A Multi-criteria Decision Making Method Based On SMAA And Vine Copula

With the rapid development of the economy,there are more and more factors that decision makers need to consider in decision-making,and close relationship may exist between these factors,so that it is impossible to draw conclusions through simple di-rect comparison.Stochastic Multi-Criteria Acceptability Analysis(SMAA)is a series of methods for multi-objective decision making that are used to give decision-making suggestion in questions where the decision maker's preferences are uncertain or missing.In these problems,the measurement uncertainty of the decision variables and the partial or missing preference information can be expressed by a variety of probability distri-bution.In many real-world problems,dependency exists between the measurement uncertainties of decision variables.However,most existing methods are not effective when handling this kind of dependency information so that when applying stochastic multi-criteria acceptability analysis,the results may not have sufficient scientific basis.However,the Copula function is a useful tool for describing the dependencies between variables and has been widely used in financial risk analysis,but it is rarely seen in multi-objective decision making analysis.From this point on,in this paper,the copula dependency analysis is combined with the stochastic multi-criteria decision analysis methods,using vine copula modeling methods to describe the uncertainty of decision variables and their dependencies.Based on the simulation experiment,we fit the joint probability distribution of the decision variables and quantify their uncertainty and their dependency.Then,the SMAA-2 method is applied to evaluate the utility of the alter-native based on the joint distribution.Finally,for other methods of dealing with the dependency relationship that have appeared in the literature,we conducted compara-tive analysis and compared their advantages and disadvantages.