Analysis on probabilistic distribution of weights calculation in the interval-based analytic hierarchy process

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.