Solving fuzzy goal programming problems

In standard goal programming (GP) it is assumed that the decision maker (DM) is able to accurately determine goal values. This is unrealistic. Imprecise DM aspiration can be expressed through fuzzy sets whose membership functions represent the DM's degree of satisfaction. When membership functions are nonlinear, the model becomes a nonlinear program that may be difficult to solve. Due to imprecise context normally the DM is not able to accurately determine the fuzzy goals membership functions. We show that few changes in membership functions produce small differences on the DM's global satisfaction degree and on the efficient frontier. Based on these results, in this paper we present a procedure to approach the nonlinear fuzzy membership functions, whatever its shape might be, through piecewise linear functions which supply a standard goal linear programming problem that, obviously, is easier to solve than the nonlinear original one. An illustrative example is also provided.