Some Topological Approaches for Generalized Rough Sets and Their Decision-Making Applications

Abu-Gdairi, Radwan; El-Gayar, Mostafa A.; Al-shami, Tareq M.; Nawar, Ashraf S.; El-Bably, Mostafa K.

doi:10.3390/sym14010095

Cited by 30 publications

(15 citation statements)

References 30 publications

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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%

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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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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

El-Gayar

Atik

2022

Complexity

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“…Recently, topology has been applied to model some real-life issues as showed in [1,11,15,16,32,46,56,64]. To study topology via S-set theory, C ¸aǧman et al [51] and Shabir and Naz [65], in 2011, introduced the concept of soft topology(ST).…”

Section: Introductionmentioning

confidence: 99%

On b-open Sets via Infra Soft Topological Spaces

Abu-Gdairi¹,

Al-Shamiri²,

Saleh³

et al. 2022

Eur. J. Pure Appl. Math.

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This work aims to present the concept of infra soft $b$-open sets(IS-b-open sets) as a generalized new class of infra open sets(IS-open sets). We first investigate their basic properties and study their behaviours under infra soft homeomorphism maps and finite product of soft spaces. Then, we establish some soft operators such as interior, closure, limit and boundary using IS-b-open sets and IS-$b$-closed sets. The relationships between them are illustrated and discussed. Finally, we display some soft maps(S-map) defined using IS-$b$-open and IS-$b$-closed sets and scrutinize their master properties.

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“…They also discussed a medical application using the concept of generalized nanotopology. Studying the interaction between topology and rough set theory was the main target for many articles such as [2,19,25,26,28,39,40,48]. This path of study also included some topology's extensions such as minimal structure [15,17] and bitopology [36].…”

Section: Introductionmentioning

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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Some Topological Approaches for Generalized Rough Sets and Their Decision-Making Applications

Cited by 30 publications

References 30 publications

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

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

On b-open Sets via Infra Soft Topological Spaces

Topological approach to generate new rough set models

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