ABSTRACT
Topology is a beneficial structure to study the approximation operators in the rough set theory. In this work, we first introduce six new types of neighborhoods with respect to finite binary relations. We study their main properties and show under what conditions they are equivalent. Then we applied these types of neighborhoods to initiate some topological spaces that are utilized to define new types of rough set models. We compare these models and prove that the best accuracy measures are obtained in the cases of i and i. Also, we illustrate that our approaches are better than those defined under one arbitrary relation. To improve rough sets’ accuracy, we define some topological spaces using the idea of ideals. With the help of examples, we demonstrate that our methods are better than some methods studied in some published literature. Finally, we give a real-life application showing the merits of the approaches followed in this manuscript.
ABSTRACT
The rough set principle was proposed as a methodology to cope with vagueness or uncertainty of data in the information systems. Day by day, this theory has proven its efficiency in handling and modeling many real-life problems. To contribute to this area, we present new topological approaches as a generalization of Pawlak’s theory by using j-adhesion neighborhoods and elucidate the relationship between them and some other types of approximations with the aid of examples. Topologically, we give another generalized rough approximation using near open sets. Also, we generate generalized approximations created from the topological models of j-adhesion approximations. Eventually, we compare the approaches given herein with previous ones to obtain a more affirmative solution for decision-making problems.