Approximate resolution of an imprecise goal programming model with nonlinear membership functions

被引:8
作者
Jiménez, M
Arenas, M
Bilbao, A
Uría, MVR
机构
[1] Univ Basque Country, Dept Appl Econ 1, San Sebastian 20018, Spain
[2] Univ Oviedo, Dept Quantitat Econ, Oviedo, Spain
关键词
multiple criteria evaluation; goal programming; fuzzy mathematical programming; fuzzy goal satisfaction; integer linear programming; decision analysis;
D O I
10.1016/j.fss.2004.05.001
中图分类号
TP301 [理论、方法];
学科分类号
081202 [计算机软件与理论];
摘要
In standard goal programming (GP) it is assumed that the decision maker (DM) is able to determine goal values accurately. This is unrealistic; usually DM expresses his/her aspirations in an imprecise way. The imprecise nature of the DM's judgments has led to an important development of the fuzzy multiobjective approaches. In this paper, we will assume that the DM's goals may be expressed through fuzzy sets and therefore we deal with an imprecise goal programming (IGP). Determining the membership functions that represent the fuzzy 'goals of the DM use to be a difficult task and it is necessary to fit them in the sense of being robust, hence, some results on sensibility analysis are established. We show that small changes in membership functions produce small differences on the DM's global satisfaction degree and on the efficient frontier. On the other hand, when membership functions are nonlinear. IGP becomes a nonlinear program that may be difficult to solve. This difficulty may be overcome by approximating each nonlinear fuzzy membership function through functions belonging to a class of simpler/easier functions. In this paper, based on the sensibility analysis that we develop, we prove the goodness of subrogated functions. An illustrative example is also provided. (C) 2004 Elsevier B.V. All rights reserved.
引用
收藏
页码:129 / 145
页数:17
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