Abstract: Stochastic multi-criteria acceptability analysis (SMAA) is a series of methods for multicriteria decision making. It is used to give decision opinions on the problem of uncertain or missing preferences of decision makers, the uncertainty of decision variables and incomplete or missing preference information can be represented by probability distribution. This method improves the past methods by considering inversely what specific parameters each decision outcome is determined by. However, the existing SMAA methods does not take into account the impact of the interdependence between these variables on the analysis results, or simply using a simple model such as a Gaussian distribution to describe these interdependencies, so that the analysis results do not have sufficient scientific basis. In order to fix this fault, this paper create an innovation by combining copula dependency analysis with stochastic multi-criteria acceptability analysis method, and uses vine copula modeling method to describe the uncertainty of decision variables and their interdependence, making the SMAA method complete and more effective. This paper introduces the basic methods of SMAA and vine copula separately, and gives the specific steps of combining the two methods. In simulation experiments, a comparative analysis is conducted between the original SMAA method and the method given in the paper to show their advantages and disadvantages under different dependency structures.

Key words: decision-making analysis, stochastic multi-criteria acceptability analysis (SMAA), dependency, copula, vines