Decision Making with Uncertain Judgments: A Stochastic Formulation of the Analytic Hierarchy Process*
针对层次分析法中判断可能出错的问题，提出用加权分层多项逻辑模型和贝叶斯推断来推导优先级，结果与特征向量法一致，且能给出对决策者有用的推断性陈述。
ABSTRACT In the analytic hierarchy process (AHP), priorities are derived via a deterministic method, the eigenvalue decomposition. However, judgments may be subject to error. A stochastic characterization of the pairwise comparison judgment task is provided and statistical models are introduced for deriving the underlying priorities. Specifically, a weighted hierarchical multinomial logit model is used to obtain the priorities. Inference is then conducted from the Bayesian viewpoint using Markov chain Monte Carlo methods. The stochastic methods are found to give results that are congruent with those of the eigenvector method in matrices of different sizes and different levels of inconsistency. Moreover, inferential statements can be made about the priorities when the stochastic approach is adopted, and these statements may be of considerable value to a decision maker. The methods described are fully compatible with judgments from the standard version of AHP and can be used to construct a stochastic formulation of it.