Authors: Šešelja, Branimir
Tepavčević, Andreja 
Title: Partially ordered and relational valued fuzzy relations I
Journal: Fuzzy Sets and Systems
Volume: 72
Issue: 2
First page: 205
Last page: 213
Issue Date: 9-Jun-1995
Rank: M51
ISSN: 0165-0114
DOI: 10.1016/0165-0114(94)00352-8
Abstract: 
The aim of the paper is to define and investigate some special properties of partially ordered and relational valued fuzzy relations. We use the concept of a fuzzy set as the mapping from an unempty set into a partially ordered set or into a suitable relational system (see [2, 3] ). Fuzzy equivalence and fuzzy order are defined by means of ordinary equivalence and ordering relations as the corresponding level relations, since the direct definitions (see [1], for example) are useless because of the absence of lattice operations. Necessary and sufficient conditions under which a collection of equivalence or ordering relations can be synthesized into the above-mentioned partially ordered fuzzy relation are given. For the relational valued fuzzy relations, it turns out that any collection of equivalences or orderings gives a relational valued fuzzy equivalence or ordering.
Keywords: Equivalence | Order | uzzy relation
Publisher: Elsevier

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