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, {mathcal {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 {mathcal {M}}_{sigma} -neighborhoods to define {mathcal {M}}_{sigma} -lower and {mathcal {M}}_{sigma} -upper approximations and elucidate which one of Pawlak’s properties are preserved (evaporated) by these approximations. Moreover, we research {mathcal {A}}_{Msigma }-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 =langle irangle . To show the importance of {mathcal {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.
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