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Solving Fuzzy Goal Programming Problems

Author

Listed:
  • Jiménez, M.

    (Universidad del País Vasco)

  • Arenas, M
  • Bilbao, A.
  • Rodríguez Uría, M. V.

    (Universidad de Oviedo)

Abstract

In standard goal programming (GP) it is assumed that the decision maker (DM) is able to accurately determine goal values. This is unrealistic. Imprecise DM aspiration can be expressed through fuzzy sets whose membership functions represent the DM´s degree of satisfaction. When membership functi-ons are nonlinear, the model becomes a nonlinear program that may be difficult to solve. Due to imprecise context normally the DM is not able to accurately determine the fuzzy goals membership functions. We show that few changes in membership functions produce small differences on the DM´s global satisfaction degree and on the efficient frontier. Based on these results, in this paper we present a procedure to approach the nonlinear fuzzy membership functions, whatever its shape might be, through piecewise linear functions which supply an standard goal linear programming problem that, obviously, is easier to solve than the nonlinear original one. An illustrative example is also provided

Suggested Citation

  • Jiménez, M. & Arenas, M & Bilbao, A. & Rodríguez Uría, M. V., 2004. "Solving Fuzzy Goal Programming Problems," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 0(1), pages 19-33, May.
    • Handle: RePEc:fzy:fuzeco:v:ix:y:2004:i:1:p:19-33
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    Cited by:

    1. Bermudez, J.D. & Segura, J.V. & Vercher, E., 2006. "A decision support system methodology for forecasting of time series based on soft computing," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 177-191, November.

    More about this item

    Keywords

    goal programming; fuzzy mathematical programming; nonlinear membership function; piecewise linear function; decision analysis.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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