On unfeasible fuzzy goal programming problems

In a Fuzzy goal programming problem (FGP), it is possible that the tolerance thresholds fixed by the decision maker (DM) for the different fuzzy goals were to be incompatible, therefore obtaining an unfeasible problem. In this case the DM doesn´t know the amount in which the tolerance thresholds have been surpassed and, so, neither which changes should be introduced in his aspiration levels to obtain an acceptable solution. To avoid this drawback, we propose to consider the fuzzy goal membership functions as piecewise defined including all the values that surpass the tolerance threshold, which logically have a satisfaction degree equal to 0. This way a problem that before was unfeasible becomes feasible, although, logically, the optimal solution will have an aggregate degree of satisfaction equal to 0. This solution can be used as a reference by the DM to decide how much the aspiration levels should be changed in order to obtain a satisfying solution.