Location of Repository

Fuzzy variable linear programming with fuzzy technical coefficients

By Sanwar Uddin Ahmad and Sadhan Kumar Sardar

Abstract

<!--[if gte mso 9]><xml> <o:OfficeDocumentSettings> <o:RelyOnVML /> <o:AllowPNG /> </o:OfficeDocumentSettings> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves /> <w:TrackFormatting /> <w:PunctuationKerning /> <w:ValidateAgainstSchemas /> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF /> <w:LidThemeOther>EN-US</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables /> <w:SnapToGridInCell /> <w:WrapTextWithPunct /> <w:UseAsianBreakRules /> <w:DontGrowAutofit /> <w:SplitPgBreakAndParaMark /> <w:DontVertAlignCellWithSp /> <w:DontBreakConstrainedForcedTables /> <w:DontVertAlignInTxbx /> <w:Word11KerningPairs /> <w:CachedColBalance /> </w:Compatibility> <m:mathPr> <m:mathFont m:val="Cambria Math" /> <m:brkBin m:val="before" /> <m:brkBinSub m:val=" " /> <m:smallFrac m:val="off" /> <m:dispDef /> <m:lMargin m:val="0" /> <m:rMargin m:val="0" /> <m:defJc m:val="centerGroup" /> <m:wrapIndent m:val="1440" /> <m:intLim m:val="subSup" /> <m:naryLim m:val="undOvr" /> </m:mathPr></w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true" DefSemiHidden="true" DefQFormat="false" DefPriority="99" LatentStyleCount="267"> <w:LsdException Locked="false" Priority="0" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Normal" /> <w:LsdException Locked="false" Priority="9" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="heading 1" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9" /> <w:LsdException Locked="false" Priority="39" Name="toc 1" /> <w:LsdException Locked="false" Priority="39" Name="toc 2" /> <w:LsdException Locked="false" Priority="39" Name="toc 3" /> <w:LsdException Locked="false" Priority="39" Name="toc 4" /> <w:LsdException Locked="false" Priority="39" Name="toc 5" /> <w:LsdException Locked="false" Priority="39" Name="toc 6" /> <w:LsdException Locked="false" Priority="39" Name="toc 7" /> <w:LsdException Locked="false" Priority="39" Name="toc 8" /> <w:LsdException Locked="false" Priority="39" Name="toc 9" /> <w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption" /> <w:LsdException Locked="false" Priority="10" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Title" /> <w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font" /> <w:LsdException Locked="false" Priority="11" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtitle" /> <w:LsdException Locked="false" Priority="22" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Strong" /> <w:LsdException Locked="false" Priority="20" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Emphasis" /> <w:LsdException Locked="false" Priority="59" SemiHidden="false" UnhideWhenUsed="false" Name="Table Grid" /> <w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text" /> <w:LsdException Locked="false" Priority="1" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="No Spacing" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 1" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 1" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 1" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 1" /> <w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision" /> <w:LsdException Locked="false" Priority="34" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="List Paragraph" /> <w:LsdException Locked="false" Priority="29" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Quote" /> <w:LsdException Locked="false" Priority="30" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Quote" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 1" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 1" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 1" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 1" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 1" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 2" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 2" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 2" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 2" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 2" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 2" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 2" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 2" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 2" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 3" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 3" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 3" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 3" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 3" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 3" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 3" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 3" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 3" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 4" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 4" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 4" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 4" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 4" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 4" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 4" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 4" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 4" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 5" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 5" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 5" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 5" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 5" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 5" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 5" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 5" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 5" /> <w:LsdException Locked="false" Priority="60" SemiHidden="false" UnhideWhenUsed="false" Name="Light Shading Accent 6" /> <w:LsdException Locked="false" Priority="61" SemiHidden="false" UnhideWhenUsed="false" Name="Light List Accent 6" /> <w:LsdException Locked="false" Priority="62" SemiHidden="false" UnhideWhenUsed="false" Name="Light Grid Accent 6" /> <w:LsdException Locked="false" Priority="63" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6" /> <w:LsdException Locked="false" Priority="64" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6" /> <w:LsdException Locked="false" Priority="65" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 1 Accent 6" /> <w:LsdException Locked="false" Priority="66" SemiHidden="false" UnhideWhenUsed="false" Name="Medium List 2 Accent 6" /> <w:LsdException Locked="false" Priority="67" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6" /> <w:LsdException Locked="false" Priority="68" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6" /> <w:LsdException Locked="false" Priority="69" SemiHidden="false" UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6" /> <w:LsdException Locked="false" Priority="70" SemiHidden="false" UnhideWhenUsed="false" Name="Dark List Accent 6" /> <w:LsdException Locked="false" Priority="71" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Shading Accent 6" /> <w:LsdException Locked="false" Priority="72" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful List Accent 6" /> <w:LsdException Locked="false" Priority="73" SemiHidden="false" UnhideWhenUsed="false" Name="Colorful Grid Accent 6" /> <w:LsdException Locked="false" Priority="19" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis" /> <w:LsdException Locked="false" Priority="21" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis" /> <w:LsdException Locked="false" Priority="31" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference" /> <w:LsdException Locked="false" Priority="32" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Intense Reference" /> <w:LsdException Locked="false" Priority="33" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Book Title" /> <w:LsdException Locked="false" Priority="37" Name="Bibliography" /> <w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading" /> </w:LatentStyles> </xml><![endif]--> <!--[if gte mso 10]> <mce:style><! /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0in; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin;} --> <!--[endif]--><span style="font-size: 12pt; line-height: 115%; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;">Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. In this paper an approximate but convenient method for solving these problems with fuzzy non-negative technical coefficient and without using the ranking functions, is proposed. With the help of numerical examples, the method is illustrated.</span

Topics: Fuzzy Linear Programming, Fuzzy Variable Linear Programming, Fuzzy Number, Optimal Solution, Decomposition Method, Statistics, HA1-4737, Social Sciences, H, Mathematics, QA1-939
Publisher: University of the Punjab
Year: 2012
DOI identifier: 10.1234/pjsor.v8i4.322
OAI identifier: oai:doaj.org/article:ad3ef2c6447f49b4a62f224b99525b39
Journal:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • https://doaj.org/toc/2220-5810 (external link)
  • https://doaj.org/toc/1816-2711 (external link)
  • http://pjsor.com/index.php/pjs... (external link)
  • https://doaj.org/article/ad3ef... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.