SOLVING FUZZY GOAL PROGRAMMING PROBLEMS

M. Jiménez, M Arenas, A. Bilbao and M. V. Rodríguez Uría
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M. Jiménez: Universidad del País Vasco
M. V. Rodríguez Uría: Universidad de Oviedo

Fuzzy Economic Review, 2004, vol. IX, issue 1, 19-33

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

Keywords: goal programming; fuzzy mathematical programming; nonlinear membership function; piecewise linear function; decision analysis. (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:fzy:fuzeco:v:ix:y:2004:i:1:p:19-33

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