Solving a Fuzzy Multiobjective Linear Programming Problem Through the Value and the Ambiguity of Fuzzy Numbers

Mariano Jiménez (), Mar Arenas (), Amelia Bilbao () and Ma Victoria Rodíguez ()
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Mariano Jiménez: Universidad del País Vasco.
Mar Arenas: Universidad de Oviedo.
Amelia Bilbao: Universidad de Oviedo.
Ma Victoria Rodíguez: Universidad de Oviedo.

A chapter in Multiobjective Programming and Goal Programming, 2009, pp 187-195 from Springer

Abstract: Abstract In this paper we solve multiobjective programming problems with fuzzy parameters and flexible constraints. To work with fuzzy numbers we use two real indices, the value and the ambiguity. In order to rank two fuzzy numbers a lexicographic ranking procedure can be used: in the first step the values of fuzzy numbers are compared, if these values are ‘approximately equal’ then we compare their ambiguities. In this paper we apply this ranking procedure to a fuzzy programming problem with fuzzy coefficients. In the first step we solve a model in which the fuzzy coefficients have been defuzzified by its corresponding value. Now the question is to determine when two solutions of the first step are approximately equal. In order to answer this question we propose to reflect the decision makers (DMs) preferences through the natural language, establishing a semantic correspondence for the different satisfaction degrees. We consider as approximately equal all the solutions whose global satisfaction degrees belong to the same linguistic label. Then, in the second step, among all the solutions that belong to the same linguistic label as the solution obtained in the first step, we find those with minimum (or maximum) ambiguity, depending on DMs attitude when faced with the risk. We use one example to illustrate this procedure.

Keywords: Fuzzy multi-objective linear programming; Fuzzy numbers; Linguistic label; Value and ambiguity of a fuzzy number (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-85646-7_18

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DOI: 10.1007/978-3-540-85646-7_18

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