<?xml version="1.0" encoding="utf-8"?>
<journal>
<title>International Journal of Applied Operational Research</title>
<title_fa>ژورنال بین المللی پژوهش عملیاتی</title_fa>
<short_title>International Journal of Applied Operational Research - An Open Access Journal</short_title>
<subject>Basic Sciences</subject>
<web_url>http://ijorlu.lahijan.iau.ir</web_url>
<journal_hbi_system_id>1</journal_hbi_system_id>
<journal_hbi_system_user>admin</journal_hbi_system_user>
<journal_id_issn>2251-6867</journal_id_issn>
<journal_id_issn_online>2251-9432</journal_id_issn_online>
<journal_id_pii>8</journal_id_pii>
<journal_id_doi>7</journal_id_doi>
<journal_id_iranmedex></journal_id_iranmedex>
<journal_id_magiran></journal_id_magiran>
<journal_id_sid>14</journal_id_sid>
<journal_id_nlai>8888</journal_id_nlai>
<journal_id_science>13</journal_id_science>
<language>en</language>
<pubdate>
	<type>jalali</type>
	<year>1401</year>
	<month>10</month>
	<day>1</day>
</pubdate>
<pubdate>
	<type>gregorian</type>
	<year>2023</year>
	<month>1</month>
	<day>1</day>
</pubdate>
<volume>11</volume>
<number>1</number>
<publish_type>online</publish_type>
<publish_edition>1</publish_edition>
<article_type>fulltext</article_type>
<articleset>
	<article>


