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On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html> <head> <meta name=renderer content=webkit> <meta http-equiv="X-UA-Compatible" content="IE=edge" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <meta name="viewport" content="width=device-width,initial-scale=1.0,maximum-scale=1.0,minimum-scale=1.0,user-scalable=no" /> <title>On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty</title> <meta name="_sowise_journalid" content="10002"/> <meta name="WT.cg_n" content="AIMS Mathematics"/> <meta name="prism.issn" content="2473-6988"/> <meta name="citation_issn" content="2473-6988"/> <meta name="journal_id" content="110"/> <meta name="dc.title" content="On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty"/> <meta name="dc.source" content="AIMS Mathematics 2022 2:2331"/> <meta name="dc.format" content="text/html"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.publicationName" content="AIMS Mathematics"/> <meta name="dc.date" content=""/> <meta name="dc.language" content="en"/> <meta name="dc.copyright" content="2022 The Author(s)"/> <meta name="dc.rightsAgent" content="mathematics@aimspress.org"/> <meta name="prism.rightsAgent" content="mathematics@aimspress.org"/> <meta name="dc.description" content="&lt;abstract&gt;&lt;p&gt;In this study, we use the robust optimization techniques to consider a class of multi-objective fractional programming problems in the presence of uncertain data in both of the objective function and the constraint functions. The components of the objective function vector are reported as ratios involving a convex non-negative function and a concave positive function. In addition, on applying a parametric approach, we establish $ \varepsilon $-optimality conditions for robust weakly $ \varepsilon $-efficient solution. Furthermore, we present some theorems to obtain a robust $ \varepsilon $-saddle point for uncertain multi-objective fractional problem.&lt;/p&gt;&lt;/abstract&gt;"/> <meta name="og:description" content="In this study, we use the robust optimization techniques to consider a class of multi-objective fractional programming problems in the presence of uncertain data in both of the objective function and the constraint functions. The components of the objective function vector are reported as ratios involving a convex non-negative function and a concave positive function. In addition, on applying a parametric approach, we establish $ \varepsilon $-optimality conditions for robust weakly $ \varepsilon $-efficient solution. Furthermore, we present some theorems to obtain a robust $ \varepsilon $-saddle point for uncertain multi-objective fractional problem."/> <meta name="description" content="&lt;abstract&gt;&lt;p&gt;In this study, we use the robust optimization techniques to consider a class of multi-objective fractional programming problems in the presence of uncertain data in both of the objective function and the constraint functions. The components of the objective function vector are reported as ratios involving a convex non-negative function and a concave positive function. In addition, on applying a parametric approach, we establish $ \varepsilon $-optimality conditions for robust weakly $ \varepsilon $-efficient solution. Furthermore, we present some theorems to obtain a robust $ \varepsilon $-saddle point for uncertain multi-objective fractional problem.&lt;/p&gt;&lt;/abstract&gt;"/> <meta name="prism.publicationDate" content=""/> <meta name="prism.volume" content="7"/> <meta name="prism.number" content="math-07-02-132"/> <meta name="prism.startingPage" content="2331"/> <meta name="prism.endingPage" content="2347"/> <meta name="prism.copyright" content="2022 The Author(s)"/> <meta name="prism.url" content="http://www.aimspress.com/article/doi/10.3934/math.2022132"/> <meta name="prism.doi" content="doi:10.3934/math.2022132"/> <meta name="citation_pdf_url" content="http://www.aimspress.com/article/doi/10.3934/math.2022132"/> <meta name="citation_fulltext_html_url" content="http://www.aimspress.com/article/doi/10.3934/math.2022132"/> <meta name="citation_journal_title" content="AIMS Mathematics"/> <meta name="citation_journal_abbrev" content="MATH"/> <meta name="citation_title" content="On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty"/> <meta name="citation_volume" content="7"/> <meta name="citation_issue" content="2"/> <meta name="citation_online_date" content=""/> <meta name="citation_firstpage" content="2331"/> <meta name="citation_lastpage" content="2347"/> <meta name="citation_article_type" content="Article"/> <meta name="citation_fulltext_world_readable" content=""/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.3934/math.2022132"/> <meta name="DOI" content="10.3934/math.2022132"/> <meta name="citation_doi" content="10.3934/math.2022132"/> <meta name="dc.subject" content="Research article"/> <!