Homotopy on Smooth Fuzzy Fréchet Manifold

Abstract

    This paper presents definition to a fuzzy FF-smooth homotopy on FF-smooth fuzzy Fréchet manifold and proves that the fuzzy FF-smooth homotopy of a fuzzy path forms an equivalence relation. The researchers also expand the study to include three types of fuzzy FF-smooth homotopy of a fuzzy path, namely a maximal fuzzy FF-smooth homotopy, an internal fuzzy FF-smooth homotopy, and local fuzzy FF-smooth homotopy admitting equivalence relations and a structure of a group.