An approach to the fuzzification of complete lattices

Article type: Research Article

Authors: Yao, Wei

Affiliations: Department of Mathematics, Hebei University of Science and Technology, Shijiazhuang, P.R. China

Note: [] Corresponding author. Wei Yao, Department of Mathematics, Hebei University of Science and Technology, Shijiazhuang 050018, P.R. China. E-mail: [email protected]

Abstract: This paper presents an approach to the fuzzification of complete lattices. This kind of fuzzification is a functor from the category of complete lattices to the category of complete L-ordered sets. It not only can be considered as an algebraic representation of the Lowen functor ωL, but also can characterize the stratification of L-topological spaces and the underlying set of Hutton unit interval.

Keywords: Stratified L-topology, complete lattice, frame, (Complete) L-ordered set, L-frame, Lowen functor $\omega_L$

DOI: 10.3233/IFS-130897

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 5, pp. 2239-2249, 2014