Paper:

# Suppression Effect of α-Cut Based Inference on Consequence Deviations

## Kiyohiko Uehara^{*}, Takumi Koyama^{*}, 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

This paper clarifies that inference based on α-cut and generalized mean (α-GEMII) is effective in suppressing consequence deviations. The suppression effect of α-GEMII is numerically evaluated in comparison to conventional inference based on the Compositional Rule of Inference (CRI). CRI-based parallel inference causes discontinuous deviations in the least upper and greatest lower bounds of deduced fuzzy sets even when it models the continuous input-output relation of a system and given facts change continuously. In contrast, α-GEMII can suppress the deviations because of its schemes originally developed for constraint propagation control. In simulations, indices are defined for numerically evaluating the degree to which deduced consequences follow the change in fuzzy outputs of given systems. Simulation results show that α-GEMII is effective in suppressing the deviations, compared to CRI-based parallel inference. In effective use of the schemes for suppressing the consequence deviations, α-GEMII can be applied to nonlinear prediction filters for complex time series, especially with fluctuations that do not always originate from a correlation between time series data.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.14, No.3, pp. 256-271, 2010.

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