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The main purpose of this paper is to introduce and study the concepts of fuzzy upper and lower α`-continuous (resp. β -`-continuous, semi-`-continuous and pre-`-continuous) multifunctions via fuzzy ideals. Several properties of these multifunctions along with their mutual relationships are established with the help of examples. Also, we give the decomposition of fuzzy upper (resp. lower) α-`-continuity and the decomposition of fuzzy upper (resp. lower) `-continuity [15]. Later, we introduce new types of r-fuzzy compactness in a fuzzy ideal topological space (X ,τ, `) based on the sense of Šostak.

On fuzzy upper and lower α-ℓ-continuity and their decomposition