Specificity shift in solving fuzzy relational equations

Abstract Studied is a system of “N” fuzzy relational equations with a max-t composition x(k)R = y(k), where the input-output fuzzy sets (x(k) and y(k)) are available while the fuzzy relation (R) needs to be determined. The solution to these equations is derived through a new paradigm of specificity shift. The main objective is to modify a level of specificity of the fuzzy sets (relational constraint) so that the modified constraints allow for the use of some standard theoretical results of the theory of fuzzy relational equations that otherwise would have been found totally unjustifiable. In more detail, the specificity of the available input fuzzy sets becomes gradually increased while an opposite tendency is observed for the output fuzzy sets. The optimization of the specificity levels is discussed in detail. Numerical studies are also included. Finally, the use of the specificity shift is discussed in a conjunction with the exploitation of standard gradient-based techniques.

[1]  J. V. Oliveira,et al.  Neuron inspired learning rules for fuzzy relational structures , 1993 .

[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 and Their Applications to Knowledge Engineering , 1989, Theory and Decision Library.

[4]  H. Trussell,et al.  Constructing membership functions using statistical data , 1986 .

[5]  W. Pedrycz.  Genetic algorithms for learning in fuzzy relational structures , 1995 .

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

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

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

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

[10]  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).

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

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

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

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

[15]  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).

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

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

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

[19]  Witold Pedrycz,et al.  Solving fuzzy relational equations through logical filtering , 1996, Fuzzy Sets Syst..