Subset neighborhood rough sets

We present a novel kind of neighborhood, named subset neighborhood and denoted asS(rho)-neighborhood. It is defined under an arbitrary binary relation using the inclusion relations between N-rho-neighborhoods. We study its relationships with some kinds of neighborhood systems given in the literature. Then, we formulate the concepts of S-rho-lower and S-rho-upper approximations, and S-rho-accuracy and roughness measures based on S-rho-neighborhoods. We show in which cases the S-rho-accuracy measure is the highest among related approximations and investigate under which conditions the S-rho-accuracy and S-rho-roughness measures are monotonic. Moreover, we compare our approach with two existing ones and elucidate the advantages of our technique to obtain accuracy measures under some specific relations. To support the obtained results, we provide two medical examples. (c) 2021 Elsevier B.V. All rights reserved.