<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332013000200007</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Lineamientos generales de solución para programación lineal con coeficientes borrosos]]></article-title>
<article-title xml:lang="en"><![CDATA[General guidelines solution for linear programming with fuzzy coefficients]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[de-los-Cobos-Silva]]></surname>
<given-names><![CDATA[Sergio G.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Terceño-Gómez]]></surname>
<given-names><![CDATA[Antonio]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gutiérrez-Andrade]]></surname>
<given-names><![CDATA[Miguel A.]]></given-names>
</name>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Autónoma Metropolitana-Iztapalapa , Departamento de Ingeniería Eléctrica ]]></institution>
<addr-line><![CDATA[ México D.F.]]></addr-line>
<country>México</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universitat Rovira i Virgili Departamento de Gestión de Empresas y Economía ]]></institution>
<addr-line><![CDATA[ Reus]]></addr-line>
<country>España</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2013</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2013</year>
</pub-date>
<volume>20</volume>
<numero>2</numero>
<fpage>203</fpage>
<lpage>214</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332013000200007&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332013000200007&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332013000200007&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[En este trabajo se introduce tanto a la Programación Posibilística como a la Programación Borrosa como paradigmas que permiten resolver problemas de optimización cuando los coeficientes del modelo de programación lineal o las restricciones del mismo se presentan como números borrosos, en lugar de números exactos (crisp, en inglés). Se presentan algunos ejemplos basados en [1].]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[This work introduce to the Possibilistic Programming and the Fuzzy Programming as paradigms that allow to resolve problems of linear programming when the coefficients of the model or the restrictions on the same are presented as fuzzy numbers, rather than exact numbers (crisp). This work presents some examples based on [1].]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Programación posibilística]]></kwd>
<kwd lng="es"><![CDATA[programación borrosa]]></kwd>
<kwd lng="es"><![CDATA[optimización]]></kwd>
<kwd lng="en"><![CDATA[Possibilistic programming]]></kwd>
<kwd lng="en"><![CDATA[fuzzy programming]]></kwd>
<kwd lng="en"><![CDATA[optimization]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <div style="text-align: justify;">     <div style="text-align: center;"><font style="font-weight: bold;"  size="4"><span style="font-family: verdana;">Lineamientos generales de soluci&oacute;n para programaci&oacute;n lineal con coeficientes borrosos</span></font><br  style="font-family: verdana; font-weight: bold;"> <br style="font-family: verdana; font-weight: bold;"> <font style="font-weight: bold;" size="4"><span  style="font-family: verdana;">General guidelines solution for linear programming with fuzzy coefficients</span></font><br  style="font-family: verdana;"> </div> <br style="font-family: verdana;">     <div style="text-align: center;">     <div style="text-align: left;">     <div style="text-align: center;"><font size="2"><span  style="font-family: verdana;">Sergio G. de-los-Cobos-Silva<sup><a  href="#1">*</a><a name="4"></a>+</sup>, Antonio Terce&ntilde;o-G&oacute;mez<sup><a href="#2">&#8224;</a><a name="5"></a>+</sup>, Miguel A. Guti&eacute;rrez-Andrade<sup><a href="#3">&#8225;</a><a name="6"></a>+</sup></span></font>    <br> </div> <font size="2"><span style="font-family: verdana;"></span></font></div> <font size="2"><span style="font-family: verdana;"><br  style="font-family: verdana;"> </span></font></div> <font size="2"><span style="font-family: verdana;"> </span></font><font size="2"><span style="font-family: verdana;"><a  name="Correspondencia2"></a>*<a href="#Correspondencia1">Direcci&oacute;n para correspondencia:</a><br style="font-family: verdana;"> </span></font> <hr style="width: 100%; height: 2px;"><font size="3"><span  style="font-family: verdana; font-weight: bold;">Resumen</span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">En este trabajo se introduce tanto a la Programaci&oacute;n Posibil&iacute;stica como a la Programaci&oacute;n Borrosa como paradigmas que permiten resolver problemas de optimizaci&oacute;n cuando los coeficientes del modelo de programaci&oacute;n lineal o las restricciones del mismo se presentan como n&uacute;meros borrosos, en lugar de n&uacute;meros exactos (crisp, en ingl&eacute;s). Se presentan algunos ejemplos basados en [1].