fuzzy ordered sets and duality for finite fuzzy distributive lattices

FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES

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 space...

A duality between fuzzy domains and strongly completely distributive $L$-ordered sets

The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...

a duality between fuzzy domains and strongly completely distributive $l$-ordered sets

the aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. all values aretaken in a fixed frame $l$. a definition of (strongly) completelydistributive $l$-ordered sets is introduced. the main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $l$-ordereds...

Representation theorem for finite intuitionistic fuzzy perfect distributive lattices

In this paper, we extend some results obtained by A. Amroune and B. Davvaz in [1]. More precisely, we will develop a representation theory of intuitionistic fuzzy perfect distributive lattices in the finite case. To that end, we introduce the notion of intuitionistic fuzzy perfect distributive lattices and the one of fuzzy perfect Priestley spaces. In this way, the results of A. Amroune and B. ...

Avoidable structures, II: finite distributive lattices and nicely-structured ordered sets

Let 〈D,≤〉 be the ordered set of isomorphism types of finite distributive lattices, where the ordering is by embeddability. We characterize the order ideals in 〈D,≤〉 that are well-quasi-ordered by embeddability, and thus characterize the members of D that belong to at least one infinite anti-chain in D.

Cardinalities of Fuzzy Sets and Fuzzy Quantifiers over Residuated Lattices