SMAA-based model for decision aiding using regret theory in discrete Z-number context

We study stochastic multi-criteria decision-aiding problems with possibilistic and probabilistic restriction information in the form of a discrete Z-number, which is regarded as the most generalized representation of uncertain but reliable real-life information. Existing multi-criteria decision-making methods dealing with inherent uncertainties, such as criteria measurements, criteria weights, and regret aversion factors, have not been simultaneously predicted on the basis of regret theory. Thus, we propose a new decision-aiding method based on stochastic multi-criteria acceptability analysis (SMAA) of the regret aversion behavior of decision makers (DM) with discrete Z-numbers. First, we construct a linear program model in the discrete Z-number context to determine the underlying probability distribution of objects. Second, we integrate the decision behavior (regret aversion) of DMs into SMAA-based models on the basis of bounded rationality and propose an SMAA-regret model for decision aiding on the basis of regret theory. We also define the central regret aversion factor, which can measure the regret aversion factor of typical DMs who favor a specific candidate. Third, we design a simulation-based interactive decision aiding system in which decision analysts guide DMs in dealing with selection issues. Finally, we provide an example by evaluating and selecting a charging facility design for electric vehicles. The rationality and validity of the proposed method are demonstrated by comparing with those of SMAA-2 and prospect theory-based SMAA.