不确定性多属性决策的新方法

A New Approach fo Uncertain Multiple Attribute Decision Making

本文研究了属性指标值,属性权重为L-R模糊数的多属性决策问题,首先在不同的α水平下将L-R模糊数转化为区间数,基于优化模型求出方案的区间属性值并利用α-截及区间数序关系的可能度,构造互补判断矩阵。提出一种新的排序公式,得到一族排序向量,然后对不同α水平下的排序向量集结,得出总的排序向量,以此对方案排序,最后通过实例说明了该方法的可行性和有效性。

The multiple attribute decision making is researched in this paper, in which the elements in attribute values matrix and attribute weights are supposed as L-R fuzzy numbers. Firstly, L-R fuzzy numbers are transformed into interval numbers under different α-levels. Synthetic values （in the form of interval numbers） of alternatives are obtained by solving the optimism models. Complementary judgment matrix is built based on α-levels and its ordering and possibility. A new formula of ranking is proposed and a family of weight vector is obtained. Then a total ranking vector is acquired by aggravating different vectors under different α-levels. Then the alternatives can be ordered based on this total vector. Finally a numerical example is given to demonstrate the feasibility and efficiency of this approach.