Fuzzy rough sets with a fuzzy ideal

Abstract

In this paper, we defined the fuzzy upper, fuzzy lower, and fuzzy boundary sets of a rough fuzzy set λ in a fuzzy approximation space (X,R). Based on λ and R, we introduced the fuzzy ideal approximation interior operator intlambdaR and the fuzzy ideal approximation closure operator $\text {cl}_{\lambda }^{R}$ cl λ R . We joined the fuzzy ideal notion with the fuzzy approximation spaces, and then introduced the fuzzy ideal approximation closure and interior operators associated to a rough fuzzy set λ. Fuzzy ideal approximation connectedness and the fuzzy ideal approximation continuity between fuzzy ideal approximation spaces are introduced.

Single-Valued Neutrosophic Roughness via Ideals

“…If the lower and the upper approximation sets are identical, then α n is then a thorough subset of F , and there is no roughness. Many of their applications appear in the studies [13][14][15][16][17][18][19]. Irfan in [20] studied the connections between fuzzy set, rough set, and Soft set notions.…”

On Proximity Spaces Constructed on Rough Sets

“…The resulting rough sets (in [10]) have fewer boundary region sets than those defined in [1,4,9], and so it is a good generalized definition. Following that generalized definition in [10], Ibedou et al [11,12] introduced two types of generalizations of rough sets in the fuzzy case. Also, in this paper, we follow the same strategy.…”