基于-切和极大极小技术的模糊系数线性分式规划方法

IF 1.9 4区数学 Q1 MATHEMATICS

Iranian Journal of Fuzzy Systems Pub Date : 2021-10-02 DOI:10.22111/IJFS.2021.6359

M. Borza, A. S. Rambely

{"title":"基于-切和极大极小技术的模糊系数线性分式规划方法","authors":"M. Borza, A. S. Rambely","doi":"10.22111/IJFS.2021.6359","DOIUrl":null,"url":null,"abstract":"This paper presents an efficient and straightforward method with less computational complexities to address the linear fractional programming with fuzzy coefficients (FLFPP). To construct the approach, the concept of α-cut is used to tackle the fuzzy numbers in addition to rank them. Accordingly, the fuzzy problem is changed into a bi-objective linear fractional programming problem (BOLFPP) by the use of interval arithmetic. Afterwards, an equivalent BOLFPPis defined in terms of the membership functions of the objectives, which is transformed into a bi-objective linear programming problem (BOLPP) applying suitable non-linear variable transformations. Max-min theory is utilized to alter the BOLPP into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an ϵ-optimal solution for the fuzzy problem. Four numerical examples are given to illustrate the method and comparisonsare made to show the efficiency.","PeriodicalId":54920,"journal":{"name":"Iranian Journal of Fuzzy Systems","volume":"18 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"(2012-6359) An approach based on -cuts and max-min technique to linear fractional programming with fuzzy coefficients\",\"authors\":\"M. Borza, A. S. Rambely\",\"doi\":\"10.22111/IJFS.2021.6359\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents an efficient and straightforward method with less computational complexities to address the linear fractional programming with fuzzy coefficients (FLFPP). To construct the approach, the concept of α-cut is used to tackle the fuzzy numbers in addition to rank them. Accordingly, the fuzzy problem is changed into a bi-objective linear fractional programming problem (BOLFPP) by the use of interval arithmetic. Afterwards, an equivalent BOLFPPis defined in terms of the membership functions of the objectives, which is transformed into a bi-objective linear programming problem (BOLPP) applying suitable non-linear variable transformations. Max-min theory is utilized to alter the BOLPP into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an ϵ-optimal solution for the fuzzy problem. Four numerical examples are given to illustrate the method and comparisonsare made to show the efficiency.\",\"PeriodicalId\":54920,\"journal\":{\"name\":\"Iranian Journal of Fuzzy Systems\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2021-10-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Iranian Journal of Fuzzy Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.22111/IJFS.2021.6359\",\"RegionNum\":4,\"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":"Iranian Journal of Fuzzy Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.22111/IJFS.2021.6359","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

本文提出了一种求解模糊系数线性分式规划(FLFPP)的有效、简单、计算复杂度低的方法。为了构造该方法，除了对模糊数进行排序外，还使用了α-切的概念来处理模糊数。据此，利用区间算法将模糊问题转化为双目标线性分式规划问题。然后，根据目标的隶属函数定义一个等效的bolfpp，并应用适当的非线性变量变换将其转化为双目标线性规划问题(BOLPP)。利用极大极小理论将BOLPP问题转化为线性规划问题(LPP)。证明了LPP的最优解是模糊问题的ϵ-optimal解。给出了四个数值算例来说明该方法的有效性，并进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

(2012-6359) An approach based on -cuts and max-min technique to linear fractional programming with fuzzy coefficients

This paper presents an efficient and straightforward method with less computational complexities to address the linear fractional programming with fuzzy coefficients (FLFPP). To construct the approach, the concept of α-cut is used to tackle the fuzzy numbers in addition to rank them. Accordingly, the fuzzy problem is changed into a bi-objective linear fractional programming problem (BOLFPP) by the use of interval arithmetic. Afterwards, an equivalent BOLFPPis defined in terms of the membership functions of the objectives, which is transformed into a bi-objective linear programming problem (BOLPP) applying suitable non-linear variable transformations. Max-min theory is utilized to alter the BOLPP into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an ϵ-optimal solution for the fuzzy problem. Four numerical examples are given to illustrate the method and comparisonsare made to show the efficiency.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Iranian Journal of Fuzzy Systems 数学-数学

CiteScore

3.50

自引率

16.70%

发文量

期刊介绍： The two-monthly Iranian Journal of Fuzzy Systems (IJFS) aims to provide an international forum for refereed original research works in the theory and applications of fuzzy sets and systems in the areas of foundations, pure mathematics, artificial intelligence, control, robotics, data analysis, data mining, decision making, finance and management, information systems, operations research, pattern recognition and image processing, soft computing and uncertainty modeling. Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.