-- more author --> <meta name="dc.creator" content="Shima Soleimani Manesh"/> <meta name="dc.creator" content="Mansour Saraj"/> <meta name="dc.creator" content="Mahmood Alizadeh"/> <meta name="dc.creator" content="Maryam Momeni"/> <!-- more refers --> <meta name="citation_reference" content="A. 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class="article-left"> <div class="article-column "> <span class="columnli">Research article</span> <!-- <span class="columnli access"> Open Access </span> --> <!-- <span class="columnli" id="article_special_show" hidden> Special Issue </span> --> </div> <div class="articleEn"> <div class="article-title left-title"> <h1>On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty</h1> </div> <ul class="article-author clear"> <li > <a href="javascript:void(0);" class="mainColor" data-relate="msaraj@scu.ac.ir; sh.s.manesh@gmail.com" data="{{author.authorNameEn}}" type="authors.authorNameEn">Shima Soleimani Manesh</a> <sup class="authorTag"> <a href="javascript:void(0);" class="com-num" data-tagVal="1">1</a> ,&nbsp; <a href="javascript:void(0);" class="com-user" title="Corresponding Author:&nbsp;Shima Soleimani Manesh,&nbsp;msaraj@scu.ac.ir; sh.s.manesh@gmail.com"></a>,&nbsp;<a href="mailto:msaraj@scu.ac.ir; sh.s.manesh@gmail.com" class="com-mail" title="mailto:&nbsp;msaraj@scu.ac.ir; sh.s.manesh@gmail.com"></a></sup>,&nbsp; </li> <li > <a href="javascript:void(0);" class="mainColor" data-relate="msaraj@scu.ac.ir; sh.s.manesh@gmail.com" data="{{author.authorNameEn}}" type="authors.authorNameEn">Mansour Saraj</a> <sup class="authorTag"> <a href="javascript:void(0);" class="com-num" data-tagVal="1,2">1,2</a> ,&nbsp; <a href="javascript:void(0);" class="com-user" title="Corresponding Author:&nbsp;Mansour Saraj,&nbsp;msaraj@scu.ac.ir; sh.s.manesh@gmail.com"></a>,&nbsp;<a href="mailto:msaraj@scu.ac.ir; sh.s.manesh@gmail.com" class="com-mail" title="mailto:&nbsp;msaraj@scu.ac.ir; sh.s.manesh@gmail.com"></a></sup>,&nbsp; </li> <li > <a href="javascript:void(0);" class="mainColor" data-relate="" data="{{author.authorNameEn}}" type="authors.authorNameEn">Mahmood Alizadeh</a> <sup class="authorTag"> <a href="javascript:void(0);" class="com-num" data-tagVal="1">1</a> </sup>,&nbsp; </li> <li > <a href="javascript:void(0);" class="mainColor" data-relate="" data="{{author.authorNameEn}}" type="authors.authorNameEn">Maryam Momeni</a> <sup class="authorTag"> <a href="javascript:void(0);" class="com-num" data-tagVal="1">1</a> </sup> </li> </ul> <ul class="about-author"> <!-- 英文作者地址 --> <li class="article-author-address"> <span class=""> 1. </span> <div class="lostOf" > Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran </div> </li> <li class="article-author-address"> <span class=""> 2. </span> <div class="lostOf" > Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran </div> </li> </ul> <ul class="about-article"> <!-- 稿件日期和基金项目0308 --> <li class="com-author-info timewrap"> <span><b>Received:</b> 09 August 2021 </span> <span><b>Accepted:</b> 26 October 2021 </span> <span><b>Published:</b> 11 November 2021 </span> </li> <li class="fundwrap"> </li> <li class="com-author-info"> <p class="com-author-info"> <b>MSC : </b> 90C17, 90C29, 90C32 </p> </li> <li class="com-author-info"> <span class="columnli" id="article_special_show" hidden> </span> </li> </p> </li> </ul> </div> </div> <ul id="myTab" class="tab-ul tab-ul-article clear"> <li class="active abs"><a href="#Abstract" data-toggle="tab">Abstract</a></li> <li class="htm"><a href="#FullTextWrap" data-toggle="tab">Full Text(HTML)</a></li> <!-- <div class="pdf-xml clearfix"> <div class="download-pdf" data="618cf88cba35de0683e3bfc7"><a href="javascript:void(0);" > Download PDF</a></div> <div class="download-xml"><a href="javascript:void(0);" onclick="toExportXML('618cf88cba35de0683e3bfc7');"> Download XML</a></div> <li class="pdf"><a href="javascript:void(0);" data-toggle="tab">Download PDF</a></li> </div> --> <li class="pdf hidden-sm hidden-xs"><div class="download-pdf" data="618cf88cba35de0683e3bfc7"><a href="javascript:void(0);" > Download PDF</a></div></li> <li class="pdf hidden-lg hidden-md"> <a href="/aimspress-data/math/2022/2/PDF/math-07-02-132.pdf" > Download PDF </a> </li> </ul> <ul class="article-tab-box tab-content" id="myTabContent"> <!-- 摘要 --> <li id="Abstract" class="articleListBox tab-pane fade in active"> <!-- <h3 class="navTitle" id="Abstract-list">Abstract</h3> --> <!-- <abstract><p>In this study, we use the robust optimization techniques to consider a class of multi-objective fractional programming problems in the presence of uncertain data in both of the objective function and the constraint functions. The components of the objective function vector are reported as ratios involving a convex non-negative function and a concave positive function. In addition, on applying a parametric approach, we establish $ \varepsilon $-optimality conditions for robust weakly $ \varepsilon $-efficient solution. Furthermore, we present some theorems to obtain a robust $ \varepsilon $-saddle point for uncertain multi-objective fractional problem.