On the infimum and supremum of simplified fuzzy inference method

Fuzzy inference has played significant role in many applications. Although simplified fuzzy inference method is currently mostly used, the problem is that the number of fuzzy rules becomes very huge and so the setup and adjustment of fuzzy rules become difficult. On the other hand, Yubazaki et al. have proposed ldquosingle input rule modules connected fuzzy inference methodrdquo (SIRMs method, for short) whose final output is obtained by summarizing the product of the importance degrees and the inference results from single input fuzzy rule module. Seki et al. have shown that simplified fuzzy inference method and SIRMs method are equal when the sum of diagonal elements in rules of simplified fuzzy inference method is equal to that of cross diagonal elements. However, the conditions of infimum and supremum between simplified fuzzy inference method and SIRMs method are not clarified. This paper clarifies the conditions for infimum and supremum of simplified fuzzy inference method using SIRMs method.