Authors: Medina, Jesus
Stepanović, Vanja
Tepavčević, Andreja 
Affiliations: Computer Science 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Solutions of matrix equations with weak fuzzy equivalence relations
Journal: Information Sciences
Volume: 629
First page: 634
Last page: 645
Issue Date: 2023
Rank: ~M21a
ISSN: 0020-0255
DOI: 10.1016/j.ins.2023.01.145
In this paper, we are solving matrix equations where the operation on matrices might not be a standard composition, but it can be any convenient binary operation. We use fuzzy (lattice valued) techniques in which a particular fuzzy weak equivalence relation and its compatibility with the matrix operation plays the central role. This fuzzy weak equivalence relation is weakly reflexive, symmetric, transitive, and compatible with the matrix operation. We obtain approximate solutions of two main types of matrix equations. We also tackle the question of the uniqueness of solutions (which are unique up to the fuzzy weak equivalence relation).
Keywords: Lattice valued | Linear equation | Matrix equations | Weak fuzzy equivalence relation
Publisher: Elsevier

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