A comparison of three types of rough fuzzy sets based on two universal sets

In this paper, using the weak fuzzy similarity relation, we propose a new similarity degree which describes the relationships between the 2-tuples in U × V . In addition, we propose the reliability of each 2-tuples and use this reliability to give the calculation method of the similarity degree between the 2-tuples and the approximation set X . Using this similarity degree, a new fuzzy rough set model is proposed. Furthermore, a new fuzzy rough entropy which describing the knowledge information in the dual-universe U × V is defined. Then, we present a decision-making model to solve the problems, in which the elements in two different universes have different attributes. Finally, we give a significant algorithm which is applied to a decision-making problem in the dual-universe, and the effectiveness of this algorithm is verified by a numerical example.INDEX TERMS Decision-making method, fuzzy rough entropy, reliability, rough set, similarity degree.

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“…Proof: We known that a weak ordering w is a fuzzy relation which is transitive and µ w (x, y) > 0 or µ w (y, x) > 0 for every x = y in [28].…”

Section: A the Similarity Degree Between 2-tuples And Approximation Sets Based On Reliabilitymentioning

confidence: 99%

“…But these models are based on using one universe to judge the classification of elements in another universe, so there is a certain classification error. Abd El-Monsef et al [28] studied this issue and proposed some models that can make the approximating sets and the approximated sets are on the same universes of discourse.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Rough Set Model Based on Reliability Over Dual-Universe and Its Applications

Shao

Gong

2019

IEEE Access

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“…e construction of topology and its concepts via relations has become a remarkable and hot role in solving many problems such as [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Closure space has been described by Cech [10] as an extension of classical topology.…”

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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“…us, varied types of fuzzy rough sets were presented and axiomatic properties of fuzzy rough approximation operators are obtained in many studies (see [17][18][19][20][21]). After then, a new model of fuzzy rough sets called Metric-based fuzzy rough sets [22] was put forward via hemimetric.…”

Section: Introductionmentioning

confidence: 99%

New Topological Approaches to Rough Sets via Subset Neighborhoods

Yildirim

2022

Journal of Mathematics

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This paper aims to obtain new types of approximations by using topological concepts. Firstly, different kinds of topologies are generated by subset neighborhoods and relationships between them are studied. Then, j-subset approximations based on these topologies are introduced and their basic properties are examined. In addition to this, S j -near open and θ β S j -open sets are defined and the connections among them are given. Later, new approximations are presented with the help of the aforementioned sets, and their main properties are investigated. Furthermore, the proposed approximations are compared both with themselves and with the previous one. From this, it is shown that the approximations based on θ β S j -open sets are more accurate than those based on S j -open and S j -near open sets under arbitrary binary relation and than those based on j-open sets under similarity relation. Finally, a real-life problem related to COVID-19 is addressed to highlight the importance of applying the proposed approximations.

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A comparison of three types of rough fuzzy sets based on two universal sets

Cited by 24 publications

References 40 publications

A Fuzzy Rough Set Model Based on Reliability Over Dual-Universe and Its Applications

A Fuzzy Rough Set Model Based on Reliability Over Dual-Universe and Its Applications

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

New Topological Approaches to Rough Sets via Subset Neighborhoods

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