (with derivatives in Hilbert spaces equation for the probability characteristic is proved. Interpretation of objects in the equations is given.
Dirac equation in very special relativity for hydrogen atom
Maluf, R V; Cruz, W T; Almeida, C A S
2014-01-01
In this work, we study the modified Dirac equation in the framework of very special relativity (VSR). The low-energy regime is accessed and the nonrelativistic Hamiltonian is obtained. It turns out that this Hamiltonian is similar to that achieved from the Standard Model Extension (SME) via coupling of the spinor field to a Lorentz-violating term, but new features arise inherited from the non-local character of the VSR. In addition, the implications of the VSR-modified Lorentz symmetry on the spectrum of a hydrogen atom is determined by calculating the first-order energy corrections in the context of standard quantum mechanics. Among the results, we highlight that the modified Hamiltonian provides non-vanishing corrections which lift the degeneracy of the energy levels and allow us to find an upper bound upon the VSR-parameter.
Dirac equation in very special relativity for hydrogen atom
R.V. Maluf
2014-11-01
Full Text Available In this work, we study the modified Dirac equation in the framework of very special relativity (VSR. The low-energy regime is accessed and the nonrelativistic Hamiltonian is obtained. It turns out that this Hamiltonian is similar to that achieved from the Standard Model Extension (SME via coupling of the spinor field to a Lorentz-violating term, but new features arise inherited from the non-local character of the VSR. In addition, the implications of the VSR-modified Lorentz symmetry on the spectrum of a hydrogen atom are determined by calculating the first-order energy corrections in the context of standard quantum mechanics. Among the results, we highlight that the modified Hamiltonian provides non-vanishing corrections which lift the degeneracy of the energy levels and allow us to find an upper bound upon the VSR-parameter.
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.
Control of convergence in a computational fluid dynamic simulation using fuzzy logic
刘训良; 陶文铨; 郑平; 何雅玲; 王秋旺
2002-01-01
A fuzzy control method was used to accelerate iteration convergence in numerical fluid dynamic simulation using SIMPLER algorithm. The residual ratio of momentum or energy equation between two successive iterations was used as the input variable. A fuzzy logic algorithm was developed in order to obtain the relative increment of the under-relaxation factor and its new value was then used for the next iteration. The algorithm was tested by four benchmark problems. In all cases considered, when the fuzzy control logic was used, convergence was achieved with nearly the minimum number of iterations, showing the feasibility of the proposed method.
Possibilistic Exponential Fuzzy Clustering
Kiatichai Treerattanapitak; Chuleerat Jaruskulchai
2013-01-01
Generally,abnormal points (noise and outliers) cause cluster analysis to produce low accuracy especially in fuzzy clustering.These data not only stay in clusters but also deviate the centroids from their true positions.Traditional fuzzy clustering like Fuzzy C-Means (FCM) always assigns data to all clusters which is not reasonable in some circumstances.By reformulating objective function in exponential equation,the algorithm aggressively selects data into the clusters.However noisy data and outliers cannot be properly handled by clustering process therefore they are forced to be included in a cluster because of a general probabilistic constraint that the sum of the membership degrees across all clusters is one.In order to improve this weakness,possibilistic approach relaxes this condition to improve membership assignment.Nevertheless,possibilistic clustering algorithms generally suffer from coincident clusters because their membership equations ignore the distance to other clusters.Although there are some possibilistic clustering approaches that do not generate coincident clusters,most of them require the right combination of multiple parameters for the algorithms to work.In this paper,we theoretically study Possibilistic Exponential Fuzzy Clustering (PXFCM) that integrates possibilistic approach with exponential fuzzy clustering.PXFCM has only one parameter and not only partitions the data but also filters noisy data or detects them as outliers.The comprehensive experiments show that PXFCM produces high accuracy in both clustering results and outlier detection without generating coincident problems.
On the relation between elementary partial difference equations and partial differential equations
van den Berg, I.P.
1998-01-01
The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential
FUZZY STABILITY ANALYSIS OF MODE COUPLING CHATTER ON CUTTING PROCESS
1998-01-01
The influence of fuzzy uncertainty factors is considered on the analysis of chatter occurring during machine tool cutting process. Using fuzzy mathematics analysis methods, a detailed discussion over fuzzy stability analysis problems is presented related to the mode coupling chatter with respect to intrinsic structure fuzzy factors, and the possibility distribution of the fuzzy stability cutting range and the confidence level expressions of the fuzzy stability cutting width are given.
A fuzzy expert system for diabetes decision support application.
Lee, Chang-Shing; Wang, Mei-Hui
2011-02-01
An increasing number of decision support systems based on domain knowledge are adopted to diagnose medical conditions such as diabetes and heart disease. It is widely pointed that the classical ontologies cannot sufficiently handle imprecise and vague knowledge for some real world applications, but fuzzy ontology can effectively resolve data and knowledge problems with uncertainty. This paper presents a novel fuzzy expert system for diabetes decision support application. A five-layer fuzzy ontology, including a fuzzy knowledge layer, fuzzy group relation layer, fuzzy group domain layer, fuzzy personal relation layer, and fuzzy personal domain layer, is developed in the fuzzy expert system to describe knowledge with uncertainty. By applying the novel fuzzy ontology to the diabetes domain, the structure of the fuzzy diabetes ontology (FDO) is defined to model the diabetes knowledge. Additionally, a semantic decision support agent (SDSA), including a knowledge construction mechanism, fuzzy ontology generating mechanism, and semantic fuzzy decision making mechanism, is also developed. The knowledge construction mechanism constructs the fuzzy concepts and relations based on the structure of the FDO. The instances of the FDO are generated by the fuzzy ontology generating mechanism. Finally, based on the FDO and the fuzzy ontology, the semantic fuzzy decision making mechanism simulates the semantic description of medical staff for diabetes-related application. Importantly, the proposed fuzzy expert system can work effectively for diabetes decision support application.
Fuzzy Ideals and Fuzzy Distributive Lattices%Fuzzy Ideals and Fuzzy Distributive Lattices*
S.H.Dhanani; Y. S. Pawar
2011-01-01
Our main objective is to study properties of a fuzzy ideals (fuzzy dual ideals). A study of special types of fuzzy ideals (fuzzy dual ideals) is also furnished. Some properties of a fuzzy ideals (fuzzy dual ideals) are furnished. Properties of a fuzzy lattice homomorphism are discussed. Fuzzy ideal lattice of a fuzzy lattice is defined and discussed. Some results in fuzzy distributive lattice are proved.
Venkatesh, B.; George, M.K. [Multimedia University (Malaysia). Faculty of Engineering and Technology; Gooi, H.B. [Nanyang Technological University (Singapore). School of Electrical and Electronics Engineering
2004-09-01
A new optimal reactive power flow (ORPF) method is proposed which considers the inclusion of unified powerflow controllers (UPFC). The modelling and inclusion of UPFC in the solution of power flow equations is presented. The ORPF problem is formulated as a fuzzy optimisation problem considering the objectives of minimising system transmission loss and obtaining the best voltage profile. The fuzzy formulation of the ORPF problem is solved using an EP algorithm. The proposed method is applied on the 6-bus and 57-bus IEEE test systems and on a 191-bus Indian electric power system. The results demonstrate the applicability of the method. (author)
Nonlinear partial differential equations: Integrability, geometry and related topics
Krasil'shchik, Joseph; Rubtsov, Volodya
2017-03-01
Geometry and Differential Equations became inextricably entwined during the last one hundred fifty years after S. Lie and F. Klein's fundamental insights. The two subjects go hand in hand and they mutually enrich each other, especially after the "Soliton Revolution" and the glorious streak of Symplectic and Poisson Geometry methods in the context of Integrability and Solvability problems for Non-linear Differential Equations.
On some functional equations related to Steffensen's inequality
Bogdan Choczewski
2004-05-01
Full Text Available We consider the problem, proposed by the second author (cf. [1] of solving functional equations stemming from the Steffensen integral inequality (S, which is applicable in actuarial problems, cf. [4]. Imposing some regularity conditions we find solutions of two equations in two variables, one with two and another with three unknown functions.
Thin-Layer Solutions of the Helmholtz and Related Equations
Ockendon, J. R.
2012-01-01
This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.
On Fuzzy Simplex and Fuzzy Convex Hull
Dong QIU; Wei Quan ZHANG
2011-01-01
In this paper,we discuss fuzzy simplex and fuzzy convex hull,and give several representation theorems for fuzzy simplex and fuzzy convex hull.In addition,by giving a new characterization theorem of fuzzy convex hull,we improve some known results about fuzzy convex hull.
The Fuzzy Set by Fuzzy Interval
Dr.Pranita Goswami
2011-01-01
Fuzzy set by Fuzzy interval is atriangular fuzzy number lying between the two specified limits. The limits to be not greater than 2 and less than -2 by fuzzy interval have been discussed in this paper. Through fuzzy interval we arrived at exactness which is a fuzzymeasure and fuzzy integral
Probability representations of fuzzy systems
LI Hongxing
2006-01-01
In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the sense of mean square. Based on different fuzzy implication operators, several typical probability distributions such as Zadeh distribution, Mamdani distribution, Lukasiewicz distribution, etc. are given. Those distributions act as "inner kernels" of fuzzy systems. Furthermore, by some properties of probability distributions of fuzzy systems, it is also demonstrated that CRI method, proposed by Zadeh, for constructing fuzzy systems is basically reasonable and effective. Besides, the special action of uniform probability distributions in fuzzy systems is characterized. Finally, the relationship between CRI method and triple I method is discussed. In the sense of construction of fuzzy systems, when restricting three fuzzy implication operators in triple I method to the same operator, CRI method and triple I method may be related in the following three basic ways: 1) Two methods are equivalent; 2) the latter is a degeneration of the former; 3) the latter is trivial whereas the former is not. When three fuzzy implication operators in triple I method are not restricted to the same operator, CRI method is a special case of triple I method; that is, triple I method is a more comprehensive algorithm. Since triple I method has a good logical foundation and comprises an idea of optimization of reasoning, triple I method will possess a beautiful vista of application.
Fuzzy-TOPSIS Method with Multi-goal
PANG Jin-hui; ZHANG Qiang
2009-01-01
To develop the technique for order preference by similarity to an ideal solution,namely,TOPSIS method with multi-goal in fuzzy decision environment.Firstly,a new approach to constructing fuzzy decision matrix by Choquet integral was proposed in muhi-goal decision system.Secondly,the concepts of fuzzy positive-ideal solution and fuzzy negative-ideal solution related to the fuzzy decision matrix were given.Finally,the credibility measure was adopted to calculate the distances to fuzzy positive-ideal solution and fuzzy negative-ideal solution.The presented fuzzy-TOPSIS method embodies well both the predetermined preferences and the weights of goals.
Gourgoulhon, Eric
2011-04-01
Numerical relativity is one of the major fields of contemporary general relativity and is developing continually. Yet three years ago, no textbook was available on this subject. The first textbook devoted to numerical relativity, by Alcubierre, appeared in 2008 [1] (cf the CQG review [2]). Now comes the second book, by Baumgarte and Shapiro, two well known players in the field. Inevitably, the two books have some common aspects (otherwise they would not deal with the same topic!). For instance the titles of the first four chapters of Baumgarte and Shapiro are very similar to those of Alcubierre. This arises from some logic inherent to the subject: chapter 1 recaps basic GR, chapter 2 introduces the 3+1 formalism, chapter 3 focuses on the initial data and chapter 4 on the choice of coordinates for the evolution. But there are also many differences between the two books, which actually make them complementary. At first glance the differences are the size (720 pages for Baumgarte and Shapiro vs 464 pages for Alcubierre) and the colour figures in Baumgarte and Shapiro. Regarding the content, Baumgarte and Shapiro address many topics which are not present in Alcubierre's book, such as magnetohydrodynamics, radiative transfer, collisionless matter, spectral methods, rotating stars and post-Newtonian approximation. The main difference regards binary systems: virtually absent from Alcubierre's book (except for binary black hole initial data), they occupy not less than five chapters in Baumgarte and Shapiro's book. In contrast, gravitational wave extraction, various hyperbolic formulations of Einstein's equations and the high-resolution shock-capturing schemes are treated in more depth by Alcubierre. In the first four chapters mentioned above, some distinctive features of Baumgarte and Shapiro's book are the beautiful treatment of Oppenheimer-Snyder collapse in chapter 1, the analogy with Maxwell's equations when discussing the constraints and the evolution equations in
Probabilistic delay differential equation modeling of event-related potentials.
Ostwald, Dirk; Starke, Ludger
2016-08-01
"Dynamic causal models" (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach.
On fractional partial differential equations related to quantum mechanics
Purohit, S. D.; Kalla, S. L.
2011-01-01
In this paper, we investigate the solutions of generalized fractional partial differential equations involving the Caputo time-fractional derivative and the Liouville space-fractional derivatives. The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms. Several special cases as solutions of one-dimensional non-homogeneous fractional equations occurring in quantum mechanics are presented in the concluding section. The results given earlier by Debnath (2003 Fract. Calc. Appl. Anal. 6 119-55), Saxena et al (2010 Appl. Math. Comput. 216 1412-7) and Pagnini and Mainardi (2010 J. Comput. Appl. Math. 233 1590-5) follow as special cases of our findings.
On fractional partial differential equations related to quantum mechanics
Purohit, S D [Department of Basic-Sciences (Mathematics), College of Technology and Engineering, M.P. University of Agriculture and Technology, Udaipur-313001 (India); Kalla, S L, E-mail: sunil_a_purohit@yahoo.com, E-mail: shyamkalla@gmail.com [Institute of Mathematics, VIHE, 15 B, Pal-Link Road, Jodhpur-342008 (India)
2011-01-28
In this paper, we investigate the solutions of generalized fractional partial differential equations involving the Caputo time-fractional derivative and the Liouville space-fractional derivatives. The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms. Several special cases as solutions of one-dimensional non-homogeneous fractional equations occurring in quantum mechanics are presented in the concluding section. The results given earlier by Debnath (2003 Fract. Calc. Appl. Anal. 6 119-55), Saxena et al (2010 Appl. Math. Comput. 216 1412-7) and Pagnini and Mainardi (2010 J. Comput. Appl. Math. 233 1590-5) follow as special cases of our findings.
Computer generation of robot dynamics equations and the related issues
Leu, M.C.; Koplik, J.
1986-01-01
Two programs have been developed using the computer algebra system REDUCE to generate the dynamics equations of motion for robot manipulators. One of these programs is based on a Lagrange formulation and the other utilizes a recursive Newton-Euler formulation. Both programs produce equivalent scalar symbolic expressions for the generalized actuator forces, but the program based on the recursive Newton-Euler formulation is more efficient for the generation of equations. These programs have been used to generate the dynamics equations of manipulators with as many as six degrees of freedom. 16 references.
Berenstein, David [Department of Applied Mathematics and Theoretical Physics,University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Department of Physics, University of California Santa Barbara,Santa Barbara, California 93106 (United States); Dzienkowski, Eric; Lashof-Regas, Robin [Department of Physics, University of California Santa Barbara,Santa Barbara, California 93106 (United States)
2015-08-27
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{sup ∗} field theory with a non-trivial charge density. The solutions we construct have a ℤ{sub 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.
Malhas, Othman Qasim
1993-10-01
The concept of “abacus logic” has recently been developed by the author (Malhas, n.d.). In this paper the relation of abacus logic to the concept of fuzziness is explored. It is shown that if a certain “regularity” condition is met, concepts from fuzzy set theory arise naturally within abacus logics. In particular it is shown that every abacus logic then has a “pre-Zadeh orthocomplementation”. It is also shown that it is then possible to associate a fuzzy set with every proposition of abacus logic and that the collection of all such sets satisfies natural conditions expected in systems of fuzzy logic. Finally, the relevance to quantum mechanics is discussed.
Consolidity analysis for fully fuzzy functions, matrices, probability and statistics
Walaa Ibrahim Gabr
2015-03-01
Full Text Available The paper presents a comprehensive review of the know-how for developing the systems consolidity theory for modeling, analysis, optimization and design in fully fuzzy environment. The solving of systems consolidity theory included its development for handling new functions of different dimensionalities, fuzzy analytic geometry, fuzzy vector analysis, functions of fuzzy complex variables, ordinary differentiation of fuzzy functions and partial fraction of fuzzy polynomials. On the other hand, the handling of fuzzy matrices covered determinants of fuzzy matrices, the eigenvalues of fuzzy matrices, and solving least-squares fuzzy linear equations. The approach demonstrated to be also applicable in a systematic way in handling new fuzzy probabilistic and statistical problems. This included extending the conventional probabilistic and statistical analysis for handling fuzzy random data. Application also covered the consolidity of fuzzy optimization problems. Various numerical examples solved have demonstrated that the new consolidity concept is highly effective in solving in a compact form the propagation of fuzziness in linear, nonlinear, multivariable and dynamic problems with different types of complexities. Finally, it is demonstrated that the implementation of the suggested fuzzy mathematics can be easily embedded within normal mathematics through building special fuzzy functions library inside the computational Matlab Toolbox or using other similar software languages.
Discovering Equations in Relation of Process to the Counseling Process
Hideaki Yanagisawa
2015-05-01
Full Text Available Each counselor understands counseling freely as all counseling theories are explained without equations. Therefore, there are two kinds of mistakes in counseling. One is counter-transference, the other is a mistake wherein the counselor forces his thought and induces certain thoughts in the client. The counselor assists in aiding the client’s real intentions to be converted to the client’s consciousness from their unconsciousness. It is equal to a process in which the methods rearrange and unify the thoughts from a chaotic state. For example, such methods include the KJ (Kawakida Jiro method, the SEIQoL-DW (Schedule for the Evaluation of Individual Quality of Life-Direct Weighting method, dialectics, the process discovering equation. In this report, the counseling process is compared with a process of discovering equations from observed values. In the process of discovering equations, it is important that the curve of equations smoothly continues. On the curve, the contact point and the gradient of the tangent line must not break off. Similarly, it is important that a counselor easily understands a client. Therefore, it is a necessary condition for counseling that the counselor’s and client’s original characters are smoothly patterned and that the communicating method of the counselor must be equal to that of the client. It will be useful for preventing two kinds of mistakes in counseling if counseling can be represented using equations and graphs.
EEG-Based Person Authentication Using a Fuzzy Entropy-Related Approach with Two Electrodes
Zhendong Mu
2016-12-01
Full Text Available Person authentication, based on electroencephalography (EEG signals, is one of the directions possible in the study of EEG signals. In this paper, a method for the selection of EEG electrodes and features in a discriminative manner is proposed. Given that EEG signals are unstable and non-linear, a non-linear analysis method, i.e., fuzzy entropy, is more appropriate. In this paper, unlike other methods using different signal sources and patterns, such as rest state and motor imagery, a novel paradigm using the stimuli of self-photos and non-self-photos is introduced. Ten subjects are selected to take part in this experiment, and fuzzy entropy is used as a feature to select the minimum number of electrodes that identifies individuals. The experimental results show that the proposed method can make use of two electrodes (FP1 and FP2 in the frontal area, while the classification accuracy is greater than 87.3%. The proposed biometric system, based on EEG signals, can provide each subject with a unique key and is capable of human recognition.
Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections
Hong Liang
2015-01-01
Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and $\\sigma$-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections and establish their fundamental properties.
On a wave map equation arising in general relativity
Ringstrom, H
2003-01-01
We consider a class of spacetimes for which the essential part of Einstein's equations can be written as a wave map equation. The domain is not the standard one, but the target is hyperbolic space. One ends up with a 1+1 non-linear system of wave equations, where the space variable belongs to the circle and the time variable belongs to the positive real numbers. In this article, we discuss the asymptotics of solutions to these equations as time tends to infinity. For each point in time, the solution defines a loop in hyperbolic space, and the first result is that the length of this loop tends to zero as time tends to infinity. In other words, the solution in some sense becomes spatially homogeneous. However, the asymptotic behaviour need not be similar to that of spatially homogeneous solutions to the equations. The orbits of such solutions are either a point or a geodesic in the hyperbolic plane. In general, the solution may oscillate around a circle inside the upper half plane. Thus, even though the solutio...
Projectively related metrics, Weyl nullity, and metric projectively invariant equations
Gover, A Rod
2015-01-01
A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity condition. The analysis is simplified by a fundamental and canonical 2-tensor invariant that we discover. It leads to a new canonical tractor connection for these geometries which is defined on a rank $(n+1)$-bundle. We show this connection is linked to the metrisability equations that govern the existence of metrics compatible with the structure. The fundamental 2-tensor also leads to a new class of invariant linear differential operators that are canonically associated to these geometries; included is a third equation studied by Gallot et al. We apply the results to study the metrisability equation, in the nullity setting described. We obtain strong local and global results on the nature of solutions and also on the nature of the geometries admitting such solutions, obtaining ...
General relativity as the equation of state of spin foam
Smolin, Lee
2012-01-01
Building on recent significant results of Frodden, Ghosh and Perez (FGP) and Bianchi, I present a quantum version of Jacobson's argument that the Einstein equations emerge as the equation of state of a quantum gravitational system. I give three criteria a quantum theory of gravity must satisfy if it is to allow Jacobson's argument to be run. I then show that the results of FGP and Bianchi provide evidence that loop quantum gravity satisfies two of these criteria and argue that the third should also be satisfied in loop quantum gravity. I also show that the energy defined by FGP is the canonical energy associated with the boundary term of the Holst action.
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.
Zadeh, Lofti A.
1988-01-01
The author presents a condensed exposition of some basic ideas underlying fuzzy logic and describes some representative applications. The discussion covers basic principles; meaning representation and inference; basic rules of inference; and the linguistic variable and its application to fuzzy control.
Anker, Thomas Boysen; Kappel, Klemens; Eadie, Douglas
2012-01-01
This article clarifies the commonplace assumption that brands make promises by developing definitions of brand promise delivery. Distinguishing between clear and fuzzy brand promises, we develop definitions of what it is for a brand to deliver on fuzzy functional, symbolic, and experiential...
