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JACIII Vol.17 No.4 pp. 647-662
doi: 10.20965/jaciii.2013.p0647
(2013)

Paper:

Multi-Level Control of Fuzzy-Constraint Propagation in Inference Based on α-Cuts and Generalized Mean

Kiyohiko Uehara* and Kaoru Hirota**

*Ibaraki University, 4-12-1 Nakanarusawa-cho, Hitachi 316-8511, Japan

**Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan

Received:
April 9, 2013
Accepted:
May 17, 2013
Published:
July 20, 2013
Keywords:
fuzzy inference, compositional rule of inference, implication, convex fuzzy set, α-cut
Abstract

An inference method is proposed, which can perform nonlinear mapping between convex fuzzy sets and present a scheme of various fuzzy-constraint propagation from given facts to deduced consequences. The basis of nonlinear mapping is provided by α-GEMII (α-level-set and generalized-mean-based inference) whereas the control of fuzzy-constraint propagation is based on the compositional rule of inference (CRI). The fuzzy-constraint propagation is controlled at the multi-level of α in its α-cut-based operations. The proposed method is named α-GEMS (α-level-set and generalized-mean-based inference in synergy with composition). Although α-GEMII can perform the nonlinear mapping according to a number of fuzzy rules in parallel, it has limitations in the control of fuzzy-constraint propagation and therefore has difficulty in constructing models of various given systems. In contrast, CRI-based inference can rather easily control fuzzy-constraint propagation with high understandability especially when a single fuzzy rule is used. It is difficult, however, to perform nonlinear mapping between convex fuzzy sets by using a number of fuzzy rules in parallel. α-GEMS can solve both of these problems. Simulation results show that α-GEMS is performed well in the nonlinear mapping and fuzzy-constraint propagation. α-GEMS is expected to be applied to modeling of given systems with various fuzzy input-output relations.

Cite this article as:
K. Uehara and K. Hirota, “Multi-Level Control of Fuzzy-Constraint Propagation in Inference Based on α-Cuts and Generalized Mean,” J. Adv. Comput. Intell. Intell. Inform., Vol.17, No.4, pp. 647-662, 2013.
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