Based On The Continuous Grey Multi-criteria Decision Making Method Of A Random Variable

With the grey system theory putting forward, some scholars began to study the multi-criteria decision making problems which’s criteria values criteria are both grey and random. So far studies about this kind of problem are still few, and the existed studies are only considering discrete grey random multi-criteria decision problems. But in real life, some criteria for decision making are difficult to divide into limited natural states, so it can only be expressed as a continuous random variable. And due to the Changeable external environment and many unknown factors, any event cannot be repeated under exactly the same conditions, exact probability under ideal laboratory conditions also will lose its meaning in real life. So for about a continuous random variable to represent the criteria values, sometimes decision-makers can only give a range in values of probability with a interval gray number. It is necessary to study the issue of continuous gray random multi-criteria decision making problems.On the basis of researches about the current domestic, international situation of relevant multi-criteria decision-making research, and the lastest achievements of research on methods for random multi-criteria decision-making, grey multi-criteria decision-making are extended to handle the problems in the domain of continuous grey random multi-criteria decision-making.Some approaches or models are proposed to solve the corresponding problems. And the details are as follows:(1) With regard to grey random uncertain MCDM problems, in which the criteria weights are complete and the criteria value of alternatives are in the form of continuous gray random numbers, we give two decision-making methods based on dominance analysis. Stochastic dominance analysis doesn’t need to set the exact utility function, and just need to know some information about utility functions to conduct a comparative analysis. So it’s more suitable for random multi-criteria decision-making. But for any two random variables, maybe there are no stochastic dominance relations between then, almost stochastic dominance can be solutions to the problem of lack of dominance relations, and the probability dominance is complementary to almost stochastic dominance. In this paper, we propose two kinds of decision-making methods by combining probability dominance and almost stochastic dominance. The first method applies the almost stochastic dominances and probability dominance to the outranking method. The valued outranking relations between the alternatives are obtained. The ranking index of every alternative according to which the alternatives are ranked is calculated through the valued outranking relations. Another method applies the almost stochastic dominances and probability dominance to the Priority intensity function to get every alternative’s superiority flow and inferiority flow. Then using every alternative’s superiority flow and inferiority flow to calculate the net flow,with which the alternatives are ranked.(2) With regard to grey random uncertain MCDM problems, in which the criteria weights are incomplete and the criteria value of alternatives are in the form of continuous gray random numbers, we give two decision-making methods based on relation analysis. Grey relation analysis is commonly used in multi-criteria decision making problems. But the traditional grey relation degree in general is positive, and it does not fully reflect the relationships between things, because there may be a negative correlation between things, so this article will propose an improved gray relation analysis, which can fully reflected the relationship between things.(3) With regard to grey random uncertain MCGDM problems, in which the criteria weights are incomplete and the criteria value of alternatives are in the form of continuous gray random numbers, we give two decision-making methods based on Grey Stochastic Multi-criteria Acceptability Analysis. The first method combines PROMETHE Ⅱ method with SMAA-2method. First calculated each alternative’s integrated priority values and rank acceptability index, then calculated each alternative’s holistic acceptability indices based on the rank acceptability index. The ranking with of alternatives appears with the help of rank acceptability index. Another method combines prospect theory with SMAA-2method.First each alternative’s prospect values and rank acceptability index are calculated, then calculated each alternative’s holistic acceptability indices based on the rank acceptability index are calculated. The ranking of alternatives appears with the help of rank acceptability index.