模糊线性规划的最优解

On Optimal Soltion of Fuzzy Linear Programming

本文说明模糊线性规划的模糊优越集C_f,在一般情况下是去掉端点x^((0))的线段。在线段上有且只有一个模糊线性规划问题的最优解。最后提出了解模糊线性规划的一个比较简便的算法。根据本文的结论,可以证明Zimmermann算法的最优值因此,Zimmermann算法的最后一步可简单地用代替,从而节省了大量的计算工作量。[3]指出,当模糊判决用乘法或凸组合运算时,导出的规划往往是非线性的,求解比较困难。然而,用本文的结论,问题能容易地得到解决。

In this paper, it will be proved that the optimal point set C_f of fuzzy linear programming is a segment missed end x^((1)) There is one and only one point x~* which is the optimal solution of fuzzy linear programming in this segment. Finally, a relative simple algorithm used to solve fuzzy linear programming will be introduced.According to results of this paper, it can be proved that the optimal value λ~* in Zimmermann's algorithm [3] is equivalent to 1/2 For this reason the last stage of Zimmermann's algorithm could be replaced with λ~*=1/2 briefly.[3] has pointed out that a nonlinear programming will always be obtained when the multiplication or the convex combination is adopted in fuzzy decision. It is a problem difficult enough to solve it. Using the results of this paper, however, it could be solved easily.