On the sensitivity of membership functions for fuzzy linear programming problems

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, modeling 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 show the convenience of using linear functions instead of other more complicated ones.