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On the structure of F-indistinguishability operators. (English) Zbl 0609.04002
The concept of F-indistinguishability operator is a generalization of the concept of equivalence relation by substituting the F-transitivity for the usual transitivity. It is proven that any F-indistinguishability operator on a set X is generated by a family of fuzzy subsets of X. This result allows the construction of F-indistinguishabilities in a more efficient way, and facilitates new applications of these relations.
The relationship between the F-indistinguishability operators and metrics is explored. The concepts of G-pseudometric as well as G-metric are defined. Fuzzy partitions are discussed from the point of view of F- indistinguishability operators.
Reviewer: Qu Yinsheng

MSC:
03E20 Other classical set theory (including functions, relations, and set algebra)
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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