On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications - I. M. Taha (Journal of Mathematics)
In the present study, we introduce and characterize the class of r-generalized fuzzy ℓ-closed sets in a fuzzy ideal topological space X,τ,ℓ in Šostak sense. Also, we show that r-generalized fuzzy closed set by Kim and Park (2002) ⟹r-generalized fuzzy ℓ-closed set, but the converse need not be true. Moreover, if we take ℓ=ℓ0, the r-generalized fuzzy ℓ-closed set and r-generalized fuzzy closed set are equivalent. After that, we define fuzzy upper (lower) generalized ℓ-continuous multifunctions, and some properties of these multifunctions along with their mutual relationships are studied with the help of examples. Finally, some separation axioms of r-generalized fuzzy ℓ-closed sets are introduced and studied. Also, the notion of r-fuzzy G∗-connected sets is defined and studied with help of r-generalized fuzzy ℓ-closed sets.