Abstract
In this paper, we propose an interactive fuzzy satisficing method for the solution of multiobjective optimal control problems in one-dimensional linear stationary distributed-parameter systems controlled by boundary control functions. In order to reduce the control problem of this distributed-parameter system to approximate multiobjective linear programming problems, we use a numerical integration formula and introduce the suitable auxiliary variables.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 the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker effiviently from a Pareto optimal solution set is presented. An illustrative numerical example is worked out to indicate the effeciency of the proposed method.