Master equation solutions in the linear regime of characteristic formulation of general relativity
M., C E Cedeño
2015-01-01
From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and M\\"adler, for a Minkowski's background, were able to show that it is possible to derive a fourth order ordinary differential equation, called master equation, for the $J$ metric variable of the Bondi-Sachs metric. Once $\\beta$, another Bondi-Sachs potential, is obtained from the field equations, and $J$ is obtained from the master equation, the other metric variables are solved integrating directly the rest of the field equations. In the past, the master equation was solved for the first multipolar terms, for both the Minkowski's and Schwarzschild's backgrounds. Also, M\\"adler recently reported a generalisation of the exact solutions to the linearised field equations when a Minkowski's background is considered, expressing the master equation family of solutions for the vacuum in terms of Bessel's functions of the first and the second kind. Here, we report new sol...
van Lith, Pascal; van Lith, P.F.; Betlem, Bernardus H.L.; Roffel, B.
2002-01-01
Hybrid fuzzy-first principles models can be a good alternative if a complete physical model is difficult to derive. These hybrid models consist of a framework of dynamic mass and energy balances, supplemented by fuzzy submodels describing additional equations, such as mass transformation and
Lith, Pascal F. van; Betlem, Ben H.L.; Roffel, Brian
2002-01-01
Hybrid fuzzy-first principles models can be a good alternative if a complete physical model is difficult to derive. These hybrid models consist of a framework of dynamic mass and energy balances, supplemented by fuzzy submodels describing additional equations, such as mass transformation and
Lith, Pascal F. van; Betlem, Ben H.L.; Roffel, Brian
2002-01-01
Hybrid fuzzy-first principles models can be a good alternative if a complete physical model is difficult to derive. These hybrid models consist of a framework of dynamic mass and energy balances, supplemented by fuzzy submodels describing additional equations, such as mass transformation and transfe
Lith, Pascal F. van; Betlem, Ben H.L.; Roffel, Brian
2002-01-01
Hybrid fuzzy-first principles models can be a good alternative if a complete physical model is difficult to derive. These hybrid models consist of a framework of dynamic mass and energy balances, supplemented by fuzzy submodels describing additional equations, such as mass transformation and transfe
On mathematical structures of fuzzy rough set algebras
WU Wei-zhi
2008-01-01
In rough set theory, the lower and upper approximation operators are important notions defined by a binary rela-tion. In this paper, we introduce a general type of relation-based fuzzy rough model determined by a triangular norm. Prop-erties of fuzzy rough approximation operators are examined. The fuzzy rough approximation operators are also characterized by axioms. A comparative study of the fuzzy rough set algebra with other mathematical structures such as fuzzy topological spaces, fuzzy measurable spaces, and fuzzy belief structures is investigated.
On the applicability of the geodesic deviation equation in General Relativity
Philipp, Dennis; Laemmerzahl, Claus
2016-01-01
Within the theory of General Relativity we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. The deviation equation is used to model satellite orbit constellations around the earth. In particular, we reconsider the deviation equation in Newtonian gravity and then determine relativistic effects within the theory of General Relativity. The deviation of nearby orbits, as constructed from exact solutions of the underlying geodesic equation, is compared to the solution of the geodesic deviation equation to assess the accuracy of the latter. Furthermore, we comment on the so-called Shirokov effect in Schwarzschild spacetime.
Complex Fuzzy Set-Valued Complex Fuzzy Measures and Their Properties
Ma, Shengquan; Li, Shenggang
2014-01-01
Let F*(K) be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance on F*(K), fuzzy complex number-valued measure on F*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous from above, autocontionuous from below, and autocontinuity of the defined fuzzy complex number-valued measures. Properties of fuzzy complex number-valued measures are studied in detail. PMID:25093202
Complex fuzzy set-valued complex fuzzy measures and their properties.
Ma, Shengquan; Li, Shenggang
2014-01-01
Let F*(K) be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance on F*(K), fuzzy complex number-valued measure on F*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous from above, autocontionuous from below, and autocontinuity of the defined fuzzy complex number-valued measures. Properties of fuzzy complex number-valued measures are studied in detail.
Corveleyn, Samuel
2014-01-01
Uncertainty quantification is playing an increasingly important role in the mathematical modeling of physical phenomena. The classical approach to the modeling of uncertainties is to use probability theory. In some cases, it can, however, be argued that probability may not be the most appropriate mathematical representation of the uncertainty. One of the modeling alternatives is then provided by fuzzy sets.The main goal of this thesis was the development and analysis of numerical methods for ...
Analysis of Helical Gear System Dynamic Response Based on Fuzzy Numbers
马亮; 李瑰贤; 杨伟君
2001-01-01
A non-linear dynamic model with the single degree of freedom of a helical gear pair introducing frzzy numbers is developed. In this proposed model, time-variant mesh stiffness, which is a non-linear parameter, mesh damping and composite error of a pair of meshing tooth of the gear pair are all included. Mesh stiffness is calculated by expressing Bo (r) as a Fourier series. Ⅱshape function is introduced as the membership function to characterize the fuzziness of the error. Fuzzy displacement dynamic response of the geared system at A- level, which is a closed interval, is ohtained by removing the fuzziness of the fuzzy differential equations and using Runge-Kutta numerical method. In fact, the fuzzy dynamic response and dynamic loading factor are aH the interval functions related λ. The result obtained here can be used to the fuzzy dynamic optimization design course of the helical gear system. The main advantage of this method is to introduce the concept of fuzzy number for the first time to the analysis of the gear system dynamics.
Wei Zhang
2014-01-01
Full Text Available The underwater recovery of autonomous underwater vehicles (AUV is a process of 6-DOF motion control, which is related to characteristics with strong nonlinearity and coupling. In the recovery mission, the vehicle requires high level control accuracy. Considering an AUV called BSAV, this paper established a kinetic model to describe the motion of AUV in the horizontal plane, which consisted of nonlinear equations. On the basis of this model, the main coupling variables were analyzed during recovery. Aiming at the strong coupling problem between the heading control and sway motion, we designed a decoupling compensator based on the fuzzy theory and the decoupling theory. We analyzed to the rules of fuzzy compensation, the input and output membership functions of fuzzy compensator, through compose operation and clear operation of fuzzy reasoning, and obtained decoupling compensation quantity. Simulation results show that the fuzzy decoupling controller effectively reduces the overshoot of the system, and improves the control precision. Through the water tank experiments and analysis of experimental data, the effectiveness and feasibility of AUV recovery movement coordinated control based on fuzzy decoupling method are validated successful, and show that the fuzzy decoupling control method has a high practical value in the recovery mission.
Simultaneous contrast improvement and denoising via diffusion-related equations
Sapiro, Guillermo; Caselles, Vicent
1995-08-01
The explicit use of partial differential equations (PDE's) in image processing became a major topic of study in the last years. In this work we present an algorithm for histogram modification via PDE's. We show that the histogram can be modified to achieve any given distribution. The modification can be performed while simultaneously reducing noise. This avoids the noise sharpening effect in classical algorithms. The approach is extended to local contrast enhancement as well. A variational interpretation of the flow is presented and theoretical results on the existence of solutions are given.
Type-2 fuzzy fractional derivatives
Mazandarani, Mehran; Najariyan, Marzieh
2014-07-01
In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann-Liouville and Caputo derivative of order β ɛ (0, 1), and based on type-2 Hukuhara difference and H2-differentiability. The existence and uniqueness of the solutions of type-2 fuzzy fractional differential equations (T2FFDEs) under Caputo type-2 fuzzy fractional derivative and the definition of Laplace transform of type-2 fuzzy number-valued functions are also given. Moreover, the approximate solution to T2FFDE by a Predictor-Evaluate-Corrector-Evaluate (PECE) method is presented. Finally, the approximate solutions of two examples of linear and nonlinear T2FFDEs are obtained using the PECE method, and some cases of T2FFDEs applications in some sciences are presented.
Fuzzy Evidence in Identification, Forecasting and Diagnosis
Rotshtein, Alexander P
2012-01-01
The purpose of this book is to present a methodology for designing and tuning fuzzy expert systems in order to identify nonlinear objects; that is, to build input-output models using expert and experimental information. The results of these identifications are used for direct and inverse fuzzy evidence in forecasting and diagnosis problem solving. The book is organised as follows: Chapter 1 presents the basic knowledge about fuzzy sets, genetic algorithms and neural nets necessary for a clear understanding of the rest of this book. Chapter 2 analyzes direct fuzzy inference based on fuzzy if-then rules. Chapter 3 is devoted to the tuning of fuzzy rules for direct inference using genetic algorithms and neural nets. Chapter 4 presents models and algorithms for extracting fuzzy rules from experimental data. Chapter 5 describes a method for solving fuzzy logic equations necessary for the inverse fuzzy inference in diagnostic systems. Chapters 6 and 7 are devoted to inverse fuzzy inference based on fu...
Symmetry reduction related with nonlocal symmetry for Gardner equation
Ren, Bo
2017-01-01
Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.
BPS relations from spectral problems and blowup equations
Grassi, Alba
2016-01-01
Recently an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi-Yau threefolds has been proposed. At the same time an exact quantization condition for the cluster integrable systems associated to these geometries has been conjectured. The consistency between the two approaches leads to an infinite set of constraints for the refined BPS invariants of the toric Calabi-Yau threefolds. We show that, for the Y^{N,m} geometries, these constraints can be derived from the K-theoretic blowup equations for SU(N) SYM with generic Chern-Simons invariant m. In particular this furnishes a proof of the BPS constraints in the case of m = 0.
Einstein's equations from Einstein's inertial motion and Newton's law for relative acceleration
Schmid, Christoph
2016-01-01
We show that Einstein's $R^{\\hat{0} \\hat{0}}$ equation for nonrelativistic matter and strong gravitational fields is identical with Newton's equation for relative radial acceleration of neighbouring freefalling particles, spherically averaged. These laws are explicitely identical with primary observer's (1) space-time slicing by radial 4-geodesics, (2) radially parallel Local Ortho-Normal Bases, LONBs, (3) Riemann normal 3-coordinates. Hats on indices denote LONBs. General relativity follows from Newton's law of relative acceleration, Einstein's inertial motion, Lorentz covariance, and energy-momentum conservation combined with Bianchi identity. The gravitational field equation of Newton-Gauss and Einstein's $R^{\\hat{0} \\hat{0}}$ equation are identical and linear in gravitational field for an inertial primary observer.--- Einstein's equivalence between fictitious forces and gravitational forces is formulated as equivalence theorem in the equations of motion. With this, the gravitational field equation of 19th...
Relationship between fuzzy controllers and PID controllers
李洪兴
1999-01-01
The internal relations between fuzzy controllers and PID controllers are revealed. First, it is pointed out that a fuzzy controller with one input and one output is just a piecewise P controller. Then it is proved that a fuzzy controller with two inputs and one output is just a piecewise PD (or I) controller with interaction between P and D (or PI). At last, the conclusion that a fuzzy controller with three inputs and one output is just a piecewise PID controller with interaction among P, I and D is given. Moreover, a kind of difference scheme of fuzzy controllers is designed.
Generalized fuzzy ideals of near-rings
ZHAN Jian-ming; Dawaz B.
2009-01-01
The concept of ((∈),(∈)V (q))-fuzzy subnear-rings (ideals) of a near-ring is introduced and some of its related properties are investigated. In particular, the relationships among ordinary fuzzy subnear-rings (ideals), (∈,∈V q)-fuzzy subnear-rings (ideals) and ((∈),(∈)V (q))-fuzzy subnearrings (ideals) of near-rings are described. Finally, some characterization of [μ]t is given by means of (∈,∈V q)-fuzzy ideals.
A new fuzzy Monte Carlo method for solving SLAE with ergodic fuzzy Markov chains
Maryam Gharehdaghi
2015-05-01
Full Text Available In this paper we introduce a new fuzzy Monte Carlo method for solving system of linear algebraic equations (SLAE over the possibility theory and max-min algebra. To solve the SLAE, we first define a fuzzy estimator and prove that this is an unbiased estimator of the solution. To prove unbiasedness, we apply the ergodic fuzzy Markov chains. This new approach works even for cases with coefficients matrix with a norm greater than one.
田森; 陈建宏
2015-01-01
Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors. In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corresponding prevention and control work, multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory are implemented to evaluate them and find out the rules of this evaluation system with 14 representative cases. The methods of multi-hierarchical fuzzy evaluation can overall consider each influence factor of risk assessment system and their mutual impact, and the index weight based on the analytic hierarchy process is relatively reasonable. Rough set theory based on dominance relation reduces each index attribute from the top down, largely simplifies the complexity of the original evaluation system, and considers the preferential information in each index. Furthermore, grey correlation theory is applied to analysis of importance of each reducted condition attribute. The results demonstrate the feasibility of the proposed safety evaluation system and the application potential.
Fuzzy weakly preopen (preclosed) function in Kubiak-Sostak fuzzy topological spaces
Zahran, A.M. [Department of Mathematics, Faculty of Science, Al azhar University, Assuit (Egypt)], E-mail: zahran15@hotmail.com; Abd-Allah, M. Azab. [Department of Mathematics, Faculty of Science, Assuit University, Assuit (Egypt)], E-mail: mazab57@yahoo.com; Abd El-Rahman, Abd El-Nasser G. [Department of Mathematics, Faculty of Science, South valley University, Qena 83523 (Egypt)], E-mail: ghareeb_nasser@yahoo.com
2009-02-15
In this paper, we introduce and characterize fuzzy weakly preopen and fuzzy weakly preclosed functions between L-fuzzy topological spaces in Kubiak-Sostak sense and also study these functions in relation to some other types of already known functions.
Weak forms of continuity in I-double gradation fuzzy topological spaces.
Ghareeb, A
2012-12-01
In this paper, we introduce and characterize double fuzzy weakly preopen and double fuzzy weakly preclosed functions between I-double gradation fuzzy topological spaces and also study these functions in relation to some other types of already known functions.
Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity
Satin, Seema; Hu, Bei Lok
2016-01-01
For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally-related spacetime is known. For example, from the Minkowski solution of Martin and Verdaguer, those of the Einstein-Langevin equations in conformally-flat spacetimes, especially for spatially-flat Friedmann-Robertson-Walker models, can be readily obtained.
Conformally related Einstein-Langevin equations for metric fluctuations in stochastic gravity
Satin, Seema; Cho, H. T.; Hu, Bei Lok
2016-09-01
For a conformally coupled scalar field we obtain the conformally related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally related spacetime is known. For example, from the Minkowski solution of Martín and Verdaguer, those of the Einstein-Langevin equations in conformally flat spacetimes, especially for spatially flat Friedmann-Robertson-Walker models, can be readily obtained.
When do L-fuzzy ideals of a ring generate a distributive lattice?
Gao Ninghua
2016-01-01
Full Text Available The notion of L-fuzzy extended ideals is introduced in a Boolean ring, and their essential properties are investigated. We also build the relation between an L-fuzzy ideal and the class of its L-fuzzy extended ideals. By defining an operator “⇝” between two arbitrary L-fuzzy ideals in terms of L-fuzzy extended ideals, the result that “the family of all L-fuzzy ideals in a Boolean ring is a complete Heyting algebra” is immediately obtained. Furthermore, the lattice structures of L-fuzzy extended ideals of an L-fuzzy ideal, L-fuzzy extended ideals relative to an L-fuzzy subset, L-fuzzy stable ideals relative to an L-fuzzy subset and their connections are studied in this paper.
Tseng, Ming-Lang; Lim, Ming; Wu, Kuo-Jui; Zhou, Li
2017-01-01
The existing literatures are lacking on the cost and benefit concerns, screening the measures and convergence of interval-valued triangular fuzzy numbers-grey relation analysis (IVTFN-GRA) weight together. Nonetheless, Green supply chain management is always suffering the linguistic preferences and system incomplete information in evaluation process to enhance the performance. Yet, those previous studies are merely based on un-converged weight results. Hence, this study proposed a hybrid meth...
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...
HUANGYi; ZHANGYin-ke
2003-01-01
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work.The linear equations were expressed in the forms similar to Biot''''''''s equations for saturated porous media.The Darcy''''''''s laws of unsaturated soil were proved.It is shown that Biot''''''''s equations of saturated porous media are the simplification of the theory.All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.
Exact solutions of the Klein-Gordon equation with Makarov potential and a recurrence relation
Zhang Min-Cang; Wang Zhen-Bang
2007-01-01
In this paper, the Klein-Gordon equation with equal scalar and vector Makarov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number e is established and some special cases of Makarov potential are discussed.
Yun-Chin Chen
2011-01-01
Full Text Available Problem statement: In the information age, the process of E-Commerce (EC operates quickly and the present enterprises of Taiwan have to face the Free Cross-Strait Market (FCSM with Mainland China, which will definitely change the model as well as the performance of the supply chain. Hence, this study focuses on the issue of supply chain performance evaluation of the wafer testing house in Taiwan. Approach: This investigation applied the Fuzzy Analytic Hierarchy Process (FAHP to derive the weights of influential indicators for evaluating the supply chain performance of the wafer testing house and the Grey Relation Analysis (GRA was used to evaluate the performance between the FCSM and EC aspects. Results: The analyzed results had identified the indicator weight of the supply chain performance evaluation in the wafer testing house and the indicator performances between different aspects were compared. The research results indicated that the FCSM aspect had better performance than EC aspect of the supply chain evaluation in the wafer testing house. Conclusion/Recommendations: Based on the analyzed results, the managers can find out the problems and improve the supply chain performance of the wafer testing house. This study not only can be a good basis for improvements of the case company, but also can be the reference for evaluating the supply chain performance of the wafer testing house.
Kadir, Norhidayah A.; Sarudin, Ezzah Suraya; Hamid, Fairus; Shamsuddin, Nor Diyana Ahmad
2014-10-01
There are various thoughts and opinions when it comes to how people think of their selected banks. Therefore, to choose the best bank with a good personal loan package can be a bit tricky especially for first time customer. This research offers a guide in choosing the right bank for applying personal loan package by highlighting the important criteria that applicants should take into consideration. In order to cater the problem above, we used Consistent Fuzzy Preference Relations (CFPR). Based on expert and public opinions, the important criteria in selecting an Islamic personal loan package are interest rate, tenure of loan, processing period and security of the loan. We developed questionnaire with the criteria mention earlier and distributed it among academic staffs and non academic staffs at Faculty of Computer and Mathematical Sciences (FSKM), UiTM Shah Alam. Based on the questionnaire, we found that four banks have been selected for multiple reasons. Before we could determine the best bank, calculations are divided into 2 phases which are criteria weights determination and ranking of alternatives. We implemented these phases to get the aggregation result and to obtain the ranking in descending order. As a result, our objectives have been achieved. As a conclusion, CFPR can help others in the decision making process.
Fuzzy Set Approximations in Fuzzy Formal Contexts
Mingwen Shao; Shiqing Fan
2006-01-01
In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept, we present a pair of rough fuzzy set approximations within fuzzy formal contexts. By the proposed rough fuzzy set approximations, we can approximate a fuzzy set according to different precision level. We discuss the properties of the proposed approximation operators in detail.
模糊集间的R0-相似关系及其性质%R0 -similarity relation between fuzzy sets and its properties
刘杰; 吴洪博
2011-01-01
将王国俊教授在R0-型逻辑系统中建立的R0-蕴涵算子应用于模糊数学理论之中,在非空集合X为论域的模糊集族F(X)上定义了一种新型运算- R0蕴含运算,并讨论了F(X)上R0-蕴含运算的一些基本性质.通过R0-蕴含运算在F(X)上定义了一个二元模糊相似关系- R0-相似关系,并对其性质进行了较为详细的讨论.在有限论域X确定的模糊集族F(X)上给出了几个R0-相似关系的具体实例.%Ro -implication operator proposed by Professor Wang Guojun in the Ro -type logic system has been applied to the fuzzy mathematical theory,and a new kind of computation- Ro -implication operation, is defined on the family F(X) of fuzzy sets, and its basic properties have been discussed.Then, a binary fuzzy similarity relation- Ro -similarity relation on F(X) is defined through the Ro implication,and its properties are discussed in detail.Finally,several examples of Ro -similarity relation are provided by the Ro implication operator on F(X) with the finite domain Xnot only the results of this paper make an application of the R0-type logic system,but also enrich the methods of studying fuzzy mathematics.
Relating fundamental creep mechanisms in Waspaloy to the Wilshire equations
Deen C.
2014-01-01
Full Text Available Creep tests of the polycrystalline nickel alloy Waspaloy have been conducted at Swansea University, for varying stress conditions at 700 ∘C. Investigation through use of Transmission Electron Microscopy at Cambridge University has examined the dislocation networks formed under these conditions, notably those with stresses above and below the yield stress. This paper highlights how the dislocation structures vary throughout creep and proposes a dislocation mechanism theory for creep in Waspaloy. In particular, the roles of recovery, tertiary gamma prime particles and dislocation foresting are examined, and related back to observations from the Wilshire fits. The virgin (untested material has been forged and heat treated, containing some recrystallised material together with areas of more heavily deformed and recovered material clustered around the grain boundaries. Observations from tests below the 0.2% proof stress show relatively low dislocation densities away from grain boundaries and dislocation movement can be seen to be governed by interactions with the γ′ precipitates. In contrast, above the 0.2% proof stress, TEM observations show a substantially greater density of dislocations. The increased density provides an increment of strength through forest hardening. At stresses above the original yield point, determined by the precipitates, the creep rate is controlled by inter-action with the dislocation forest and results in an apparent activation energy change. It is proposed that the activation energy change is related to the stress increment provided by work hardening, as can be observed from Ti, Ni and steel results.
Minimal solution of general dual fuzzy linear systems
Abbasbandy, S. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34194-288 (Iran, Islamic Republic of)], E-mail: abbasbandy@yahoo.com; Otadi, M.; Mosleh, M. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh (Iran, Islamic Republic of)
2008-08-15
Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered.
