Different kinds of generalized rough sets based on neighborhoods with a medical application

Approximation space can be said to play a critical role in the accuracy of the set's approximations. The idea of approximation space was introduced by Pawlak in 1982 as a core to describe information or knowledge induced from the relationships between objects of the universe. The main objective of this paper is to create new types of rough set models through the use of different neighborhoods generated by a binary relation. New approximations are proposed representing an extension of Pawlak's rough sets and some of their generalizations, where the precision of these approximations is substantially improved. To elucidate the effectiveness of our approaches, we provide some comparisons between the proposed methods and the previous ones. Finally, we give a medical application of lung cancer disease as well as provide an algorithm which is tested on the basis of hypothetical data in order to compare it with current methods.

Automated summary

The paper aims to create new rough set models by using different neighborhoods generated by a binary relation, proposing new approximations that extend Pawlak's rough sets and some generalizations, with significantly improved precision. It also provides comparisons between the proposed methods and previous ones, as well as a medical application on lung cancer disease and an algorithm tested on hypothetical data for comparison with current methods.