Research On Method And Application Of Grey Taget Decision Making

Grey target decision making method is an important part of grey system theory, and it is widely used in many areas, such as society, economics, management and military. Although grey target decision making methods have achieved some achievements, there are many fields about theory and application for improvement. With the development of the society, decision making problems are becoming more and more complicated, information collection is becoming more and more difficult, which make the information is uncertain. This dissertation depicts the uncertain by grey numbers, and systematically studies the grey target decision making methods under grey numbers, expands the decision making method to multi-dimensional data sequences, and widens the application range.The main research results are summarized as follows:(1) Study on ranking method, distance measure of grey numbers. Based on the principle of information persisting, the projection rule from ordinary interval grey numbers to standard grey numbers in universe of discourse [0,1] is designed. Moreover, the concepts of relative kernel and degree of accuracy are put forward aiming at standard grey number. And then, the new ranking method and distance measure of grey numbers are presented. Moreover, a new method of the possibility ranking method based on gravity center, midpoint, and the length of three-parameter interval numbers is proposed. Then, the distance formula of three-parameter numbers is established according to the most likely appearing characteristic of gravity center.(2) Study on dynamic grey target decision making method based on grey number information. Comprehensively considering the existing state in every stage and change trend of alternatives in the whole period, the dynamic grey target decision making methods with grey numbers and three-parameter grey numbers are proposed based on the concepts of approaching degree and bull’s-eye distance. For dynamic risk decision-making problems, considering the decision maker’s risk attitude, prospect matrixes are calculated by using the average value of all attributes’ values as the preference point. Every attribute’s weight is obtained from a programming model based on the maximum entropy based on the comprehensive prospect matrix. Furthermore, the new ellipsoid grey target models are constructed, then the distances between every project and ideal, unsatisfactory target-center are computed, which are aggregated to comprehensive ones to rank projects.(3) Study on group decision making method based on grey number information. Firstly, a method to obtain the attribute weights based on intrinsic relationship of attributes and information distribution is proposed. Then, three different methods to obtain the decision makers’ weights are put forward based on group consistency requirements, characteristics of uncertain information, and the effect of maxmam and minimum evaluation on deviation of the decision results. For the phenomenon that every decision maker has an expected grey target about every attribute, the prospect value functions of alternatives’ attributes are defined letting the expected grey target, the zero point under the linear operator with the features of the “Rewarding good and punishing bad ” be the reference points, separately. Consequently, two different grey target methods based on prospect theory are presented. Finally, the alternatives hit the bull’s eye or not are judged by the comprehensive prospect values.(4) Study on dynamic group grey target decision making method based on grey number information. For the psychological behavior that every decision maker has an expected grey target about every attribute, a grey target decision making method is presented based on prospect theory. Furthermore, weight model of stages, which is based on the principle of new information priority, the requirement of stable fluctuations of alternatives, and charicaratics of information distribution, is suggested. Meanwhile, weight model of decision makers, which is based on the requirement of difference of alternatives and the maximum entropy principle, is suggested. Finally, the alternatives which hit the bull’s eye are judged by the comprehensive prospect values.(5) Study on matrix grey target decision making model based on multi-dimensional data sequences. The grey target decision making models are extended to 3-dimentional space and 4-dimentional space. In 3-dimentional space, the data of alternatives in other two number axes are represented by matrices, the ideal and unsatisfactory bull’s eye matrix is composed of the corresponding optimal and worst values. In 4-dimentional space, the data of alternatives in other three number axes are represented by set of matrices, the ideal and unsatisfactory bull’s eye matrices of attributes are composed of the corresponding optimal and worst attribute values. The bull’s eye deviation degrees of alternatives in 3-dimentional space, bull’s eye deviation degrees of attributes of alternatives in 4-dimentional space are both defined by matrix norm. Finally, the ranking of alternatives is obtained by comprehensive bull’s eye deviation degree.(6) Study on application of grey target decision making method in selection of component suppliers of complex equipment. The evaluation index system of component suppliers of complex equipment is established aiming at the characteristics of complex equipment, and then the component suppliers of complex equipment are evaluated by dynamic group grey target decision making method from two aspects about the existing state of alternatives in every stage and change trend of alternatives in the whole period. Finally, the evaluation of component suppliers combining both the two aspects are carried out based on the decision maker’s emphasis on the different aspects.