Research On Decision-making Models And Applications Based On Grey Number Information

Along with the development of social and economic, in which decision making environment is becoming more and more complex, and because of the complexity and uncertainty of the actual problems as well as the limitations of human knowledge, then the decision-making information is usually small sample and poor information that is partial information known and the other unknown. In this case, the value of evaluated object is usually grey number, and then the decision-making problem that contains a grey number or general model and grey model is called grey decision-making problem. In recent years, the decision-making method and model with grey information have made a lot of research results, and have been widely used in the social, economic, and military and other fields, but there is still certain research space for further development. With regard to multi-attribute decision-making problems with grey information, this paper have studied from the differences and interaction of evaluation attribute sets, weight discrimination degree, the risk decision making, information fusion. It can provide new ideas, new methods for grey decision-making technique expand the range of application, enrich the grey decision-making system.The main research contents of dissertation and research results are as follows:(1) Research on multiple attribute decision-making problem with interval grey number. Fristly, with regard to the differences of evaluation attribute sets, the concept of grey soft set was defined, and the modeling method was proposed based on grey soft set and proves the weights of synthesis attributes set. Secondly, considering interaction of attribute set, the discrete Choquet integral of degree of greyness of interval grey number is defined, and some of its properties are investigated, and then the optimization model based on the discrete Choquet integral of interval grey number. Finaly, aim at risk decision-making problem under interval grey number information, TODIM method is introduced into the multiple attribute decision making problem under interval grey number information combined with random dominant, then a improved TODIM method is proposed by analysising insufficient of the classic TODIM method.(2) Research on multiple attribute decision-making problem with three-parameter interval grey number. Fristly, according to the characteristics of the classic gray correlation analysis, the grey relative correlation coefficient of the alternative with respect to ideal optimal alternative evaluation vector is defined, and then a multi-index grey-target decision-making approach based on grey relative entropy is proposed. Secondly, the point bull’s-eye distance of the alternative with respect to positive and negative bull’s-eye under a certain attributes is defined, and the optimization model is established based on point bull’s-eye distance by using D-S evidence theory to reduce the uncertainty of decision results. Thirdly, the grey relative correlation coefficient of the alternative with respect to critical alternative evaluation vector is defined, and the prospect value function is defined based on the grey relative correlation coefficient, and a multi-attribute optimization model which satisfies maximum integrated grey prospect value relative can be built to solve the optimal weight vector. Finaly, taking into account the problem that the dispersion of index objective weights derived from entropy weighting method is not high, a normalized decision matrix method based on adjusting coefficient was proposed, and the optimizing entropy model was established to determine the index objective weights. The mean area method was applied to convert index subjective weights into real number, and the D-S combination rule was utilized to integrate the subjective and objective weights into comprehensive weights, then a multi-index grey-target decision-making approach based on adjustment coefficient.(3) Research on risk type dynamic multiple attribute decision making problems with grey number. Fristly, with regard to risk type dynamic multi-attribute decision-making problems, in which the attribute values of the alternatives are interval grey number, an optimized model based on entropy and time degree is built to determine time weight. Considering that the risk attitude of policy-makers often has an impact on multi-attribute decision making, the prospect value function is determined, an optimization model with reference to each other is established to calculate optimal weight vector, then risk type dynamic multiple attribute decision making model with interval grey number is put forward. Secondly, with regard to risk type dynamic multi-attribute decision-making problems, in which the attribute value of alternatives are three-parameter interval grey number,considering the previous distance formula of three-parameters interval grey number can’t reflect the characteristics of the three-parameters interval grey numbers gravity point and risk preference of decision makers facing risk, the distance measure and ranking method of three-parameters interval grey numbers is defined.In view of differences and volatility of the evaluation objects in the timing, an optimized model based on variance and time degree is built to determine time weight; the prospect value function is determined with reference to each other alternatives, and a multi-index optimization model can be built to solve the optimum weight vector, then risk type dynamic multiple attribute decision making model with three-parameter interval grey number is put forward.(4) Taking improve TODIM method as the basic tool, the evaluation problem of haze weather of five cities in the south of Jiangsu is studied, and according to the results of evaluation, the rationality of the evaluation results is analysised from the data, the condition of air quality, the main source of haze to provide theoretical basis for the governance haze weather.