Paper:

# Fuzzy Inference with Schemes for Guaranteeing Convexity and Symmetricity in Consequences Based on α-Cuts

## Kiyohiko Uehara^{*}, Takumi Koyama^{*}, and Kaoru Hirota^{**}

^{*} Ibaraki University, Hitachi 316-8511, Japan

^{**} Tokyo Institute of Technology, Yokohama 226-8502, Japan

A fuzzy inference method is proposed on the basis of α-cuts, which can mathematically prove to deduce consequences in both convex and symmetric forms under the required conditions, studied here, when fuzzy sets in the consequent parts of fuzzy rules are all convex and symmetric. The inference method can reflect the distribution forms of fuzzy sets in consequent parts of fuzzy rules, guaranteeing the convexity in deduced consequences. It also has a control scheme for the fuzziness and specificity in deduced consequences. The controllability provides a way to suppress excessive fuzziness increase and specificity decrease in deduced consequences. Simulation studies show that the proposed method can deduce consequences in convex and symmetric forms under the required conditions. It is also demonstrated that the distribution forms of consequent parts are reflected to deduced consequences. Moreover, it is found that the fuzziness and specificity of deduced consequences can be effectively controlled in the simulations.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.13, No.2, pp. 135-149, 2009.

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