On L-Fuzzy Topological Spaces Determined by Implicators

Abstract

This paper is towards the study of [Formula: see text]-fuzzy topological spaces, [Formula: see text]-fuzzy pretopological spaces and their corresponding operators determined by general implicators. We show that the results regarding one-to-one correspondence between [Formula: see text]-fuzzy reflexive approximation spaces and [Formula: see text]-fuzzy pretopological spaces as well as [Formula: see text]-fuzzy preorder approximation spaces and [Formula: see text]-fuzzy topological spaces heavily depend on implicators. Finally, we establish a relationship between category of [Formula: see text]-fuzzy pretopological spaces and category of [Formula: see text]-fuzzy topological spaces by using category of [Formula: see text]-fuzzy approximation spaces.