Novel Concepts of Domination in Vague Graphs with Application in Medicine

Qiang, Xiaoli; Akhoundi, Maryam; Kou, Zheng; Liu, Xinyue; Kosari, Saeed

doi:10.1155/2021/6121454

Cited by 13 publications

(8 citation statements)

References 49 publications

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“…The concept of domination in rough fuzzy digraphs was described by [42]. Similarly, domination in several types of vague graphs was discussed in [43][44][45][46]. Domination in IFGs was discussed by Parvathi [47], while double domination in IFGs was described by Nagoorgani [48].…”

Section: Introductionmentioning

confidence: 99%

Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs

Guan,

Khan,

Fida

et al. 2024

Mathematics

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In this manuscript, we introduce a few new types of dominations in intuitionistic fuzzy directed graphs (IFDGs) based on different types of strong arcs (SAs). Our work is not only a direct extension of domination in directed fuzzy graphs (DFGs) but also fills the gap that exists in the literature regarding the dominations in different extended forms of fuzzy graphs (FGs). In the beginning, we introduce several types of strong arcs in IFDGs, like semi-β strong arcs, semi-δ strong arcs, etc. Then, we introduce the concepts of domination in IFDGs based on these strong arcs and discuss its various useful characteristics. Moreover, the dominating set (DS), minimal dominating set (MDS), etc., are described with some fascinating results. We also introduce the concept of an independent set in IFDGs and investigate its relations with the DS, minimal independent set (MIS) and MDS. We also provide numerous important characterizations of domination in IFDGs based on minimal and maximal dominating sets. In this context, we discuss the lower and upper dominations of some IFDGs. In addition, we introduce the terms status and structurally equivalent and examine a few relationships with the dominations in IFDGs. Finally, we investigate the most expert (influential) person in the organization by utilizing the concepts of domination in IFGs.

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Section: Introductionmentioning

confidence: 99%

Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs

Guan,

Khan,

Fida

et al. 2024

Mathematics

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“…The notion of a VG is a new mathematical attitude to model the ambiguity and uncertainty in decision-making issues. Study on VG and results from these graphs were introduced by Kosari et al [7][8][9][10]. Furthermore, a review was carried out on different types of FGs, and the new results were studied [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

A Novel Domination in Vague Influence Graphs with an Application

Shi,

Cai,

Talebi

et al. 2024

Axioms

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Vague influence graphs (VIGs) are well articulated, useful and practical tools for managing the uncertainty preoccupied in all real-life difficulties where ambiguous facts, figures and explorations are explained. A VIG gives the information about the effect of a vertex on the edge. In this paper, we present the domination concept for VIG. Some issues and results of the domination in vague graphs (VGs) are also developed in VIGs. We defined some basic notions in the VIGs such as the walk, path, strength of In-pair , strong In-pair, In-cut vertex, In-cut pair (CP), complete VIG and strong pair domination number in VIG. Finally, an application of domination in illegal drug trade was introduced.

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“…Dey et al [19][20][21] introduced the fuzzy minimum spanning tree with an interval type 2 fuzzy arc length and an interval type 2 FS in a fuzzy shortest path problem. Qiang et al [22] expressed a novel description of VG structure and also investigated the new results of it. Some types of FGs were studied in [23,24].…”

Section: Introductionmentioning

confidence: 99%

A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application

Rao,

Lei,

Talebi

et al. 2023

Symmetry

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Many problems of practical interest can be modeled and solved by using interval-valued fuzzy graph (IVFG) algorithms. An IVFG is a very useful and effective tool for studying various calculations, fields of intelligence, and computer science, such as networking, imaging, and other fields, such as biological sciences. In different applications, they present an appropriate construction means. There were limitations in the definition of fuzzy graphs (FGs), which prompted us to propose a new definition for IVFGs. Some interesting properties related to the new IVFGs are investigated, and enough conditions under which the level graph on IVFGs is equivalent are obtained. Therefore, in this study, we present the properties of a level graph (LG) of an IVFG, and four operations, the Cartesian product (CP), composition (CO), union, and join, are investigated on it. Today, in a treatment system, one of the issues that can be very valuable and important to the quality of service to patients is finding qualified and efficient people in each department, which is not an easy task. But the interval-valued fuzzy graph, as an important fuzzy graph, can help us by considering the ability of each person in the form of intervals of numbers and the effectiveness of each one on the other (according to the relationships between them) in order to find the most worthy people. So, an application of IVFG to find the most effective person in a hospital information system has been introduced.

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Novel Concepts of Domination in Vague Graphs with Application in Medicine

Cited by 13 publications

References 49 publications

Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs

Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs

A Novel Domination in Vague Influence Graphs with an Application

A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application

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