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Fuzzy Parameters Multiobjective Linear Programming Problem: Solution Analysis

  • M. Arenas
  • A. Bilbao
  • M. V. Rodríguez
  • M. Jiménez
Chapter
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 465)

Abstract

In decision making problems, the estimate of the parameters defining the model is a difficult task. They are usually defined by the Decision Maker in an uncertain way or by means of language statements. Therefore, it is suitable to represent those parameters by fuzzy numbers, defined by their possibility distribution.

The fuzziness and/or inaccuracy of the parameters give rise to a problem whose solution will also be fuzzy as we saw in [1] and is defined by its possibility distribution, being the component of the same a fuzzy number.

In this paper we aim to find a decision vector which approximates as much as possible the fuzzy goals to the fuzzy solutions previously obtained. In order to solve this problem, we shall define an Interval Goal Programming Problem. Our proposal will be illustrated by an example.

Keywords

Multiobjective programming decision making fuzzy programming possibility distribution fuzzy number. 

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References

  1. [1]
    Arenas Parra, M.; Bilbao Terol, A.; Jiménez, M.; Rodrí guez Uría M.V., “A Fuzzy Approach to a Fuzzy Linear Goal Programming Problem”. Lectures Notes in Economics and Mathematical Systems 448: Multiple Criteria Decision Making, pp: 255–264. Springer, 1997.Google Scholar
  2. [2]
    Heilpern, S. (1992): “The expected value of a fuzzy number”, Fuzzy Sets and Systems 47 81–86.CrossRefGoogle Scholar
  3. [3]
    Ignizio, J.P.(1976): Goal Programming and Extensions, Lexington Books.Google Scholar
  4. [4]
    Jiménez M. (1994): Modelos matemáticos aplicados a la toma de decisiones financieras en condiciones de incertidumbre. Tesis Doctoral, Universidad del País Vasco, Bilbao.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • M. Arenas
    • 1
  • A. Bilbao
    • 1
  • M. V. Rodríguez
    • 1
  • M. Jiménez
    • 2
  1. 1.Dto. MatemáticasUniv. de OviedoSpain
  2. 2.Dto. Econ. Aplicada IUniv. del País VascoSpain

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