Study Of Probability To Determine The Gray Randomized, Multi-criteria Decision Making Approach

Grey random multi-criteria decision-making problem is a subdivision of stochastic multi-criteria decision-making problem and it can be used to describe some decision-making problems in the social and economic activities more properly. Briefly speaking, it is the kind of multi-criteria problem in which evaluations of alternatives with respect to criteria are in the form of grey random variables, and how to select, rank or classify the alternatives is the focus of the problems. Because of the grey indeterminacy and random indeterminacy in the real practice of decision-making, it is normal that the evaluations of alternatives are grey random variables and some information of the decision-making factors, such as the weights and the preference given by the decision-maker, may be incomplete. As for these problems, rare literatures are focused. Therefore, the academic value of systemic research on theory or methods for grey random multi-criteria decision-making is worthy. In practical application, stochastic department can apply those approaches, so it can assist relevant managers in making decision more scientifically and improving risk management quality more significantly. Therefore, they are of great application value.Based on comprehensive research on the current domestic and international situation of relevant multi-criteria decision-making research, and for some situations in which the evaluations of alternatives under each criterion are interval grey numbers with certain probabilities, there exists the problem wihich can be concluded as probability-known grey random multi-criteria decision-making problem, and one type grey random variable can be defined. Then the latest achievements of research on methods for grey system theory and multi-criteria decision-making are extended to handle the problems in the domain of grey random multi-criteria decision-making, and approaches or models are proposed correspondingly. At the end, these methods are all applied effectively to solve the according problems. The main productions are organized as follows:(1) One discrete grey random variable, which will be called grey random variable for short in the rest of the dissertation, is defined, and its probability density function, expected value and standard deviation are also defined according to operation laws of interval grey number. On the basis of comparison rules for interval grey number, the probability distribution function of grey random variable is defined and corresponding properties are studied.(2)Applying the expected utility theory is the first major way to deal with the problems in grey random multi-criteria decision-making in the third chapter of this paper. As for these problems with completely certain weights and grey random variable type value of alternatives with respect to criteria, the corresponding standard expected value is calculated to substitute as the evaluation value for each alternative under the criteria firstly. And then a standard expected value decision-making matrix can be formed. Finally, the order of the alternatives can be listed by using the calculation method of probability degree of interval grey numbers. Considering the multi-criteria decision-making problems with completely unknown weights and the grey random variable type value of alternatives, the evaluation value of each alternative under every criterion is replaced by the expected value of grey random variable firstly. And then after calculating the grey relation indexes of every alternative with respect to the ideal scheme, the total deviations of grey relation indexes of all alternatives under every criterion can be attained. Based on the maximizing deviations principle, an optimal programming model can be enacted to get the weights. Finally, the order of the alternatives can be listed by using grey relation analysis method.(3)Extending the stochastic dominance is the second major way to handle the problems in the fourth chapter of this paper. With respect to the grey random multi-criteria problems with completely certain weights and grey random variable type value of alternatives, the stochastic dominance method is combined effectively with the SIR method at the first beginning. Secondly, after taking generalized criterion into account, superiority matrix and inferiority matrix for the alternatives can be attained. Finally, the order of the alternatives can be listed by comparing the superiority flow and the inferiority flow of each alternative. With regard to the problems with completely unknown weights and grey random variable type value of alternatives, stochastic dominance method and PROMETHEEⅡmethod are integrated firstly. Secondly, multi-criteria preference indexes for the alternatives can be attained by transforming the stochastic dominance relation for every pair of alternatives. And then a multi-objective optimization model, which is based on the maximum of satisfying degree of each alternative, can be enacted to get the weights. Finally, the order of the alternatives can be listed.(4) Introducing the complementary judgment matrix is the last but not the least major way to work out the grey random multi-criteria decision-making problems in the fifth chapter of this paper. As far as these problems are concerned, which has incompletely certain weights and grey random variable type value of alternatives under the criteria, the expected probability degree is defined and its meaning studied at the beginning. Then the expected probability judgment matrix is defined, and some properties of the judgment matrix are studied. Following these definitions, the evaluation value of alternatives can be transformed to comprise the judgment matrix, based on which a non-linear programming model can be enacted. At the end, the genetic algorithm is used to solve the model to attain the criteria weights, and the order of alternatives can be listed consequently.