	<language>en</language>
	<article_id_doi></article_id_doi>
	<title_fa></title_fa>
	<title>A two- phase approach for solving fuzzy flexible linear programming problems with fuzzy objective coefficients</title>
	<subject_fa>عمومى</subject_fa>
	<subject>General</subject>
	<content_type_fa>گزارش مورد</content_type_fa>
	<content_type>case report</content_type>
	<abstract_fa>-</abstract_fa>
	<abstract>&lt;span style=&quot;font-size:11pt&quot;&gt;&lt;span style=&quot;text-autospace:none&quot;&gt;&lt;span style=&quot;unicode-bidi:embed&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span calibri=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span new=&quot;&quot; roman=&quot;&quot; style=&quot;font-family:&quot; times=&quot;&quot;&gt;In this paper, new concepts of &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;m:omath&gt;&lt;m:acc&gt;&lt;m:accpr&gt;&lt;m:chr m:val=&quot;̅&quot;&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span cambria=&quot;&quot; math=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;font-style:italic&quot;&gt;&lt;m:ctrlpr&gt;&lt;/m:ctrlpr&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/m:chr&gt;&lt;/m:accpr&gt;&lt;m:e&gt;&lt;i&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span cambria=&quot;&quot; math=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;m:r&gt;&amp;alpha;&lt;/m:r&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;/m:e&gt;&lt;/m:acc&gt;&lt;/m:omath&gt;&lt;span style=&quot;font-size:11.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span calibri=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;position:relative&quot;&gt;&lt;span style=&quot;top:5.5pt&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span new=&quot;&quot; roman=&quot;&quot; style=&quot;font-family:&quot; times=&quot;&quot;&gt;-feasibility and &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;m:omath&gt;&lt;m:acc&gt;&lt;m:accpr&gt;&lt;m:chr m:val=&quot;̅&quot;&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span cambria=&quot;&quot; math=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;font-style:italic&quot;&gt;&lt;m:ctrlpr&gt;&lt;/m:ctrlpr&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/m:chr&gt;&lt;/m:accpr&gt;&lt;m:e&gt;&lt;i&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span cambria=&quot;&quot; math=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;m:r&gt;&amp;alpha;&lt;/m:r&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;/m:e&gt;&lt;/m:acc&gt;&lt;/m:omath&gt;&lt;span style=&quot;font-size:11.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span calibri=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;position:relative&quot;&gt;&lt;span style=&quot;top:5.5pt&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span new=&quot;&quot; roman=&quot;&quot; style=&quot;font-family:&quot; times=&quot;&quot;&gt;-efficiency of solutions for fuzzy mathematical programming problems are used, where &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;m:omath&gt;&lt;m:acc&gt;&lt;m:accpr&gt;&lt;m:chr m:val=&quot;̅&quot;&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span cambria=&quot;&quot; math=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;font-style:italic&quot;&gt;&lt;m:ctrlpr&gt;&lt;/m:ctrlpr&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/m:chr&gt;&lt;/m:accpr&gt;&lt;m:e&gt;&lt;i&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span cambria=&quot;&quot; math=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;m:r&gt;&amp;alpha;&lt;/m:r&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;/m:e&gt;&lt;/m:acc&gt;&lt;/m:omath&gt;&lt;span style=&quot;font-size:11.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span calibri=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;position:relative&quot;&gt;&lt;span style=&quot;top:5.5pt&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span new=&quot;&quot; roman=&quot;&quot; style=&quot;font-family:&quot; times=&quot;&quot;&gt;&amp;nbsp;is a vector of distinct satisfaction degrees. Recently, a special kind of fuzzy mathematical programming entitled Fuzzy Flexible Linear programming (FFLP) is attracted much interest. Using the mentioned concepts, we propose a two-phase approach to solve FFLP. In the first phase, the original FFLP problem converts to a Multi-Objective Linear Programming (MOLP) problem, and then in phase II a weighting technique for the reduced program is introduced. We saw that it was observed that using this concept as a generalization of the parametric approach in linear programming provides a more appropriate tool for modeling real problems and improving the solving process. Thus, by using this two-phase approach, we achieve better utilization of available resources. Further, the solution resulting from these two approaches is always an &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;m:omath&gt;&lt;m:acc&gt;&lt;m:accpr&gt;&lt;m:chr m:val=&quot;̅&quot;&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span cambria=&quot;&quot; math=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;font-style:italic&quot;&gt;&lt;m:ctrlpr&gt;&lt;/m:ctrlpr&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/m:chr&gt;&lt;/m:accpr&gt;&lt;m:e&gt;&lt;i&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span cambria=&quot;&quot; math=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;m:r&gt;&amp;alpha;&lt;/m:r&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;/m:e&gt;&lt;/m:acc&gt;&lt;/m:omath&gt;&lt;span style=&quot;font-size:11.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span calibri=&quot;&quot; style=&quot;font-family:&quot;&gt;&lt;span style=&quot;position:relative&quot;&gt;&lt;span style=&quot;top:5.5pt&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;&lt;span style=&quot;line-height:115%&quot;&gt;&lt;span new=&quot;&quot; roman=&quot;&quot; style=&quot;font-family:&quot; times=&quot;&quot;&gt;-efficient solution. Finally, an example in the real world is described to express this approach.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;</abstract>
	<keyword_fa></keyword_fa>
	<keyword>Fuzzy Linear Programming, Triangular Fuzzy Numbers, Multi-Objective Linear Programming, Feasibility and Efficiency.</keyword>
	<start_page>11</start_page>
	<end_page>19</end_page>
	<web_url>http://ijorlu.lahijan.iau.ir/browse.php?a_code=A-10-484-1&amp;slc_lang=en&amp;sid=1</web_url>


<author_list>
	<author>
	<first_name>S.H.</first_name>
	<middle_name></middle_name>
	<last_name>Nasseri</last_name>
	<suffix></suffix>
	<first_name_fa></first_name_fa>
	<middle_name_fa></middle_name_fa>
	<last_name_fa></last_name_fa>
	<suffix_fa></suffix_fa>
	<email>nhadi57@gmail.com</email>
	<code>10031947532846001752</code>
	<orcid>10031947532846001752</orcid>
	<coreauthor>Yes
</coreauthor>
	<affiliation>Department of Mathematics and Big Data, Foshan University, Foshan, China and Department of mathematics, University of  Mazandaran, Babolsar, Iran</affiliation>
	<affiliation_fa></affiliation_fa>
	 </author>


	<author>
	<first_name>S</first_name>
	<middle_name></middle_name>
	<last_name>Mansouri</last_name>
	<suffix></suffix>
	<first_name_fa></first_name_fa>
	<middle_name_fa></middle_name_fa>
	<last_name_fa></last_name_fa>
	<suffix_fa></suffix_fa>
	<email>samira.mansory1372@gmail.com</email>
	<code>10031947532846001753</code>
	<orcid>10031947532846001753</orcid>
	<coreauthor>No</coreauthor>
	<affiliation>Department of mathematics, University of  Mazandaran, Babolsar, Iran</affiliation>
	<affiliation_fa></affiliation_fa>
	 </author>


</author_list>


	</article>
</articleset>
</journal>
