ANALYTICAL RESOLUTION AND NUMERICAL IDENTIFICATION OF FUZZY RELATIONAL SYSTEMS

Since Sanchez's seminal paper on fuzzy relational equations, both thei r theories and applications have been continuously exploited by resear chers. However, the solvable conditions of a system of fuzzy relationa l equations, also known as a fuzzy relational system (FRS), are still poorly established and their relationship with the methods for obtaini ng approximate solutions are unclear. When the FRS is adopted to model a fuzzy system, most of the existing identification algorithms focus on parameter estimation and less on the structure identification. In t his paper, these two issues are addressed. New theoretical understandi ngs on solving a system of fuzzy relational equations exactly and appr oximately are presented and their implications on the use of FRS to en code fuzzy rulebases are highlighted. Based upon the guided evolutiona ry simulated annealing (GESA) algorithm [11], an evolutionary identifi cation formulation called EVIDENT capable for both parameter and struc ture identifications in fuzzy system models is proposed. As demonstrat ed by the simulation results, the new algorithm not only is effective in determining the structure of the systems, but also identifies a bet ter parametric solution, as compared with that of the existing FRS ide ntification algorithms.