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 25 publications

(8 citation statements)

References 28 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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“…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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“…Atanassov [17] defined intuitionistic fuzzy sets as one of the intriguing generalizations of fuzzy sets with excellent application. Applications of intuitionistic fuzzy sets can be found in a variety of domains, including optimization issues, decisionmaking, and medical diagnostics [22][23][24]. However, in many circumstances, the decision maker may assign degrees of membership and non-membership to a given attribute such that their aggregate is larger than one.…”

Section: Introductionmentioning

confidence: 99%

n<SUP>th</SUP> Power Root Fuzzy Sets and Its Topology

Al-shami¹,

Ibrahim²,

Mhemdi³

et al. 2022

IJFIS

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One of the most useful expansions of fuzzy sets for coping with information uncertainties is the q-rung orthopair fuzzy sets. In such circumstances, in this article, we define a novel extension of fuzzy sets called n th power root fuzzy set (briefly, nPR-fuzzy set) and elucidate their relationship with intuitionistic fuzzy sets, SR-fuzzy sets, CR-fuzzy sets and q-rung orthopair fuzzy sets. Then, we provide the necessary set of operations for nPR-fuzzy sets as well as study their various features. Furthermore, we familiarize the concept of nPR-fuzzy topology and investigate the basic aspects of this topology. In addition, we define separated nPR-fuzzy sets and then present the concept of disconnected nPR-fuzzy sets. Moreover, we study and characterize nPR-fuzzy continuous maps in great depth. Finally, we establish T 0 and T 1 in nPR-fuzzy topologies and discover the links between them.

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

Cited by 25 publications

References 28 publications

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

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

Topological approach to generate new rough set models

n<SUP>th</SUP> Power Root Fuzzy Sets and Its Topology

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