DIFFUSIVE-DISPERSIVE TRAVELING WAVES AND KINETIC RELATIONS IV.COMPRESSIBLE EULER EQUATIONS
无
2003-01-01
The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are taken into account. A typical example of nonconvex con-stitutive equation for fluids is Van der Waals' equation. The first order terms of these partialdifferential equations form a nonlinear system of mixed (hyperbolic-elliptic) type. For a class ofnonconvex equations of state, an existence theorem of traveling waves solutions with arbitrarylarge amplitude is established here. The authors distinguish between classical (compressive) andnonclassical (undercompressive) traveling waves. The latter do not fulfill Lax shock inequali-ties, and are characterized by the so-called kinetic relation, whose properties are investigatedin this paper.
Differential Equations Related to the Williams-Bjerknes Tumour Model
F Martinez; A R Villena
2000-08-01
We investigate an initial value problem which is closely related to the Williams-Bjerknes tumour model for a cancer which spreads through an epithelial basal layer modeled on ⊂ 2. The solution of this problem is a family =(()), where each () could be considered as an approximation to the probability that the cell situated at is cancerous at time . We prove that this problem has a unique solution, it is defined on [0, + ∞], and, for some relevant situations, lim → ∞ ()=1 for all ∈ . Moreover, we study the expected number of cancerous cells at time .
Hesitant Fuzzy Soft Subalgebras and Ideals in BCK/BCI-Algebras
Jun, Young Bae; Ahn, Sun Shin
2014-01-01
As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories in BCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (closed) hesitant fuzzy soft ideals are introduced, and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra and a (closed) hesitant fuzzy soft ideal are discussed. Conditions for a hesitant fuzzy soft set to be a hesitant fuzzy soft subalgebra are given, and conditions for a hesitant fuzzy soft subalgebra to be a hesitant fuzzy soft ideal are provided. Characterizations of a (closed) hesitant fuzzy soft ideal are considered. PMID:25405234
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...
Mackey, Lester [Department of Statistics, Stanford University,Stanford, CA 94305 (United States); Nachman, Benjamin [Department of Physics, Stanford University,Stanford, CA 94305 (United States); SLAC National Accelerator Laboratory, Stanford University,2575 Sand Hill Rd, Menlo Park, CA 94025 (United States); Schwartzman, Ariel [SLAC National Accelerator Laboratory, Stanford University,2575 Sand Hill Rd, Menlo Park, CA 94025 (United States); Stansbury, Conrad [Department of Physics, Stanford University,Stanford, CA 94305 (United States)
2016-06-01
Collimated streams of particles produced in high energy physics experiments are organized using clustering algorithms to form jets. To construct jets, the experimental collaborations based at the Large Hadron Collider (LHC) primarily use agglomerative hierarchical clustering schemes known as sequential recombination. We propose a new class of algorithms for clustering jets that use infrared and collinear safe mixture models. These new algorithms, known as fuzzy jets, are clustered using maximum likelihood techniques and can dynamically determine various properties of jets like their size. We show that the fuzzy jet size adds additional information to conventional jet tagging variables in boosted topologies. Furthermore, we study the impact of pileup and show that with some slight modifications to the algorithm, fuzzy jets can be stable up to high pileup interaction multiplicities.
On discrete fractional integral operators and related Diophantine equations
Kim, Jongchon
2011-01-01
In this paper we show that an arithmetic property of a hypersurface in $\\zn{k+1}$ (a map $\\gamma:\\zn{k} \\to \\mathbb{Z}$) gives $l^p \\to l^q$ bounds of a Radon-type discrete fractional integral operator along the hypersurface. As a corollary, we prove $l^p \\to l^q$ bounds of a Radon-type discrete fractional integral operator along paraboloids in $\\zn{3}$ and some other related operators. As a by-product of this approach, we show that the statement $r_{s,k}(N) = O(N^\\epsilon)$ for any $\\epsilon>0$ is false if $s>k$, where $r_{s,k}(N)$ denotes the number of representations of a positive integer $N$ as a sum of s positive $k$-th powers.
Dr.Pranita Goswami
2011-01-01
The Partial Fuzzy Set is a portion of the Fuzzy Set which is again a Fuzzy Set. In the Partial Fuzzy Set the baseline is shifted from 0 to 1 to any of its α cuts . In this paper we have fuzzified a portion of the Fuzzy Set by transformation
New Definition and Properties of Fuzzy Entropy
Qing Ming; Qin Yingbing
2006-01-01
Let X = (x1,x2 ,…,xn ) and F(X) be a fuzzy set on a universal set X. A new definition of fuzzy entropy about a fuzzy set A on F(X), e*, is defined based on the order relation "≤" on [0,1/2] n. It is proved that e* is a σ-entropy under an additional requirement. Besides, some entropy formulas are presented and related properties are discussed.
Propagators of Generalized Schrödinger Equations Related by First-order Supersymmetry
A. Schulze-Halberg
2011-01-01
Full Text Available We construct an explicit relation between propagators of generalized Schrödinger equations that are linked by a first-order supersymmetric transformation. Our findings extend and complement recent results on the conventional case [1].
Wang Lihe; Zhou Shulin
2006-01-01
In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a nonlinear parabolic partial differential equation, which is related to the Malik-Perona model in image analysis.
Jensen, E W; Nebot, A; Caminal, P;
1999-01-01
The aim of this study was to identify a possible relationship between haemodynamic variables, auditory evoked potentials (AEP) and inspired fraction of isoflurane (ISOFl). Two different models (isoflurane and mean arterial pressure) were identified using the fuzzy inductive reasoning (FIR......) methodology. A fuzzy model is able to identify non-linear and linear components of a causal relationship by means of optimization of information content of available data. Nine young female patients undergoing hysterectomy under general anaesthesia were included. Mean arterial pressure (MAP), heart rate (HR...
Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)
2005-01-28
Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample
HUANGYi; ZHANGYin-ke
2003-01-01
The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory.The soils were treated as the mixture composed of three constituents.First ,from the researches of soil mechanics,some basic assumptions about the unsaturated soil mixture were mode,and the entropy inequality unsaturated soil mixture was derived.Then,with the common method usually used to deal with the constitutive problems in mixture theory,the nonlinear constitutive equations were obtained.Finally,putting the constiutive equtions of constituents into the balance equations of momentum,the nonlinear field equations of constitutents into the balance equations of momentum,the nonliear field equations of constitutents were set up.The balance equation of energy of unsaturated soil was also given,and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.
Properties of fuzzy hyperplanes
ZHANG Zhong; LI Chuandong; WU Deyin
2004-01-01
Some properties of closed fuzzy matroid and those of its hyperplanes are investigated. A fuzzy hyperplane property,which extends the analog of a crisp matroid from crisp set systems to fuzzy set systems, is proved.
Statistical mechanics of fuzzy random polymer networks
陈晓红
1995-01-01
A statistical mechanics framework of fuzzy random polymer networks is established based on the theories of fuzzy systems. The entanglement effect is manifested quantitatively by introducing an entanglement tensor and membership function and the amorphous structure is treated as the fuzzy random network made up of macromolecular coils entangled randomly. A random tetrahedral entangled-crosslinked cell is chosen as an average representative unit of the fuzzy random polymer network structure. By making use of the theory of fuzzy probability and statistical mechanics, the expression for the free energy of deformation is given, which fits well with the experimental data on rubber elasticity under various deformation modes. Both classical statistical theory and Mooney-Rivlin equation can be taken as its special cases.
On Rough Intuitionistic Fuzzy Ideals(Filters) in Lattices
HE Peng-fei; YANG Yong-wei; XIN Xiao-long
2014-01-01
In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such ideals(filters).
Bonissone CIDU Presentation: Design of Local Fuzzy Models
National Aeronautics and Space Administration — After reviewing key background concepts in fuzzy systems and evolutionary computing, we will focus on the use of local fuzzy models, which are related to both kernel...
Mathematical Foundation of Basic Algorithms of Fuzzy Reasoning
潘正华
2005-01-01
Algorithm of fuzzy reasoning has been successful applied in fuzzy control, but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper, structure of basic algorithms of fuzzy reasoning was studied, its rationality was discussed from the viewpoint of logic and mathematics, and three theorems were proved. These theorems shows that there always exists a mathematical relation (that is, a bounded real function) between the premises and the conclusion for fuzzy reasoning, and in fact various algorithms of fuzzy reasoning are specific forms of this function. Thus these results show that algorithms of fuzzy reasoning are theoretically reliable.
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...... prediction of outputs. This article presents an overview of some of the most popular clustering methods, namely Fuzzy Cluster-Means (FCM) and its generalizations to Fuzzy C-Lines and Elliptotypes. The algorithms for computing cluster centers and principal directions from a training data-set are described....... A method to obtain an optimized number of clusters is outlined. Based upon the cluster's characteristics, a behavioural model is formulated in terms of a rule-base and an inference engine. The article reviews several variants for the model formulation. Some limitations of the methods are listed...
王坚强; 吴佳亭
2015-01-01
Hesitant fuzzy linguistic sets is an extension of both linguistic term sets and hesitant fuzzy sets. Motivated by the idea of traditional Electre methods, an Electre method for hesitant fuzzy linguistic information is introduced. Firstly, the Hausdorff distance of hesitant fuzzy linguistic numbers are proposed. Then, the outranking relation for hesitant fuzzy linguistic numbers under each criterion is developed, based on which, a method for hesitant fuzzy linguistic multi-criteria decision-making based on the outranking relation is proposed. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed method.%犹豫模糊语言集是语言集和犹豫模糊集的扩展,受传统Electre方法的启发,构建基于优序关系的犹豫模糊语言多准则决策方法. 首先,给出犹豫模糊语言数的Hausdorff距离公式;然后,基于每一准则下方案评价的对比,建立犹豫模糊语言数的优序关系,并在此基础上,提出一种基于优序关系的犹豫模糊语言多准则决策方法;最后,通过算例表明了所提出方法的有效性和可行性.
Jørgensen, Jacob Høj
by Eric von Hippel to a network innovation perspective and discusses the different concepts as a method when identifying industrial customers for network based innovation. This is done in order to provide insights in how the Fuzzy Front-End of network based innovation can become more efficient. ...
FUZZY MODEL FOR TWO-DIMENSIONAL RIVER WATER QUALITY SIMULATION UNDER SUDDEN POLLUTANTS DISCHARGED
无
2007-01-01
Based on the fuzziness and impreciseness of water environmental system, the fuzzy arithmetic was used to simulate the fuzzy and imprecise relations in modeling river water quality. By defining the parameters of water quality model as symmetrical triangular fuzzy numbers, a two-dimensional fuzzy water quality model for sudden pollutant discharge is established. From the fuzzy model, the pollutant concentrations, corresponding to the specified confidence level of α, can be obtained by means of the α-cut technique and arithmetic operations of triangular fuzzy numbers. Study results reveal that it is feasible in theory and reliable on calculation applying triangular fuzzy numbers to the simulation of river water quality.
m-Polar fuzzy sets: an extension of bipolar fuzzy sets.
Chen, Juanjuan; Li, Shenggang; Ma, Shengquan; Wang, Xueping
2014-01-01
Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and [0,1](2)-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion of m-polar fuzzy set (actually, [0,1] (m)-set which can be seen as a generalization of bipolar fuzzy set, where m is an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case of m-polar fuzzy sets. We also give examples to show how to apply m-polar fuzzy sets in real world problems.
黄义; 张引科
2003-01-01
The nonlinear constitutive equations and field equations of unsaturated soils were cons tructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.
Fuzzy Functional Dependencies and Bayesian Networks
LIU WeiYi(刘惟一); SONG Ning(宋宁)
2003-01-01
Bayesian networks have become a popular technique for representing and reasoning with probabilistic information. The fuzzy functional dependency is an important kind of data dependencies in relational databases with fuzzy values. The purpose of this paper is to set up a connection between these data dependencies and Bayesian networks. The connection is done through a set of methods that enable people to obtain the most information of independent conditions from fuzzy functional dependencies.
Intuitionistic Fuzzy Cycles and Intuitionistic Fuzzy Trees
Alshehri, N. O.
2014-01-01
Connectivity has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. The structural properties of intuitionistic fuzzy graphs provide a tool that allows for the solution of operations research problems. In this paper, we introduce various types of intuitionistic fuzzy bridges, intuitionistic fuzzy cut vertices, intuitionistic fuzzy cycles, and intuitionistic fuzzy trees in intuitionistic fuzzy graphs and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types. PMID:24701155
XIE Yin-Li; YANG Xin-Fang; JIA Li-Qun
2011-01-01
Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied.The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given.Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained.Finally, an example is given to illustrate the application of the results.PACS numbers: 11.30.-j, 45.20.Jj, 02.20.Sv
A Novel Empirical Equation for Relative Permeability in Low Permeability Reservoirs☆
Yulei Ge; Shurong Li; Kexin Qu
2014-01-01
In this paper, a novel empirical equation is proposed to calculate the relative permeability of low permeability res-ervoir. An improved item is introduced on the basis of Rose empirical formula and Al-Fattah empirical formula, with one simple model to describe oil/water relative permeability. The position displacement idea of bare bones particle swarm optimization is applied to change the mutation operator to improve the RNA genetic algorithm. The param-eters of the new empirical equation are optimized with the hybrid RNA genetic algorithm (HRGA) based on the ex-perimental data. The data is obtained from a typical low permeability reservoir wel 54 core 27-1 in GuDong by unsteady method. We carry out matlab programming simulation with HRGA. The comparison and error analysis show that the empirical equation proposed is more accurate than the Rose empirical formula and the exponential model. The generalization of the empirical equation is also verified.
Fuzzy Morphological Polynomial Image Representation
Chin-Pan Huang
2010-01-01
Full Text Available A novel signal representation using fuzzy mathematical morphology is developed. We take advantage of the optimum fuzzy fitting and the efficient implementation of morphological operators to extract geometric information from signals. The new representation provides results analogous to those given by the polynomial transform. Geometrical decomposition of a signal is achieved by windowing and applying sequentially fuzzy morphological opening with structuring functions. The resulting representation is made to resemble an orthogonal expansion by constraining the results of opening to equate adapted structuring functions. Properties of the geometric decomposition are considered and used to calculate the adaptation parameters. Our procedure provides an efficient and flexible representation which can be efficiently implemented in parallel. The application of the representation is illustrated in data compression and fractal dimension estimation temporal signals and images.
Encoding spatial images: A fuzzy set theory approach
Sztandera, Leszek M.
1992-01-01
As the use of fuzzy set theory continues to grow, there is an increased need for methodologies and formalisms to manipulate obtained fuzzy subsets. Concepts involving relative position of fuzzy patterns are acknowledged as being of high importance in many areas. In this paper, we present an approach based on the concept of dominance in fuzzy set theory for modelling relative positions among fuzzy subsets of a plane. In particular, we define the following spatial relations: to the left (right), in front of, behind, above, below, near, far from, and touching. This concept has been implemented to define spatial relationships among fuzzy subsets of the image plane. Spatial relationships based on fuzzy set theory, coupled with a fuzzy segmentation, should therefore yield realistic results in scene understanding.
A recurrent fuzzy network for fuzzy temporal sequence processing and gesture recognition.
Juang, Chia-Feng; Ku, Ksuan-Chun
2005-08-01
A fuzzified Takagi-Sugeno-Kang (TSK)-type recurrent fuzzy network (FTRFN) for handling fuzzy temporal information is proposed in this paper. The FTRFN extends our previously proposed network, TRFN, to deal with fuzzy temporal signals represented by Gaussian or triangular fuzzy numbers. In the precondition part of FTRFN, matching degrees between input fuzzy variables and fuzzy antecedent sets is performed by similarity measure. In the TSK-type consequence, a linear combination of fuzzy variables is computed, where two sets of combination coefficients, one for the center and the other for the width of each fuzzy number, are used. Derivation of the linear combination results and final network output is based on left-right fuzzy number operation. There are no rules in FTRFN initially; they are constructed online by concurrent structure and parameter learning, where all free parameters in the precondition/consequence of FTRFN are all tunable. FTRFN can be applied on a variety of domains related to fuzzy temporal information processing. In this paper, it has been applied on one-dimensional and two-dimensional fuzzy temporal sequence prediction and CCD-based temporal gesture recognition. The performance of FTRFN is verified from these examples.
The relation between Maxwell, Dirac, and the Seiberg-Witten equations
Waldyr A. Rodrigues
2003-01-01
Full Text Available We discuss unsuspected relations between Maxwell, Dirac, and the Seiberg-Witten equations. First, we present the Maxwell-Dirac equivalence (MDE of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field the equation F=ψγ21ψ˜, where F is a given electromagnetic field. Such task is presented and it permits to clarify some objections to the MDE which claim that no MDE may exist because F has six (real degrees of freedom and ψ has eight (real degrees of freedom. Also, we review the generalized Maxwell equation describing charges and monopoles. The enterprise is worth, even if there is no evidence until now for magnetic monopoles, because there are at least two faithful field equations that have the form of the generalized Maxwell equations. One is the generalized Hertz potential field equation (which we discuss in detail associated with Maxwell theory and the other is a (nonlinear equation (of the generalized Maxwell type satisfied by the 2-form field part of a Dirac-Hestenes spinor field that solves the Dirac-Hestenes equation for a free electron. This is a new result which can also be called MDE of the second kind. Finally, we use the MDE of the first kind together with a reasonable hypothesis to give a derivation of the famous Seiberg-Witten equations on Minkowski spacetime. A physical interpretation for those equations is proposed.
Li, Zhaowen; Wen, Guoqiu; Xie, Ningxin
2015-07-01
The existing methods of fuzzy soft sets in decision making are mainly based on different kinds of level soft sets, and it is very difficult for decision makers to select a suitable level soft set in most instances. The goal of this paper is to present an approach to fuzzy soft sets in decision making to avoid selecting a suitable level soft set and to apply this approach to solve medical diagnosis problems. This approach combines grey relational analysis with the Dempster-Shafer theory of evidence. It first utilizes grey relational analysis to calculate the grey mean relational degree, by which we calculate the uncertain degree of various parameters. Then, on the basis of the uncertain degree, the suitable basic probability assignment function of each independent alternative with each parameter can be obtained. Next, we apply Dempster-Shafer rule of evidence fusion to aggregate these alternatives into a collective alternative, by which these alternatives are ranked and the best alternative is obtained. Finally, we compare this approach with the mean potentiality approach. The results demonstrate the effectiveness and feasibility of this approach vis-a-vis the mean potentiality approach, Feng's method, Analytical Hierarchy Process and Naive Bayes' classification method because the measure of performance of this approach is the same as that of the mean potentiality approach, and the belief measure of the whole uncertainty falls from the initial mean 0.3821 to 0.0069 in an application of medical diagnosis. An approach to fuzzy soft sets in decision making by combining grey relational analysis with Dempster-Shafer theory of evidence is introduced. The advantages of this approach are discussed. A practical application to medical diagnosis problems is given. Copyright © 2015 Elsevier B.V. All rights reserved.
Research on the Equation of DF Relation%DF关系方程的研究
无
2004-01-01
This paper gives out the basic concept of DF matrix. In this base it researches the basic theories and the answers of the equation of DF relation in the norm system further. It proves the importance and effect of these basic productions with using the basic concept. And this paper enriches and develops the content of DE relation through the research on it.
GATE TYPE SELECTION BASED ON FUZZY MAPPING
无
2002-01-01
Gate type selection is very important for mould design. Improper gate type may lead to poor product quality and low production efficiency. Although numerical simulation approach could be used to optimize gate location, the determination of gate type is still up to designers' experience. A novel method for selecting gate type based on fuzzy logic is proposed. The proposed methodology follows three steps:Design requirements for gate is extracted and generalized; Possible gate types (design schemes) are presented; The fuzzy mapping relationship between gate design requirements and gate design scheme is established based on fuzzy composition and fuzzy relation transition matrices that are assigned by domain experts.
Fuzzy controlofanylonpolymerizationsemi-batchreactor
Wakabayashi, C; Embiruçu, Marcelo; Fontes, Cristiano; Kalid, Ricardo
2009-01-01
Acesso restrito: Texto completo. p. 537-553 Batch and semi-batch polymerization reactors with specified trajectories for certain process variables present challenging control problems. This work reports, results and procedures related to the application of PI (proportional and integral) fuzzy control in a semi-batch reactor for the production of nylon 6. Closed loop simulation results were based on a phenomenological model adjusted for a commercial reactor and they attest to the potential ...
曹立明
1990-01-01
By the similarity between the syllogism in logic and a path proposition in graph theory,a new concept,fuzzy reasoning graph G has been given in this paper. Transitive closure has been studied and used to do reasoning related to self-loop in G,and an algorithm has been designed to cope with reasoning in other cycles in G. Both approaches are applicable and efficient.
Vedic Mathematics: 'Vedic' or 'Mathematics' -- A Fuzzy and Neutrosophic Analysis
2006-01-01
In this book the authors probe into Vedic Mathematics (a concept that gained renown in the period of the religious fanatic and revivalist Hindutva rule in India): and explore whether it is really 'Vedic' in origin or 'Mathematics' in content. We analyzed this problem using fuzzy models like Fuzzy Cognitive Maps (FCM), Fuzzy Relational Maps (FRM) and the newly constructed fuzzy dynamical system (and its Neutrosophic analogue) that can analyze multi-experts opinion at a time using a single mode...
Precise analysis of pion-pion scattering data from Roy equations and forward dispersion relations
Peláez, J R; Kaminski, R; Ynduráin, F J
2008-01-01
We review our recent analysis of pion-pion scattering data in terms of Roy equations and Forward Dispersion Relations, and present some preliminary results in terms of a new set of once-subtracted coupled equations for partial waves. The first analysis consists of independent fits to the different pion-pion channels that satisfies rather well the dispersive representation. In the second analysis we constrain the fit with the dispersion relations. The latter provides a very precise and model independent description of data using just analyticity, causality and crossing.
