FUZZY RELATIONAL EQUATIONS: BRIDGING THEORY, METHODOLOGY AND PRACTICE

This study delivers a general overview of the theory and practice of fuzzy relational equations. We discuss various methods leading to the solutions of these equations starting from analytical approaches, moving through semi-analytic methods and finally elaborating on the neural-like style of finding solutions to relational constructs. The paper addresses important aspects of knowledge representation worked out by these equations and proposes a number of structural enhancements of the existing relational architectures.

[1]  J. Goguen L-fuzzy sets , 1967 .

[2]  A. Alouani,et al.  Prediction of complex systems' behavior described by fuzzy relational equations , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[3]  W. Pedrycz,et al.  Fuzzy relation equations on a finite set , 1982 .

[4]  M. Sugeno,et al.  Fuzzy relational equations and the inverse problem , 1985 .

[5]  Witold Pedrycz,et al.  Fuzzy-set based models of neurons and knowledge-based networks , 1993, IEEE Trans. Fuzzy Syst..

[6]  D. Ruan,et al.  A novel neural algorithm and its application in solving fuzzy relation equations , 1997, 1997 Annual Meeting of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.97TH8297).

[7]  Witold Pedrycz,et al.  Fuzzy control and fuzzy systems , 1989 .

[8]  W. Pedrycz,et al.  Fuzzy relation equations theory as a basis of fuzzy modelling: an overview , 1991 .

[9]  Witold Pedrycz,et al.  Estimation of fuzzy relational matrix by using probabilistic descent method , 1993 .

[10]  Witold Pedrycz,et al.  Fuzzy sets engineering , 1995 .

[11]  W. Pedrycz Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data , 1985 .

[12]  W. Pedrycz,et al.  Fuzzy Relation Equations and Their Applications to Knowledge Engineering , 1989, Theory and Decision Library.

[13]  G. Klir,et al.  Resolution of finite fuzzy relation equations , 1984 .

[14]  Salvatore Sessa,et al.  On the set of solutions of composite fuzzy relation equations , 1983 .

[15]  C. Desoer,et al.  Linear System Theory , 1963 .

[16]  Chang-Chieh Hang,et al.  The delta rule and learning for min-max neural networks , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[17]  W. Bandler,et al.  The use of trapezoidal function in a linguistic fuzzy relational neural network for speech recognition , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[18]  Sergiu Rudeanu Boolean functions and equations , 1974 .

[19]  Witold Pedrycz,et al.  Fuzzy system identification via probabilistic sets , 1982, Inf. Sci..

[20]  W. Pedrycz Numerical and applicational aspects of fuzzy relational equations , 1983 .

[21]  Elie Sanchez,et al.  Resolution of Composite Fuzzy Relation Equations , 1976, Inf. Control..

[22]  Witold Pedrycz,et al.  Neurocomputations in Relational Systems , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  János Fodor,et al.  A new look at fuzzy connectives , 1993 .

[24]  Alexandru Agapie,et al.  Genetic Algorithms for Solving Systems of Fuzzy Relational Equations , 1997, Fuzzy Days.

[25]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

[26]  W Pedrycz,et al.  Solvability of fuzzy relational equations and manipulation of fuzzy data , 1986 .

[27]  Witold Pedrycz,et al.  Fuzzy neural networks and neurocomputations , 1993 .

[28]  Siegfried Gottwald,et al.  On the existence of solutions of systems of fuzzy equations , 1984 .