Many valued lattices and their representations

Authors:
Hongbin Zhao;Dexue Zhang
Affiliations:
Department of Mathematics, Sichuan University, Chengdu 610064, China;Department of Mathematics, Sichuan University, Chengdu 610064, China
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

This paper presents an investigation of many valued lattices from the point of view of enriched category theory. For a bounded partially ordered set P, the conditions for P to become a lattice can be postulated as existence of certain adjunctions. Reformulating these adjunctions, by aid of enriched category theory, in many valued setting, two kinds of many valued lattices, weak @W-lattices and @W-lattices, are introduced. It is shown that the notion of @W-lattices coincides with that of lattice fuzzy orders of Belohlavek; and the notion of weak @W-lattices coincides with that of vague lattices of Demirci.