On r -Generalized Fuzzy ℓ -Closed Sets: Properties and Applications

Abstract

In the present study, we introduce and characterize the class of $r$ -generalized fuzzy $\ell$ -closed sets in a fuzzy ideal topological space $\left(X,\tau ,\ell \right)$ in Šostak sense. Also, we show that $r$ -generalized fuzzy closed set by Kim and Park (2002) $⟹$ $r$ -generalized fuzzy $\ell$ -closed set, but the converse need not be true. Moreover, if we take $\ell ={\ell }_0$ , the $r$ -generalized fuzzy $\ell$ -closed set and $r$ -generalized fuzzy closed set are equivalent. After that, we define fuzzy upper (lower) generalized $\ell$ -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 $\ell$ -closed sets are introduced and studied. Also, the notion of $r$ -fuzzy $G^{\ast }$ -connected sets is defined and studied with help of $r$ -generalized fuzzy $\ell$ -closed sets.