On the equivalence of single input type fuzzy inference methods

This paper addresses equivalence of fuzzy inference methods. It first presents single input type fuzzy inference methods: the single input rule modules connected type fuzzy inference method (SIRMs method) and single input connected fuzzy inference method (SIC method). Secondly, the equivalence conditions of the SIRMs method and SIC method are shown. Finally, this paper also discusses the equivalence conditions between the single input type fuzzy inference methods and the conventional fuzzy inference methods like the simplified fuzzy inference method, product-sum-gravity method and fuzzy singleton-type inference method which are all widely used as fuzzy control methods.