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Fuzzy ordered sets and duality for finite fuzzy distributive lattices. (English) Zbl 1260.06015

Summary: The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley spaces is equivalent to the dual of the category of finite fuzzy distributive lattices. Several examples are also presented.

MSC:

06D72 Fuzzy lattices (soft algebras) and related topics
06A75 Generalizations of ordered sets
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