On Characterization of Rough Type-2 Fuzzy Sets
Tao Zhao
2016-01-01
Full Text Available Rough sets theory and fuzzy sets theory are important mathematical tools to deal with uncertainties. Rough fuzzy sets and fuzzy rough sets as generalizations of rough sets have been introduced. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle high uncertainties. In this paper, the rough type-2 fuzzy set model is proposed by combining the rough set theory with the type-2 fuzzy set theory. The rough type-2 fuzzy approximation operators induced from the Pawlak approximation space are defined. The rough approximations of a type-2 fuzzy set in the generalized Pawlak approximation space are also introduced. Some basic properties of the rough type-2 fuzzy approximation operators and the generalized rough type-2 fuzzy approximation operators are discussed. The connections between special crisp binary relations and generalized rough type-2 fuzzy approximation operators are further examined. The axiomatic characterization of generalized rough type-2 fuzzy approximation operators is also presented. Finally, the attribute reduction of type-2 fuzzy information systems is investigated.
Some Additions to the Fuzzy Convergent and Fuzzy Bounded Sequence Spaces of Fuzzy Numbers
Şengönül, M.; Z. Zararsız
2011-01-01
Some properties of the fuzzy convergence and fuzzy boundedness of a sequence of fuzzy numbers were studied in Choi (1996). In this paper, we have consider, some important problems on these spaces and shown that these spaces are fuzzy complete module spaces. Also, the fuzzy α-, fuzzy β-, and fuzzy γ-duals of the fuzzy module spaces of fuzzy numbers have been computeded, and some matrix transformations are given.
Sharma Animesh
2007-01-01
Full Text Available Abstract Background The four heterogeneous childhood cancers, neuroblastoma, non-Hodgkin lymphoma, rhabdomyosarcoma, and Ewing sarcoma present a similar histology of small round blue cell tumor (SRBCT and thus often leads to misdiagnosis. Identification of biomarkers for distinguishing these cancers is a well studied problem. Existing methods typically evaluate each gene separately and do not take into account the nonlinear interaction between genes and the tools that are used to design the diagnostic prediction system. Consequently, more genes are usually identified as necessary for prediction. We propose a general scheme for finding a small set of biomarkers to design a diagnostic system for accurate classification of the cancer subgroups. We use multilayer networks with online gene selection ability and relational fuzzy clustering to identify a small set of biomarkers for accurate classification of the training and blind test cases of a well studied data set. Results Our method discerned just seven biomarkers that precisely categorized the four subgroups of cancer both in training and blind samples. For the same problem, others suggested 19–94 genes. These seven biomarkers include three novel genes (NAB2, LSP1 and EHD1 – not identified by others with distinct class-specific signatures and important role in cancer biology, including cellular proliferation, transendothelial migration and trafficking of MHC class antigens. Interestingly, NAB2 is downregulated in other tumors including Non-Hodgkin lymphoma and Neuroblastoma but we observed moderate to high upregulation in a few cases of Ewing sarcoma and Rabhdomyosarcoma, suggesting that NAB2 might be mutated in these tumors. These genes can discover the subgroups correctly with unsupervised learning, can differentiate non-SRBCT samples and they perform equally well with other machine learning tools including support vector machines. These biomarkers lead to four simple human interpretable
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
Xi-Zhong, Liu
2012-01-01
In this paper, We derive the symmetry group theorem to the Lin-Tsien equation by using the modified CK's direct method, from which we obtain the corresponding symmetry group. More importantly, conservation laws corresponding to the Kac-Moody-Virasoro symmetry algebra of Lin-Tsien equation is obtained up to second order group invariants.
Fuzzy ta/2 symmetries of straight chain conjugate polyene molecules
无
2009-01-01
On the basis of our recent studies on the molecular fuzzy point group symmetry,we further probe into the more complicated planar one-dimensional fuzzy periodic molecules-straight chain conjugate polyene.Except for the fuzzy translation transformation,the space transformation of the fuzzy screw rotation and the glide plane will be referred to.In addition,other fuzzy point symmetry transformation lain in the space transformation is discussed.Usually there is a correlation between the fuzzy symmetry characterization caused by the transition of the point symmetry elements and by certain space symmetry transformation.For the molecular orbital,the irreducible representation component is analyzed besides the membership function of the fuzzy symmetry transformation.Also,we inquire into the relativity between some molecular property and the fuzzy symmetry characterization.
Fuzziness in Chang's fuzzy topological spaces
1999-01-01
It is known that fuzziness within the concept of openness of a fuzzy set in a Chang's fuzzy topological space (fts) is absent. In this paper we introduce a gradation of openness for the open sets of a Chang jts (X, $\\mathcal{T}$) by means of a map $\\sigma\\;:\\; I^{x}\\longrightarrow I\\left(I=\\left[0,1\\right]\\right)$, which is at the same time a fuzzy topology on X in Shostak 's sense. Then, we will be able to avoid the fuzzy point concept, and to introduce an adeguate theory f...
Representation Theorems for Fuzzy Random Sets and Fuzzy Stochastic Processes
无
1999-01-01
The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set-valued random sets, fuzzy random elements and fuzzy set-valued stochastic processes are obtained.
Homeopathic drug selection using Intuitionistic fuzzy sets.
Kharal, Athar
2009-01-01
Using intuitionistic fuzzy set theory, Sanchez's approach to medical diagnosis has been applied to the problem of selection of single remedy from homeopathic repertorization. Two types of Intuitionistic Fuzzy Relations (IFRs) and three types of selection indices are discussed. I also propose a new repertory exploiting the benefits of soft-intelligence.
Kosko, Bart
1991-01-01
Mappings between fuzzy cubes are discussed. This level of abstraction provides a surprising and fruitful alternative to the propositional and predicate-calculas reasoning techniques used in expert systems. It allows one to reason with sets instead of propositions. Discussed here are fuzzy and neural function estimators, neural vs. fuzzy representation of structured knowledge, fuzzy vector-matrix multiplication, and fuzzy associative memory (FAM) system architecture.
S. Nazmul
2014-03-01
Full Text Available Notions of Lowen type fuzzy soft topological space are introduced and some of their properties are established in the present paper. Besides this, a combined structure of a fuzzy soft topological space and a fuzzy soft group, which is termed here as fuzzy soft topological group is introduced. Homomorphic images and preimages are also examined. Finally, some definitions and results on fuzzy soft set are studied.
Immink, G. K.
1994-10-01
This paper is concerned with applications of the Mellin transformation in the study of homogeneous linear differential and difference equations with polynomial coefficients. We begin by considering a differential equation (D) with regular singularities at O and ∞ and arbitrary singularities in the rest of the complex plane, and the difference equation (Δ‧) obtained from (D) by a variant of the formal Mellin transformation. We define fundamental systems of solutions of (Δ‧), analytic in either a right or a left half plane. by the use of Mellin transforms of microsolutions of (D). The relations between these fundamental systems are expressed in terms of central connection matrices of (D). Second, we study the differential equation (D1) obtained from (D) by means of a formal Laplace transformation and the difference equation (Δ1) obtained from (D1) by a formal Mellin transformation. We use Mellin transforms of "ordinary" solutions of (D1) with moderate growth at ∞ to construct fundamental systems of solutions of (Δ1). The relation between these fundamental systems involves certain Stokes multipliers and a formal monodromy matrix of (D1).
Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Khan, Yasir; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustin Leobardo; Castaneda-Sheissa, Roberto; Pereyra-Diaz, Domitilo; Cervantes-Perez, Juan; Agustin Perez-Sesma, Jose Antonio; Hernandez-Machuca, Sergio Francisco; Cuellar-Hernandez, Leticia
2014-01-01
In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.
Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation
Prentice, J. S. C.
2012-01-01
An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…
无
2010-01-01
In this paper, we study an even order neutral differential equation with deviating arguments, and obtain new oscillation results without the assumptions which were required for related results given before. Our results extend and improve many known oscillation criteria, based on the standard integral averaging technique.
An estimator for the relative entropy rate of path measures for stochastic differential equations
Opper, Manfred
2017-02-01
We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.
NEW OSCILLATION CRITERIA RELATED TO EULER S INTEGRAL FOR CERTAIN NONLINEAR DIFFERENTIAL EQUATION
无
2011-01-01
Using the integral average technique and a new function,some new oscillation criteria related to Euler integral are obtained for second order nonlinear differential equations with damping and forcing. Our results are of a higher degree of generality than some previous results. Information about the distribution of the zeros of solutions to the system is also obtained.
Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Khan, Yasir; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustin Leobardo; Castaneda-Sheissa, Roberto; Pereyra-Diaz, Domitilo; Cervantes-Perez, Juan; Agustin Perez-Sesma, Jose Antonio; Hernandez-Machuca, Sergio Francisco; Cuellar-Hernandez, Leticia
2014-01-01
In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.
An Introduction to Relativistic Quantum Mechanics. I. From Relativity to Dirac Equation
De Sanctis, M
2007-01-01
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear algebra are employed for the development of the present work.
Cao, Buwen; Luo, Jiawei; Liang, Cheng; Wang, Shulin; Ding, Pingjian
2016-10-01
Identifying overlapping protein complexes in protein-protein interaction (PPI) networks can provide insight into cellular functional organization and thus elucidate underlying cellular mechanisms. Recently, various algorithms for protein complexes detection have been developed for PPI networks. However, majority of algorithms primarily depend on network topological feature and/or gene expression profile, failing to consider the inherent biological meanings between protein pairs. In this paper, we propose a novel method to detect protein complexes using pseudo-clique extension based on fuzzy relation (PCE-FR). Our algorithm operates in three stages: it first forms the nonoverlapping protein substructure based on fuzzy relation and then expands each substructure by adding neighbor proteins to maximize the cohesive score. Finally, highly overlapped candidate protein complexes are merged to form the final protein complex set. Particularly, our algorithm employs the biological significance hidden in protein pairs to construct edge weight for protein interaction networks. The experiment results show that our method can not only outperform classical algorithms such as CFinder, ClusterONE, CMC, RRW, HC-PIN, and ProRank +, but also achieve ideal overall performance in most of the yeast PPI datasets in terms of composite score consisting of precision, accuracy, and separation. We further apply our method to a human PPI network from the HPRD dataset and demonstrate it is very effective in detecting protein complexes compared to other algorithms.
Input-output relations in biological systems: measurement, information and the Hill equation.
Frank, Steven A
2013-01-01
Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system's overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.
Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model
Zhao, Y; Liu, Y; Yuan, W; Chang, Lei; Liu, Yu-xin; Yuan, Wei; Zhao, Yue
2006-01-01
We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the possibility of the chiral phase transition in NJL model.
REGULARITY RESULTS FOR LINEAR ELLIPTIC PROBLEMS RELATED TO THE PRIMITIVE EQUATIONS
无
2002-01-01
The authors study the regularity of solutions of the GFD-Stokes problem and of some second order linear elliptic partial differential equations related to the Primitive Equations of the ocean.The present work generalizes the regularity results in [18] by taking into consideration the nonhomogeneous boundary conditions and the dependence of solutions on the thickness ε of the domain occupied by the ocean and its varying bottom topography. These regularity results are important tools in the study of the PEs (see e.g. [6]),and they seem also to possess their own interest.
Huang, Jeng-Sheng; Chao, Paul C.-P.; Fung, Rong-Fong; Lai, Cheng-Liang
2003-06-01
This study is dedicated to design effective control schemes to suppress transverse vibration of an axially moving string system by adjusting the axial tension of the string. To this end, a continuous model in the form of partial differential equations is first established to describe the system dynamics. Using an energy-like system functional as a Lyapunov function, a sliding-mode controller (SMC) is designed to be applied when the level of vibration is not small. Due to non-analyticity of the SMC control effort generated as vibration level becoming small, two intelligent control schemes are proposed to complete the task — fuzzy sliding-mode control (FSMC) and fuzzy neural network control (FNNC). Both control approaches are based on a common structure of fuzzy control, taking switching function and its derivative as inputs and tension variation as output to reduce the transverse vibration of the string. In the framework of FSMC, genetic algorithm (GA) is utilized to search for the optimal scalings for the inputs; in addition, the technique of regionwise linear fuzzy logic control (RLFLC) is employed to simplify the computation procedure of the fuzzy reasoning. On the other hand, FNNC is proposed for conducting on-line tuning of control parameters to overcome model uncertainty. Numerical simulations are conducted to verify the effectiveness of controllers. Satisfactory stability and vibration suppression are attained for all controllers with the findings that the FSMC assisted by GA holds the advantage of fast convergence with a precise model while the FNNC is robust to model uncertainty and environmental disturbance although a relatively slower convergence could be present.
Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc
2012-12-11
The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.
Quantum corrected Friedmann equations from loop quantum black holes entropy-area relation
Silva, C A S
2015-01-01
The Friedmann equations govern the evolution of space in homogeneous and isotropic models of the universe within the context of general relativity. Such equations can be derived by using Clausius relation to the apparent horizon of Friedmann-Robertson-Walker (FRW) universe, in which entropy is assumed to be proportional to its horizon area \\cite{Cai:2005ra}. Such demonstration follows the spirit of the results obtained by Jacobson that assuming the proportionality between entropy and horizon area, demonstrated that the spacetime can be viewed as a gas of atoms with a related entropy given by the Bekenstein-Hawking formula and the Einstein equation is a equation of state of this gas \\cite{Jacobson:1995ab}. Loop Quantum Gravity is a theory that propose a way to model the atomic behavior of spacetime. One recent prediction of this theory is the existence of sub-Planckian black holes called self-dual black holes. Among the interesting features of loop quantum black holes is the fact that they give rise to a modif...
A review of some basic aspects related to integration of airplane’s equations of motion
Dan TURCANU
2017-09-01
Full Text Available Numerical integration of the airplane’s equations of motion has long been considered among the most fundamental calculations in airplane’s analysis. Numerical algorithms have been implemented and experimentally validated. However, the need for superior speed and accuracy is still very topical, as, nowadays, various optimization algorithms rely heavily on data generated from the integration of the equations of motion and having access to larger amounts of data can increase the quality of the optimization. Now, for a number of decades, engineers have relied heavily on commercial codes based on automatically selected integration steps. However, optimally chosen constant integration steps can save time and allows for larger numbers of integrations to be performed. Yet, the basic papers that presented the fundamentals of numerical integration, as applied to airplane’s equations of motion are nowadays not easy to locate. Consequently, this paper presents a review of basic aspects related to the integration of airplane’s equation of motion. The discussion covers fundamentals of longitudinal and lateral-directional motion as well as the implementation of some numerical integration methods. The relation between numerical integration steps, accuracy, computational resource usage, numerical stability and their relation with the parameters describing the dynamic response of the airplane is considered and suggestions are presented for a faster yet accurate numerical integration.
Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”
A. Favini
2015-01-01
Full Text Available The concept of “white noise,” initially established in finite-dimensional spaces, is transferred to infinite-dimensional case. The goal of this transition is to develop the theory of stochastic Sobolev type equations and to elaborate applications of practical interest. To reach this goal the Nelson-Gliklikh derivative is introduced and the spaces of “noises” are developed. The Sobolev type equations with relatively sectorial operators are considered in the spaces of differentiable “noises.” The existence and uniqueness of classical solutions are proved. The stochastic Dzektser equation in a bounded domain with homogeneous boundary condition and the weakened Showalter-Sidorov initial condition is considered as an application.
Intuitionistic supra fuzzy topological spaces
Abbas, S.E. E-mail: sabbas73@yahoo.com
2004-09-01
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 ECCENTRICITY AND GROSS ERROR IDENTIFICATION
无
2006-01-01
The dominant and recessive effect made by exceptional interferer is analyzed in measurement system based on responsive character, and the gross error model of fuzzy clustering based on fuzzy relation and fuzzy equipollence relation is built. The concept and calculate formula of fuzzy eccentricity are defined to deduce the evaluation rule and function of gross error, on the base of them, a fuzzy clustering method of separating and discriminating the gross error is found. Utilized in the dynamic circular division measurement system, the method can identify and eliminate gross error in measured data, and reduce measured data dispersity. Experimental results indicate that the use of the method and model enables repetitive precision of the system to improve 80% higher than the foregoing system, to reach 3.5 s, and angle measurement error is less than 7 s.
Dirac-Kahler equation in curved space-time, relation between spinor and tensor formulations
Red'kov, V M
2011-01-01
A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then spinor equations for fermions. In that context, a very interesting problem is of extension a wave equation for Dirac--K\\"{a}hler field (Ivanenko--Landau field was historically first term, also the term a vector field of general type was used). The article relates a generally covariant tensor formalism to a spinor one when these both are applied to description of the Dirac-K\\"ahler field in a Rimannian space-time. Both methods are taken to be equivalent and the tensor equations are derived from spinor ones. It is shown that, for characterization of Dirac-K\\"ahler's tensor components, two alternative approaches are suitable: these are whether a tetrad-based pseudo tensor classification or a generally coordinate pseudo tensor one. By imposing definite restrictions on the the Di...
Fault Diagnosis and Reliability Analysis Using Fuzzy Logic Method
Miao Zhinong; Xu Yang; Zhao Xiangyu
2006-01-01
A new fuzzy logic fault diagnosis method is proposed. In this method, fuzzy equations are employed to estimate the component state of a system based on the measured system performance and the relationship between component state and system performance which is called as "performance-parameter" knowledge base and constructed by expert. Compared with the traditional fault diagnosis method, this fuzzy logic method can use humans intuitive knowledge and dose not need a precise mapping between system performance and component state. Simulation proves its effectiveness in fault diagnosis. Then, the reliability analysis is performed based on the fuzzy logic method.
R. Ezzati
2014-09-01
Full Text Available We propose an approach for computing an approximate nonnegative symmetric solution of some fully fuzzy linear system of equations, where the components of the coefficient matrix and the right hand side vector are nonnegative fuzzy numbers, considering equality of the median intervals of the left and right hand sides of the system. We convert the m×n fully fuzzy linear system to two m×n real linear systems, one being related to the cores and the other being concerned with spreads of the solution. We propose an approach for solving the real systems using the modified Huang method of the Abaffy-Broyden-Spedicato (ABS class of algorithms. An appropriate constrained least squares problem is solved when the solution does not satisfy nonnegative fuzziness conditions, that is, when the obtained solution vector for the core system includes a negative component, or the solution of the spread system has at least one negative component, or there exists an index for which the component of the spread is greater than the corresponding component of the core. As a special case, we discuss fuzzy systems with the components of the coefficient matrix as real crisp numbers. We finally present two computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems.
Ningxin Xie
2014-01-01
Full Text Available A method based on grey relational analysis and D-S theory of evidence is proposed for fuzzy soft sets in decision making. Firstly, grey relational analysis is used to calculate grey mean relational degrees and determine uncertain degrees of parameters. Then based on uncertain degrees, suitable mass functions of different independent alternatives with different parameters can be constructed. Next, D-S rule of evidence combination is applied to aggregate these alternatives into a collective alternative. Finally, these alternatives are ranked and the best alternative(s are obtained. Moreover, the effectiveness and feasibility of this method are demonstrated by comparing with the mean potentiality approach and giving an application to medical diagnosis.
Xie, Ningxin; Wen, Guoqiu; Li, Zhaowen
2014-01-01
A method based on grey relational analysis and D-S theory of evidence is proposed for fuzzy soft sets in decision making. Firstly, grey relational analysis is used to calculate grey mean relational degrees and determine uncertain degrees of parameters. Then based on uncertain degrees, suitable mass functions of different independent alternatives with different parameters can be constructed. Next, D-S rule of evidence combination is applied to aggregate these alternatives into a collective alternative. Finally, these alternatives are ranked and the best alternative(s) are obtained. Moreover, the effectiveness and feasibility of this method are demonstrated by comparing with the mean potentiality approach and giving an application to medical diagnosis.
Liu Chunping
2003-06-02
Using a direct algebraic method, more new exact solutions of the Kolmogorov-Petrovskii-Piskunov equation are presented by formula form. Then a theorem concerning the relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations is given. Finally, the applications of the theorem to several well-known equations in physics are also discussed.
Fuzzy Clustering with Novel Separable Criterion
无
2006-01-01
Fuzzy clustering has been used widely in pattern recognition, image processing, and data analysis. An improved fuzzy clustering algorithm was developed based on the conventional fuzzy c-means (FCM) to obtain better quality clustering results. The update equations for the membership and the cluster center are derived from the alternating optimization algorithm. Two fuzzy scattering matrices in the objective function assure the compactness between data points and cluster centers, and also strengthen the separation between cluster centers in terms of a novel separable criterion. The clustering algorithm properties are shown to be an improvement over the FCM method's properties. Numerical simulations show that the clustering algorithm gives more accurate clustering results than the FCM method.
Pierseaux, Yves
2010-01-01
We suggest the following solution of Friedman's equations: parameter of curvature K=0, scale factor R(t)=1 and non-null Cosmological Constant(CC). In this case Robertson-Walker's metric becomes Minkowskian. This special solution of Einstein's equation of General Relativity forces therefore us into renormalizing Einstein's Special Relativity (SR) with non-null CC. By introducing a maximal interval (Hyperbolic Horizon), we deduce the law of Hubble and transform in this way SR into HCR (Hyperbolic Cosmological Relativity). Euclidean Einstein's rigid ruler is replaced with Lobatchevskian LIGHT-distance. Both basic parameters of Cosmology, H (Hubble) and q (acceleration) are deduced on the only basis of Lorentz Transformation. Usual ad hoc Lemaitre's scale factor R(t) is replaced with Bondi's "scale factor k". We induce a global principle of equivalence between centrifugal (hyperbolic) acceleration and repulsive gravitation. Hidden density of dark energy is a relativistic effect of globally curved Minkowski's spac...
Lim, C. W.; Wu, B. S.; He, L. H.
2001-12-01
A novel approach is presented for obtaining approximate analytical expressions for the dispersion relation of periodic wavetrains in the nonlinear Klein-Gordon equation with even potential function. By coupling linearization of the governing equation with the method of harmonic balance, we establish two general analytical approximate formulas for the dispersion relation, which depends on the amplitude of the periodic wavetrain. These formulas are valid for small as well as large amplitude of the wavetrain. They are also applicable to the large amplitude regime, which the conventional perturbation method fails to provide any solution, of the nonlinear system under study. Three examples are demonstrated to illustrate the excellent approximate solutions of the proposed formulas with respect to the exact solutions of the dispersion relation. (c) 2001 American Institute of Physics.
