{"title":"高效求解费尔马特模糊固体运输问题的扩展 Vogel 近似算法","authors":"Shivani, Deepika Rani","doi":"10.1007/s00500-024-09812-x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper aims to solve a solid transportation problem, wherein the uncertain parameters related to the problem are represented using triangular Fermatean fuzzy numbers. Fermatean fuzzy sets offer a relatively novel and wider alternative by providing the decision-makers with more versatile means of managing the uncertain information throughout the decision-making process. As per our literature survey, no algorithm exists in the literature for fuzzy solid transportation problems with parameters as triangular Fermatean fuzzy numbers. Therefore, in this study, the existing Vogel’s approximation method for the initial basic feasible solution (IBFS) of the traditional transportation problems is extended for the Fermatean fuzzy solid transportation problems. Further, a new method for getting the optimal solution from the obtained IBFS is proposed. The computational complexity and operational efficacy of the proposed algorithm are also discussed. Two application examples have been solved to illustrate the practicality of the proposed algorithm. For the comparative study, the problems are also solved with LINGO 20.0 software. The obtained results of IBFS are found to be significantly lower than those obtained by certain existing methods and the optimal values are comparable with those generated by the LINGO 20.0 optimization solver. Through a comparative analysis, it has been found that the proposed algorithm consistently produces optimal transportation costs for both application examples, adding to the novelty of the proposed work. Finally, the conclusion and future scope of this study are described.</p><h3 data-test=\"abstract-sub-heading\">Graphical abstract</h3><p>Graphical depiction of abstract</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"15 1","pages":""},"PeriodicalIF":3.1000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems\",\"authors\":\"Shivani, Deepika Rani\",\"doi\":\"10.1007/s00500-024-09812-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>This paper aims to solve a solid transportation problem, wherein the uncertain parameters related to the problem are represented using triangular Fermatean fuzzy numbers. Fermatean fuzzy sets offer a relatively novel and wider alternative by providing the decision-makers with more versatile means of managing the uncertain information throughout the decision-making process. As per our literature survey, no algorithm exists in the literature for fuzzy solid transportation problems with parameters as triangular Fermatean fuzzy numbers. Therefore, in this study, the existing Vogel’s approximation method for the initial basic feasible solution (IBFS) of the traditional transportation problems is extended for the Fermatean fuzzy solid transportation problems. Further, a new method for getting the optimal solution from the obtained IBFS is proposed. The computational complexity and operational efficacy of the proposed algorithm are also discussed. Two application examples have been solved to illustrate the practicality of the proposed algorithm. For the comparative study, the problems are also solved with LINGO 20.0 software. The obtained results of IBFS are found to be significantly lower than those obtained by certain existing methods and the optimal values are comparable with those generated by the LINGO 20.0 optimization solver. Through a comparative analysis, it has been found that the proposed algorithm consistently produces optimal transportation costs for both application examples, adding to the novelty of the proposed work. Finally, the conclusion and future scope of this study are described.</p><h3 data-test=\\\"abstract-sub-heading\\\">Graphical abstract</h3><p>Graphical depiction of abstract</p>\",\"PeriodicalId\":22039,\"journal\":{\"name\":\"Soft Computing\",\"volume\":\"15 1\",\"pages\":\"\"},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Soft Computing\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s00500-024-09812-x\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Soft Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00500-024-09812-x","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems
Abstract
This paper aims to solve a solid transportation problem, wherein the uncertain parameters related to the problem are represented using triangular Fermatean fuzzy numbers. Fermatean fuzzy sets offer a relatively novel and wider alternative by providing the decision-makers with more versatile means of managing the uncertain information throughout the decision-making process. As per our literature survey, no algorithm exists in the literature for fuzzy solid transportation problems with parameters as triangular Fermatean fuzzy numbers. Therefore, in this study, the existing Vogel’s approximation method for the initial basic feasible solution (IBFS) of the traditional transportation problems is extended for the Fermatean fuzzy solid transportation problems. Further, a new method for getting the optimal solution from the obtained IBFS is proposed. The computational complexity and operational efficacy of the proposed algorithm are also discussed. Two application examples have been solved to illustrate the practicality of the proposed algorithm. For the comparative study, the problems are also solved with LINGO 20.0 software. The obtained results of IBFS are found to be significantly lower than those obtained by certain existing methods and the optimal values are comparable with those generated by the LINGO 20.0 optimization solver. Through a comparative analysis, it has been found that the proposed algorithm consistently produces optimal transportation costs for both application examples, adding to the novelty of the proposed work. Finally, the conclusion and future scope of this study are described.
期刊介绍：
Soft Computing is dedicated to system solutions based on soft computing techniques. It provides rapid dissemination of important results in soft computing technologies, a fusion of research in evolutionary algorithms and genetic programming, neural science and neural net systems, fuzzy set theory and fuzzy systems, and chaos theory and chaotic systems.
Soft Computing encourages the integration of soft computing techniques and tools into both everyday and advanced applications. By linking the ideas and techniques of soft computing with other disciplines, the journal serves as a unifying platform that fosters comparisons, extensions, and new applications. As a result, the journal is an international forum for all scientists and engineers engaged in research and development in this fast growing field.
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