On the Infimum and Supremum of Fuzzy Inference by Single Input Type Fuzzy Inference

Hirosato SEKI  Hiroaki ISHII 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E92-A  No.2  pp.611-617
Publication Date: 2009/02/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: General Fundamentals and Boundaries
Keyword: 
fuzzy inference,  T-S fuzzy inference method,  simplified fuzzy inference method,  SIRMs connected fuzzy inference method,  infimum and supremum, 

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Summary: 
Fuzzy inference has played a significant role in many applications. Although the 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 a "single input rule modules connected fuzzy inference method" (SIRMs method) 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 the simplified fuzzy inference method and the SIRMs method are equivalent when the sum of diagonal elements in rules of the simplified fuzzy inference method is equal to that of cross diagonal elements. This paper clarifies the conditions for the infimum and supremum of the fuzzy inference method using the single input type fuzzy inference method, from the view point of fuzzy inference.