A new dispersion-relation preserving method for integrating the classical Boussinesq equation
Jang, T. S.
2017-02-01
In this paper, a dispersion-relation preserving method is proposed for nonlinear dispersive waves, starting from the oldest weakly nonlinear dispersive wave mathematical model in shallow water waves, i.e., the classical Boussinesq equation. It is a semi-analytic procedure, however, which preserves, as a distinctive feature, the dispersion-relation imbedded in the model equation without adding (unwelcome) numerical effects, i.e., the proposed method has the same dispersion-relation as the original classical Boussinesq equation. This remarkable (dispersion-relation) preserving property is proved mathematically for small wave motion in present study. The property is also numerically examined by observing both the local wave number and the local frequency of a slowly varying water-wave group. The dispersion-relation preserving method proposed here is powerful as well for observing nonlinear wave phenomena such as solitary waves and their collision. In fact, the main features of nonlinear wave characteristics are clearly seen through not only a single propagating solitary wave but counter-propagating (head-on) solitary wave collisions. They are compared with known (exact) nonlinear solutions, the results of which represent a major improvement over existing solution formulations in the literature.
Wang, Yan; Xi, Chengyu; Zhang, Shuai; Yu, Dejian; Zhang, Wenyu; Li, Yong
2014-01-01
The recent government tendering process being conducted in an electronic way is becoming an inevitable affair for numerous governmental agencies to further exploit the superiorities of conventional tendering. Thus, developing an effective web-based bid evaluation methodology so as to realize an efficient and effective government E-tendering (GeT) system is imperative. This paper firstly investigates the potentiality of employing fuzzy analytic hierarchy process (AHP) along with fuzzy gray relational analysis (GRA) for optimal selection of candidate tenderers in GeT process with consideration of a hybrid fuzzy environment with incomplete weight information. We proposed a novel hybrid fuzzy AHP-GRA (HFAHP-GRA) method that combines an extended fuzzy AHP with a modified fuzzy GRA. The extended fuzzy AHP which combines typical AHP with interval AHP is proposed to obtain the exact weight information, and the modified fuzzy GRA is applied to aggregate different types of evaluation information so as to identify the optimal candidate tenderers. Finally, a prototype system is built and validated with an illustrative example for GeT to confirm the feasibility of our approach.
On the Rate of Relaxation for the Landau Kinetic Equation and Related Models
Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong
2017-08-01
We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.
Life insurance risk assessment using a fuzzy logic expert system
Carreno, Luis A.; Steel, Roy A.
1992-01-01
In this paper, we present a knowledge based system that combines fuzzy processing with rule-based processing to form an improved decision aid for evaluating risk for life insurance. This application illustrates the use of FuzzyCLIPS to build a knowledge based decision support system possessing fuzzy components to improve user interactions and KBS performance. The results employing FuzzyCLIPS are compared with the results obtained from the solution of the problem using traditional numerical equations. The design of the fuzzy solution consists of a CLIPS rule-based system for some factors combined with fuzzy logic rules for others. This paper describes the problem, proposes a solution, presents the results, and provides a sample output of the software product.
FUZZY-GENETIC CONTROL OF QUADROTOR UNMANNED AERIAL VEHICLES
Attila Nemes
2016-03-01
Full Text Available This article presents a novel fuzzy identification method for dynamic modelling of quadrotor unmanned aerial vehicles. The method is based on a special parameterization of the antecedent part of fuzzy systems that results in fuzzy-partitions for antecedents. This antecedent parameter representation method of fuzzy rules ensures upholding of predefined linguistic value ordering and ensures that fuzzy-partitions remain intact throughout an unconstrained hybrid evolutionary and gradient descent based optimization process. In the equations of motion the first order derivative component is calculated based on Christoffel symbols, the derivatives of fuzzy systems are used for modelling the Coriolis effects, gyroscopic and centrifugal terms. The non-linear parameters are subjected to an initial global evolutionary optimization scheme and fine tuning with gradient descent based local search. Simulation results of the proposed new quadrotor dynamic model identification method are promising.
Fuzzy logic applied to the modeling of water dynamics in an Oxisol in northeastern Brazil
Antônio Cláudio Marques Afonso
2014-04-01
Full Text Available Modeling of water movement in non-saturated soil usually requires a large number of parameters and variables, such as initial soil water content, saturated water content and saturated hydraulic conductivity, which can be assessed relatively easily. Dimensional flow of water in the soil is usually modeled by a nonlinear partial differential equation, known as the Richards equation. Since this equation cannot be solved analytically in certain cases, one way to approach its solution is by numerical algorithms. The success of numerical models in describing the dynamics of water in the soil is closely related to the accuracy with which the water-physical parameters are determined. That has been a big challenge in the use of numerical models because these parameters are generally difficult to determine since they present great spatial variability in the soil. Therefore, it is necessary to develop and use methods that properly incorporate the uncertainties inherent to water displacement in soils. In this paper, a model based on fuzzy logic is used as an alternative to describe water flow in the vadose zone. This fuzzy model was developed to simulate the displacement of water in a non-vegetated crop soil during the period called the emergency phase. The principle of this model consists of a Mamdani fuzzy rule-based system in which the rules are based on the moisture content of adjacent soil layers. The performances of the results modeled by the fuzzy system were evaluated by the evolution of moisture profiles over time as compared to those obtained in the field. The results obtained through use of the fuzzy model provided satisfactory reproduction of soil moisture profiles.
The Paradox of the Fuzzy Disambiguation in the Information Retrieval
Anna Bryniarska
2013-09-01
Full Text Available Current methods of data mining, word sense disambiguation in the information retrieval, semantic relation, fuzzy sets theory, fuzzy description logic, fuzzy ontology and their implementation, omit the existence of paradox called here the paradox of the fuzzy disambiguation. The paradox lies in the fact that due to fuzzy data and the experts knowledge it can be obtained precise knowledge. In this paper to describe this paradox, is introduced a conceptual apparatus. Moreover, there is formulated an information retrieval logic. There are suggested certain applications of this logic to search information on the Web.
L-fuzzy Roughness of n-ary Polygroups
Yun Qiang YIN; Jian Ming ZHAN; P. CORSINI
2011-01-01
In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of (normal) TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of v-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called (normal) TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the (strong) homomorphism of v-lower and T-upper L-fuzzy rough approximation operators is studied.
Improvement on fuzzy controller design techniques
Wang, Paul P.
1993-01-01
This paper addresses three main issues, which are somewhat interrelated. The first issue deals with the classification or types of fuzzy controllers. Careful examination of the fuzzy controllers designed by various engineers reveals distinctive classes of fuzzy controllers. Classification is believed to be helpful from different perspectives. The second issue deals with the design according to specifications, experiments related to the tuning of fuzzy controllers, according to the specification, will be discussed. General design procedure, hopefully, can be outlined in order to ease the burden of a design engineer. The third issue deals with the simplicity and limitation of the rule-based IF-THEN logical statements. The methodology of fuzzy-constraint network is proposed here as an alternative to the design practice at present. It is our belief that predicate calculus and the first order logic possess much more expressive power.
Flows in networks under fuzzy conditions
Bozhenyuk, Alexander Vitalievich; Kacprzyk, Janusz; Rozenberg, Igor Naymovich
2017-01-01
This book offers a comprehensive introduction to fuzzy methods for solving flow tasks in both transportation and networks. It analyzes the problems of minimum cost and maximum flow finding with fuzzy nonzero lower flow bounds, and describes solutions to minimum cost flow finding in a network with fuzzy arc capacities and transmission costs. After a concise introduction to flow theory and tasks, the book analyzes two important problems. The first is related to determining the maximum volume for cargo transportation in the presence of uncertain network parameters, such as environmental changes, measurement errors and repair work on the roads. These parameters are represented here as fuzzy triangular, trapezoidal numbers and intervals. The second problem concerns static and dynamic flow finding in networks under fuzzy conditions, and an effective method that takes into account the network’s transit parameters is presented here. All in all, the book provides readers with a practical reference guide to state-of-...
Clinical effect of fuzzy numbers based on center of gravity
Jane
2011-10-05
Oct 5, 2011 ... the extension principle, if M is a fuzzy number with membership function i ... On the other hand, from Equation (5) each constraint of the problem (. ) ... objective function using linear programming algorithms such as the simplex ...
Fuzzy logic mode switching in helicopters
Sherman, Porter D.; Warburton, Frank W.
1993-01-01
The application of fuzzy logic to a wide range of control problems has been gaining momentum internationally, fueled by a concentrated Japanese effort. Advanced Research & Development within the Engineering Department at Sikorsky Aircraft undertook a fuzzy logic research effort designed to evaluate how effective fuzzy logic control might be in relation to helicopter operations. The mode switching module in the advanced flight control portion of Sikorsky's motion based simulator was identified as a good candidate problem because it was simple to understand and contained imprecise (fuzzy) decision criteria. The purpose of the switching module is to aid a helicopter pilot in entering and leaving coordinated turns while in flight. The criteria that determine the transitions between modes are imprecise and depend on the varied ranges of three flight conditions (i.e., simulated parameters): Commanded Rate, Duration, and Roll Attitude. The parameters were given fuzzy ranges and used as input variables to a fuzzy rulebase containing the knowledge of mode switching. The fuzzy control program was integrated into a real time interactive helicopter simulation tool. Optimization of the heading hold and turn coordination was accomplished by interactive pilot simulation testing of the handling quality performance of the helicopter dynamic model. The fuzzy logic code satisfied all the requirements of this candidate control problem.
Intuitionistic fuzzy segmentation of medical images.
Chaira, Tamalika
2010-06-01
This paper proposes a novel and probably the first method, using Attanassov intuitionistic fuzzy set theory to segment blood vessels and also the blood cells in pathological images. This type of segmentation is very important in detecting different types of human diseases, e.g., an increase in the number of vessels may lead to cancer in prostates, mammary, etc. The medical images are not properly illuminated, and segmentation in that case becomes very difficult. A novel image segmentation approach using intuitionistic fuzzy set theory and a new membership function is proposed using restricted equivalence function from automorphisms, for finding the membership values of the pixels of the image. An intuitionistic fuzzy image is constructed using Sugeno type intuitionistic fuzzy generator. Local thresholding is applied to threshold medical images. The results showed a much better performance on poor contrast medical images, where almost all the blood vessels and blood cells are visible properly. There are several fuzzy and intuitionistic fuzzy thresholding methods, but these methods are not related to the medical images. To make a comparison with the proposed method with other thresholding methods, the method is compared with six nonfuzzy, fuzzy, and intuitionistic fuzzy methods.
On Fuzzy Interior Ideals in Semigroups%半群的模糊内理想
詹建明; 马学玲
2008-01-01
The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set.With this new concept,the interval valued (∈,∈ Vq)-fuzzy interior ideal in semigroups is introduced.In fact,this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups.In this paper,this kind of fuzzy interior ideals and related properties will be investigated.Moreover,the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.
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.
Need for fuzzy morphology: erosion as a fuzzy marker
Dougherty, Edward R.; Sinha, Divyendu
1992-03-01
The need for fuzzy mathematical morphology is explained in terms of the need for fuzzy erosion in certain types of applications, especially where erosion is serving as a marker, as with hit-or-miss shape recognition. Since erosion is defined by fitting, there at once arises a need for relating fuzzified set inclusion and mathematical morphology. The result is a very general class of Minkowski algebras based upon an axiomatic description of indicator functions that yield acceptable set-inclusion fuzzifications and a subclass of richer Minkowski algebras resulting from an analytic formulation for indicators that is constrained by the axioms.
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.
Fuzzy Logic for Incidence Geometry.
Tserkovny, Alex
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects "as if they were points." Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation "extended lines sameness" is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy "degree of indiscernibility" and "discernibility measure" of extended points.
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Implicit-Relation-Type Cyclic Contractive Mappings and Applications to Integral Equations
Hemant Kumar Nashine
2012-01-01
Full Text Available We introduce an implicit-relation-type cyclic contractive condition for a map in a metric space and derive existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the paper, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.
Theoretical and experimental FUZZY modelling of building thermal dynamic response
Skrjanc, Igor; Zupancic, Borut [Ljubljana Univ., Faculty of Electrical Engineering, Ljubljana (Slovenia); Furlan, Bostjan; Krainer, Ales [Ljubljana Univ., Faculty of Civil Engineering, Ljubljana (Slovenia)
2001-11-01
In this paper this main advantages and disadvantages of two different types of modelling: theoretical and experimental are presented and discussed. The theoretical modelling is based on energy balances, which gives the overall model described by differential equations. On the basis of developed theoretical model a complex simulator in the MATLAB-Simulink environment was implemented. The second part is devoted to experimental modelling. In this paper a fuzzy model represented by non-linear relations between input and output variables obtained by least-squares optimisation method is investigated. (Author)
Xie Yin-Li; Jia Li-Qun; Luo Shao-Kai
2011-01-01
Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.
Ruspini, Enrique H.
1991-01-01
Summarized here are the results of recent research on the conceptual foundations of fuzzy logic. The focus is primarily on the principle characteristics of a model that quantifies resemblance between possible worlds by means of a similarity function that assigns a number between 0 and 1 to every pair of possible worlds. Introduction of such a function permits one to interpret the major constructs and methods of fuzzy logic: conditional and unconditional possibility and necessity distributions and the generalized modus ponens of Zadeh on the basis of related metric relationships between subsets of possible worlds.
Fuzzy logic based robotic controller
Attia, F.; Upadhyaya, M.
1994-01-01
Existing Proportional-Integral-Derivative (PID) robotic controllers rely on an inverse kinematic model to convert user-specified cartesian trajectory coordinates to joint variables. These joints experience friction, stiction, and gear backlash effects. Due to lack of proper linearization of these effects, modern control theory based on state space methods cannot provide adequate control for robotic systems. In the presence of loads, the dynamic behavior of robotic systems is complex and nonlinear, especially where mathematical modeling is evaluated for real-time operators. Fuzzy Logic Control is a fast emerging alternative to conventional control systems in situations where it may not be feasible to formulate an analytical model of the complex system. Fuzzy logic techniques track a user-defined trajectory without having the host computer to explicitly solve the nonlinear inverse kinematic equations. The goal is to provide a rule-based approach, which is closer to human reasoning. The approach used expresses end-point error, location of manipulator joints, and proximity to obstacles as fuzzy variables. The resulting decisions are based upon linguistic and non-numerical information. This paper presents a solution to the conventional robot controller which is independent of computationally intensive kinematic equations. Computer simulation results of this approach as obtained from software implementation are also discussed.
Transformation and entropy for fuzzy rough sets
无
2008-01-01
A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given.The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed.This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.
The Einstein-Klein-Gordon Equations, Wave Dark Matter, and the Tully-Fisher Relation
Goetz, Andrew S
2015-01-01
We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. These two equations together are known as the Einstein-Klein-Gordon system. In the low-field, non-relativistic limit, the Einstein-Klein-Gordon system reduces to the Poisson-Schr\\"odinger system. We describe the simplest solutions of these systems in spherical symmetry, the spherically symmetric static states, and some scaling properties they obey. We also describe some approximate analytic solutions for these states. The EKG system underlies a theory of wave dark matter, also known as scalar field dark matter (SFDM), boson star dark matter, and Bose-Einstein condensate (BEC) dark matter. We discuss a possible connection between the theory of wave dark matter and the baryonic Tully-Fisher relation, which is a scaling relation observed to hold for disk galaxies in the universe across many decades in mass. We show how fixing boundary conditions at the edge of the spherically symmetric static states implies T...
On the Operator ⨁Bk Related to Bessel Heat Equation
Wanchak Satsanit
2010-01-01
Full Text Available We study the equation (∂/∂tu(x,t=c2⊕Bku(x,t with the initial condition u(x,0=f(x for x∈Rn+. The operator ⊕Bk is the operator iterated k-times and is defined by ⊕Bk=((∑i=1pBxi4-(∑j=p+1p+qBxi4k, where p+q=n is the dimension of the Rn+, Bxi=∂2/∂xi2+(2vi/xi(∂/∂xi, 2vi=2αi+1, αi>-1/2, i=1,2,3,…,n, and k is a nonnegative integer, u(x,t is an unknown function for (x,t=(x1,x2,…,xn,t∈Rn+×(0,∞, f(x is a given generalized function, and c is a positive constant. We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.
刘叙华; 邓安生
1994-01-01
A new approach of operator fuzzy logic, Boolean operator fuzzy logic (BOFL) based on Boolean algebra, is presented. The resolution principle is also introduced into BOFL. BOFL is a natural generalization of classical logic and can be applied to the qualitative description of fuzzy knowledge.
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...
Fuzzy Linguistic Topological Spaces
Kandasamy, W B Vasantha; Amal, K
2012-01-01
This book has five chapters. Chapter one is introductory in nature. Fuzzy linguistic spaces are introduced in chapter two. Fuzzy linguistic vector spaces are introduced in chapter three. Chapter four introduces fuzzy linguistic models. The final chapter suggests over 100 problems and some of them are at research level.
Howard, Ayanna
2005-01-01
The Fuzzy Logic Engine is a software package that enables users to embed fuzzy-logic modules into their application programs. Fuzzy logic is useful as a means of formulating human expert knowledge and translating it into software to solve problems. Fuzzy logic provides flexibility for modeling relationships between input and output information and is distinguished by its robustness with respect to noise and variations in system parameters. In addition, linguistic fuzzy sets and conditional statements allow systems to make decisions based on imprecise and incomplete information. The user of the Fuzzy Logic Engine need not be an expert in fuzzy logic: it suffices to have a basic understanding of how linguistic rules can be applied to the user's problem. The Fuzzy Logic Engine is divided into two modules: (1) a graphical-interface software tool for creating linguistic fuzzy sets and conditional statements and (2) a fuzzy-logic software library for embedding fuzzy processing capability into current application programs. The graphical- interface tool was developed using the Tcl/Tk programming language. The fuzzy-logic software library was written in the C programming language.
Relations between low-lying quantum wave functions and solutions of the Hamilton-Jacobi equation
Friedberg, R; Zhao Wei Qin
1999-01-01
We discuss a new relation between the low lying Schroedinger wave function of a particle in a one-dimentional potential V and the solution of the corresponding Hamilton-Jacobi equation with -V as its potential. The function V is $\\geq 0$, and can have several minina (V=0). We assume the problem to be characterized by a small anhamornicity parameter $g^{-1}$ and a much smaller quantum tunneling parameter $\\epsilon$ between these different minima. Expanding either the wave function or its energy as a formal double power series in $g^{-1}$ and $\\epsilon$, we show how the coefficients of $g^{-m}\\epsilon^n$ in such an expansion can be expressed in terms of definite integrals, with leading order term determined by the classical solution of the Hamilton-Jacobi equation. A detailed analysis is given for the particular example of quartic potential $V={1/2}g^2(x^2-a^2)^2$.
Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients
Khmelnytskaya, K V; González, A
2009-01-01
We consider two closely related Riccati equations of constant parameters whose particular solutions are used to construct the corresponding class of supersymmetrically-coupled second-order differential equations. We solve analytically these parametric periodic problems along the positive real axis. Next, the analytically solved model is used as a case study for a powerful numerical approach that is employed here for the first time in the investigation of the energy band structure of periodic not necessarily regular potentials. The approach is based on the well-known self-matching procedure of James (1949) and implements the spectral parameter power series solutions introduced by Kravchenko (2008). We obtain additionally an efficient series representation of the Hill discriminant based on Kravchenko's series
Some weakly mappings on intuitionistic fuzzy topological spaces
Zhen-Guo Xu; Fu-Gui Shi
2008-01-01
In this paper, we shall introduce concepts of fuzzy semiopen set, fuzzy semiclosed set, fuzzy semiinterior, fuzzy semiclosure on intuitionistic fuzzy topological space and fuzzy open (fuzzy closed) mapping, fuzzy irresolute mapping, fuzzy irresolute open (closed) mapping, fuzzy semicontinuous mapping and fuzzy semiopen (semiclosed) mapping between two intuitionistic fuzzy topological spaces. Moreover, we shall discuss their some properties.
Hierarchical fuzzy identification of MR damper
Wang, Hao; Hu, Haiyan
2009-07-01
Magneto-rheological (MR) dampers, recently, have found many successful applications in civil engineering and numerous area of mechanical engineering. When an MR damper is to be used for vibration suppression, an inevitable problem is to determine the input voltage so as to gain the desired restoring force determined from the control law. This is the so-called inverse problem of MR dampers and is always an obstacle in the application of MR dampers to vibration control. It is extremely difficult to get the inverse model of MR damper because MR dampers are highly nonlinear and hysteretic. When identifying the inverse model of MR damper with simple fuzzy system, there maybe exists curse of dimensionality of fuzzy system. Therefore, it will take much more time, and even the inverse model may not be identifiable. The paper presents two-layer hierarchical fuzzy system, that is, two-layer hierarchical ANFIS to deal with the curse of dimensionality of the fuzzy identification of MR damper and to identify the inverse model of MR damper. Data used for training the model are generated from numerical simulation of nonlinear differential equations. The numerical simulation proves that the proposed hierarchical fuzzy system can model the inverse model of MR damper much more quickly than simple fuzzy system without any reduction of identification precision. Such hierarchical ANFIS shows the higher priority for the complicated system, and can also be used in system identification and system control for the complicated system.
Mathematics of Fuzzy Sets and Fuzzy Logic
Bede, Barnabas
2013-01-01
This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy infer...
How we pass from fuzzy $po$-semigroups to fuzzy $po$-$\\Gamma$-semigroups
Kehayopulu, Niovi
2014-01-01
The results on fuzzy ordered semigroups (or on fuzzy semigroups) can be transferred to fuzzy ordered gamma (or to fuzzy gamma) semigroups. We show the way we pass from fuzzy ordered semigroups to fuzzy ordered gamma semigroups.
Orlov A. I.
