Authors: Ignjatović, Jelena
Ćirić, Miroslav
Šešelja, Branimir
Tepavčević, Andreja 
Title: Fuzzy relational inequalities and equations, fuzzy quasi-orders, closures and openings of fuzzy sets
Journal: Fuzzy Sets and Systems
Volume: 260
First page: 1
Last page: 24
Issue Date: 1-Jan-2015
Rank: M21a
ISSN: 0165-0114
DOI: 10.1016/j.fss.2014.05.006
The paper deals with systems of fuzzy relation equations known in the literature as eigen fuzzy set equations, as well as with systems of related fuzzy relation inequalities. Our main results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities, and algorithms for computing the greatest solutions to the considered systems of fuzzy relation equations. The systems are studied in the framework of complete residuated lattices as the structure of membership values, by means of fuzzy quasi-orders and closures and openings on a collection of fuzzy sets.
Keywords: Closures | Complete residuated lattices | Eigen fuzzy sets | Fuzzy quasi-orders | Fuzzy relation equations | Fuzzy relation inequalities | Fuzzy relations | Openings
Publisher: Elsevier
Project: Development of methods of computation and information processing: theory and applications 

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