多目标线性规划的模糊折衷算法

通过推广求解多目标线性规划问题的平均算子法,提出了多目标线性规划的模糊折衷算法,证明了多目标线性规划的模糊折衷算法求得的解是有效解.此外,提出了多目标线性规划的两阶段算法,即:若多目标线性规划的模糊折衷算法指定的最小满意度不恰当,则可能会导致交互过程复杂化;若用最小算子法求得的解作为多目标线性规划模糊折衷算法中决策者指定的目标函数最小满意度,则可能使多目标线性规划的模糊折衷算法的计算量减小,另一方面能够弥补最大(最小)算子法求得的解可能为非有效解的不足.此外,用实例验证了多目标线性规划两阶段算法求得的解为有效解.

Fuzzy compromise method for multiobjective linear programming problems

In this paper, average operator approach for solving multiple objective linear programming problems, i.e., fuzzy compromise approach, was deduced, and the efficient solution obtained by fuzzy compromise approach was proved. When the minimum satisfaction degree of objective funciton chosen by decision-maker is too great, it will lead to the result of no solution. Though minimum satisfaction degree for getting feasible solution, i.e. fuzzy efficient solution, can be adjusted, it sometimes makes the process of interaction more complicated. Two-phase approach on the basis of fuzzy compromise approach and max-min operator was proposed.