A representation theorem for infinite fuzzy distributive lattices

Article type: Research Article

Authors: Amroune, Abdelaziz^* | Oumhani, Ali

Affiliations: Laboratory of pure and applied Mathematics, Department of Mathematics, University Mohamed Boudiaf, M’sila, Algeria

Correspondence: [*] Corresponding author. Abdelaziz Amroune, Laboratory of pure and applied Mathematics, Department of Mathematics, University Mohamed Boudiaf, P.O. Box 166, M’sila 28000, Algeria. Tel.: +213 6 64 60 23 78; Fax: +213 35 389245; E-mail: [email protected].

Abstract: In this paper, we show that the category of infinite fuzzy Priestley spaces is equivalent to the dual of the category of infinite fuzzy distributive lattices. A representation theorem for the infinite fuzzy distributive lattices is also given.

Keywords: Fuzzy ordered relation, fuzzy ordered set, fuzzy lattice, fuzzy Priestley space, homomorphism of fuzzy lattices, homomorphism of fuzzy Priestley spaces

DOI: 10.3233/JIFS-151029

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 35-42, 2017