判断矩阵的区间权向量及其方案排序

Interval weight vector of judgment matrix and ranking of the alternatives

针对当层次分析法中判断矩阵不满足一致性时,特征根法等传统方法导出的权向量只能近似反映排序结果,有时甚至可能出错的问题,通过建立线性规划模型求解判断矩阵的区间权向量,结果更具柔性.定义了一种反映决策者满意度的区间数序关系,基于该序关系将所有方案进行充分排序.最后给出算例.

When a judgment matrix is inconsistent in the analytic hierarchy process, the weight vector educed from it by traditional methods such as eigenvalue method can only reflect an approximate sort result. Sometimes the result may be even error. Aimed at this problem, an interval weight vector is obtained from the judgment matrix through a linear programming model. As a result, the solution becomes more flexible. In the following an order relation between interval numbers is proposed which reflects the decision maker's satisfaction with the order. Based on this a full ranking is made on all the alternatives. Finally an example is given.