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 tak ing part in it. For the sake of simplicity often linear membership fun ctions are supposed, but this seems a poor reason. Here it is shown th at in the case of fuzzy linear programming problems, whether or not a fuzzy optimal solution has been found by using linear membership funct ions modeling the constraints, possible further changes of those membe rship functions do not affect the former optimal solution. This sensit ivity analysis performed for those membership functions and the corres ponding solutions shows the convenience of using linear functions inst ead of other more complicated ones.