A fuzzy multiobjective program with quasiconcave membership functions and fuzzy coefficients

Zimmermann has shown that the fuzzy multi-objective program (FMOP) can be reduced to a standard linear program. While a linear membership function allows an easy conversion of FMOP into a linear programming problem, it should be obvious that such a function may be unsuitable for certain problems. It is generally admitted that membership functions are most likely nonlinear. One of the promising methods of linearizing nonlinear membership functions is the piecewise linear programming. However, the conventional methods require using complicated ways to represent a general piecewise membership function in FMOP. This always involves a dramatic increase in the number of constraints and may cause heavy computational burden when the number of break points becomes large. In this study an efficient piecewise linearization method for solving FMOP is proposed. The proposed method has the following features: (i) it expresses a general piecewise linear membership function more efficiently; (ii) fewer binary variables are used. The computational experiments are provided to demonstrate the superiority of the proposed models. The illustrative examples are also provided to show the usefulness of the proposed method.