Minimal structure approximation space and some of its application

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.

Section: Introductionmentioning

confidence: 99%

Topological approach to generate new rough set models

2022

Complex Intell. Syst.

“…In recent years, it has been exploited some topological generalizations such as infra topology Al-shami and Mhemdi ( 2022 ), minimal structure (Azzam et al. 2020 ; El-Sharkasy 2021 ) and bitopology Salama ( 2020 ) to deal with rough set concepts and address some medical problems. Following this line, we suggest novel kinds of rough set models inspired by another abstract structure called “supra-topology”.…”

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.

“…Moreover, it was applied rough set concepts induced from some generalizations of topology such as minimal structure (Azzam et al. 2020 ; El-Sharkasy 2021 ) and bitopology (Salama 2020b ) to cope with some medical problems.…”

Section: Introductionmentioning

confidence: 99%

Approximation operators and accuracy measures of rough sets from an infra-topology view

Mhemdi

2022

Soft Comput

In this work, our target point is to focus on rough approximation operators generated from infra-topology spaces and examine their features. First, we show how infra-topology spaces are constructed from -neighborhood systems under an arbitrary relation. Then, we exploit these infra-topology spaces to form new rough set models and scrutinize their master characterizations. The main advantages of these models are to preserve all properties of Pawlak approximation operators and produce accuracy values higher than those given in several methods published in the literature. One of the unique characterizations of the current approach is that all the approximation operators and accuracy measures produced by the current approach are identical under a symmetric relation. Finally, we present two medical applications of the current methods regarding Dengue fever and COVID-19 pandemic. Some debates regarding the pros and cons of the followed technique are given as well as some upcoming work are proposed.