A fuzzy multiobjective program with quasiconcave membership functions and fuzzy coefficients

A method is proposed for solving a fuzzy multi-objective linear programming problem (FMP) with quasiconcave membership functions and fuzzy coefficients. The proposed method first expresses a piecewise function as the summation of absolute terms. Then we search for the interval where the optimal solution is allocated by finding the corresponding points with same value of membership functions. After that, the problem is solved by goal programming techniques. Comparing with other FMP methods, the proposed method does not need to add extra zero-one variables, to divide the original problem into several sub-problems, or transforming all original quasiconcave functions into concave functions. In addition, the proposed method could solve a FMP problem with fuzzy coefficients to obtain a solution closing to a global optimum.