Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

Abstract. This paper extends some essential topological properties in general topological spaces in to the I-rough topological spaces, the topology of the rough universe. I-rough compactness and I-rough Hausdorffness are introduced and several properties are investigated. I-rough compactness of subsets of I-rough Hausdorff spaces are studied. Also the paper establishes I-rough connectedness in ...

The concept of an M-approximative system is introduced. Basic properties of the category of M-approximative systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximative systems. Keywords— Approximative operator...

The main goal of this paper is to introduce a new bitopological approaches to rough sets. Suggested approaches depend on two topologies, generated by a general relation. The first topology is a right topology whose subbase is the family of right neighborhoods and a subbase of the other topology, left topology, is the family of left neighborhoods, with respect to that general relation. Some Pawl...

Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relat...

Rough set theory, a mathematical tool to deal with vague concepts, has originally described the indiscernibility of elements by equivalence relations. Covering-based rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as subbase, neighborhood and separation axioms have bee...