Fuzzy power structures |
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Authors: | George Georgescu |
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Institution: | (1) Faculty of Mathematics, Bucharest University, Str. Academiei 14, Bucharest, Romania |
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Abstract: | Power structures are obtained by lifting some mathematical structure (operations, relations, etc.) from an universe X to its power set . A similar construction provides fuzzy power structures: operations and fuzzy relations on X are extended to operations and fuzzy relations on the set of fuzzy subsets of X. In this paper we study how this construction preserves some properties of fuzzy sets and fuzzy relations (similarity, congruence,
etc.). We define the notions of good, very good, Hoare good and Smith good fuzzy relation and establish some connections between
them, generalizing some results of Brink, Bošnjak and Madarász on power structures. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 03B52 03B50 |
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