Paper:

# Noise Reduction with Inference Based on Fuzzy Rule Interpolation at an Infinite Number of Activating Points: Toward Fuzzy Rule Learning in a Unified Inference Platform

## Kiyohiko Uehara^{*} and Kaoru Hirota^{**}

^{*}Ibaraki University

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

^{**}Beijing Institute of Technology

5 South Zhongguancun Street, Haidian District, Beijing 100081, China

In order to provide a unified platform for fuzzy inference and fuzzy rule learning with noise-corrupted data, a method is proposed for reducing noise in learning data on the basis of a fuzzy inference method called α-GEMINAS (α-level-set and generalized-mean-based inference with fuzzy rule interpolation at an infinite number of activating points). It is expected to prevent fuzzy rules from overfitting to noise in learning data, especially when there is less learning data available for fuzzy rule optimization. The proposed method is named α-GEMI-ES (α-GEMINAS-based local-evolution toward slight linearity for global smoothness) in this paper. α-GEMI-ES iteratively performs α-GEMINAS and reduces the noise in each iteration. This paper mathematically proves that α-GEMI-ES effectively reduces the noise. The noise-reduction process is decisive and thus relies less on trial-and-error-based progress. The noise is reduced by a large amount in the early iterations and the amount of its reduction is decelerated in the later iterations where the deviation in the learning data is suppressed to a great extent. This property makes it easy to determine the termination conditions for the iterative process. Simulation results demonstrate that α-GEMI-ES properly reduces noise as the mathematical proof suggests. The above-mentioned properties indicate that α-GEMI-ES is feasible in practice for the unified platform.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.22, No.6, pp. 883-899, 2018.

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