Stochastic Group Preference Analysis Framework for Interval Multiplicative Preference Relations

In group decision making (GDM), preferences are typically treated as fixed values by conventional approaches when handling interval multiplicative preference relations (IMPRs), thereby ignoring the stochastic characteristics of preference relations and resulting in the loss of original information. To account for the stochastic and dynamic characteristics of preference relations, this paper introduces a stochastic group preference analysis framework for IMPRs based on preference ranking organization method for enrichment evaluations II (PROMETHEE II). Specifically, stochastic multiplicative preference relations (MPRs) are extracted from IMPRs using a specific density function, and a stochastic priority preference comprehensive matrix is constructed by preference priority weight vectors which are determined using the eigenvector method. Moreover, an algorithm for calculating the stochastic net outranking flow is designed to synthesize the preferences of decision makers (DMs), and the stochastic preference relation judgment space is derived using Monte Carlo simulation. Then, additional analyses are conducted to ascertain the stochastic preference ranking acceptability index and the expected rank confidence degree, ultimately deriving the optimal preference ranking. Furthermore, the stochastic group preference analysis framework is proposed to deal with GDM with IMPRs. Finally, the validity and feasibility of the proposed method are demonstrated through a numerical example and comparison analyses.