A Study on Interval‐Valued Fuzzy Graph with Application in Energy Industry Management

Qiang, Xiaoli; Xiao, Qian-Ru; Khan, Aysha; Talebi, Ali Asghar; Sivaraman, Arun Kumar; Mojahedfar, Masomeh

doi:10.1155/2022/8499577

Cited by 1 publication

(1 citation statement)

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“…Specific properties of a VFGS are investigated, including the order of a VFGS, the degree of a vertex, and various types of energy in VFGS. Talebi et al [30] studied the interval-valued fuzzy graph with an application in energy industry management.…”

Section: Introductionmentioning

confidence: 99%

Energy of Vague Fuzzy Graph Structure and Its Application in Decision Making

Wan

Talebi

et al. 2022

Symmetry

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Vague graphs (VGs), belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. The notion of a VG is a new mathematical attitude to model the ambiguity and uncertainty in decision-making issues. A vague fuzzy graph structure (VFGS) is the generalization of the VG. It is a powerful and useful tool to find the influential person in various relations. VFGSs can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problems where fuzzy graphs may fail to reveal satisfactory results. Moreover, VGSs are very useful tools for the study of different domains of computer science such as networking, social systems, and other issues such as bioscience and medical science. The subject of energy in graph theory is one of the most attractive topics that is very important in biological and chemical sciences. Hence, in this work, we extend the notion of energy of a VG to the energy of a VFGS and also use the concept of energy in modeling problems related to VFGS. Actually, our purpose is to develop a notion of VFGS and investigate energy and Laplacian energy (LE) on this graph. We define the adjacency matrix (AM) concept, energy, and LE of a VFGS. Finally, we present three applications of the energy in decision-making problems.

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Section: Introductionmentioning

confidence: 99%