A New Notion of Fuzzy Local Function and Some Applications

Abstract

In this paper, a new notion of fuzzy local function called r-fuzzy local function is introduced, and some properties are given in a fuzzy ideal topological space X,τ,ℓ in Šostak sense. After that, the concepts of fuzzy upper (resp., lower) almost ℓ-continuous, weakly ℓ-continuous, and almost weakly ℓ-continuous multifunctions are introduced. Some properties and characterizations of these multifunctions along with their mutual relationships are discussed with the help of examples.