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Article

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

1
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
2
Department of Mathematics, University of Mazandaran, Babolsar 4741613534, Iran
3
School of Physics, Damghan University, Damghan 3671641167, Iran
*
Author to whom correspondence should be addressed.
Symmetry 2023, 15(12), 2106; https://doi.org/10.3390/sym15122106
Submission received: 13 October 2023 / Revised: 15 November 2023 / Accepted: 21 November 2023 / Published: 23 November 2023
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

Abstract

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.
Keywords: fuzzy set; interval-valued fuzzy graph; level graph; Cartesian product; composition; join fuzzy set; interval-valued fuzzy graph; level graph; Cartesian product; composition; join

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MDPI and ACS Style

Rao, Y.; Lei, S.; Talebi, A.A.; Mojahedfar, M. A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application. Symmetry 2023, 15, 2106. https://doi.org/10.3390/sym15122106

AMA Style

Rao Y, Lei S, Talebi AA, Mojahedfar M. A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application. Symmetry. 2023; 15(12):2106. https://doi.org/10.3390/sym15122106

Chicago/Turabian Style

Rao, Yongsheng, Siran Lei, Ali Asghar Talebi, and Masomeh Mojahedfar. 2023. "A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application" Symmetry 15, no. 12: 2106. https://doi.org/10.3390/sym15122106

APA Style

Rao, Y., Lei, S., Talebi, A. A., & Mojahedfar, M. (2023). A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application. Symmetry, 15(12), 2106. https://doi.org/10.3390/sym15122106

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