A Novel Framework to Group Decision Making Problems With Interval Multiplicative Preference Relations by Using Stochastic Simulation

Group decision making (GDM) problems with interval multiplicative preference relations (IMPRs) contain uncertain preference information from the decision makers (DMs). To help the DMs make decision quickly and accurately, this article proposes a novel framework to GDM problems with IMPRs by combining the ELECTRE III method with stochastic simulation. First, the stochastic multiplicative preference relations are derived by stochastic simulation, then the individual stochastic priority vector and the group stochastic priority matrix are defined. Second, the group stochastic net credibility degree is presented to evaluate all alternatives. Third, several optimal group measurements are proposed, including the group stochastic rank acceptability degree, the optimal preference rank, the group stochastic central weight vector, and the group stochastic optimal confidence factor. Moreover, a novel framework for GDM problems with IMPRs is put forward by using the stochastic simulation with the ELECTRE III method. The proposed approach retains the initial opinions of DMs and reduces the influence of DMs’ subjectivity, besides considers the ranking possibility of all alternatives from an expected perspective. Finally, a medicine decision example of Wilson disease is analyzed, comparison analysis and sensitivity analysis are conducted to verify the validity and feasibility of the proposed approach.