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 $\left(X,\tau ,\ell \right)$ in Šostak sense. After that, the concepts of fuzzy upper (resp., lower) almost $\ell$ -continuous, weakly $\ell$ -continuous, and almost weakly $\ell$ -continuous multifunctions are introduced. Some properties and characterizations of these multifunctions along with their mutual relationships are discussed with the help of examples.