Inverses of fuzzy relation matrices with addition-min composition

This paper mainly considers the post-inverse matrix of a fuzzy relation matrix in terms of addition-min composition. A necessary and sufficient condition for the consistency of the inverse matrix problem is given by transforming the problem into a series of particular fuzzy relation equations. The u...

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Bibliographic Details
Published in:	Fuzzy sets and systems Vol. 490; p. 109037
Main Authors:	Guo, Fang-Fang, Fu, Rong, Shen, Jie
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 15-08-2024
Subjects:	Addition-min composition Fuzzy relation equation Fuzzy relation matrix Post-inverse Fuzzy relation matrix Fuzzy relation equation Post-inverse Addition-min composition
Online Access:	Get full text
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Summary:	This paper mainly considers the post-inverse matrix of a fuzzy relation matrix in terms of addition-min composition. A necessary and sufficient condition for the consistency of the inverse matrix problem is given by transforming the problem into a series of particular fuzzy relation equations. The uniqueness of the post-inverse is also investigated. Furthermore, it is proved that the search for the minimal solutions of the particular fuzzy relation equations can be converted into solving a linear system. Based on these discussions, an algorithm is constructed for solving a post-inverse of a given fuzzy relation matrix.
ISSN:	0165-0114 1872-6801
DOI:	10.1016/j.fss.2024.109037