Fuzzy arithmetic-based interpolative reasoning for nonlinear dynamic fuzzysystems

FAIR (fuzzy arithmetic-based interpolative reasoning)-a fuzzy reasoning sch eme based on fuzzy arithmetic, is presented here. Linguistic rules of the M amdani type, with fuzzy numbers as consequents, are used in an inference me chanism similar to that of a Takagi-Sugeno model. The inference result is a weighted sum of fuzzy numbers, calculated by means of the extension princi ple. Both fuzzy and crisp inputs and outputs can be used, and the chaining of rule bases is supported without increasing the spread of the output fuzz y sets in each step. This provides a setting for modeling dynamic fuzzy sys tems using fuzzy recursion. The matching in the rule antecedents is done by means of a compatibility measure that can be selected to suit the applicat ion at hand. Different compatibility measures can be used for different ant ecedent variables, and reasoning with sparse rule bases is supported. The a pplication of FAIR to the modeling of a nonlinear dynamic system based on a combination of knowledge-driven and data-driven approaches is presented as an example. (C) 1998 Elsevier Science Ltd. All rights reserved.