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doi:10.1016/0020-0255(88)90044-8 
Copyright © 1988 Published by Elsevier Science Inc.
Convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing
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Ario Ohsato and Takashi Sekiguchi
Received 4 May 1987.
Abstract
This paper presents some theoretical results on a set of the convexly combined fuzzy relational equations represented in the form λ·(x(k)Δ 2)+ −λ· (x(k) · R) = y(k) (k = 1,2,…, K), where xk and yk denote fuzzy sets, R and 2 fuzzy relations, · the sup · min compositional operator, Δ the inf · max one, and λ a fuzzy convex combinator whose complement is −λ. Furthermore, we propose a method to formulate the fuzzy information processing approximately by means of the convexly combined fuzzy relational equations, focusing our attention on the modeling of fuzzy input-output systems, normality of fuzzy sets characterizing fuzzy input, fuzzy logical aspects of systems, and association between fuzzy information. Finally, it is suggested that the proposed method is suitable for the modelling of several types of fuzzy systems.
