A linear output structure for fuzzy logic controllers

In this paper, the output structure of multiple-input-single-output fuzzy logic controller (FLCr) is studied. The input and output variables of the FLCr are all characterized by normal triangular-shaped membership functions and fuzzy partitions are considered for corresponding universes of discourse. A special mapping, linear rule mapping [(Fuzzy Sets and Systems 57 (1993) 149)], which describes the relationship between the input variables and the output variables of one rule is used. The conclusion proposed is that the output of multiple-input-single-output FLCr can be represented by the convex linear combination of its crisp input variables. A precise mathematical model of FLCr, which is helpful to analyze fuzzy control and tune the fuzzy logic controller, is given.