Double stochastic preference analysis on group decision making with interval additive preference relations

Abstract

Interval additive preference relations (IAPRs) provide a valuable framework for representing uncertain pairwise comparisons among alternatives in group decision-making (GDM). Conventional GDM methods that incorporate IAPRs often treat preference values as uniform entities and establish dedicated conflict or consensus mechanisms for amalgamating individual opinions while overlooking the stochastic preferences and lacking the flexibility to address diverse decision requirements. Therefore, to account for the stochastic characteristics in both preference representation and group preference aggregation, this paper introduces an innovative double stochastic preference analysis for GDM with IAPRs. In the initial phase, stochastic additive preference relations are extracted from IAPRs using a specific density function. A best preference matrix is then constructed through a logarithmic consistency minimum deviation model. In the second phase, preference comparison intervals are synthesized to encapsulate the collective viewpoints of decision-makers. Subsequently, ranking acceptability indices and preference confidence degrees are computed through processing of the preference ranking judgment space, leading to the derivation of the final preference rankings. The experimental results, obtained through Monte Carlo simulations for a site selection case in Anhui Province, China, demonstrate the effectiveness and validity of the proposed method. The ranking results achieved a confidence degree exceeding 89%, offering insights into decision-makers’ weight distribution for various ranking scenarios.