We present a novel kind of neighborhood, named subset neighborhood and denoted as Sρ-neighborhood. It is defined under an arbitrary binary relation using the inclusion relations between Nρ-neighborhoods. We study its relationships with some kinds of neighborhood systems given in the literature. Then, we formulate the concepts of Sρ-lower and Sρ-upper approximations, and Sρ-accuracy and roughness measures based on Sρ-neighborhoods. We show in which cases the Sρ-accuracy measure is the highest among related approximations and investigate under which conditions the Sρ-accuracy and Sρ-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.
Al-shami, T., Ciucci, D. (2022). Subset neighborhood rough sets. KNOWLEDGE-BASED SYSTEMS, 237(15 February 2022) [10.1016/j.knosys.2021.107868].
Subset neighborhood rough sets
Ciucci D.
2022
Abstract
We present a novel kind of neighborhood, named subset neighborhood and denoted as Sρ-neighborhood. It is defined under an arbitrary binary relation using the inclusion relations between Nρ-neighborhoods. We study its relationships with some kinds of neighborhood systems given in the literature. Then, we formulate the concepts of Sρ-lower and Sρ-upper approximations, and Sρ-accuracy and roughness measures based on Sρ-neighborhoods. We show in which cases the Sρ-accuracy measure is the highest among related approximations and investigate under which conditions the Sρ-accuracy and Sρ-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.
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