2016-05-01
Full Text Available Fuzzy sets are the special form of objects of nonnumeric nature. Therefore, in the processing of the sample, the elements of which are fuzzy sets, a variety of methods for the analysis of statistical data of any nature can be used - the calculation of the average, non-parametric density estimators, construction of diagnostic rules, etc. We have told about the development of our work on the theory of fuzziness (1975 - 2015. In the first of our work on fuzzy sets (1975, the theory of random sets is regarded as a generalization of the theory of fuzzy sets. In non-fiction series "Mathematics. Cybernetics" (publishing house "Knowledge" in 1980 the first book by a Soviet author fuzzy sets is published - our brochure "Optimization problems and fuzzy variables". This book is essentially a "squeeze" our research of 70-ies, ie, the research on the theory of stability and in particular on the statistics of objects of non-numeric nature, with a bias in the methodology. The book includes the main results of the fuzzy theory and its note to the random set theory, as well as new results (first publication! of statistics of fuzzy sets. On the basis of further experience, you can expect that the theory of fuzzy sets will be more actively applied in organizational and economic modeling of industry management processes. We discuss the concept of the average value of a fuzzy set. We have considered a number of statements of problems of testing statistical hypotheses on fuzzy sets. We have also proposed and justified some algorithms for restore relationships between fuzzy variables; we have given the representation of various variants of fuzzy cluster analysis of data and variables and described some methods of collection and description of fuzzy data
刘晶; 裴峥; 周斌
2014-01-01
An ordering method of fuzzy evaluating linguistic values based on equivalence relation was proposed, and its properties were analyzed.It was proved that the ordering method could make a linear ordering among fuzzy evaluating linguistic values, which meaned that the ordering method could provide the unique optimal solution of fuzzy multi-crite-ria linguistic decision-making.Example analysis showed that the proposed method could be used to avoid the drawback of pre-order relation, which could be an alternative method of fuzzy multi-criteria linguistic decision-making method.%提出一种基于等价关系的模糊评价语言值排序方法，分析该排序方法的相关性质，证明了该排序方法确保模糊评价语言值之间的序关系是一种线性序关系，从而保证模糊多属性语言决策最优解的唯一性。实例分析表明，本研究提出的排序方法能够克服已有预序关系带来的不足，是一种可选的模糊多属性语言决策方法。
Pressure-velocity relations in reservoir rocks: Modified MacBeth's equation
Grana, Dario
2016-09-01
The knowledge of the saturation and pressure effects on elastic properties is a key factor in reservoir monitoring. The relation between saturation changes and velocity variations is well known in rock physics and at seismic frequency it can be satisfactorily described by Gassmann's equations. The pressure effect still requires deeper investigations in order to be included in rock physics models for 4D studies. Theoretical models of velocity-pressure relations often do not match lab measurements, or contain empirical constants or theoretical parameters that are difficult to calibrate or do not have a precise physical meaning. In this work, I present a new model to describe the pressure sensitivity of elastic moduli for clastic rocks. The proposed model is an extension of MacBeth's relations. These equations are then integrated within a complete rock physics model to describe the relation between rock properties (porosity and clay content), dynamic attributes (saturation and pressure) and elastic properties. The proposed model is calibrated with laboratory measurements of dry samples over a wide range of pressure variations and then applied to well data to simulate different production scenarios. The complete rock physics model can then be used in time-lapse inversion to predict the distribution of dynamic property changes in the reservoir within an inversion workflow for reservoir monitoring.
Xu, Peng
2016-01-01
With continuous advances in technologies related to deep space ranging and satellite gravity gradiometry, corrections from general relativity to the dynamics of relative orbital motions will certainly become important. In this work, we extend,in a systematic way, the Hill-Clohessy-Wiltshire Equations to include the complete first order post-Newtonian effects from general relativity. Within certain short time limit, post-Newtonian corrections to general periodic solutions of the Hill-Clohessy-Wiltshire Equations are also worked out.
EXTENSION OF THE PROJECTION THEOREM ON HILBERT SPACE TO FUZZY HILBERT SPACE OVER FUZZY NUMBER SPACE
K. P. DEEPA; Dr.S.Chenthur Pandian
2012-01-01
In this paper, we extend the projection theorem on Hilbert space to its fuzzy version over fuzzy number space embedded with fuzzy number mapping. To prove this we discuss the concepts of fuzzy Hilbert space over fuzzy number space with fuzzy number mapping. The fuzzy orthogonality, fuzzy orthonormality, fuzzy complemented subset property etc. of fuzzy Hilbert space over fuzzy number space using fuzzy number mapping also been discussed.
Mahanta, J.; P. K. Das
2012-01-01
A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.
Compactness in intuitionistic fuzzy topological spaces
S. E. Abbas
2005-02-01
Full Text Available We introduce fuzzy almost continuous mapping, fuzzy weakly continuous mapping, fuzzy compactness, fuzzy almost compactness, and fuzzy near compactness in intuitionistic fuzzy topological space in view of the definition of Ã…Â ostak, and study some of their properties. Also, we investigate the behavior of fuzzy compactness under several types of fuzzy continuous mappings.
On the quasi-controllability of continuous-time dynamic fuzzy control systems
Feng Yuhu [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)]. E-mail: yhfeng@dhu.edu.cn; Hu Liangjian [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)
2006-10-15
This paper gives the controllability analysis of continuous-time dynamic fuzzy control system from the aspect of fuzzy differential equations. The fuzzy state is different from the crisp state, as the counterpart of the controllability concept in the classical control theory, the controllable target state must be restricted within some limits. Hence, the concepts of admissible controllable state subset and quasi-controllability are introduced to describe the controllability property for fuzzy control system. The sufficient and necessary conditions for the fuzzy control system to be quasi-controllable are obtained and some examples are given to demonstrate the problems discussed in this paper.
Image Edge Extraction via Fuzzy Reasoning
Dominquez, Jesus A. (Inventor); Klinko, Steve (Inventor)
2008-01-01
A computer-based technique for detecting edges in gray level digital images employs fuzzy reasoning to analyze whether each pixel in an image is likely on an edge. The image is analyzed on a pixel-by-pixel basis by analyzing gradient levels of pixels in a square window surrounding the pixel being analyzed. An edge path passing through the pixel having the greatest intensity gradient is used as input to a fuzzy membership function, which employs fuzzy singletons and inference rules to assigns a new gray level value to the pixel that is related to the pixel's edginess degree.
Vector-valued fuzzy multifunctions
Ismat Beg
2001-01-01
Full Text Available Some of the properties of vector-valued fuzzy multifunctions are studied. The notion of sum fuzzy multifunction, convex hull fuzzy multifunction, close convex hull fuzzy multifunction, and upper demicontinuous are given, and some of the properties of these fuzzy multifunctions are investigated.
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-04-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-02-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Rare event simulation for stochastic fixed point equations related to the smoothing transform
Collamore, Jeffrey F.; Vidyashankar, Anand N.; Xu, Jie
2013-01-01
In several applications arising in computer science, cascade theory, and other applied areas, it is of interest to evaluate the tail probabilities of non-homogeneous stochastic fixed point equations. Recently, techniques have been developed for the related linear recursions, yielding tail estimates...... and importance sampling methods for these recursions. However, such methods do not routinely generalize to non-homogeneous recursions. Drawing on techniques from the weighted branching process literature, we present a consistent, strongly efficient importance sampling algorithm for estimating the tail...... probabilities for the case of non-homogeneous recursions....
The Neutron Star Mass-Radius Relation and the Equation of State of Dense Matter
Steiner, Andrew W; Brown, Edward F
2012-01-01
The equation of state (EOS) of dense matter has been a long-sought goal of nuclear physics. Equations of state generate unique mass versus radius (M-R) relations for neutron stars, the ultra-dense remnants of stellar evolution. In this work, we determine the neutron star mass-radius relation and, based on recent observations of both transiently accreting and bursting sources, we show that the radius of a 1.4 solar mass neutron star lies between 10.4 and 12.9 km, independent of assumptions about the composition of the core. We show, for the first time, that these constraints remain valid upon removal from our sample of the most extreme transient sources or of the entire set of bursting sources; our constraints also apply even if deconfined quark matter exists in the neutron star core. Our results significantly constrain the dense matter EOS and are, furthermore, consistent with constraints from both heavy-ion collisions and theoretical studies of neutron matter. We predict a relatively weak dependence of the s...
Sourie, Aurélien; Novak, Jérôme
2016-01-01
We present a numerical model for uniformly rotating superfluid neutron stars, for the first time with realistic microphysics including entrainment, in a fully general relativistic framework. We compute stationary and axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rates around a common axis. Both fluids are coupled by entrainment, a non-dissipative interaction which in case of a non-vanishing relative velocity between the fluids, causes the fluid momenta being not aligned with the respective fluid velocities. We extend the formalism by Comer and Joynt (2003) in order to calculate the equation of state (EoS) and entrainment parameters for an arbitrary relative velocity. The resulting entrainment matrix fulfills all necessary sum rules and in the limit of small relative velocity our results agree with Fermi liquid theory ones, derived to lowest order in the velocity. This formalism is applied t...
Application of fuzzy grey relational analysis in fault tree analysis%模糊灰关联分析方法在故障树分析中的应用
周真; 马德仲; 于晓洋; 樊尚春
2012-01-01
针对传统的故障树分析方法在分析具有模糊性、灰色性特点的多状态不确定性复杂系统时存在的不足,提出利用模糊灰关联分析方法对传统的故障树分析方法进行改进:用三角模糊数来表示基本事件的模糊概率；计算顶上事件模糊概率和基本事件的模糊重要度；以基本事件模糊重要度作为参考列,以最小割集组成的特征矩阵作为比较列,通过计算关联系数进而求出最小割集所代表的故障模式与顶上事件之间的灰色关联度.应用该方法对风力发电机系统中风轮叶片故障树进行分析,找出了系统的薄弱环节,为预防事故的发生,改进系统可靠性和安全性提供了理论依据.%It is unsatisfactory to apply the classical fault tree analysis (FTA) to the multi-state uncertainty complex system with fuzzy and grey characteristics. So the method, fuzzy grey relational analysis, was applied to improve the FTA. The triangular fuzzy number was used to denote the fuzzy probability of the basic event. The fuzzy probability of the top event and fuzzy significances of basic events were calculated. Then, the set made up of fuzzy significances of basic events was taken as a reference sequence and the characteristic matrix made up of minimal cut sets was taken as a comparative sequence, grey relation degrees between the top event and minimal cut sets were computed after getting incidence coefficients between them. The fault tree of rotor blades in the wind power generation was analyzed by this method. The results can provide theoretical bases for finding out weaknesses, preventing faults, improving reliability and safety of the system.
Arendonk, van J.A.M.
1991-01-01
Profit equations or functions that reflect the realized profitability of cows have been used in the literature to determine the relative importance of different variables such as milk yield and herd life. In all profit equations, the opportunity cost of postponed replacement, which reflects the prof
On fuzzy almost continuous convergence in fuzzy function spaces
A.I. Aggour
2013-10-01
Full Text Available In this paper, we study the fuzzy almost continuous convergence of fuzzy nets on the set FAC(X, Y of all fuzzy almost continuous functions of a fuzzy topological space X into another Y. Also, we introduce the notions of fuzzy splitting and fuzzy jointly continuous topologies on the set FAC(X, Y and study some of its basic properties.
A New Type Fuzzy Module over Fuzzy Rings
Ece Yetkin
2014-01-01
Full Text Available A new kind of fuzzy module over a fuzzy ring is introduced by generalizing Yuan and Lee’s definition of the fuzzy group and Aktaş and Çağman’s definition of fuzzy ring. The concepts of fuzzy submodule, and fuzzy module homomorphism are studied and some of their basic properties are presented analogous of ordinary module theory.
Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations
Chakraverty, S.; Smita, Tapaswini
2014-12-01
The fractional diffusion equation is one of the most important partial differential equations (PDEs) to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases.
Nursing and fuzzy logic: an integrative review.
Jensen, Rodrigo; Lopes, Maria Helena Baena de Moraes
2011-01-01
This study conducted an integrative review investigating how fuzzy logic has been used in research with the participation of nurses. The article search was carried out in the CINAHL, EMBASE, SCOPUS, PubMed and Medline databases, with no limitation on time of publication. Articles written in Portuguese, English and Spanish with themes related to nursing and fuzzy logic with the authorship or participation of nurses were included. The final sample included 21 articles from eight countries. For the purpose of analysis, the articles were distributed into categories: theory, method and model. In nursing, fuzzy logic has significantly contributed to the understanding of subjects related to: imprecision or the need of an expert; as a research method; and in the development of models or decision support systems and hard technologies. The use of fuzzy logic in nursing has shown great potential and represents a vast field for research.
A New Fuzzy Set Theory Satisfying All Classical Set Formulas
Qing-Shi Gao; Xiao-Yu Gao; Yue Hu
2009-01-01
A new fuzzy set theory, C-fuzzy set theory, is introduced in this paper. It is a particular case of the classical set theory and satisfies all formulas of the classical set theory. To add a limitation to C-fuzzy set system, in which all fuzzy sets must be "non-uniform inclusive" to each other, then it forms a family of sub-systems, the Z-fuzzy set family. It can be proved that the Z0-fuzzy set system, one of Z-fuzzy set systems, is equivalent to Zadeh's fuzzy set system. Analysis shows that 1) Zadeh's fuzzy set system defines the relations A = B and A ∈B between two fuzzy sets A and B as "Vu e U,(u A E (u)=μB(U))" and "Au ∈ U, (μA(U) ≤μB(μ))" respectively is inappropriate, because it makes all fuzzy sets be "non-uniformly inclusive"; 2) it is also inappropriate to define two fuzzy sets' union and intersection operations as the max and rain of their grades of membership, because this prevents fuzzy set's ability to correctly reflect different kinds of fuzzy phenomenon in the natural world. Then it has to work around the problem by invent unnatural functions that are hard to understand, such as augmenting max and min for union and intersection to min{a + b, 1} and max{a + b - 1, 0}, but these functions are incorrect on inclusive case. If both pairs of definitions are used together, not only are they unnatural, but also they are still unable to cover all possible set relationships in the natural world; and 3) it is incorrect to define the set complement as 1 -μA(μ), because it can be proved that set complement cannot exist in Zadeh's fuzzy set, and it causes confusion in logic and thinking. And it is seriously mistaken to believe that logics of fuzzy sets necessarily go against classical and normal thinking, logic, and conception. The C-fuzzy set theory proposed in this paper overcomes all of the above errors and shortcomings, and more reasonably reflects fuzzy phenomenon in the natural world. It satisfies all relations, formulas, and operations of the
Didactic derivation of the special theory of relativity from Klein-Gordon equation
Arodź, H
2014-01-01
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity $\\textbf{v}$ of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound $|\\textbf{v}|
Decision making with fuzzy probability assessments and fuzzy payoff
Song Yexin; Yin Di; Chen Mianyun
2005-01-01
A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate the fuzzy expected payoff of alternatives. The level sets of each fuzzy expected payoff are then obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and a numerical integration formula (Newton-Cotes formula), an effective approach to rank the fuzzy expected payoff of alternatives is also developed to determine the best alternative. Finally, a numerical example is provided to illustrate the proposed method.
LI Jiang-tao; XUN Chen; CUI Chun-li; WANG Hui-fang; WU Yi-tai; YUN Ai-hong; JIANG Xiao-feng; MA Jun
2012-01-01
Background The new Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was developed to address the systematic underestimation of glomerular filtration rate (GFR) by the Modification of Diet in Renal Disease (MDRD) Study equation in patients with relatively well-preserved kidney function.Performance of the new equation in the Chinese population is unknown.The goal of the present study was to compare performance of these two equations in Chinese patients with chronic kidney disease (CKD).Methods We enrolled 450 Chinese patients (239 women and 211 men) with CKD in the present study.The renal dynamic imaging method was used to measure the referenced standard GFR (rGFR) for comparison with estimations using the two equations.Their overall performance was assessed with the Bland-Altman method and receiver-operating characteristics (ROC) analysis.Performance of the two equations in lower and higher estimated GFR (eGFR) subgroups was further investigated.Results Both eGFRs correlated well with rGFR (r=0.88,0.81,P＜0.05).In overall performance,the CKD-EPI equation showed less bias,higher precision and improved accuracy,and was better for detecting CKD.In the higher-eGFR subgroup,the CKD-EPI equation corrected the underestimation of GFR by the abbreviated MDRD equation.Conclusions The CKD-EPI equation outperformed the abbreviated MDRD equation not only in overall performance but also in the subgroups studied.For the present,the CKD-EPI equation appears to be the first-choice prediction equation for estimating GFR.
Park, Han-Earl; Kim, Young-Rok
2016-01-01
A relative navigation method for autonomous formation flying using the state-dependent Riccati equation filter (SDREF) is presented. In the SDREF, nonlinear relative dynamics, including J2 perturbation, are parameterized into a state-dependent coefficient (SDC) form without any loss of nonlinearity. The relative navigation algorithm is established based on the carrier-phase differential GPS (CDGPS) and single-frequency GPS data, in which the SDREF is used as a nonlinear estimator. To evaluate the SDREF performance, two different extended Kalman filters (EKFR1 and EKFR2) are introduced. The dynamic models of all the filters are based on relative motion including J2 perturbation. However, the SDREF and the EKFR1 use linear state propagation, whereas EKFR2 employs nonlinear state propagation. The navigation simulation is performed for each filter using live GPS signals simulated by a GPS signal generator, and the result is analyzed in terms of estimation accuracy and computational load. As a result, the SDREF provides a relative navigation solution with 3-D RMS accuracies of 6.0 mm and 0.153 mm/s for position and velocity, respectively, for a separation of 50 km with a computation time of approximately 34 s. The simulation results demonstrate that the SDREF estimates the relative states as rapidly as the EKFR1 and as accurately as the EKFR2, which means that the developed SDREF combines the strong points of EKFR1 and EKFR2 and overcomes their disadvantages.
Fault Diagnosis in Deaerator Using Fuzzy Logic
S Srinivasan
2007-01-01
Full Text Available In this paper a fuzzy logic based fault diagnosis system for a deaerator in a power plant unit is presented. The system parameters are obtained using the linearised state space deaerator model. The fuzzy inference system is created and rule base are evaluated relating the parameters to the type and severity of the faults. These rules are fired for specific changes in system parameters and the faults are diagnosed.
K-Fuzzy赋范空间与WF-Fuzzy赋范空间%K-Fuzzy Normed Space and WF-Fuzzy Normed Space
方锦暄; 郭翀琦
2000-01-01
The relations between the K-fuzzy norme d sp ace and the WF-fuzzy normed space are further considered.The Hausdorff K -fuzzy normed space and the WF-fuzzy normed space are essentially consis tent.%研究了K-fuzzy赋范空间与WF-fuzzy赋范空间之间的关系,证明了Hausdorff的K-fuzzy赋范空间与WF-fuzzy赋范空间本质上是一致的.
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.
Constraint-Based Fuzzy Models for an Environment with Heterogeneous Information-Granules
K. Robert Lai; Yi-Yuan Chiang
2006-01-01
A novel framework for fuzzy modeling and model-based control design is described. Based on the theory of fuzzy constraint processing, the fuzzy model can be viewed as a generalized Takagi-Sugeno (TS) fuzzy model with fuzzy functional consequences. It uses multivariate antecedent membership functions obtained by granular-prototype fuzzy clustering methods and consequent fuzzy equations obtained by fuzzy regression techniques. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. The fuzzy-constraint-based approach provides the following features. 1) The knowledge base of a constraint-based fuzzy model can incorporate information with various types of fuzzy predicates. Consequently, it is easy to provide a fusion of different types of knowledge. The knowledge can be from data-driven approaches and/or from controlrelevant physical models. 2) A corresponding inference mechanism for the proposed model can deal with heterogeneous information granules. 3) Both numerical and linguistic inputs can be accepted for predicting new outputs.The proposed techniques are demonstrated by means of two examples: a nonlinear function-fitting problem and the well-known Box-Jenkins gas furnace process. The first example shows that the proposed model uses fewer fuzzy predicates achieving similar results with the traditional rule-based approach, while the second shows the performance can be significantly improved when the control-relevant constraints are considered.
The forms of three-order Lagrangian equation in relative motion
Ma Shan-Jun; Liu Ming-Ping; Huang Pei-Tian
2005-01-01
In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented.
Color-image retrieval based on fuzzy correlation
ZHAI Hongchen; LIANG Yanmei; MU Guoguang
2004-01-01
We report a method of color-image retrieval based on fuzzy correlation, in which α-cut relations in fuzzy set theory are applied to defining color match and height match of color peaks for synthesizing fuzzy correlation of two color histograms, and RGB space is partitioned into six sub-regions in the experiment for the regional color comparisons. Experimental results show that the efficiency of the color-image retrieval can be effectively improved by this approach.
The fuzzy space construction kit
Sykora, Andreas
2016-01-01
Fuzzy spaces like the fuzzy sphere or the fuzzy torus have received remarkable attention, since they appeared as objects in string theory. Although there are higher dimensional examples, the most known and most studied fuzzy spaces are realized as matrix algebras defined by three Hermitian matrices, which may be seen as fuzzy membrane or fuzzy surface. We give a mapping between directed graphs and matrix algebras defined by three Hermitian matrices and show that the matrix algebras of known two-dimensional fuzzy spaces are associated with unbranched graphs. By including branchings into the graphs we find matrix algebras that represent fuzzy spaces associated with surfaces having genus 2 and higher.
Fuzzy Model for Trust Evaluation
Zhang Shibin; He Dake
2006-01-01
Based on fuzzy set theory, a fuzzy trust model is established by using membership function to describe the fuzziness of trust. The trust vectors of subjective trust are obtained based on a mathematical model of fuzzy synthetic evaluation. Considering the complicated and changeable relationships between various subjects, the multi-level mathematical model of fuzzy synthetic evaluation is introduced. An example of a two-level fuzzy synthetic evaluation model confirms the feasibility of the multi-level fuzzy synthesis evaluation model. The proposed fuzzy model for trust evaluation may provide a promising method for research of trust model in open networks.
