In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are introduced to describe the uncertainty of the decision makers. Secondly, a satisfactory solution is derived by updating the minimum satisfactory degrees with considerations of the overall satisfactory balance among all levels. In addition, the steps of the proposed method are given in this paper. Finally, numerical examples illustrate the feasibility of this method.
In this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is concerned.Using the KKT optimality conditions of the lower level problem,this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization problem.Then,a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is introduced.It is shown that the Pareto optimal solutions(stationary points)of the approximate problems converge to a Pareto optimal solution(stationary point)of the original bilevel multiobjective programming problem.Numerical results showing the viability of the smoothing approach are reported.
