Analytic hierarchical process with stochastic uncertainty: A case study of governmental audits in China

Abstract

Techniques for collecting preferences in the framework of analytical hierarchy process (AHP) have been widely developed. But the resultant uncertainty has not been paid sufficient attention. A stochastic AHP is proposed based on theoretical development. The development is driven by a practical case regarding the evaluations in China’s governmental audits, in which the collected opinions are with high uncertainty degrees and low consistency indices. First of all, the proposed process measures uncertainty degrees within the pair-wise comparisons based on their variances, checks the uncertainty degrees of a stochastic comparison matrix (SCM) based on random uncertainty degrees. For uncertainty reduction, an algorithm is proposed to re-estimate the probabilistic distributions of the entries whose uncertainty degrees are not acceptable. Then, the consistency of a SCM is measured by its similarity to an ideal comparison matrix. Priority vector of a set of SCMs is then obtained by programming models which maximize the consistency indices. Quantitative comparisons clarify that the proposed process is supported by interesting theoretical properties, provides admissible results due to the consideration of uncertainties, outputs interpretable results which could be easily understood and accepted by experts.