1994 Volume 6 Issue 6 Pages 1202-1210
In this paper, we propose a fuzzy programming method for the solution of multiobjective linear continuous optimal control problems. When a system of differential equations is linear, the state variables of the system at any fixed time are described by definite integrals, whose integrand is linear in the control functions. Upon use of a suitable numerical integration formula, each of the definite integrals is approximately replaced by a weighted sum of a finite number of variables, we can formulate approximate linear multiobjective programming problems. 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 worked out to indicate the efficiency of the proposed method.