</span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;"><span  style="font-weight: bold;">Palabras clave:</span> Programaci&oacute;n posibil&iacute;stica, programaci&oacute;n borrosa, optimizaci&oacute;n.</span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="3"><span style="font-family: verdana; font-weight: bold;">Abstract</span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">This work introduce to the Possibilistic Programming and the Fuzzy Programming as paradigms that allow to resolve problems of linear programming when the coefficients of the model or the restrictions on the same are presented as fuzzy numbers, rather than exact numbers (crisp). This work presents some examples based on [1].</span></font><br style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;"><span  style="font-weight: bold;">Keywords:</span> Possibilistic programming, fuzzy programming, optimization.</span></font><br  style="font-family: verdana;"> <br style="font-family: verdana; font-weight: bold;"> <font size="2"><span style="font-family: verdana;"><span  style="font-weight: bold;">Mathematics Subject Classification:</span> 65J05, 90C05, 90C70, 65K05, 65K99.    <br> </span></font> <hr style="width: 100%; height: 2px;"><font  style="color: rgb(0, 0, 0); font-family: verdana; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: justify; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; background-color: rgb(255, 255, 255);"  size="-1">    <br> Ver contenido disponible en pdf</font><span  style="color: rgb(0, 0, 0); font-family: verdana; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: justify; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; background-color: rgb(255, 255, 255); display: inline ! important; float: none;"><span  class="Apple-converted-space"> </span></span>    <br> <font size="2"><span style="font-family: verdana;"><br  style="font-family: verdana;"> </span></font> <hr style="width: 100%; height: 2px;">    <!-- ref --><br> <font size="3"><span style="font-family: verdana; font-weight: bold;">Referencias</span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">[1] De Andr&eacute;s S&aacute;nchez J.; Terce&ntilde;o G&oacute;mez A.,(2002) &#8220;Programaci&oacute;n matem&aacute;tica y regresi&oacute;n lineal con instrumentos de la teor&iacute;a de los subconjuntos borrosos&#8221;, Departamento de Gesti&oacute;n de Empresas, Facultad de Ciencias Econ&oacute;micas y Empresariales. Universidad Rovira i Virgili.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951744&pid=S1409-2433201300020000700001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --></span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">[2] Fuller, R. (1986) &#8220;On a spetial type of fuzzy linear programming&#8221;, <span style="font-style: italic;">Colloquia Mathematica Societatis Janos Bolyai </span>49.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951745&pid=S1409-2433201300020000700002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><br>     <!-- ref --><br> [3] Kaufmann, A.; Gil Aluja, J.; Terce&ntilde;o, A. (1994), &#8220;Matem&aacute;tica para la econom&iacute;a y la gesti&oacute;n de empresas&#8221;. Foro Cient&iacute;fico, Barcelona.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951747&pid=S1409-2433201300020000700003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --></span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;"></span></font><font  size="2"><span style="font-family: verdana;">[4] Lai, Y.J.; Hwang, C.L. (1992) &#8220;A new approach to some possibilistic linear programming problem&#8221;, <span style="font-style: italic;">Fuzzy sets and systems</span> 49.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951748&pid=S1409-2433201300020000700004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --> </span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">[5] Lai, Y.L.; Hwang, C.L. (1996) &#8220;Fuzzy Multiple Objective Decision Making&#8221;. Springer-Verlag, Berlin.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951749&pid=S1409-2433201300020000700005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --></span></font><br style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">[6] Lai, Y.L; Hwang, C.L. (1992)&#8220;Fuzzy Mathematical Programming&#8221;. Springer-Verlag, Berlin.