Sets of solution-set-invariant coefficient matrices of simple fuzzy relation equations
type: Item
instance of: scholarly article
title: Sets of solution-set-invariant coefficient matrices of simple fuzzy relation equations
zbMATH Open document ID: 0649.04003
DOI: 10.1016/0165-0114(87)90153-9
author: Masaaki Miyakoshi
author: Masaru Shimbo
published in: Fuzzy Sets and Systems
publication date: 1987-01-01T00:00:00Z
review text: Let x, b be two fuzzy sets and A, A' be two fuzzy relations such that the finite fuzzy equations \(x\circ A=b\) and \(x\circ A'=b\) hold, where ``\(\circ ''\) denotes the max-min composition, A, A' are assigned and x is unknown. If the membership values of b are ordered in strictly decreasing sense, then the above equations are called simple. Let X and X', respectively, be the sets of the solutions of the above equations. Using results of \textit{Wang Peizhuang}, \textit{S. Sessa}, the reviewer, and \textit{W. Pedrycz} [Busefal 18, 67-74 (1984; Zbl 0581.04001)], the authors give an iff condition in order to have \(X=X'\). Further results on the number of the distinct elements of X are established.
Mathematics Subject Classification ID: 03E99
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 4059402
zbMATH Keywords: simple fuzzy relation equations
zbMATH Keywords: fuzzy relations
zbMATH Keywords: max-min composition
reviewed by: Antonio Di Nola
MaRDI profile type: Publication
full work available at URL: 0165-0114(87)90153-9
OpenAlex ID: W2067522369
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description: scientific article; zbMATH DE number 4059402