A New Approach to Rough Set Based on Remote Neighborhood Systems

J Ambient Intell Human Comput

2022

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.

“… 2018 ; Sun et al. 2019 ); Explore -neighborhoods system in the areas of soft rough set and fuzzy rough sets. …”

Section: Discussionmentioning

confidence: 99%

“…Sun et al. ( 2019 ) defined the dual idea of neighborhood systems under the name of remote neighborhood systems. Recently, Al-shami et al.…”

Section: Introductionmentioning

confidence: 99%

Maximal rough neighborhoods with a medical application

J Ambient Intell Human Comput

2022

“…In an attempt to solve such unreasonableness, some extensions under various relations were proposed such as [46,47]. To different purposes including improving the set's accuracy values, new types of neighborhoods were introduced such as minimal right (left) neighborhoods [4,5], intersection (union) neighborhoods B Tareq M. Al-shami tareqalshami83@gmail.com 1 Department of Mathematics, Sana'a University, Sana'a, Yemen [1], maximal neighborhoods [18], remote neighborhood [42], P j -neighborhoods [29], E j -neighborhoods [12], C jneighborhoods [7], and recently S j -neighborhoods [10].…”

Section: Introductionmentioning

confidence: 99%

Topological approach to generate new rough set models

2022

Complex Intell. Syst.

In this paper, we introduce a topological method to produce new rough set models. This method is based on the idea of “somewhat open sets” which is one of the celebrated generalizations of open sets. We first generate some topologies from the different types of $$N_\rho $$ N ρ -neighborhoods. Then, we define new types of rough approximations and accuracy measures with respect to somewhat open and somewhat closed sets. We study their main properties and prove that the accuracy and roughness measures preserve the monotonic property. One of the unique properties of these approximations is the possibility of comparing between them. We also compare our approach with the previous ones, and show that it is more accurate than those induced from open, $$\alpha $$ α -open, and semi-open sets. Moreover, we examine the effectiveness of the followed method in a problem of Dengue fever. Finally, we discuss the strengths and limitations of our approach and propose some future work.

“…( 2018 ), core neighborhoods defined using equality relation Mareay ( 2016 ), and remote neighborhood Sun et al. ( 2019 ). Admittedly, they were created with the goal of improving approximation operators, increasing accuracy measures, and handling some practical problems.…”

Section: Introductionmentioning

confidence: 99%

Rough sets models inspired by supra-topology structures

Alshammari

2022

Artif Intell Rev

Our aim of writing this manuscript is to found novel rough-approximation operators inspired by an abstract structure called “supra-topology”. This approach is more relaxed than topological ones and extends the scope of applications because an intersection condition of topology is dispensed. Firstly, we generate eight types of supra-topologies using -neighborhood systems induced from any arbitrary relation. We elucidate the relationships between them and investigate the conditions under which some of them are identical. Then, we create new rough sets models from these supra-topologies and present the main characterizations of their lower and upper approximations. We apply these approximations to classify the regions of the subset and compute its accuracy measures. The master merits of the current approach are to produce the highest accuracy values compared with all approaches given in the published literature under a reflexive relation as well as preserve the monotonicity property of accuracy and roughness measures. Moreover, we demonstrate the good performance of the followed technique through analysis of some data of dengue fever disease. Ultimately, we debate the advantages and disadvantages of the followed approach and make a plan for some upcoming work.