Maximal rough neighborhoods with a medical application

Abstract

In this paper, we focus on the main concepts of rough set theory induced from the idea of neighborhoods. First, we put forward new types of maximal neighborhoods (briefly, $M_{\sigma }$ -neighborhoods) and explore master properties. We also reveal their relationships with foregoing neighborhoods and specify the sufficient conditions to obtain some equivalences. Then, we apply $M_{\sigma }$ -neighborhoods to define $M_{\sigma }$ -lower and $M_{\sigma }$ -upper approximations and elucidate which one of Pawlak's properties are preserved (evaporated) by these approximations. Moreover, we research $A_{M\sigma }$ -accuracy measures and prove that they keep the monotonic property under any arbitrary relation. We provide some comparisons that illustrate the best approximations and accuracy measures are obtained when $\sigma =⟨i⟩$ . To show the importance of $M_{\sigma }$ -neighborhoods, we present a medical application of them in classifying individuals of a specific facility in terms of their infection with COVID-19. Finally, we scrutinize the strengths and limitations of the followed technique in this manuscript compared with the previous ones.

Keywords: M σ -neighborhood; N σ -neighborhood; Accuracy measure; Lower and upper approximations; Rough set.