On F-homotopy and F-fundamental group

In general, there are two main ways to define fuzzy topological spaces: (1) given a set X we can take a family of fuzzy subsets of X which satisfies special axioms of topology in X or (2) if τ is a topology at X in the usual sense and A is a fuzzy subset of X, we can consider the special family of fuzzy subsets τ* generated by τ in such way that (A, τ*) is a fuzzy topological space. We present a formalization of the concept of homotopy considering the first point of view of fuzzy topological spaces. We start by making a comparison between the definitions of fuzzy topological spaces in the sense of Morderson and Gunduz, as well as their respective concepts of continuity. Furthermore, we investigate issues related to homotopy, function spaces and fundamental group considering this point of view of homotopy.