<rdf:RDF xmlns:rdf="http://www.openarchives.org/OAI/2.0/rdf/" xmlns:ow="http://www.ontoweb.org/ontology/1#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:ds="http://dspace.org/ds/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:doc="http://www.lyncode.com/xoai" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/rdf/ http://www.openarchives.org/OAI/2.0/rdf.xsd">
   <ow:Publication rdf:about="oai:digibug.ugr.es:10481/64825">
      <dc:title>Lexicographic Methods for Fuzzy Linear Programming</dc:title>
      <dc:creator>Pérez Cañedo, Boris</dc:creator>
      <dc:creator>Verdegay Galdeano, José Luis</dc:creator>
      <dc:creator>Concepción Morales, Eduardo René</dc:creator>
      <dc:creator>Rosete, Alejandro</dc:creator>
      <dc:subject>Fuzzy linear programming</dc:subject>
      <dc:subject>Fully fuzzy linear programming</dc:subject>
      <dc:subject>Fully fuzzy multi-objective linear programming</dc:subject>
      <dc:subject>Fuzzy linear assignment problem</dc:subject>
      <dc:subject>Fuzzy number</dc:subject>
      <dc:subject>Fuzzy inequality constraint</dc:subject>
      <dc:subject>Lexicographic ranking criteria</dc:subject>
      <dc:description>Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world&#xd;
decision-making problems that arise in uncertain and ever-changing environments since its&#xd;
introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming&#xd;
(LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development.&#xd;
Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can&#xd;
appear in the model components in different ways. Hence, despite fifty years of research,&#xd;
new formulations of FLP problems and solution methods are still being proposed. Among the&#xd;
existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables&#xd;
for handling inexactness and vagueness in data have experienced a remarkable development in&#xd;
recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions&#xd;
and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is&#xd;
to present an updated review of advances in this particular area. Consequently, the paper briefly&#xd;
examines well-known models and methods for FLP, and expands on methods for fuzzy single- and&#xd;
multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the&#xd;
fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical&#xd;
relevance. For this case, computer codes are provided that can be used to reproduce results presented&#xd;
in the paper and for practical applications. The paper demonstrates that FLP that is focused on&#xd;
lexicographic methods is an active area with promising research lines and practical implications.</dc:description>
      <dc:date>2020-12-11T10:43:03Z</dc:date>
      <dc:date>2020-12-11T10:43:03Z</dc:date>
      <dc:date>2020-09-09</dc:date>
      <dc:type>info:eu-repo/semantics/article</dc:type>
      <dc:identifier>Pérez-Cañedo, B.; Verdegay, J.L.; Concepción-Morales, E.R.; Rosete, A. Lexicographic Methods for Fuzzy Linear Programming. Mathematics 2020, 8, 1540. [doi:10.3390/math8091540]</dc:identifier>
      <dc:identifier>http://hdl.handle.net/10481/64825</dc:identifier>
      <dc:identifier>10.3390/math8091540</dc:identifier>
      <dc:language>eng</dc:language>
      <dc:rights>http://creativecommons.org/licenses/by/3.0/es/</dc:rights>
      <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
      <dc:rights>Atribución 3.0 España</dc:rights>
      <dc:publisher>Mdpi</dc:publisher>
   </ow:Publication>
</rdf:RDF>