An approach to the fuzzification of complete lattices

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 ω_L, but also can characterize the stratification of L-topological spaces and the underlying set of Hutton unit interval.