A stochastic AHP decision making methodology for imprecise preferences

Existing decision making methodologies like the Analytic Hierarchy Process (AHP) address imprecise pairwise comparisons by modeling crisp pairwise comparisons as fuzzy sets or a single type of probability distribution (e.g., uniform, triangular). However, one common issue faced by decision makers (DMs) is bounded rationality. That is, DMs have limited cognitive powers in specifying their preferences over multiple pairwise comparisons. This result to crisp as well as imprecise pairwise comparisons. Furthermore, given the ultimate goal of imprecise AHP is to make the decision, computing weights for the criteria and the alternatives from the imprecise preferences is a must. Hence, these various types of pairwise comparisons must be modeled using a single probability distribution for easy computation of the weights. In this research, a beta distribution is proposed to model the varying stochastic preferences of the DM. The method-of-moments methodology is used to fit the varying stochastic preferences of the DM into beta stochastic pairwise comparisons since it can represent a wide variety of probability distributions. Additionally, a non-linear programming model is then developed that calculates weights which maximize the preferences of the DM while maintaining a level of consistency. Comparison experiments are conducted using datasets collected from literature to validate the proposed methodology.