Some Connectivity Parameters of Interval-Valued Intuitionistic Fuzzy Graphs with Applications

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-12-13 DOI:10.3390/axioms12121120

Hao Guan, Waheed Ahmad Khan, Shazia Saleem, Waqar Arif, J. Shafi, Aysha Khan

{"title":"Some Connectivity Parameters of Interval-Valued Intuitionistic Fuzzy Graphs with Applications","authors":"Hao Guan, Waheed Ahmad Khan, Shazia Saleem, Waqar Arif, J. Shafi, Aysha Khan","doi":"10.3390/axioms12121120","DOIUrl":null,"url":null,"abstract":"Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity parameters related to interval-valued intuitionistic fuzzy graphs (IVIFGs). These are the generalizations of the parameters defined for fuzzy graphs, interval-valued fuzzy graphs, and intuitionistic fuzzy graphs. First, we introduce interval-valued intuitionistic fuzzy bridges (IVIF bridges) and interval-valued intuitionistic fuzzy cut-nodes (IVIF cut-nodes). We discuss the many characteristics of these terms as well as establish the necessary and sufficient conditions for an arc to become an IVIF-bridge and a vertex to be an IVIF-cutnode. Furthermore, we initiate the concepts of interval-valued intuitionistic fuzzy cycles (IVIFCs) and interval-valued intuitionistic fuzzy trees (IVIFTs) and explore few relationships among them. In addition, we introduce the notions of fuzzy blocks and fuzzy block graphs and extend these terms as interval-valued fuzzy blocks (IVF-blocks) and interval-valued intuitionistic fuzzy block graphs (IVIF-block graphs). Finally, we provide the application of interval-valued intuitionistic fuzzy trees (IVIFTs) in a road transport network.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"9 2","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Axioms","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3390/axioms12121120","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity parameters related to interval-valued intuitionistic fuzzy graphs (IVIFGs). These are the generalizations of the parameters defined for fuzzy graphs, interval-valued fuzzy graphs, and intuitionistic fuzzy graphs. First, we introduce interval-valued intuitionistic fuzzy bridges (IVIF bridges) and interval-valued intuitionistic fuzzy cut-nodes (IVIF cut-nodes). We discuss the many characteristics of these terms as well as establish the necessary and sufficient conditions for an arc to become an IVIF-bridge and a vertex to be an IVIF-cutnode. Furthermore, we initiate the concepts of interval-valued intuitionistic fuzzy cycles (IVIFCs) and interval-valued intuitionistic fuzzy trees (IVIFTs) and explore few relationships among them. In addition, we introduce the notions of fuzzy blocks and fuzzy block graphs and extend these terms as interval-valued fuzzy blocks (IVF-blocks) and interval-valued intuitionistic fuzzy block graphs (IVIF-block graphs). Finally, we provide the application of interval-valued intuitionistic fuzzy trees (IVIFTs) in a road transport network.

查看原文本刊更多论文

区间值直观模糊图的一些连接性参数及其应用

图中的连接性有助于描述神经网络、计算机网络等不同类型的通信系统。在设计任何网络时，都必须根据连接的强度对其进行评估。在本手稿中，我们全面描述了与区间值直观模糊图（IVIFG）相关的各种连接性参数。这些参数是对模糊图、区间值模糊图和直观模糊图所定义参数的概括。首先，我们介绍了区间值直观模糊桥（IVIF 桥）和区间值直观模糊切节点（IVIF 切节点）。我们讨论了这些术语的许多特点，并建立了弧成为 IVIF 桥和顶点成为 IVIF 切节点的必要条件和充分条件。此外，我们还提出了区间值直观模糊循环（IVIFC）和区间值直观模糊树（IVIFT）的概念，并探讨了它们之间的一些关系。此外，我们还介绍了模糊块和模糊块图的概念，并将这些术语扩展为区间值模糊块（IVF-blocks）和区间值直观模糊块图（IVIF-block graphs）。最后，我们介绍了区间值直观模糊树（IVIFT）在公路交通网络中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.