An interactive fuzzy satisficing method for multiobjective optimal controlproblems in linear distributed-parameter systems

In this paper, we propose an interactive fuzzy satisficing method for the s olution of a multiobjective optimal control problem in a linear distributed -parameter system governed by a heat conduction equation. In order to reduc e the control problem of this distributed-parameter system to an approximat e multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. By considering th e vague nature of human judgements, we assume that the decision maker may h ave fuzzy goals for the objective functions. Having elicited the correspond ing linear membership functions through the interaction with the decision m aker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minima x problems. Then a linear programming-based interactive fuzzy satisficing m ethod for deriving a satisficing solution for the decision maker efficientl y from a Pareto optimal solution set is presented. An illustrative numerica l example is worked out to indicate the efficiency of the proposed method. (C) 1999 Elsevier Science B.V. All rights reserved.