Authors: Stepanović, Vanja
Tepavčević, Andreja
Affiliations: Computer Science 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Fuzzy sets (in)equations with a complete codomain lattice
Journal: Kybernetika
Volume: 58
Issue: 2
First page: 145
Last page: 162
Issue Date: 2022
Rank: ~M23
ISSN: 0023-5954
DOI: 10.14736/kyb-2022-2-0145
Abstract: 
The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of fuzzy sets (in)equations, in a special case of a meet-continuous complete codomain lattice.
Keywords: fuzzy relations | fuzzy set equations | fuzzy set inequations | monotonous operator | upper continuous lattice
Publisher: The Institute of Information Theory and Automation (UTIA), Czech Academy of Sciences

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