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Keywords:
poset valued fuzzy set; cut; equivalent fuzzy sets; Dedekind- MacNeille completion
poset valued fuzzy set; cut; equivalent fuzzy sets; Dedekind- MacNeille completion
Summary:
Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Relationship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.
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