区间层次分析法权重计算中的概率分布分析

Analysis on Probabilistic Distribution of Weights Calculation in the Interval-Based AHP

在区间层次分析法(IAHP)的两两比较判断中,专家不但能够给出取值范围,还能描述范围内取值的“优劣”,即区间内取值与实际情况相符的可能程度.而现有的IAHP模型不能描述区间内取值的可能性.为此,文中基于随机模拟法研究了IAHP权重计算过程中的概率分布规律.研究表明,当判断矩阵元素为平均分布和正态分布时,所求得的权重均为正态分布.权重计算对数据分布具有明显的压缩作用,经过计算,区间平均宽度显著减小,数据分布更加集中,不确定性程度减小.

In pair-wise comparison of an interval-based analytic hierarchy process (IAHP), an expert usually not only gives the range of his judgment, but also describes the fitness of each point within this range, which is the probabilities on how these points comply to the real situation. However, the regular IAHP model cannot describe the probability with an interval number. To solve this problem, research was made on the probabilistic distribution of the weights calculation in IAHP, based on the method of random simulation. It has been found that interval weights are normally distributed, whether the judgment matrix elements are homogeneously or normally distributed. The weights calculation has an obvious effect of compression on data distribution. Through the calculation, the average width of interval has decreased obviously, data has been more congregated, and the degree of uncertainty has reduced.