ON r-fuzzy ℓ-open sets and continuity of fuzzy multifunctions via fuzzy ideals

Abstract

In this paper, the concepts of r-fuzzy ℓ-open, r-fuzzy semi-ℓ-open, r-fuzzy pre-ℓ-open, r-fuzzy α-ℓ- open and r-fuzzy β-ℓ-open sets are introduced in a fuzzy ideal topological space (X, τ, ℓ) based on the sense of Sostak. Also, the relations of these sets with each other are investigated with the help of examples. Moreover, the concepts of fuzzy upper (resp. lower) ℓ-continuous, almost ℓ-continuous and weakly ℓ-continuous multifunctions are introduced and some properties of these multifunctions along with their mutual relationships are specified.