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Similarity and fuzzy tolerance spaces. (English) Zbl 1067.03057

The paper studies fuzzy tolerance relations. Fuzzy tolerances and fuzzy tolerance spaces are presented and their properties are investigated. Natural grouping of elements induced by the similarity, as well as induced relations by a fuzzy tolerance on \(X\), are studied. Examples complete the exposition. Attention is paid to algorithms for generating all fuzzy tolerance classes of a fuzzy tolerance relation.

MSC:

03E72 Theory of fuzzy sets, etc.
03B52 Fuzzy logic; logic of vagueness
08A72 Fuzzy algebraic structures
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