Topological approaches to rough approximations based on closure operators

The main goal of this paper is to integrate the relationships among rough set theory and topology. We introduce different closure operators by using binary relations. Using these operators, we construct generalized approximation operators in the theory of rough sets. In addition, new methods for generating different topologies from any binary relation (without using base or subbase) are provided. The main properties of suggested structures are investigated. Comparisons among the suggested operations and the previous works are constructed. The suggested methods depend, basically, on the “j-neighborhood space” that given by (Abd El-Monsef et al., Int J Granul Comput Rough Sets Intell Syst 3:292–305, 2014). These methods generate new granulation for rough sets. Finally, a practical example is introduced as a simple application for the suggested structures. We think that at the level of theoretical foundations and real-life implementations, the proposed approaches place emphasis on ties between rough sets, granular computing, and information discovery and data mining.