区间层次分析法的权重求解方法初探

为综合比较各种区间层次分析法的权重求解方法,通过对计算结果的定性分析和定量比较,对其中5种方法的精度以及在综合评判决策中的适用性作出了评价,并指出其在实际中应用的原则。实际综合评判决策多为离线计算,对每个判断矩阵都可调用多种方法计算权重及其误差,取误差最小的权重作为结果。针对以往文献中迭代算法的缺陷提出了改进方法;研究了随机模拟法中样本容量与精度的关系及分布规律;分析了LM模型无解的原因并给出了相应的处理方法,并提出了LM模型是否存在可行解可作为区间判断矩阵一致性校验的一种方法。

Exploration on the methods of weight calculation in the interval-based AHP

For comparing the accuracies of different methods of weight calculation in interval-based analytic hierarchy process (IAHP), five methods are studied. By comparison and analysis of the results, accuracy of these methods is evaluated and the principle of applying different methods to practical multi-attribute decision-making (MADM) is concluded. In case of off-time MADM, various algorithms can be invoked and the weights with the minimal error will be the final results. In addition, some improvements are made to increase the accuracey of the iteration algorithm. As to random simulation method, the relationship between accuracy and sample capacity and the rules of probability distribution are studied. In addition, the reason that the lower model (LM) algorithm has no solution in some cases is found; and a method to avoid this situation is also proposed. It has been shown that whether the LM has a solution is a new method to determine the consistence of a judgment matrix.