On the Monotonicity of Single Input Type Fuzzy Reasoning Methods

Hirosato SEKI  Hiroaki ISHII  Masaharu MIZUMOTO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.7   pp.1462-1468
Publication Date: 2007/07/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.7.1462
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: General Fundamentals and Boundaries
fuzzy reasoning,  single input rule modules (SIRMs),  fuzzy sets,  monotonicity,  

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Yubazaki et al. have proposed "single input rule modules connected type fuzzy reasoning method" (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. Another type of single input type fuzzy reasoning method proposed by Hayashi et al. (we call it "Single Input Connected fuzzy reasoning method" (SIC method, for short) in this paper) uses rule modules to each input item as well as SIRMs method. We expect that inference results of SIRMs method and SIC method have monotonicity if the antecedent parts and consequent parts of fuzzy rules in SIRMs rule modules have monotonicity. However, this paper points out that even if fuzzy rules in SIRMs rule modules have monotonicity, the inference results do not necessarily have monotonicity. Moreover, it clarifies the conditions for the monotonicity of inference results by SIRMs method and SIC method.