A fuzzy satisficing method for multiobjective linear optimal control problems

In this paper, we propose ct fuzzy satisficing method for the solution of multiobjective linear continuous optimal control problems. To solve these multiobjective linear continuous optimal control problems, we first discretize the time and replace the system of differential equations by difference equations. By introducing suitable auxiliary variables, approximate linear multiobjective programming problems are formulated. Then by considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if we adopt the fuzzy decision for combining them, it is shown that the formulated problem can be reduced to a linear programming problem and the satisficing solution for the decision maker can be obtained through the simplex method of linear programming. An Illustrative numerical example is provided to indicate the efficiency of the proposed method.