A new approach to compute measures of connectivity in rough fuzzy network models

Akram, Muhammad; Zafar, Fariha

doi:10.3233/jifs-181751

Cited by 18 publications

(13 citation statements)

References 31 publications

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“…Definition 2.9 (Akram and Zafar 2019b) Let G = (G, G) be a DRFG. An edge w 0 w 1 ∈ E is defined to be strong directed rough fuzzy edge (strong DRF-edge) of G if it is strong directed fuzzy edge (strong DF-edge) in G as well as in G, that is…”

Section: Example 25 Considermentioning

confidence: 99%

“…A DRFG can be helpful in uncertain problems with incomplete knowledge to obtain finer and more accurate results. Recently, Akram and Zafar (2019b) proposed the concept of strength or intensity of the connection between each pair of vertices in DRFGs and addressed several essential concepts such as strongest DRF-path, strong DRF-path and DRF-bridge, α strong DRF-edge, β strong DRFedge, δ DRF-edge, and so on. Connectivity (power of connection) analysis deals with decision-making problems.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Example 25 Considermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Directed rough fuzzy graph with application to trade networking

Ahmad

Nawaz

2022

Comp. Appl. Math.

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“…DRFG also introduced basic operations and outcomes such as union, intersection, Cartesian product and composition, and so on. Akram and Zafar [7] introduced the approach of SC among the set of vertices in DRFGs and handled numerous notions like strongest path, strong path and bridge, strong edges, weak edges, and so on. Furthermore, they presented the concept of CI, average connectivity index (ACI), and associated findings in DRFGs.…”

Section: Introductionmentioning

confidence: 99%

Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

Ahmad

Nawaz

2023

Granul. Comput.

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The directed rough fuzzy graph (DRFG) is a fusion of rough and fuzzy theory, because it deals with incomplete and vague information simultaneously. Connection or the strength of connectivity (SC) is vital in the realm of circuits or networks that are linked to the real world. As a result, SC is one of the most essential aspects of a directed rough fuzzy network system. The neighborhood connectivity index (N CI) is one such parameter that has a variety of applications in network theory. In this paper, we discuss the notion of N CI in DRFGs using the strength of vertices to their neighbor vertices. We provide several lower and upper bounds on the N CI of DRFGs with reference to other graph invariants such as the number of vertices, edges, and degree distance. When we study N CI in operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG provides a confusing picture. Therefore, a mechanism to determine the N CI for DRFG operations is needed. Therefore, generalized formulas for N CI of DRFGs obtained by operations such as union, composition, and Cartesian product are also developed. An algorithm for obtaining N CI of DRFGs is also proposed. In addition, an application of N CI of DRFGs in traffic flow networks was discussed to identify the busiest intersection using the proposed algorithm. Finally, we gave a complete comparative evaluation and analysis table for a similar human trafficking system, comparing the results for connectivity index (CI), Wiener index (WI), and N CI.

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“…Industrial Information Integration Engineering (IIIE) is a set of foundational concepts and techniques that facilitate the industrial information integration process using fuzzy techniques, the detailed survey is given by Chen (Chen, 2020). Zafar and Akram (Akram & Zafar, 2019; Akram & Zafar, n.d.) discussed rough fuzzy digraphs and connectivity in rough fuzzy network models. Feng et al (Feng et al, 2011) investigated the concept of soft rough set.…”

Section: Introductionmentioning

confidence: 99%

Group decision‐making analysis based on distance measures under rough environment

Fatima

Sarwar²,

Zafar

et al. 2022

Expert Systems

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A rough set as a superset of a crisp set is a mathematical tool to cope with uncertainty using initial data without additional assumptions and pre-defined parameters.Using the technique of upper and lower approximations, rough models provide a complete description of the problem. This paper aims to introduce the notion of distance function, which is a metric, in rough graphs. We establish formulae of distance function, degree and radius of certain products of rough graphs in terms of initial given rough graphs. We discuss the concepts of weak isomorphism and isomorphism in rough graphs, and describe the properties of isomorphic rough graphs. We demonstrate the significance and importance of the distance function with an application to a decision making problem concerning organ trafficking networks. An application of rough matrices in steam valve systems is discussed, and we show how they can help to identify the potential failures and risk components during the power generation process. The results obtained under the rough model are compared with existing extensions of graphs and fuzzy based approaches.

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A new approach to compute measures of connectivity in rough fuzzy network models

Cited by 18 publications

References 31 publications

Directed rough fuzzy graph with application to trade networking

Directed rough fuzzy graph with application to trade networking

Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

Group decision‐making analysis based on distance measures under rough environment

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