Fuzzy interior and fuzzy closure of fuzzy set with extended definition of fuzzy set

Abstract

The main purpose of this work is to construct a basic concept of fuzzy topology. In this article, we will try to give definition of fuzzy topology, fuzzy open set, fuzzy closed set, fuzzy interior of a fuzzy set, fuzzy closure of a fuzzy set in fuzzy topology and also, we will try to prove some theorems on fuzzy interior and fuzzy closure of a fuzzy topology with the help of extended definition of fuzzy sets and complement of a fuzzy sets.