</p></abstract> --> <div class="article-abstract"> <abstract><p>In this study, we use the robust optimization techniques to consider a class of multi-objective fractional programming problems in the presence of uncertain data in both of the objective function and the constraint functions. The components of the objective function vector are reported as ratios involving a convex non-negative function and a concave positive function. In addition, on applying a parametric approach, we establish $ \varepsilon $-optimality conditions for robust weakly $ \varepsilon $-efficient solution. Furthermore, we present some theorems to obtain a robust $ \varepsilon $-saddle point for uncertain multi-objective fractional problem.</p></abstract> </div> <ul class="article-keyword article-info-en"> <b>Keywords:</b> <li><a class="underHigh mainColor" href="javascript:void(0);" data="multi-objective fractional programming problem" type="keywords.keywordEn">multi-objective fractional programming problem</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" data="robust optimization" type="keywords.keywordEn">robust optimization</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" data="robust weakly $ \varepsilon $-efficient solution" type="keywords.keywordEn">robust weakly $ \varepsilon $-efficient solution</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" data="robust $ \varepsilon $-saddle point theorem" type="keywords.keywordEn">robust $ \varepsilon $-saddle point theorem</a>, </li> <li><a class="underHigh mainColor" href="javascript:void(0);" data="$ \varepsilon $-optimality theorem" type="keywords.keywordEn">$ \varepsilon $-optimality theorem</a> </li> </ul> <p class="citation-p"><b class="subtit-b">Citation:</b> Shima Soleimani Manesh, Mansour Saraj, Mahmood Alizadeh, Maryam Momeni. On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty[J]. AIMS Mathematics, 2022, 7(2): 2331-2347. doi: 10.3934/math.2022132</p> <!-- 相关文章 --> <div id="RelatedPages" class="articleListBox"> <h3><b class="subtit-b">Related Papers:</b></h3> <div id="RelatedPagesHtml"></div> </div> </li> <!-- 全文 --> <li id="FullTextWrap" class="articleListBox FullText-all tab-pane fade in"> <h3 class="navTitle" id="Abstract-list">Abstract</h3> <!-- changedby qmn:20210416 //CDATA域字符--> <div class="article-abstract"> <abstract><p>In this study, we use the robust optimization techniques to consider a class of multi-objective fractional programming problems in the presence of uncertain data in both of the objective function and the constraint functions. The components of the objective function vector are reported as ratios involving a convex non-negative function and a concave positive function. In addition, on applying a parametric approach, we establish $ \varepsilon $-optimality conditions for robust weakly $ \varepsilon $-efficient solution. Furthermore, we present some theorems to obtain a robust $ \varepsilon $-saddle point for uncertain multi-objective fractional problem.</p></abstract> </div> <br /> <div class="nodeTitle"><b></b></div> <br /> <div class="nodeContent"> </div> <div id="FullText" > <img style="display:block;margin:10px auto;" src="/style/web/images/article/1.gif" alt="加载中" /> </div> <!-- 缩写 --> </br> <!-- 致谢 --> <!-- 利益冲突 --> </br> <h3 class="navTitle" id="References-list">References</h3> <div id="References"> <div class="References-wrap"> <table class="reference-tab"> <tr class="document-box" id="b1"> <td valign="top" class="td1"> [1] </td> <td class="td2"> <!-- A. Beck, A. Ben-Tal, Duality in robust optimization primal worst equals dual best, <i>Oper. Res. Lett.</i>, <b>37</b> (2009), 1–6. doi: <a href="http://dx.doi.org/10.1016/j.orl.2008.09.010" target="_blank">10.1016/j.orl.2008.09.010</a>. --> A. Beck, A. Ben-Tal, Duality in robust optimization primal worst equals dual best, <i>Oper. Res. Lett.</i>, <b>37</b> (2009), 1–6. doi: <a href="http://dx.doi.org/10.1016/j.orl.2008.09.010" target="_blank">10.1016/j.orl.2008.09.010</a>. </td> </tr> <tr class="document-box" id="b2"> <td valign="top" class="td1"> [2] </td> <td class="td2"> <!-- A. Ben-Tal, EL. Ghaoui, A. Nemirovski, <i>Robust optimization</i>, Princeton Series in Applied Mathematics, 2009. --> A. Ben-Tal, EL. Ghaoui, A. Nemirovski, <i>Robust optimization</i>, Princeton Series in Applied Mathematics, 2009. </td> </tr> <tr class="document-box" id="b3"> <td valign="top" class="td1"> [3] </td> <td class="td2"> <!-- R. Bokrantz, A.Fredriksson, Necessary and Sufficient conditions for pareto efficiency in robust multiobjective optimization, <i>Eur. J. Oper. 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On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty[J]. AIMS Mathematics, 2022, 7(2): 2331-2347. doi: 10.3934/math.2022132</div> <span class="info citationEn" id=""> Shima Soleimani Manesh, Mansour Saraj, Mahmood Alizadeh, Maryam Momeni. 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