An interactive fuzzy satisfying method for multiobjective optimal control problems in linear distributed-parameter systems

摘要

In this paper, we propose an interactive fuzzy satisfying method for the solution of a multi objective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order to reduce the control problem of this distributed-parameter system to an approximate multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. 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 Parrot optimal solution can be obtained by solving the minimal problems. Then a linear programming-based interactive fuzzy satisfying method for deriving a satisfying solution for the decision maker efficiently from a Parrot optimal solution set is presented. An illustrative numerical example is worked out to indicate the efficiency of the proposed method.