On the Equivalence Conditions of Fuzzy Inference Methods—Part 1: Basic Concept and Definition

This paper addresses equivalence of fuzzy inference methods. It first presents several well-known fuzzy inference methods: the product-sum-gravity method, the simplified fuzzy inference method, the fuzzy singleton-type inference method, the single input rule modules connected type fuzzy inference method (SIRMs method), and the single input connected fuzzy inference method (SIC method). Second, three fuzzy inference methods of the product-sum-gravity method, simplified fuzzy inference method, and fuzzy singleton-type inference method, which are all widely used as fuzzy control methods, are shown to be equivalent to each other. Third, the equivalence conditions between the SIRMs method and the SIC method, known as single input type fuzzy inference method, are shown. Finally, it also gives the equivalence conditions between the single input type fuzzy inference methods and the previous three fuzzy inference methods. Investigating the equivalence among various fuzzy inference methods would help to understand the relationship of those fuzzy inference methods.