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On the sensitivity of membership functions for fuzzy linear programming problems. (English) Zbl 0804.90137

Summary: For a fuzzy linear programming problem it is usually assumed that the decision-maker exactly knows the shape of the membership functions taking part in it. For the sake of simplicity often linear membership functions are supposed, but this seems a poor reason. Here it is shown that in the case of fuzzy linear programming problems, whether or not a fuzzy optimal solution has been found by using linear membership functions modelling the constraints, possible further changes of those membership functions do not affect the former optimal solution. This sensitivity analysis performed for those membership functions and the corresponding solutions shows the convenience of using linear functions instead of other more complicated ones.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C05 Linear programming
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References:

[1] Delgado, M.; Verdegay, J. L.; Vila, M. A., A general model for fuzzy linear programming, Fuzzy Sets and Systems, 29, 21-29 (1989) · Zbl 0662.90049
[2] Garcia-Aguado, C., Sensitivity of the membership functions for optimization problems with fuzzy constraints, (Thesis (1990), Universidad de Granada) · Zbl 0804.90137
[3] Hamacher, H.; Leberling, H.; Zimmermann, H. J., Sensitivity analysis in fuzzy linear programming, Fuzzy Sets and Systems, 1, 269-281 (1978) · Zbl 0408.90051
[4] Verdegay, J. L., Fuzzy mathematical programming, (Gupta, M. M.; Sanchez, E., Fuzzy Information and Decision Processes (1982), North-Holland: North-Holland Amsterdam), 231-237 · Zbl 0504.90056
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