A new approach based on intuitionistic fuzzy rough graphs for decision-making

Malik, Hafsa Masood; Akram, Muhammad

doi:10.3233/jifs-171395

Cited by 15 publications

(7 citation statements)

References 25 publications

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“…A full soft set S from A on V can be defined in tabular form in Table 5 as follows: Table 5. Full soft set S. Hence, SN=(S(N),S(N)) is a soft rough neutrosophic set on V. Let E={v 11 ,v 15 ,v 16 ,v 23 ,v 25 ,v 34 ,v 41 ,v 43 , v 56 ,v 62 ,v 63 }⊆Ṽ and L={a 12 ,a 13 ,a 21 ,a 23 ,a 31 }⊆Ã. Then a full soft set R on E (from L to E) can be defined in Table 6 as follows: Figure 1: Soft rough neutrosophic graph G = (G, G) finition 2.9.…”

Section: Definitionmentioning

confidence: 99%

“…Therefore, it is necessary to develop hybrid models by incorporating the advantages of many other different mathematical models dealing uncertainty. Recently, new hybrid models, including rough fuzzy graphs [40,41], fuzzy rough graphs [42], intuitionistic fuzzy rough graphs [43,44], rough neutrosophic graphs [45] and neutrosophic soft rough graphs [46] are constructed. For other notations and definitions, the readers are refereed to [47][48][49][50][51].…”

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confidence: 99%

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Soft Rough Neutrosophic Influence Graphs with Application

2018

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In this paper, we apply the notion of soft rough neutrosophic sets to graph theory. We develop certain new concepts, including soft rough neutrosophic graphs, soft rough neutrosophic influence graphs, soft rough neutrosophic influence cycles and soft rough neutrosophic influence trees. We illustrate these concepts with examples, and investigate some of their properties. We solve the decision-making problem by using our proposed algorithm. Mathematics 2018, 6, 125 2 of 37 Kaufmann [22]. Later, Rosenfeld [23] considered fuzzy graphs and obtained analogs of several graph theoretical concepts. Mordeson and Peng [24] defined some operations on fuzzy graphs. Mathew and Sunitha [25,26] presented some new concepts on fuzzy graphs. Gani et al. [27-30] discussed several concepts, including size, order, degree, regularity and edge regularity in fuzzy graphs and intuitionistic fuzzy graphs. Parvathi and Karunambigai [31] described some operation on intuitionistic fuzzy graph. Recently, Akram et al. [32][33][34][35][36] has introduced several extensions of fuzzy graphs with applications. Denish [37] considered the idea of fuzzy incidence graph. Fuzzy incidence graphs were further studied in [38,39]. Due to the limitation of humans knowledge to understand the complex problems, it is very difficult to apply only a single type of uncertainty method to deal with such problems. Therefore, it is necessary to develop hybrid models by incorporating the advantages of many other different mathematical models dealing uncertainty. Recently, new hybrid models, including rough fuzzy graphs [40,41], fuzzy rough graphs [42], intuitionistic fuzzy rough graphs [43,44], rough neutrosophic graphs [45] and neutrosophic soft rough graphs [46] are constructed. For other notations and definitions, the readers are refereed to [47][48][49][50][51]. In this paper, we apply the notion of soft rough neutrosophic sets to graph theory. We develop certain new concepts, including soft rough neutrosophic graphs, soft rough neutrosophic influence graphs, soft rough neutrosophic influence cycles and soft rough neutrosophic influence trees. We illustrate these concepts with examples, and investigate some of their properties. We solve decision-making problem by using our proposed algorithm. This paper is organized as follows. In Section 2, some definitions and some properties of soft rough neutrosophic graphs are given. In Section 3, soft rough neutrosophic influence graphs, soft rough neutrosophic influence cycles and soft rough neutrosophic influence trees are discussed. In Section 4, an application is presented. Finally, we conclude our contribution with a summary in Section 5 and an outlook for the further research.

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Section: Definitionmentioning

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Soft Rough Neutrosophic Influence Graphs with Application

2018

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“…Recently, Akram and Arshad ( 2018 ) apply the concept of fuzzy rough sets to graphs. Malik and Akram ( 2018 ) and Zhan et al. ( 2019 ) studied intuitionistic fuzzy rough graph and its applications to decision-making.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Akram and Arshad (2018) apply the concept of fuzzy rough sets to graphs. Malik and Akram (2018) and Zhan et al (2019) studied intuitionistic fuzzy rough graph and its applications to decision-making. In networks, directed fuzzy graphs (DFGs) are unable to cope with real networks with incomplete data information.…”

Section: Introductionmentioning

confidence: 99%

Directed rough fuzzy graph with application to trade networking

Ahmad

Nawaz

2022

Comp. Appl. Math.

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In the realm of linking networks to the real world, connectivity (strength of connectedness) plays a crucial role. In this article, we introduce three types of vertices based on the indegree and outdegree of the vertices of directed rough fuzzy networks (DRFNs). We also define the concept of strength-reducing sets ( ) of DRF-vertices, DRF-edges, and important related results using the strongest path in directed rough fuzzy graphs (DRFGs). We generalize the idea of Menger’s theorem of vertices and edges in directed fuzzy graphs to directed rough fuzzy graphs which are appropriate for dealing with uncertainty in information systems. Furthermore, we use strong DRF-edges, strong DRF-edges and DRF-edges to identify developing countries most affected by trade deficits during COVID-19. Finally, our research results are compared with existing methods to demonstrate their applicability and productivity.

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“…Tong He introduced further rough theoretic properties of rough graphs [18] and representation forms of rough graphs [19]. Some other hybrid structures of rough graphs like soft rough graphs, neutrosophic soft rough graphs, intuitionistic fuzzy rough graphs are also introduced in [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Vertex rough graphs

Mathew

John

Garg

2020

Complex Intell. Syst.

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This article introduces the notion of vertex rough graph and discusses certain basic graph theoretic definitions and examples. Adjacency of vertices is used to create a matrix corresponding to a vertex rough graph. Also, the membership function of a vertex rough graph is introduced with the help of Pawlak's Rough set theory, and using this certain results are obtained. The concepts of rough precision and rough similarity degree are extended to vertex rough graphs.

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A new approach based on intuitionistic fuzzy rough graphs for decision-making

Cited by 15 publications

References 25 publications

Soft Rough Neutrosophic Influence Graphs with Application

Soft Rough Neutrosophic Influence Graphs with Application

Directed rough fuzzy graph with application to trade networking

Vertex rough graphs

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