Fuzzy roughness via ideals

Abstract

In this paper, we join the notion of fuzzy ideal to the notion of fuzzy approximation space to define the notion of fuzzy ideal approximation spaces. We introduce the fuzzy ideal approximation interior operator int Φ λ and the fuzzy ideal approximation closure operator cl Φ λ , and moreover, we define the fuzzy ideal approximation preinterior operator p int Φ λ and the fuzzy ideal approximation preclosure operator p cl Φ λ with respect to that fuzzy ideal defined on the fuzzy approximation space (X, R) associated with some fuzzy set λ ∈ IX. Also, we define fuzzy separation axioms, fuzzy connectedness and fuzzy compactness in fuzzy approximation spaces and in fuzzy ideal approximation spaces as well, and prove the implications in between.

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.…”