Fuzzy power structures

Archive for Mathematical Logic 47 (3):233-261 (2008)
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Power structures are obtained by lifting some mathematical structure (operations, relations, etc.) from an universe X to its power set ${\mathcal{P}(X)}$ . A similar construction provides fuzzy power structures: operations and fuzzy relations on X are extended to operations and fuzzy relations on the set ${\mathcal{F}(X)}$ 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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Citations of this work

Good fuzzy preorders on fuzzy power structures.Hongliang Lai & Dexue Zhang - 2010 - Archive for Mathematical Logic 49 (4):469-489.

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References found in this work

Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.
Metamathematics of Fuzzy Logic.P. Hájek - 2002 - Studia Logica 72 (3):433-437.
Universal Algebra.George Grätzer - 1982 - Studia Logica 41 (4):430-431.

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