Stochastic Multi-criteria Decision Making Method Based On Prospect Theory Research

Stochastic multi-criteria decision-making problem is an important research field of uncertain, and is widely applied in engineering design, economy management, and military affairs. For the fuzziness of the world and lack of knowledge, a number of stochastic multi-criteria decision making problems exist where the criteria value of alternatives are stochastic variable and the criteria weight and the decision maker’s subjective preferences are uncertain. Consequently, the decision maker can not make decision completely rational under uncertain circumstances. At present, there are few literatures focused on these problems. Therefore, it is necessary to explore theories and methods for stochastic multi-criteria making problems. Based on the previous research about stochastic multi-criteria problems and prospect theory, this study aims to explore the methods for stochastic multi-criteria with the consideration of the preferences of decision maker’s subjective risk. The main results are as follows:Stochastic multi-criteria decision-making problems that the decision information from the same period or stage arestudied. According to different decision making situations, three methods are proposed with the consideration of preferences of decision-maker’s subjective risk:(1) For stochastic problems in which the criteria weight is known and the value of criteria was discrete stochastic variable, a method is suggested based on the judgment matrix. Firstly, all the stochastic variables of the same criterion can be compared with each other to construct judgment matrixes of all criteria. Then, the comprehensive judgment matrix is calculated by aggregation operator. Finally, the alternatives are sorted according to Promethee Ⅱ.(2) For problems that the criteria weight is uncertain and the criteria values are normally distributed, a new method is developed based on the degree of closeness. The prospect value is calculated with the given distribution functions. Then, an optimal model is constructed to get the weight of criteria.Finally, the alternatives are ranked with the degree of closeness. (3) Another method is proposed based on the prospect theory that the criteria weight is unknown and part of the criteria values are missing. BayesBoostrap method is firstly employed to stimulate the empirical distribution function and the prospect values are computed with distribution functions. Then, criteria weight is determined based on information entropy. Finally, the alternatives are sorted according to the comprehensive prospect value.Then, stochastic multi-criteria decision-making problems that the decision information from different periods or stages are explored. Bsed on the decision maker’s risk preferences, the uncertainty during decision making process is quantified.(1)A new method based on prospect theory and stochastic dominance is proposed for decision-making problems that the level of decision maker’s preferences is derived by double threshold. Firstly, calculate the prospect values of different periods in line with given distribution functions. Then, obtain the weight of time series by normally distribution and aggregate the prospect value of different periods with aggregation operations. Furthermore, an optimal model based on maximizing deviation method is constructed to get the optimal criteria weight. Finally, the stochastic dominance of different alternatives is determined by stochastic dominant rules, and then the alternatives are sorted by ELECTRE III.(2) As for the dynamic stochastic problems that the criteria weight is partly unknown and the criteria values are in the form of random distribution variables, a method is proposed combined prospect theory and conjoint analysis. First, compute the prospect value of different periods with distribution functions. Then, calculate the weights of time series by exponential distribution and integrate values by aggregation operator. Finally, the criteria weights are determined by conjoint analysis and the comprehensive prospect value can be got, thus sorted the alternatives in a descending sequence.(3) For the problems that the criteria weight is completely unknown, a new method is developed based on the prospect theory and set pair analysis. Firstly, the prospect values of alternatives are calculated on all criteria at different periods. Secondly, the time series weight is derived based on the binomial distribution probability density function. The criteria weight is ascertained by the algorithm of maximizing deviation. Then, the concepts of identity degree, contrary degree, set pair potential is employed and thus the order of alternatives can be determined consequently. Finally, an example of risk investment illustrates the effectiveness of this method.In addition, the feasibility, effectiveness, and science of above mentioned methods are verified with corresponding instances. The results could provide useful references for application in practice.