Grey Number-based Stochastic Decision-making Method With Its Application

Abstract:The stochastic decision-making problem based on grey numbers is a description of poor information and random uncertainty in the world. Due to the complexity and the limitations of human cognition, etc., people are faced with a large number of grey stochastic multi-criteria decision making (MCDM) problems which the states perform to be certain, incomplete or uncertain, and the value of criterion is expressed with extended grey number. It is against this backdrop that some methods were provided and applied accordingly. The main work and details are as follows:(1) A discrete extended grey random variable was defined and its expected value and standard deviation were given. The possibility degree of extended grey number was defined, as well as its Hausdorff distance was introduced.(2) Grey stochastic MCDM problem with certain probability was studied in this dissertation. For this sort of problem, the expected value of each criterion was calculated firstly. Then, the distance between each alternative and positive or negative ideal solution was calculated. Finally, these alternatives were ranked according to the relative degree of closeness to positive ideal solution. In the case of bounded rationality being considered when making decision, a method of grey stochastic MCDM based prospect theory was proposed. Firstly, the paper presented a method of comparing criteria values with reference value. Combined with the results of weight function and the prospect function, the prospect value of each alternative under each criterion can be obtained. Further, we ranked those alternatives according to the comprehensive prospect value. Finally, the proposed method was compared with the expected utility method based on the same illustrative example to confirm its feasibility and rationality.(3) Grey stochastic MCDM problem with incomplete probability was discussed. For the decision-making problem with interval probability, the initial interval probability should be processed to be accurate. Then we transformed the accurate probability into point. Thus the expected value of extended grey random variable can be obtained. Next we built the outranking relations of interval grey numbers and extended grey numbers, and calculated concordance index and credibility index to obtain ranking index. Finally, ranking results can be achieved. For the decision-making problem with ordered probability, we defined criterion-regret function. The expected regret can be considered as the regret value when choosing one alternative while abandoning others. Thus the ranking of these alternatives can be obtained. In the end, the proposed method was compared with the expected utility method based on the same illustrative example to confirm its feasibility and rationality.(4) Grey stochastic MCDM problem with uncertain probability was researched. In this situation which the probability is unknown, the model of Hurwicz criterion based on extended grey numbers was proposed. Choosing the optimum solution depends on the attitude towards decision-maker, that is he or she is optimistic, or pessimism or between the former and the latter. Therefore, firstly, the value of parameter should be confirmed by the attitude towards decision-maker. Then the comprehensive utility of each alternative can be calculated by using OWA operator. At last, the ranking of these alternatives were obtained according to the comprehensive utilitv.