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951750&pid=S1409-2433201300020000700006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --></span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">[7] Ramik, J.; Rimanek, J. (1985) &#8220;Active decision making in fuzzy linear optimization problems&#8221;, <span style="font-style: italic;">European Journal of Operational Research</span> 41.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951751&pid=S1409-2433201300020000700007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --></span></font><br style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">[8] Rommelfanger, H.; Hanuscheck, R.; Wolf, J. (1989) &#8220;Linear programming with fuzzy objectives&#8221;,<span  style="font-style: italic;"> Fuzzy Sets and Systems</span> 29.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951752&pid=S1409-2433201300020000700008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --> </span></font><br  style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">[9] Tanaka, H.; Asai, K. (1984) &#8220;Fuzzy linear programming with fuzzy numbers&#8221;, <span  style="font-style: italic;">Fuzzy Sets and Systems</span> 13.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951753&pid=S1409-2433201300020000700009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --></span></font><br style="font-family: verdana;"> <br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">[10] Zimmermann, H.-J. (1991) &#8220;Fuzzy Set Theory and Its Applications&#8221;. Kluwer Academic, Dordrecht. Rev.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1951754&pid=S1409-2433201300020000700010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><br>     <br> <a name="Correspondencia1"></a><a href="#Correspondencia2">*</a>Correspondencia a:    <br> </span></font><font size="2"><span style="font-family: verdana;"></span></font><font  size="2"><span style="font-family: verdana;">Sergio G. de-los-Cobos-Silva. </span></font><font size="2"><span  style="font-family: verdana;">Universidad Aut&oacute;noma Metropolitana-Iztapalapa, Departamento de Ingenier&iacute;a El&eacute;ctrica, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, M&eacute;xico D.F., C.P. 09340, M&eacute;xico. E-Mail: cobos@xanum.uam.mx</span></font><br style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">Antonio Terce&ntilde;o-G&oacute;mez. </span></font><font size="2"><span  style="font-family: verdana;">Universitat Rovira i Virgili, Departamento de Gesti&oacute;n de Empresas y Econom&iacute;a, Avinguda de la Universitat 1, 43204, Reus, Espa&ntilde;a. E-MAil: atg@fcee.urv.es</span></font><br  style="font-family: verdana;"> <font size="2"><span style="font-family: verdana;">Miguel A. Guti&eacute;rrez-Andrade. </span></font><font size="2"><span  style="font-family: verdana;">Misma direcci&oacute;n que/Same address as: S. de-los-Cobos-Silva. E-Mail: gamma@xanum.uam.mx    <br> </span></font><font size="2"><span style="font-family: verdana;"><a  name="1"></a><a href="#4">*</a>Universidad Aut&oacute;noma Metropolitana-Iztapalapa, Departamento de Ingenier&iacute;a El&eacute;ctrica, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, M&eacute;xico D.F., C.P. 09340, M&eacute;xico. E-Mail: cobos@xanum.uam.mx    <br> <a name="2"></a><a href="#5">&#8224;</a>Universitat Rovira i Virgili, Departamento de Gesti&oacute;n de Empresas y Econom&iacute;a, Avinguda de la Universitat 1, 43204, Reus, Espa&ntilde;a. E-MAil: atg@fcee.urv.es    <br> <a name="3"></a><a href="#6">&#8225;</a>Misma direcci&oacute;n que/Same address as: S. de-los-Cobos-Silva. E-Mail: gamma@xanum.uam.mx</span></font><br  style="font-family: verdana;"> </div> <hr style="width: 100%; height: 2px;">     <div style="text-align: center;"><font size="2"><span  style="font-family: verdana; font-weight: bold;">Received: 14/Nov/2011; Revised: 20/May/2013; Accepted: 27/May/2013</span></font><br  style="font-family: verdana;"> </div> <font size="2"> </font>      ]]></body><back>
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<given-names><![CDATA[K.]]></given-names>
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</person-group>
<article-title xml:lang="en"><![CDATA[&#8220;Fuzzy linear programming with fuzzy numbers&#8221;]]></article-title>
<source><![CDATA[Fuzzy Sets and Systems]]></source>
<year>1984</year>
<volume>13</volume>
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<ref id="B10">
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<person-group person-group-type="author">
<name>
<surname><![CDATA[Zimmermann]]></surname>
<given-names><![CDATA[H.-J.]]></given-names>
</name>
</person-group>
<source><![CDATA[&#8220;Fuzzy Set Theory and Its Applications&#8221;]]></source>
<year>1991</year>
<publisher-name><![CDATA[Kluwer Academic]]></publisher-name>
</nlm-citation>
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</article>
