Maximal rough neighborhoods with a medical application

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, [Formula: see text] -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 [Formula: see text] -neighborhoods to define [Formula: see text] -lower and [Formula: see text] -upper approximations and elucidate which one of Pawlak’s properties are preserved (evaporated) by these approximations. Moreover, we research [Formula: see text] -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 [Formula: see text] . To show the importance of [Formula: see text] -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.