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 inFuzzy sets and systems Vol. 490; p. 109037
Main Authors Guo, Fang-Fang, Fu, Rong, Shen, Jie
Format Journal Article
LanguageEnglish
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
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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