{"title":"用LR型模糊数求解完全模糊线性规划问题的一种直接方法","authors":"Z. Gong, Wencui Zhao, Kun Liu","doi":"10.15807/JORSJ.61.172","DOIUrl":null,"url":null,"abstract":"The fuzzy linear programming problem with triangular fuzzy numbers in its objective functions or constraints has been discussed by many scholars based on using Zadeh’s decomposition theorem of fuzzy numbers and transforming it into some crisp linear programming problems. However, the existing methods and the results will be limited when the objective functions (or the constraint functions) of a fuzzy linear programming contain generalized fuzzy numbers. In this paper, we first investigate the approximate representation of the fully fuzzy constraints and the transformation theorem of the fully fuzzy linear programming problem by means of the definition of the extended LR-fuzzy numbers. At the same time, the fully fuzzy linear programming problem is solved by transforming it into a multi-objective linear programming problem under a new ordering of GLR-fuzzy numbers proposed in this paper. Finally, the results obtained are compared with the existing work, and some numerical examples are given.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"61 1","pages":"172-185"},"PeriodicalIF":0.0000,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.61.172","citationCount":"19","resultStr":"{\"title\":\"A STRAIGHTFORWARD APPROACH FOR SOLVING FULLY FUZZY LINEAR PROGRAMMING PROBLEM WITH LR-TYPE FUZZY NUMBERS\",\"authors\":\"Z. Gong, Wencui Zhao, Kun Liu\",\"doi\":\"10.15807/JORSJ.61.172\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The fuzzy linear programming problem with triangular fuzzy numbers in its objective functions or constraints has been discussed by many scholars based on using Zadeh’s decomposition theorem of fuzzy numbers and transforming it into some crisp linear programming problems. However, the existing methods and the results will be limited when the objective functions (or the constraint functions) of a fuzzy linear programming contain generalized fuzzy numbers. In this paper, we first investigate the approximate representation of the fully fuzzy constraints and the transformation theorem of the fully fuzzy linear programming problem by means of the definition of the extended LR-fuzzy numbers. At the same time, the fully fuzzy linear programming problem is solved by transforming it into a multi-objective linear programming problem under a new ordering of GLR-fuzzy numbers proposed in this paper. Finally, the results obtained are compared with the existing work, and some numerical examples are given.\",\"PeriodicalId\":51107,\"journal\":{\"name\":\"Journal of the Operations Research Society of Japan\",\"volume\":\"61 1\",\"pages\":\"172-185\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.15807/JORSJ.61.172\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Operations Research Society of Japan\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15807/JORSJ.61.172\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Decision Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Operations Research Society of Japan","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15807/JORSJ.61.172","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Decision Sciences","Score":null,"Total":0}
A STRAIGHTFORWARD APPROACH FOR SOLVING FULLY FUZZY LINEAR PROGRAMMING PROBLEM WITH LR-TYPE FUZZY NUMBERS
The fuzzy linear programming problem with triangular fuzzy numbers in its objective functions or constraints has been discussed by many scholars based on using Zadeh’s decomposition theorem of fuzzy numbers and transforming it into some crisp linear programming problems. However, the existing methods and the results will be limited when the objective functions (or the constraint functions) of a fuzzy linear programming contain generalized fuzzy numbers. In this paper, we first investigate the approximate representation of the fully fuzzy constraints and the transformation theorem of the fully fuzzy linear programming problem by means of the definition of the extended LR-fuzzy numbers. At the same time, the fully fuzzy linear programming problem is solved by transforming it into a multi-objective linear programming problem under a new ordering of GLR-fuzzy numbers proposed in this paper. Finally, the results obtained are compared with the existing work, and some numerical examples are given.
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The journal publishes original work and quality reviews in the field of operations research and management science to OR practitioners and researchers in two substantive categories: operations research methods; applications and practices of operations research in industry, public sector, and all areas of science and engineering.
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