Research On A Class Of Stochastic Multi-Criteria Decision Making Model

Multi-criteria decision making(MCDM)refers to the evaluation and selection among multiple alternative.Multi-criteria decision making process involves many participants,including decision analyst(DA)and decision maker(DM).In the multi-criteria decisionmaking process,the information used by decision-makers needs to be unambiguous in operation to ensure the good operation of MCDM system.However,in the realistic evaluation process,the lack of accurate preference and weight information is a common problem.In practical problems,the loss or uncertainty of various information such as criteria value,criteria weight and decision-maker’s preference can easily lead to the failure of decision-making process.Based on these reasons,this paper introduces a stochastic multi-criteria decision-making method that can deal with random variables and preference information.The purpose of stochastic multi-criteria decision making is to solve the problem that there is no accurate criteria value or weight in the evaluation process.Stochastic multi-criteria acceptability analysis(SMAA)model is a multi-criteria decision making model for Stochastic data environment.By selecting criteria values and weight vectors in the form of stochastic variables for many times,the acceptability of each individual is calculated and the evaluation results are obtained.Based on SMAA model,this paper studies several key issues,such as the construction of utility function,the definition of preference space,and the treatment of risk variables.The specific contents are as follows:(1)SMAA model is combined with the aggregation method of VIKOR model to calculate the group profit value and individual regret value to obtain the basic utility function,which solves the problem that the original SMAA model only uses simple weights and aggregation indicators to cause inaccurate evaluation results.Meanwhile,the definition of VIKOR compromise solution which can be applied to SMAA model is proposed.Decision makers can use the compromise solution to form a mixed strategy to solve the consequences caused by decision failure in random data environment.(2)The preference space of decision-maker’s preference for gain and loss is defined by prospect theory and the utility function of TODIM model,which replaces expected utility theory in the original model.Defining the utility of decision-maker in different decisionmaking scenarios depends on the difference between the individual value of evaluation based on the reference value point of the corresponding index.At the same time,in view of the gain or loss of the relative reference point,it causes different utility effects on decision-maker,which solves the problem of inaccurate definition of decision-maker preference information in the decision-making process.(3)This paper proposes a definition of risk preference based on frame effect,which adjusts the utility value of random variables according to their different performances under different risk preference backgrounds,quantifies the considerations of different decision-makers in assessing alternative risk,and solves the problem of alternative instability or risk preference in probability distribution.