Fuzzy pretopogenous structure based on way below relation

Abstract

This paper aims to define fuzzy pretopogenous structure based on way below relation (or an L-fuzzifying pretopogenous structure (LFPT structure, for short), where L is a completely distributive complete lattice) and study some of its properties. Also, the concepts of L-fuzzifying pre-neighborhood, L-fuzzifying pre-interior and L-fuzzifying pre-closure operators are established. Furthermore, the relation between L-fuzzifying pretopogenous and L-fuzzifying topology is obtained. Finally, the maps between L-fuzzifying pretopogenous structures and initial fuzzifying structures are investigated.