Linear programming with fuzzy constraints based on nonlinear membership function

In this article, a new kind of method is proposed for solving linear programming (LP) problem with fuzzy constraints whose membership function are nonlinear. Firstly, a new target set is defined to characterize the optimal solution in fuzzy environment and some advantages of the new definition are presented. Secondly, through study the location of the fuzzy decision under the new target set, the fuzzy decision λ_* ≥ 0.5 is pointed out for several common nonlinear membership functions. Finally, an algorithm for solving fuzzy linear programming (FLP) is given, as well as the validity of the new target set is illustrated by numerical examples.