Paper:

# Inference with Governing Schemes for Propagation of Fuzzy Convex Constraints 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 governing scheme is proposed for fuzzy constraint propagation from given facts to consequences in convex forms, which is applied to the inference method based on α-cuts and generalized mean. The governing is performed by self-tuning which can reflect the distribution forms of fuzzy sets in consequent parts to the forms of deduced consequences. Thereby, the proposed scheme can solve the problems in the conventional inference based on the compositional rule of inference that deduces fuzzy sets with excessive fuzziness increase and specificity decrease. In simulations, it is confirmed that the proposed scheme can effectively perform the constraint propagation from given facts to consequences in convex forms while reflecting fuzzy-set distributions in consequent parts. It is also demonstrated that consequences are deduced without excessively large fuzziness and small specificity.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.13, No.3, pp. 321-330, 2009.

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