Fuzzy Dynamic Discrimination Algorithms for Distributed Knowledge Management Systems
Vasile MAZILESCU
2010-12-01
Full Text Available A reduction of the algorithmic complexity of the fuzzy inference engine has the following property: the inputs (the fuzzy rules and the fuzzy facts can be divided in two parts, one being relatively constant for a long a time (the fuzzy rule or the knowledge model when it is compared to the second part (the fuzzy facts for every inference cycle. The occurrence of certain transformations over the constant part makes sense, in order to decrease the solution procurement time, in the case that the second part varies, but it is known at certain moments in time. The transformations attained in advance are called pre-processing or knowledge compilation. The use of variables in a Business Rule Management System knowledge representation allows factorising knowledge, like in classical knowledge based systems. The language of the first-degree predicates facilitates the formulation of complex knowledge in a rigorous way, imposing appropriate reasoning techniques. It is, thus, necessary to define the description method of fuzzy knowledge, to justify the knowledge exploiting efficiency when the compiling technique is used, to present the inference engine and highlight the functional features of the pattern matching and the state space processes. This paper presents the main results of our project PR356 for designing a compiler for fuzzy knowledge, like Rete compiler, that comprises two main components: a static fuzzy discrimination structure (Fuzzy Unification Tree and the Fuzzy Variables Linking Network. There are also presented the features of the elementary pattern matching process that is based on the compiled structure of fuzzy knowledge. We developed fuzzy discrimination algorithms for Distributed Knowledge Management Systems (DKMSs. The implementations have been elaborated in a prototype system FRCOM (Fuzzy Rule COMpiler.
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.
Jantzen, Jan
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......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...
Jantzen, Jan
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......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...... 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...
Regional fuzzy chain model for evapotranspiration estimation
Güçlü, Yavuz Selim; Subyani, Ali M.; Şen, Zekai
2017-01-01
Evapotranspiration (ET) is one of the main hydrological cycle components that has extreme importance for water resources management and agriculture especially in arid and semi-arid regions. In this study, regional ET estimation models based on the fuzzy logic (FL) principles are suggested, where the first stage includes the ET calculation via Penman-Monteith equation, which produces reliable results. In the second phase, ET estimations are produced according to the conventional FL inference system model. In this paper, regional fuzzy model (RFM) and regional fuzzy chain model (RFCM) are proposed through the use of adjacent stations' data in order to fill the missing ones. The application of the two models produces reliable and satisfactory results for mountainous and sea region locations in the Kingdom of Saudi Arabia, but comparatively RFCM estimations have more accuracy. In general, the mean absolute percentage error is less than 10%, which is acceptable in practical applications.
Time-series prediction based on global fuzzy measure in social networks
Li-ming YANG; Wei ZHANG; Yun-fang CHEN
2015-01-01
Social network analysis (SNA) is among the hottest topics of current research. Most measurements of SNA methods are certainty oriented, while in reality, the uncertainties in relationships are widely spread to be overridden. In this paper, fuzzy concept is introduced to model the uncertainty, and a similarity metric is used to build a fuzzy relation model among individuals in the social network. The traditional social network is transformed into a fuzzy network by replacing the traditional relations with fuzzy relation and calculating the global fuzzy measure such as network density and centralization. Finally, the trend of fuzzy network evolution is analyzed and predicted with a fuzzy Markov chain. Experimental results demonstrate that the fuzzy network has more superiority than the traditional network in describing the network evolution process.
Multilayer perceptron, fuzzy sets, and classification
Pal, Sankar K.; Mitra, Sushmita
1992-01-01
A fuzzy neural network model based on the multilayer perceptron, using the back-propagation algorithm, and capable of fuzzy classification of patterns is described. The input vector consists of membership values to linguistic properties while the output vector is defined in terms of fuzzy class membership values. This allows efficient modeling of fuzzy or uncertain patterns with appropriate weights being assigned to the backpropagated errors depending upon the membership values at the corresponding outputs. During training, the learning rate is gradually decreased in discrete steps until the network converges to a minimum error solution. The effectiveness of the algorithm is demonstrated on a speech recognition problem. The results are compared with those of the conventional MLP, the Bayes classifier, and the other related models.
Fuzzy logic applications in engineering science
Harris, J
2006-01-01
Fuzzy logic is a relatively new concept in science applications. Hitherto, fuzzy logic has been a conceptual process applied in the field of risk management. Its potential applicability is much wider than that, however, and its particular suitability for expanding our understanding of processes and information in science and engineering in our post-modern world is only just beginning to be appreciated. Written as a companion text to the author's earlier volume "An Introduction to Fuzzy Logic Applications", the book is aimed at professional engineers and students and those with an interest in exploring the potential of fuzzy logic as an information processing kit with a wide variety of practical applications in the field of engineering science and develops themes and topics introduced in the author's earlier text.
Rough Set Theory over Fuzzy Lattices
Guilong Liu
2006-01-01
Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of roug h sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set, and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices, respectively, based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak's rough sets and fuzzy rough sets.
Fuzzy Case-Based Reasoning System
Jing Lu
2016-06-01
Full Text Available In this paper, we propose a fuzzy case-based reasoning system, using a case-based reasoning (CBR system that learns from experience to solve problems. Different from a traditional case-based reasoning system that uses crisp cases, our system works with fuzzy ones. Specifically, we change a crisp case into a fuzzy one by fuzzifying each crisp case element (feature, according to the maximum degree principle. Thus, we add the “vague” concept into a case-based reasoning system. It is these somewhat vague inputs that make the outcomes of the prediction more meaningful and accurate, which illustrates that it is not necessarily helpful when we always create accurate predictive relations through crisp cases. Finally, we prove this and apply this model to practical weather forecasting, and experiments show that using fuzzy cases can make some prediction results more accurate than using crisp cases.
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....
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 t......, 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....
Decomposition of Fuzzy Soft Sets with Finite Value Spaces
Jun, Young Bae
2014-01-01
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter. PMID:24558342
Decomposition of fuzzy soft sets with finite value spaces.
Feng, Feng; Fujita, Hamido; Jun, Young Bae; Khan, Madad
2014-01-01
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter.
Forward dispersion relations and Roy equations in $\\pi\\pi$ scattering
Kaminski, R; Ynduráin, F J
2007-01-01
We review results of an analysis of pipi interactions in S, P and D waves for two-pion effective mass from threshold to about 1.4 GeV. In particular we show a recent improvement of this analysis above the K anti-K threshold using more data for phase shifts and including the S0 wave inelasticity from pipi -> K anti-K. In addition, we have improved the fit to the f2(1270) resonance and used a more flexible P wave parametrization above the K anti-K threshold and included an estimation of the D2 wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42 GeV. We have checked that the pipi scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations.
Numerical study of a parametric parabolic equation and a related inverse boundary value problem
Mustonen, Lauri
2016-10-01
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the nonhomogeneous diffusion coefficient in the interior of an object. The method in this paper relies on solving the forward problem for a whole family of diffusivities by using a spectral Galerkin method in the high-dimensional parameter domain. The evaluation of the parametric solution and its derivatives is then completely independent of spatial and temporal discretizations. In the case of a quadratic approximation for the parameter dependence and a direct solver for linear least squares problems, we show that the evaluation of the parametric solution does not increase the complexity of any linearized subproblem arising from a Gauss-Newtonian method that is used to minimize a Tikhonov functional. The feasibility of the proposed algorithm is demonstrated by diffusivity reconstructions in two and three spatial dimensions.
Evaluating the Relative Impact of Monetary and Fiscal Policy in Nigeria using the St. Louis Equation
Michael Adebayo Ajayi
2017-02-01
Full Text Available The controversy existing on the efficacy of monetary and fiscal policy to influence the economy is unending. This study evaluates the relative impact of monetary and fiscal policy in Nigeria from 1986 to 2014 using a modified St. Louis equation. Employing the Ordinary Least Squares estimation method, this study reveals that growth in money supply and export have a positive and significant effect on growth in output of the economy while growth in government expenditure has a negative and insignificant effect. This study provides evidence that monetary policy has a greater growth-stimulating effect on the economy than fiscal policy. It recommends that monetary policy rather than fiscal policy should be relied upon by the Nigerian government as an economic stabilisation tool.
Pediatric health-related quality of life: a structural equation modeling approach.
Ester Villalonga-Olives
Full Text Available OBJECTIVES: One of the most referenced theoretical frameworks to measure Health Related Quality of Life (HRQoL is the Wilson and Cleary framework. With some adaptions this framework has been validated in the adult population, but has not been tested in pediatric populations. Our goal was to empirically investigate it in children. METHODS: The contributory factors to Health Related Quality of Life that we included were symptom status (presence of chronic disease or hospitalizations, functional status (developmental status, developmental aspects of the individual (social-emotional behavior, and characteristics of the social environment (socioeconomic status and area of education. Structural equation modeling was used to assess the measurement structure of the model in 214 German children (3-5 years old participating in a follow-up study that investigates pediatric health outcomes. RESULTS: Model fit was χ2 = 5.5; df = 6; p = 0.48; SRMR = 0.01. The variance explained of Health Related Quality of Life was 15%. Health Related Quality of Life was affected by the area education (i.e. where kindergartens were located and development status. Developmental status was affected by the area of education, socioeconomic status and individual behavior. Symptoms did not affect the model. CONCLUSIONS: The goodness of fit and the overall variance explained were good. However, the results between children' and adults' tests differed and denote a conceptual gap between adult and children measures. Indeed, there is a lot of variety in pediatric Health Related Quality of Life measures, which represents a lack of a common definition of pediatric Health Related Quality of Life. We recommend that researchers invest time in the development of pediatric Health Related Quality of Life theory and theory based evaluations.
A New Approach for Solving Fully Fuzzy Linear Systems
Amit Kumar
2011-01-01
Full Text Available Several authors have proposed different methods to find the solution of fully fuzzy linear systems (FFLSs that is, fuzzy linear system with fuzzy coefficients involving fuzzy variables. But all the existing methods are based on the assumption that all the fuzzy coefficients and the fuzzy variables are nonnegative fuzzy numbers. In this paper a new method is proposed to solve an FFLS with arbitrary coefficients and arbitrary solution vector, that is, there is no restriction on the elements that have been used in the FFLS. The primary objective of this paper is thus to introduce the concept and a computational method for solving FFLS with no non negative constraint on the parameters. The method incorporates the principles of linear programming in solving an FFLS with arbitrary coefficients and is not only easier to understand but also widens the scope of fuzzy linear equations in scientific applications. To show the advantages of the proposed method over existing methods we solve three FFLSs.
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.
无
2005-01-01
The typical BDI (belief desire intention) model of agent is not efficiently computable and the strict logic expression is not easily applicable to the AUV (autonomous underwater vehicle) domain with uncertainties. In this paper, an AUV fuzzy neural BDI model is proposed. The model is a fuzzy neural network composed of five layers: input ( beliefs and desires) , fuzzification, commitment, fuzzy intention, and defuzzification layer. In the model, the fuzzy commitment rules and neural network are combined to form intentions from beliefs and desires. The model is demonstrated by solving PEG (pursuit-evasion game), and the simulation result is satisfactory.
(α,β)-fuzzy Subalgebras of Q-algebras
Arsham Borumand Saeid
2008-01-01
In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets,the notion of (α,β)-fuzzy Q-algebras,the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q.Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras.The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined,and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.
On logical, algebraic, and probabilistic aspects of fuzzy set theory
Mesiar, Radko
2016-01-01
The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the fiel...
RANDOM VARIABLE WITH FUZZY PROBABILITY
吕恩琳; 钟佑明
2003-01-01
Mathematic description about the second kind fuzzy random variable namely the random variable with crisp event-fuzzy probability was studied. Based on the interval probability and using the fuzzy resolution theorem, the feasible condition about a probability fuzzy number set was given, go a step further the definition arid characters of random variable with fuzzy probability ( RVFP ) and the fuzzy distribution function and fuzzy probability distribution sequence of the RVFP were put forward. The fuzzy probability resolution theorem with the closing operation of fuzzy probability was given and proved. The definition and characters of mathematical expectation and variance of the RVFP were studied also. All mathematic description about the RVFP has the closing operation for fuzzy probability, as a result, the foundation of perfecting fuzzy probability operation method is laid.
Aristophanes Dimakis
2011-12-01
Full Text Available The non-autonomous chiral model equation for an m×m matrix function on a two-dimensional space appears in particular in general relativity, where for m=2 a certain reduction of it determines stationary, axially symmetric solutions of Einstein's vacuum equations, and for m=3 solutions of the Einstein-Maxwell equations. Using a very simple and general result of the bidifferential calculus approach to integrable partial differential and difference equations, we generate a large class of exact solutions of this chiral model. The solutions are parametrized by a set of matrices, the size of which can be arbitrarily large. The matrices are subject to a Sylvester equation that has to be solved and generically admits a unique solution. By imposing the aforementioned reductions on the matrix data, we recover the Ernst potentials of multi-Kerr-NUT and multi-Deminski-Newman metrics.
Results on fuzzy soft topological spaces
Mahanta, J
2012-01-01
B. Tanay et. al. introduced and studied fuzzy soft topological spaces. Here we introduce fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space. We also study fuzzy soft closure and fuzzy soft interior. Separation axioms and connectedness are introduced and investigated for fuzzy soft topological spaces.
Relation between body mass index and depression: a structural equation modeling approach
Akhtar-Danesh Noori
2007-04-01
Full Text Available Abstract Background Obesity and depression are two major diseases which are associated with many other health problems such as hypertension, dyslipidemia, diabetes mellitus, coronary heart disease, stroke, myocardial infarction, heart failure in patients with systolic hypertension, low bone mineral density and increased mortality. Both diseases share common health complications but there are inconsistent findings concerning the relationship between obesity and depression. In this work we used the structural equation modeling (SEM technique to examine the relation between body mass index (BMI, as a proxy for obesity, and depression using the Canadian Community Health Survey, Cycle 1.2. Methods In this SEM model we postulate that 1 BMI and depression are directly related, 2 BMI is directly affected by the physical activity and, 3depression is directly influenced by stress. SEM was also used to assess the relation between BMI and depression separately for males and females. Results The results indicate that higher BMI is associated with more severe form of depression. On the other hand, the more severe form of depression may result in less weight gain. However, the association between depression and BMI is gender dependent. In males, the higher BMI may result in a more severe form of depression while in females the relation may not be the same. Also, there was a negative relationship between physical activity and BMI. Conclusion In general, use of SEM method showed that the two major diseases, obesity and depression, are associated but the form of the relation is different among males and females. More research is necessary to further understand the complexity of the relationship between obesity and depression. It also demonstrated that SEM is a feasible technique for modeling the relation between obesity and depression.
Li, Shih-Yu; Tam, Lap-Mou; Tsai, Shang-En; Ge, Zheng-Ming
2015-09-11
Ge and Li proposed an alternative strategy to model and synchronize two totally different nonlinear systems in the end of 2011, which provided a new version for fuzzy modeling and has been applied to several fields to simplify their modeling works and solve the mismatch problems [1]-[17]. However, the proposed model limits the number of nonlinear terms in each equation so that this model could not be used in all kinds of nonlinear dynamic systems. As a result, in this paper, a more efficient and comprehensive advanced-Ge-Li fuzzy model is given to further release the limitation and improve the effectiveness of the original one. The novel fuzzy model can be applied to all kinds of complex nonlinear systems--this is the universal strategy and only m x 2 fuzzy rules as well as two linear subsystems are needed to simulate nonlinear behaviors (m is the number of states in a nonlinear dynamic system), whatever the nonlinear terms are copious or complicated. Further, the fuzzy synchronization of two nonlinear dynamic systems with totally distinct structures can be achieved via only two sets of control gains designed through the novel fuzzy model as well as its corresponding fuzzy synchronization scheme. Two complicated dynamic systems are designed to be the illustrations, Mathieu-Van der pol system with uncertainties and Quantum-cellular neural networks nano system with uncertainties, to show the effectiveness and feasibility of the novel fuzzy model.
Fuzzy fault tree analysis of roller oscillating tooth gear drive
李瑰贤; 杨伟君; 张欣; 李笑; 刘福利
2002-01-01
Conventional fault tree and reliability analysis do not reflect the characteristics of basic events asnon-stationary and ergodic process. To overcome these drawbacks, theory of fuzzy sets is employed to run faulttree analysis(FTA) of roller oscillating tooth gear drive( ROTGD), the relative frequencies of basic events areconsidered as symmetrical normal fuzzy numbers, from the logical relationship between different events in thefault tree and fuzzy operators AND and OR, fuzzy probability of top event is solved. Finally, an example is giv-en to demonstrate a real ROTGD system.
Redefined generalized fuzzy ideals of near-rings
ZHAN Jian-ming; YIN Yun-qiang
2010-01-01
With a new idea,we redefine generalized fuzzy subnear-rings (ideals) of a near-ring and investigate some of its related properties.Some new characterizations are given,In particular,we introduce the concepts of strong prime (or semiprime) (∈,∈∨q)-fuzzy ideals of near-rings,and discuss the relationship between strong prime (or semiprime) (∈,∈∨q)-fuzzy ideals and prime (or semiprime) (∈,∈∨q)-fuzzy ideals of near-rings.
Takagi-Sugeno fuzzy modeling and chaos control of partial differential systems.
Vasegh, Nastaran; Khellat, Farhad
2013-12-01
In this paper a unified approach is presented for controlling chaos in nonlinear partial differential systems by a fuzzy control design. First almost all known chaotic partial differential equation systems are represented by Takagi-Sugeno fuzzy model. For investigating design procedure, Kuramoto-Sivashinsky (K-S) equation is selected. Then, all linear subsystems of K-S equation are transformed to ordinary differential equation (ODE) systems by truncated Fourier series of sine-cosine functions. By solving Riccati equation for each ODE systems, parallel stabilizing feedback controllers are determined. Finally, a distributed fuzzy feedback for K-S equation is designed. Numerical simulations are given to show that the distributed fuzzy controller is very easy to design, efficient, and capable to extend.
Takagi-Sugeno fuzzy modeling and chaos control of partial differential systems
Vasegh, Nastaran; Khellat, Farhad
2013-12-01
In this paper a unified approach is presented for controlling chaos in nonlinear partial differential systems by a fuzzy control design. First almost all known chaotic partial differential equation systems are represented by Takagi-Sugeno fuzzy model. For investigating design procedure, Kuramoto-Sivashinsky (K-S) equation is selected. Then, all linear subsystems of K-S equation are transformed to ordinary differential equation (ODE) systems by truncated Fourier series of sine-cosine functions. By solving Riccati equation for each ODE systems, parallel stabilizing feedback controllers are determined. Finally, a distributed fuzzy feedback for K-S equation is designed. Numerical simulations are given to show that the distributed fuzzy controller is very easy to design, efficient, and capable to extend.
Studying on the Fuzzy-QFD System Based on Database Class Encapsulation Technology
FANG Xifeng; ZHANG Shengwen; LU Yuping; WU Hongtao
2006-01-01
Complicated product QFD system design information including design and manufacturing, operation and maintenance as well as relative supply information, all are tightly related to the product life cycle cooperative design and the process of establishing the QFD system. In the early stage of product design, we can only get the fuzzy and unreliable information. With design going, the fuzzy and unreliable information become less and less. The defect of the traditional QFD is not deal with the fuzzy contents very well. Adopt database class encapsulation and fuzzy inference technology, and then discuss the realization of QFD system based on VFP database. The structure of the fuzzy QFD system based on database class's encapsulation is built and the work flow of fuzzy algorithm based on VFP software is presented. In the analysis of fuzzy QFD process, fuzzy inference is adopted. A developed prototype system and an example have verified some presented techniques and the research results are the basis of the future development.
Some properties of fuzzy soft proximity spaces.
Demir, İzzettin; Özbakır, Oya Bedre
2015-01-01
We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities.
Some Properties of Fuzzy Soft Proximity Spaces
Demir, İzzettin; Özbakır, Oya Bedre
2015-01-01
We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities. PMID:25793224
Adom Giffin
2014-09-01
Full Text Available In this paper, we continue our efforts to show how maximum relative entropy (MrE can be used as a universal updating algorithm. Here, our purpose is to tackle a joint state and parameter estimation problem where our system is nonlinear and in a non-equilibrium state, i.e., perturbed by varying external forces. Traditional parameter estimation can be performed by using filters, such as the extended Kalman filter (EKF. However, as shown with a toy example of a system with first order non-homogeneous ordinary differential equations, assumptions made by the EKF algorithm (such as the Markov assumption may not be valid. The problem can be solved with exponential smoothing, e.g., exponentially weighted moving average (EWMA. Although this has been shown to produce acceptable filtering results in real exponential systems, it still cannot simultaneously estimate both the state and its parameters and has its own assumptions that are not always valid, for example when jump discontinuities exist. We show that by applying MrE as a filter, we can not only develop the closed form solutions, but we can also infer the parameters of the differential equation simultaneously with the means. This is useful in real, physical systems, where we want to not only filter the noise from our measurements, but we also want to simultaneously infer the parameters of the dynamics of a nonlinear and non-equilibrium system. Although there were many assumptions made throughout the paper to illustrate that EKF and exponential smoothing are special cases ofMrE, we are not “constrained”, by these assumptions. In other words, MrE is completely general and can be used in broader ways.
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.
Derivation of a viscous KP including surface tension, and related equations
Meur, Hervé Le
2015-01-01
The aim of this article is to derive surface wave models in the presence of surface tension and viscosity. Using the Navier-Stokes equations with a free surface, flat bottom and surface tension, we derive the viscous 2D Boussinesq system with a weak transverse variation. The assumed transverse variation is on a larger scale than along the main propagation direction. This Boussinesq system is only an intermediate result that enables us to derive the Kadomtsev-Petviashvili (KP) equation which is a 2D generalization of the KdV equation. In addition, we get the 1D KdV equation, and lastly the Boussinesq equation. All these equations are derived for non-vanishing initial conditions.
