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

Different Neighbourhoods via Ideals on Graphs

“…In future work, one can be focused on new types of approximations to obtain higher accuracy measures than those given in the literature by using different neighbourhoods such as S j -neighbourhoods [12] and maximal rough neighbourhoods [13] on graphs. Also, the methods that we obtained can be applied to various real-life problems.…”

“…Also, Al-Shami and Ciucci [12] studied the notions of S j -neighbourhoods using j-neighbourhoods and investigated their properties. Lastly, Al-Shami [13] de ned and studied a new class of neighbourhoods system which is called M j -neighbourhoods.…”

Improvement of Approximation Spaces Using Maximal Left Neighborhoods and Ideals

“…Then the approximations induced from these relations have the monotonic property if Acc δ2 (V ) ≤ Acc δ1 (V ). Definition 2.5: [4], [9], [35], [36] Take δ as an arbitrary binary relation on a finite set U = φ and let ν ∈ U . Then, 1) the right neighborhood of ν, denoted by N r (ν) is given by N r (ν) = {λ ∈ U : (ν, λ) ∈ δ}.…”

“…Theorem 2.1: [4] Let U be a universal set and δ 1 , δ 2 be two binary relations on U. If δ 1 ⊆ δ 2 , then θ 1l (ν) ⊆ θ 2l (ν), ∀ν ∈ U.…”

“…Following the pioneering works of Yao, many researchers and scholars interested in the rough set theory introduced novel sorts of neighborhood systems and applied to establish new generalized rough set paradigms. Among these neighborhood systems, minimal left neighborhoods and minimal right neighborhoods [2], intersection of minimal left and right neighborhoods [25], and maximal neighborhoods [4], [9].…”