Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Topology, one of the most important subjects in mathematics, provides mathematical tools and interesting topics in studying information systems and rough sets. In this paper, we present the topological characterizations to three types of covering approximation operators. F...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

fuzzy rough n-ary subhypergroups are introduced and characterized.

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhoodbased generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures...

Rough sets are often induced by descriptions of objects based on the precise observations of an insufficient number of attributes. In this paper, we study generalizations of rough sets to incomplete information systems, involving imprecise observations of attributes. The precise role of covering-based approximations of sets that extend the standard rough sets in the presence of incomplete infor...

The theory of generalized neighborhood system-based approximation operators plays an important role in the theory of generalized rough sets since it includes both the neighborhood-based approximation operators and the covering-based approximation operators as its special circumstances. The theory of reduction is one of the most significant directions in rough sets. In this work, the reduction o...

Rough set theory has been extensively discussed in the domain of machine learning and data mining. Pawlak’s rough set theory offers a formal theoretical framework for attribute reduction and rule learning from nominal data. However, this model is not applicable to numerical data, which widely exist in real-world applications. In this work, we extend this framework to numerical feature spaces by...