A fuzzy multilevel programming method for hierarchical decision making

This paper describes a fuzzy programming method for multilevel programming problems in a large hierarchical decision making organization. In the proposed approach, first the objectives at different decision making units are described fuzzily by setting an imprecise aspiration level to each of them. Then the defined fuzzy goals for the objective functions and the control vectors of the upper-level units are characterized by membership functions for measuring the degree of satisfaction of the decision makers located at different hierarchical levels. In the solution process, a linear programming formulation of the problem for minimizing the group regret of degree of dissatisfaction of the decision makers using the distance function is considered first. Then the linear programming problem is transformed into a priority based fuzzy goal programming problem to achieve the most satisfactory decision for overall benefit of the organization. To illustrate the approach, a numerical example studied [1] previously is solved and compared the solution with the conventional [1, 11] approaches.