Study On The Analytic Methods For Grey Decision-Making

This dissertation is composed of six parts. Part 1. The analytical methods of the grey interval incidence degree and grey interval cluster for grey decision-making are studied. The incidence degree coefficient formula and relative incidence degree coefficient formula for interval grey numbers are presented, and three types of incidence degree decision-making algorithms are put forward. Grey incidence decision-making with incomplete information is researched. Firstly, an algorithm is established to deal with the inadequacy of objective weight and preferential information of decision-making. Secondly, based on the satisfactory degree, an algorithm is established for grey interval incidence decision-making in the case of project objective value with null, and then with theory and method given to fulfill the null. Finally, the grey interval clustering decision algorithm is studied. Concepts and formulas are introduced for predominance strength, relative predominance strength and predominance comparative matrix between alternatives, and then an eigenvector decision algorithm is established for the case of the unknown attribute weight and preferential information of decision-making. Examples show the rationality, practicability and validity of the algorithms presented above. Part 2. On the basis of classical grey programming, the grey dynamic programming, grey multiple objective programming and grey polynomial geometric programming are studied. Firstly, grey dynamic programming model, θ dynamic positioned programming model and the definition of their optimum solution are put forward. The grey dynamic programming algorithm and θ dynamic positioned programming algorithm are also developed. Secondly, a method to objectively determine objective weights of grey multiple objective programming is given,and whitenization weight function of sub-object for obtaining optimum values is introduced. An algorithm for obtaining optimal point of grey multiple objective programming is constructed. Finally, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are presented. At the same time, an algorithm for the problem is also developed. Examples are offered to show the rationality and validity of the algorithms presented above. Part 3. Grey risk decision-making method is discussed. Firstly, a conception of grey multi-criteria risk decision-making is offered, and the risk multi- criteria decision-making problems are studied in which criteria weights are unknown and criteria values are interval grey numbers. Two algorithms based on grey fuzzy relation and two points method are respectively given to get the priorities of alternatives. In these algorithms, criteria weights are obtained by the use of information entropy, which ensures that the algorithm confirms to objective desire. Then the definitions and investment priorities corresponding to them are given to explain efficient solution, critical optimum solution and mean whitenization optimum solution of grey portfolio selection model with transaction costs. An algorithm for grey portfolio selection model with transaction costs is presented. The given examples prove the rationality and the feasibility of the algorithms above. Part 4. Grey fuzzy relation decision-making method is discussed. Firstly, based on the grey fuzzy relation, the conception of multiple attribute decision-making is presented, and a corresponding algorithm is developed which is more precise and reliable than those methods used before since its basic weight and upper bound are directly determined by grey fuzzy decision-making matrix. Secondly, the conception of grey group decision-making is put forward and the solutions to the problem are developed as well. The feasibility of the solution is shown by the example. Thirdly, a method for multi-attribute group decision-making is presented based on the theory of grey fuzzy relation and furthermore two practical algorithms are given, in which attribute weights are known o...