On the Generalization of Single Input Rule Modules Connected Type Fuzzy Reasoning Method

Yubazaki have proposed a “single input rule modules connected type fuzzy reasoning method (SIRMs method)” in which its final output is obtained by summarizing the product of importance degree and inference result from single input fuzzy rule modules. This paper proposes a “functional-type SIRMs method,” which is an extended version of the SIRMs method, and clarifies the relationship between the Takagi--Sugeno (T--S) reasoning method and the functional-type SIRMs method. The functional-type SIRMs method can be shown to be transformed to the T--S reasoning method, but generally the conversion to functional-type SIRMs method from the T--S reasoning method is impossible. It is shown, however, that the T--S reasoning method can be transformed to the functional-type SIRMs method when the T--S reasoning method fills some conditions. For this reason, it is shown that the functional-type SIRMs method is the subset of the T--S reasoning method.