Derivation of Klein-Gordon-Fock equation from General relativity in a time-space symmetrical model
Van Thuan, Vo
2016-01-01
Following a bi-cylindrical model of geometrical dynamics, in the present study we show that Einstein gravitational equation leads to bi-geodesic description in an extended symmetrical time-space which fit Hubble expansion in a "microscopic" cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, as the squared Dirac equations of leptons and as a sub-solution with pseudo-axion. This result would serve an explicit approach to consistency between quantum mechanics and general relativity.
Brustein, Ram; Hadad, Merav
2009-09-04
We show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation deltaQ=TdeltaS. Our proof relies on extending previous arguments by using a more general definition of the Noether charge entropy. We have thus completed the implementation of Jacobson's proposal to express Einstein's equations as a thermodynamic equation of state. Additionally, we find that the Noether charge entropy obeys the second law of thermodynamics if the energy-momentum tensor obeys the null energy condition. Our results support the idea that gravitation on a macroscopic scale is a manifestation of the thermodynamics of the vacuum.
On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
Nikolai N. Bogoliubov (Jr.
2007-01-01
Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
Dhakal, Y. P.; Kunugi, T.; Suzuki, W.; Aoi, S.
2014-12-01
Many of the empirical ground motion prediction equations (GMPE) also known as attenuation relations have been developed for absolute acceleration or pseudo relative velocity response spectra. For a small damping, pseudo and absolute acceleration response spectra are nearly identical and hence interchangeable. It is generally known that the relative and pseudo relative velocity response spectra differ considerably at very short or very long periods, and the two are often considered similar at intermediate periods. However, observations show that the period range at which the two spectra become comparable is different from site to site. Also, the relationship of the above two types of velocity response spectra with absolute velocity response spectra are not discussed well in literature. The absolute velocity response spectra are the peak values of time histories obtained by adding the ground velocities to relative velocity response time histories at individual natural periods. There exists many tall buildings on huge and deep sedimentary basins such as the Kanto basin, and the number of such buildings is growing. Recently, Japan Meteorological Agency (JMA) has proposed four classes of long-period ground motion intensity (http://www.data.jma.go.jp/svd/eew/data/ltpgm/) based on absolute velocity response spectra, which correlate to the difficulty of movement of people in tall buildings. As the researchers are using various types of response spectra for long-period ground motions, it is important to understand the relationships between them to take appropriate measures for disaster prevention applications. In this paper, we, therefore, obtain and discuss the empirical attenuation relationships using the same functional forms for the three types of velocity response spectra computed from observed strong motion records from moderate to large earthquakes in relation to JMA magnitude, hypocentral distance, sediment depths, and AVS30 as predictor variables at periods between
Clustering Association Rules with Fuzzy Concepts
Steinbrecher, Matthias; Kruse, Rudolf
Association rules constitute a widely accepted technique to identify frequent patterns inside huge volumes of data. Practitioners prefer the straightforward interpretability of rules, however, depending on the nature of the underlying data the number of induced rules can be intractable large. Even reasonably sized result sets may contain a large amount of rules that are uninteresting to the user because they are too general, are already known or do not match other user-related intuitive criteria. We allow the user to model his conception of interestingness by means of linguistic expressions on rule evaluation measures and compound propositions of higher order (i.e., temporal changes of rule properties). Multiple such linguistic concepts can be considered a set of fuzzy patterns (Fuzzy Sets and Systems 28(3):313-331, 1988) and allow for the partition of the initial rule set into fuzzy fragments that contain rules of similar membership to a user’s concept (Höppner et al., Fuzzy Clustering, Wiley, Chichester, 1999; Computational Statistics and Data Analysis 51(1):192-214, 2006; Advances in Fuzzy Clustering and Its Applications, chap. 1, pp. 3-30, Wiley, New York, 2007). With appropriate visualization methods that extent previous rule set visualizations (Foundations of Fuzzy Logic and Soft Computing, Lecture Notes in Computer Science, vol. 4529, pp. 295-303, Springer, Berlin, 2007) we allow the user to instantly assess the matching of his concepts against the rule set.
Nonlocal Symmetry of the Lax Equation Related to Riccati-Type Pseudopotential
Wang, Yun-Hu; Chen, Yong; Xin, Xiang-Peng
2012-12-01
We investigate the Lax equation that can be employed to describe motions of long waves in shallow water under gravity. A nonlocal symmetry of this equation is given and used to find exact solutions and derive lower integrable models from higher ones. It is interesting that this nonlocal symmetry links with its corresponding Riccati-type pseudopotential. By introducing suitable and simple auxiliary dependent variables, the nonlocal symmetry is localized and used to generate new solutions from trivial solutions. Meanwhile, this equation is reduced to an ordinary differential equation by means of this nonlocal symmetry and some local symmetries.
宋斌恒; 袁聪
2002-01-01
We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equationsl.Comsequently,we prove that a function in such a class is continuous.As an application,we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form,including the anisotropic porous equations.
Nguyen, Huu-Tho; Md Dawal, Siti Zawiah; Nukman, Yusoff; Aoyama, Hideki; Case, Keith
2015-01-01
Globalization of business and competitiveness in manufacturing has forced companies to improve their manufacturing facilities to respond to market requirements. Machine tool evaluation involves an essential decision using imprecise and vague information, and plays a major role to improve the productivity and flexibility in manufacturing. The aim of this study is to present an integrated approach for decision-making in machine tool selection. This paper is focused on the integration of a consistent fuzzy AHP (Analytic Hierarchy Process) and a fuzzy COmplex PRoportional ASsessment (COPRAS) for multi-attribute decision-making in selecting the most suitable machine tool. In this method, the fuzzy linguistic reference relation is integrated into AHP to handle the imprecise and vague information, and to simplify the data collection for the pair-wise comparison matrix of the AHP which determines the weights of attributes. The output of the fuzzy AHP is imported into the fuzzy COPRAS method for ranking alternatives through the closeness coefficient. Presentation of the proposed model application is provided by a numerical example based on the collection of data by questionnaire and from the literature. The results highlight the integration of the improved fuzzy AHP and the fuzzy COPRAS as a precise tool and provide effective multi-attribute decision-making for evaluating the machine tool in the uncertain environment.
Huu-Tho Nguyen
Full Text Available Globalization of business and competitiveness in manufacturing has forced companies to improve their manufacturing facilities to respond to market requirements. Machine tool evaluation involves an essential decision using imprecise and vague information, and plays a major role to improve the productivity and flexibility in manufacturing. The aim of this study is to present an integrated approach for decision-making in machine tool selection. This paper is focused on the integration of a consistent fuzzy AHP (Analytic Hierarchy Process and a fuzzy COmplex PRoportional ASsessment (COPRAS for multi-attribute decision-making in selecting the most suitable machine tool. In this method, the fuzzy linguistic reference relation is integrated into AHP to handle the imprecise and vague information, and to simplify the data collection for the pair-wise comparison matrix of the AHP which determines the weights of attributes. The output of the fuzzy AHP is imported into the fuzzy COPRAS method for ranking alternatives through the closeness coefficient. Presentation of the proposed model application is provided by a numerical example based on the collection of data by questionnaire and from the literature. The results highlight the integration of the improved fuzzy AHP and the fuzzy COPRAS as a precise tool and provide effective multi-attribute decision-making for evaluating the machine tool in the uncertain environment.
Browder's Fixed Point Theorem and Some Interesting Results in Intuitionistic Fuzzy Normed Spaces
Cancan M
2010-01-01
Full Text Available We define and study Browder's fixed point theorem and relation between an intuitionistic fuzzy convex normed space and a strong intuitionistic fuzzy uniformly convex normed space. Also, we give an example to show that uniformly convex normed space does not imply strongly intuitionistic fuzzy uniformly convex.
Spatial object model[l]ing in fuzzy topological spaces : with applications to land cover change
Tang, Xinming
2004-01-01
The central topic of this thesis focuses on the accommodation of fuzzy spatial objects in a GIS. Several issues are discussed theoretically and practically, including the definition of fuzzy spatial objects, the topological relations between them, the modeling of fuzzy spatial objects, the generatio
ON (∈, ∈∨q)-FUZZY FILTERS OF BL-ALGEBRAS
Xueling MA; Jianming ZHAN
2008-01-01
The authors introduce the notions of (∈, ∈∨q)-fuzzy Boolean (implicative, positive implica-tive, and fantastic) filters in BL-algebras, present some characterizations on these generalized fuzzy filters, and describe the relations among these generalized fuzzy filters. It is proved that an (∈, ∈∨q)-fuzzy filter in a BL-algebra is Boolean (implicative) if and only if it is both positive implicative and fantastic.
Generalized (∈,∈∨q)-fuzzy Ideals in BCK-algebras
LIU Chun-hui
2015-01-01
In this paper, as a generalization of the notion of (∈,∈∨q)-fuzzy ideals, we introduced the notion of (∈,∈∨qδ)-fuzzy ideals and investigated their properties in BCK-algebras. Several equivalent characterizations of (∈,∈∨qδ)-fuzzy ideals are obtained and relations between (∈,∈∨qδ)-fuzzy ideals and ideals are discussed in BCK-algebras.
Classical integrable systems and soliton equations related to eleven-vertex R-matrix
A. Levin
2014-10-01
Full Text Available In our recent paper we suggested a natural construction of the classical relativistic integrable tops in terms of the quantum R-matrices. Here we study the simplest case – the 11-vertex R-matrix and related gl2 rational models. The corresponding top is equivalent to the 2-body Ruijsenaars–Schneider (RS or the 2-body Calogero–Moser (CM model depending on its description. We give different descriptions of the integrable tops and use them as building blocks for construction of more complicated integrable systems such as Gaudin models and classical spin chains (periodic and with boundaries. The known relation between the top and CM (or RS models allows to rewrite the Gaudin models (or the spin chains in the canonical variables. Then they assume the form of n-particle integrable systems with 2n constants. We also describe the generalization of the top to 1+1 field theories. It allows us to get the Landau–Lifshitz type equation. The latter can be treated as non-trivial deformation of the classical continuous Heisenberg model. In a similar way the deformation of the principal chiral model is described.
Classical integrable systems and soliton equations related to eleven-vertex R-matrix
Levin, A., E-mail: alevin@hse.ru [NRU HSE, Department of Mathematics, Myasnitskaya str. 20, Moscow, 101000 (Russian Federation); ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); Olshanetsky, M., E-mail: olshanet@itep.ru [ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); MIPT, Institutskii per. 9, Dolgoprudny, Moscow Region, 141700 (Russian Federation); Zotov, A., E-mail: zotov@mi.ras.ru [Steklov Mathematical Institute RAS, Gubkina str. 8, Moscow, 119991 (Russian Federation); ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); MIPT, Institutskii per. 9, Dolgoprudny, Moscow Region, 141700 (Russian Federation)
2014-10-15
In our recent paper we suggested a natural construction of the classical relativistic integrable tops in terms of the quantum R-matrices. Here we study the simplest case – the 11-vertex R-matrix and related gl{sub 2} rational models. The corresponding top is equivalent to the 2-body Ruijsenaars–Schneider (RS) or the 2-body Calogero–Moser (CM) model depending on its description. We give different descriptions of the integrable tops and use them as building blocks for construction of more complicated integrable systems such as Gaudin models and classical spin chains (periodic and with boundaries). The known relation between the top and CM (or RS) models allows to rewrite the Gaudin models (or the spin chains) in the canonical variables. Then they assume the form of n-particle integrable systems with 2n constants. We also describe the generalization of the top to 1+1 field theories. It allows us to get the Landau–Lifshitz type equation. The latter can be treated as non-trivial deformation of the classical continuous Heisenberg model. In a similar way the deformation of the principal chiral model is described.
Classical integrable systems and soliton equations related to eleven-vertex R-matrix
Levin, A.; Olshanetsky, M.; Zotov, A.
2014-10-01
In our recent paper we suggested a natural construction of the classical relativistic integrable tops in terms of the quantum R-matrices. Here we study the simplest case - the 11-vertex R-matrix and related gl2 rational models. The corresponding top is equivalent to the 2-body Ruijsenaars-Schneider (RS) or the 2-body Calogero-Moser (CM) model depending on its description. We give different descriptions of the integrable tops and use them as building blocks for construction of more complicated integrable systems such as Gaudin models and classical spin chains (periodic and with boundaries). The known relation between the top and CM (or RS) models allows to rewrite the Gaudin models (or the spin chains) in the canonical variables. Then they assume the form of n-particle integrable systems with 2n constants. We also describe the generalization of the top to 1+1 field theories. It allows us to get the Landau-Lifshitz type equation. The latter can be treated as non-trivial deformation of the classical continuous Heisenberg model. In a similar way the deformation of the principal chiral model is described.
Classical integrable systems and soliton equations related to eleven-vertex R-matrix
Levin, A; Zotov, A
2014-01-01
In our recent paper we suggested a natural construction of the classical relativistic integrable tops in terms of the quantum $R$-matrices. Here we study the simplest case -- the 11-vertex $R$-matrix and related ${\\rm gl}_2$ rational models. The corresponding top is equivalent to the 2-body Ruijsenaars-Schneider (RS) or the 2-body Calogero-Moser (CM) model depending on its description. We give different descriptions of the integrable tops and use them as building blocks for construction of more complicated integrable systems such as Gaudin models and classical spin chains (periodic and with boundaries). The known relation between the top and CM (or RS) models allows to re-write the Gaudin models (or the spin chains) in the canonical variables. Then they assume the form of $n$-particle integrable systems with $2n$ constants. We also describe the generalization of the top to 1+1 field theories. It allows us to get the Landau-Lifshitz type equation. The latter can be treated as non-trivial deformation of the cla...
Natalia K. Prykarpatska
2005-01-01
Full Text Available The geometric structure of characteristic surfaces related with partial differential equations of first and higher orders is studied making use the vector field technique on hypersurfaces. It is shown, that corresponding characteristics are defined uniquely up to some smooth tensor fields, thereby supplying additional information about the suitable set of their solutions. In particular, it may be very useful for studying asymptotic properties of solutions to our partial differential equations under some boundary conditions.
A Discrete Lax-Integrable Coupled System Related to Coupled KdV and Coupled mKdV Equations
LIU Ping; JIA Ma; LOU Sen-Yue
2007-01-01
A modified Korteweg-de Vries (mKdV) lattice is found to be also a discrete Korteweg-de Vries (KdV) equation.A discrete coupled system is derived from the single lattice equation and its Lax pair is proposed. The coupled system is shown to be related to the coupled KdV and coupled mKdV systems which are widely used in physics.
Properties of Bipolar Fuzzy Hypergraphs
M. Akram; 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.
Fuzzy Markov chains: uncertain probabilities
2002-01-01
We consider finite Markov chains where there are uncertainties in some of the transition probabilities. These uncertainties are modeled by fuzzy numbers. Using a restricted fuzzy matrix multiplication we investigate the properties of regular, and absorbing, fuzzy Markov chains and show that the basic properties of these classical Markov chains generalize to fuzzy Markov chains.
Achieving of Fuzzy Automata for Processing Fuzzy Logic
SHU Lan; WU Qing-e
2005-01-01
At present, there has been an increasing interest in neuron-fuzzy systems, the combinations of artificial neural networks with fuzzy logic. In this paper, a definition of fuzzy finite state automata (FFA) is introduced and fuzzy knowledge equivalence representations between neural networks, fuzzy systems and models of automata are discussed. Once the network has been trained, we develop a method to extract a representation of the FFA encoded in the recurrent neural network that recognizes the training rules.
Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
Dagmar Markechová
2016-01-01
Full Text Available In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.
Jantzen, Jan
1998-01-01
A logic based on the two truth values True and False is sometimes inadequate when describing human reasoning. Fuzzy logic uses the whole interval between 0 (False) and 1 (True) to describe human reasoning. As a result, fuzzy logic is being applied in rule based automatic controllers, and this paper...
Extended Fuzzy Clustering Algorithms
U. Kaymak (Uzay); M. Setnes
2000-01-01
textabstractFuzzy clustering is a widely applied method for obtaining fuzzy models from data. It has been applied successfully in various fields including finance and marketing. Despite the successful applications, there are a number of issues that must be dealt with in practical applications of fuz
12. workshop fuzzy systems. Proceedings; 12. Workshop Fuzzy Systeme. Proceedings
Mikut, R.; Reischl, M. (eds.)
2002-11-01
This annual workshop is a forum for discussing new methods and industrial applications in fuzzy logic and related fields like artificial neuronal nets and evolutionary algorithms. The focus is on applications in automation, e.g. in chemical engineering, energy engineering, automobile engineering, robotics and medical engineering. Other areas of interest are, e.g. data mining for technical and non-technical applications. [German] Der jaehrliche Workshop unseres Fachausschusses bietet ein Forum zur Diskussion neuer methodischer Ansaetze und industrieller Anwendungen auf dem Gebiet der Fuzzy-Logik und in angrenzenden Gebieten wie Kuenstlichen Neuronalen Netzen und Evolutionaeren Algorithmen. Besondere Schwerpunkte sind automatisierungstechnische Anwendungen, z.B. in der Verfahrenstechnik, Enegietechnik, Kfz-Technik, Robotik und Medizintechnik, aber auch Loesungen in anderen Problemgebieten (z.B. Data Mining fuer technische und nichttechnische Anwendungen) sind von Interesse. (orig.)
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
Myrzakulov, R.; Mamyrbekova, G.K.; Nugmanova, G.N.; Yesmakhanova, K.R. [Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India)
2014-06-13
Motion of curves and surfaces in R{sup 3} lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R{sup 3} in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs.
RBSDE's with jumps and the related obstacle problems for integral-partial differential equations
FAN; Yulian
2006-01-01
The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.
A Problem in Information Retrieval with Fuzzy Sets.
Buell, Duncan A.
1985-01-01
Discussion of problems with fuzzy subsets in document retrieval highlights attempts to invent a system of weighted fuzzy queries in which weights correspond to relative importance of each term in query as whole, and use of Kantor's Logic for Retrieval as an alternative to Boolean queries. Six references are cited. (EJS)
Axiomatic of Fuzzy Complex Numbers
Angel Garrido
2012-01-01
Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead ...
MODELING FUZZY GEOGRAPHIC OBJECTS WITHIN FUZZY FIELDS
无
2001-01-01
To improve the current GIS functions in describing geographic objects w ith fuzziness,this paper begins with a discussion on the distance measure of sp atial objects based on the theory of sets and an introduction of dilation and er osion operators.Under the assumption that changes of attributes in a geographic region are gradual,the analytic expressions for the fuzzy objects of points,l ines and areas,and the description of their formal structures are presented.Th e analytic model of geographic objects by means of fuzzy fields is developed.We have shown that the 9-intersection model proposed by Egenhofer and Franzosa (19 91) is a special case of the model presented in the paper.
Forward dispersion relations and Roy equations in {pi}{pi} scattering
Kaminski, R. [Polish Academy of Sciences, Department of Theoretical Physics Henryk Niewodniczanski Institute of Nuclear Physics, Krakow (Poland); Pelaez, J.R. [Universidad Complutense de Madrid, Departamento de Fisica Teorica, II (Metodos Matematicos), Facultad de Ciencias Fisicas, Madrid (Spain); Yndurain, F.J. [Universidad Autonoma de Madrid, Canto Blanco, Departamento de Fisica Teorica, Madrid (Spain)
2007-03-15
We first review the results of an analysis of {pi}{pi} interactions in S, P and D waves for the two-pion effective mass from threshold to about 1.4 GeV. In particular, we show a recent improvement of this analysis above the K anti K threshold using more data for phase shifts and including the S0-wave inelasticity from {pi}{pi}{yields}K anti K. In addition, we have improved the fit to the f{sub 2}(1270)-resonance and used a more flexible P-wave parametrization above the K anti K threshold and included an estimation of the D2-wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42 GeV. Finally, in this work we check that the {pi}{pi} scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations. (orig.)
A structured modeling approach for dynamic hybrid fuzzy-first principles models
Lith, van Pascal F.; Betlem, Ben H.L.; Roffel, Brian
2002-01-01
Hybrid fuzzy-first principles models can be attractive if a complete physical model is difficult to derive. These hybrid models consist of a framework of dynamic mass and energy balances, supplemented with fuzzy submodels describing additional equations, such as mass transformation and transfer rate
Nadernejad, Ehsan; Forchhammer, Søren; Korhonen, Jari
2011-01-01
Fuzzy filtering is one of the recently developed methods for reducing distortion in compressed images and video. In this paper, we combine the powerful anisotropic diffusion equations with fuzzy filtering in order to reduce the impact of artifacts. Based on the directional nature of the blocking ...
On , qk -intuitionistic (fuzzy ideals, fuzzy soft ideals of subtraction algebras
Madad Khan
2015-08-01
Full Text Available The intent of this article is to study the concept of an , k q -intuitionistic fuzzy ideal and , qk -intuitionistic fuzzy soft ideal of subtraction algebras and to introduce some related properties. 2010 AMS Classification: 06F35, 03G25, 08A72.
Development of single-chip fuzzy controller based on FFSI in binary
张吉礼; 欧进萍; 孙德兴
2003-01-01
Length and concise structure of fuzzy logic reasoning program and its real-time reasoning characteris-tic have their effect on the performance of a digital single-chip fuzzy controller. The control effect of a digitalfuzzy controller based on looking up fuzzy control responding table is only relative to the table and not relative tothe fuzzy control rules in the practical control process. Aiming at above problem and having combined fuzzy log-ic reasoning with digital operational characteristics of a single-chip microcomputer, functioning-fuzzy-subset in-ference (FFSI) in binary, in which triangle membership functions of error and error-in-change are all represen-ted in binary and singleton membership functions of control variable is binary too, has been introduced. The cir-cuit principle plans of a single-chip fuzzy controller have been introduced for development of its hardware, andthe primary program structure, fuzzy logic reasoning subroutine, serial communication subroutine with PC andreliability design of the fuzzy controller are all discussed in detail. The control of indoor temperature by a fuzzycontroller has been conducted using a testing-room thermodynamic system. Research results show that the FFSIin binary can exercise a concise fuzzy control in a single-chip fuzzy controller, and the fuzzy controller is there-fore reliable and possesses a high performance-price ratio.