&lt;i&gt;θβ&lt;/i&gt;-ideal approximation spaces and their applications

Nawar, Ashraf S.; El-Gayar, Mostafa A.; El-Bably, Mostafa K.; Hosny, Rodyna A.

doi:10.3934/math.2022139

Cited by 19 publications

(10 citation statements)

References 35 publications

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“…(ii) Familiarize the concepts displayed herein in the frame of soft rough set. (iii) Improve the given results by adding the ideals to the topological structures such those presented in [11,21,22,30].…”

Section: Discussionmentioning

confidence: 99%

Topological approach to generate new rough set models

Al-shami

2022

Complex Intell. Syst.

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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.

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Section: Discussionmentioning

confidence: 99%

Topological approach to generate new rough set models

Al-shami

2022

Complex Intell. Syst.

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“… 2020 ; Nawar et al. 2022 ). limitations The present approach is generally incomparable with the topological approach introduced in Abd El-Monsef et al.…”

Section: Discussion: Strengths and Limitationsmentioning

confidence: 99%

Rough sets models inspired by supra-topology structures

Al-shami

Alshammari

2022

Artif Intell Rev

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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.

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“…e second part is devoted to the application of the closure operators, proposed in the current paper, in the notion of rough sets. In fact, we have presented three models to approximate the rough sets, which are generalizations of previously presented methods (such as [2,4,8,11,13,20,22,23,[26][27][28][29][30][31][32][33][34][35][36][37][38][39]). We studied the properties of these approximations, and we were able to demonstrate all of Pawlak's properties, which were not fulfilled in some other generalizations such as Yao [26] without adding any conditions to the relation.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Rough set theory was established by computer scientist Pawlak [24,25] based on several difficulties in computer science to overcome this challenge by a modal approximation of a crisp set in the expressions of a pair of sets called the rough approximations of it. Many writers have focused on generalization rough sets [2,4,8,11,13,20,22,23,[26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Topological Models of Rough Sets and Decision Making of COVID‐19

El-Gayar

Atik

2022

Complexity

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The basic methodology of rough set theory depends on an equivalence relation induced from the generated partition by the classification of objects. However, the requirements of the equivalence relation restrict the field of applications of this philosophy. To begin, we describe two kinds of closure operators that are based on right and left adhesion neighbourhoods by any binary relation. Furthermore, we illustrate that the suggested techniques are an extension of previous methods that are already available in the literature. As a result of these topological techniques, we propose extended rough sets as an extension of Pawlak’s models. We offer a novel topological strategy for making a topological reduction of an information system for COVID-19 based on these techniques. We provide this medical application to highlight the importance of the offered methodologies in the decision-making process to discover the important component for coronavirus (COVID-19) infection. Furthermore, the findings obtained are congruent with those of the World Health Organization. Finally, we create an algorithm to implement the recommended ways in decision-making.

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<i>θβ</i>-ideal approximation spaces and their applications

Cited by 19 publications

References 35 publications

Topological approach to generate new rough set models

Topological approach to generate new rough set models

Rough sets models inspired by supra-topology structures

Topological Models of Rough Sets and Decision Making of COVID‐19

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