Authors: Šešelja, Branimir
Tepavčević, Andreja 
Title: Weak fuzzy equivalence and equality relations
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 5909 LNCS
First page: 134
Last page: 139
Conference: 3rd International Conference on Pattern Recognition and Machine Intelligence, PReMI 2009; New Delhi; India; 16 December 2009 through 20 December 2009
Issue Date: 1-Dec-2009
Rank: M33
ISBN: 978-3-642-11164-8
ISSN: 0302-9743
DOI: 10.1007/978-3-642-11164-8_22
Weak fuzzy (lattice valued) equivalences and equalities are introduced by weakening the reflexivity property. Every weak fuzzy equivalence relation on a set determines a fuzzy set on the same domain. In addition, its cut relations are crisp equivalences on the corresponding cut subsets. Analogue properties of weak fuzzy equalities are presented. As an application, fuzzy weak congruence relations and fuzzy identities on algebraic structures are investigated.
Keywords: Block | Cut | Fuzzy equality | Fuzzy equivalence | Fuzzy identity | Lattice-valued fuzzy relation | Lattice-valued fuzzy set
Publisher: Springer Link

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