Authors: Tepavčević, Andreja 
Šešelja, Branimir
Title: On a generalization of fuzzy algebras and congruences
Journal: Fuzzy Sets and Systems
Volume: 65
Issue: 1
First page: 85
Last page: 94
Issue Date: 11-Jul-1994
Rank: M21
ISSN: 0165-0114
DOI: 10.1016/0165-0114(94)90249-6
Partially ordered fuzzy algebras are mappings from an algebra to a partially ordered set, with the property that every level subset is an ordinary subalgebra. Similar definitions are induced for P-valued congruences and weak congruences. Necessary and sufficient conditions under which an arbitrary collection of subalgebras (congruences) enables construction of a P-valued fuzzy subalgebra (congruence) are given. Any P-valued weak congruence uniquely determines a P-valued subalgebra of the same algebra. Finally, any collection of subalgebras or congruences of a given algebra can be used for the construction of a relational valued fuzzy algebra or congruence. This seems to be the most general way to obtain a fuzzy algebra (congruence) out of the collection of the ordinary subalgebras (congruences).
Keywords: Fuzzy algebra | Fuzzy congruence
Publisher: Elsevier

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