Paper:

# Fuzzy Inference Based on α-Cuts and Generalized Mean: Relations Between the Methods in its Family and their Unified Platform

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

^{*}Ibaraki University

Hitachi 316-8511, Japan

^{**}Beijing Institute of Technology

Beijing 100081, China

This paper clarifies the relations in properties and structures between fuzzy inference methods based on α-cuts and the generalized mean. The group of the inference methods is named the α-GEM (α-cut and generalized-mean-based inference) family. A unified platform is proposed for the inference methods in the α-GEM family by the effective use of the above-mentioned relations. For the unified platform, a criterion is made clear to uniquely determine the value of a parameter in fuzzy-constraint propagation control for facts given by singletons. Moreover, conditions are derived to make the inference methods in the α-GEM family equivalent to singleton-consequent-type fuzzy inference which has been successfully applied to a wide variety of fields. Thereby, the unified platform can contribute to the construction of an inference engine for both the methods in the α-GEM family and singleton-consequent-type fuzzy inference. Such scheme of the inference engine provides an effective way to make these inference methods transformed into each other in learning for selecting the inference methods as well as for optimizing fuzzy rules.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.21, No.4, pp. 597-615, 2017.

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