{"title":"费尔马特模糊图分析及其在汽车公司中的应用","authors":"Prabuddha Giri, Sk Amanathulla, Kalyani Maity Das","doi":"10.1007/s12190-024-02094-4","DOIUrl":null,"url":null,"abstract":"<p>Fuzzy graphs find numerous applications in real life. One of the extensions of fuzzy graphs is Fermatean fuzzy graphs. Here, we introduce the concepts of Fermatean fuzzy set to the domain of graph theory and obtain a novel type of graph, referred to as Fermatean fuzzy graph (<span>\\(\\textit{FFG}\\)</span>). The article establishes fundamental terms such as strong <span>\\(\\textit{FFG}\\)</span>, complete <span>\\(\\textit{FFG}\\)</span>, regular <span>\\(\\textit{FFG}\\)</span>, path, degree, total degree, homomorphism, and isomorphism of <span>\\(\\textit{FFG}\\)</span>, as well as the complement of <span>\\(\\textit{FFG}\\)</span>. Alongside the introduction of these concepts, their important properties, theorems, and illustrative examples are defined and discussed. Finally, an application has surfaced suggesting the utilization of <span>\\(\\textit{FFG}\\)</span>s to scrutinize the key factors affecting the productivity of Tata Motors, paving the way for a comprehensive analysis of the company’s operational efficiency using score function.</p>","PeriodicalId":15034,"journal":{"name":"Journal of Applied Mathematics and Computing","volume":"43 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An analysis of Fermatean fuzzy graph and its application in a car company\",\"authors\":\"Prabuddha Giri, Sk Amanathulla, Kalyani Maity Das\",\"doi\":\"10.1007/s12190-024-02094-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Fuzzy graphs find numerous applications in real life. One of the extensions of fuzzy graphs is Fermatean fuzzy graphs. Here, we introduce the concepts of Fermatean fuzzy set to the domain of graph theory and obtain a novel type of graph, referred to as Fermatean fuzzy graph (<span>\\\\(\\\\textit{FFG}\\\\)</span>). The article establishes fundamental terms such as strong <span>\\\\(\\\\textit{FFG}\\\\)</span>, complete <span>\\\\(\\\\textit{FFG}\\\\)</span>, regular <span>\\\\(\\\\textit{FFG}\\\\)</span>, path, degree, total degree, homomorphism, and isomorphism of <span>\\\\(\\\\textit{FFG}\\\\)</span>, as well as the complement of <span>\\\\(\\\\textit{FFG}\\\\)</span>. Alongside the introduction of these concepts, their important properties, theorems, and illustrative examples are defined and discussed. Finally, an application has surfaced suggesting the utilization of <span>\\\\(\\\\textit{FFG}\\\\)</span>s to scrutinize the key factors affecting the productivity of Tata Motors, paving the way for a comprehensive analysis of the company’s operational efficiency using score function.</p>\",\"PeriodicalId\":15034,\"journal\":{\"name\":\"Journal of Applied Mathematics and Computing\",\"volume\":\"43 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics and Computing\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12190-024-02094-4\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02094-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
模糊图在现实生活中应用广泛。Fermatean 模糊图是模糊图的扩展之一。在此，我们将费马特模糊集的概念引入图论领域，并得到了一种新型图，即费马特模糊图（Fermatean fuzzy graph）。文章建立了一些基本术语，如强（strong \textit{FFG}\）、完全（complete \textit{FFG}\）、规则（regular \textit{FFG}\）、路径（path）、度（degree）、总度（total degree）、同构（homomorphism）和同构（isomorphism of \textit{FFG}\），以及（the complement of \textit{FFG}\）。在介绍这些概念的同时，还定义并讨论了它们的重要性质、定理和示例。最后，一个应用浮出水面，建议利用（\textit{FFG}\）来仔细研究影响塔塔汽车公司生产率的关键因素，为使用分数函数全面分析该公司的运营效率铺平道路。
An analysis of Fermatean fuzzy graph and its application in a car company
Fuzzy graphs find numerous applications in real life. One of the extensions of fuzzy graphs is Fermatean fuzzy graphs. Here, we introduce the concepts of Fermatean fuzzy set to the domain of graph theory and obtain a novel type of graph, referred to as Fermatean fuzzy graph (\(\textit{FFG}\)). The article establishes fundamental terms such as strong \(\textit{FFG}\), complete \(\textit{FFG}\), regular \(\textit{FFG}\), path, degree, total degree, homomorphism, and isomorphism of \(\textit{FFG}\), as well as the complement of \(\textit{FFG}\). Alongside the introduction of these concepts, their important properties, theorems, and illustrative examples are defined and discussed. Finally, an application has surfaced suggesting the utilization of \(\textit{FFG}\)s to scrutinize the key factors affecting the productivity of Tata Motors, paving the way for a comprehensive analysis of the company’s operational efficiency using score function.
期刊介绍：
JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.
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