Stochastic Multi-criteria Decision-making Model With Grey Information And Its Applications

In the actual decision-making process,people are faced with a large number of decision making problems that the coexistence of greyness and randomness,owing to the ambiguity of the things themselves,the complexity of environment,the limitations of human cognition,etc..At present,there are few researches on grey stochastic multi-criteria decision-making problems.Therefore,it is of great theoretical and practical significance to study grey stochastic multi-criteria decision-making problems with different grey information.The main results of this paper are as follows:(1)For the stochastic multi-criteria decision-making problems in which the criterion value and the state probability are the interval grey numbers,the criterion weight coefficient is not completely determines,we use prospect theory to obtain the prospect matrix.On this basis,we define the three-unit connection number of the standard interval grey number based on the set pair analysis.The optimization model is established and solved,and the optimal scheme is obtained by comparing the values of the closeness of the alternative schemes with respect to the positive ideal scheme.Then,a grey stochastic multi-criteria decision-making model with interval grey number is established.(2)For the dynamic stochastic multi-criteria decision-making problems in which the criterion values are three-parameter interval grey numbers and criteria have different natural states,we combine Markov Chain theory with the importance of old and new information to deal with dynamic time information.In order to reduce the influence of interactive interference of information between decisions on decision-making results,the “matching” idea is used to construct an optimization model.Then,a grey stochastic multi-criteria decision-making model with three-parameter interval grey number is established.(3)For the stochastic multi-criteria decision-making problems with grey heterogeneous data,we give the definition of degree of greyness of extended grey number and grey heterogeneous data sets.On this basis,the kernel vector and degree of greyness vector of grey heterogeneous data are defined according to the principle of information utilization and combining with the common characteristics of grey heterogeneous data.Then,the consistency coefficient geometric plane die length sorting method and the relative compromise distance sorting method are constructed.Then,a grey stochastic multi-criteria decision-making model with grey heterogeneity data is established.(4)For the grey stochastic multi-criteria decision-making problems with multi-source heterogeneous data,we construct the K-G space according to the common characteristics of multi-source heterogeneous data information.The mapping transformation rule of the multi-source heterogeneous criterion values in K-G space is proposed.On this basis,the heterogeneous degree of incidence is given.And the optimization model is constructed to obtain structurally the criterion weights,which makes the decision result more practical.Then,a grey stochastic multi-criteria decision-making model with multi-source heterogeneous data is established.(5)The above new models are applied to the assessment of drought resistance,the drought risk assessment and the drought vulnerability risk management respectively in Henan Province.Then,the results test the rationality,scientificity and effectiveness of these models.