|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||Abstract:||
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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