Research On Order Method And Multi-attribute Decision Making

Order relation is one of the basis for decision making analysis, in the decision making analysis, an object for comparison and ordering are frequently encountered, which is an order relation from the viewpoint of the relationship. The various order relations and axiomatized order theories promoted by linear order play an important role in some practical problems. With the emergence of a wide variety of nonlinear problems in management science, biology, economics, engineering, mathematics and so on, nonlinear analysis has become one of the most important researches in modern science, while the partial order method, one of the basic method to research nonlinear problems, plays a very important role.In this dissertation, there are some important new results by studying on the order methods and multi-attribute decision making. The main contents are as follows:The first chapter introduces the historical background, current situation and the required prior knowledge in this dissertation about the partial order in nonlinear analysis and multi-attribute decision making; describes the main issues of this study and research significance of this dissertation.The second chapter describes the main order relations in mathematics and economic management science and the nature of these order relations; the relationship between the cone and partial order, wedge and quasi-order are described in this chapter.Chapter three studies some nonlinear operator problems with the order methods. First of all, there comes to the corresponding fixed point theorems through studying the existence of fixed points for nonlinear operator with partial order method. Then, it proposes the new concept of n times reasonable expansive operator and discusses its existence of fixed points to get some new fixed point theorems, promoting some important conclusions. At last, it conducts a discussion on the existence of solutions of a class of nonlinear equations with partial order method and monotone iterative technique and studys their Min-max solution and Max-min solution.The fourth chapter addresses the relationship between the wedge and quasi-preferences, and studies the existence of solutions to a class of operator equations and problems about set-valued increasing operator with the sense of quasi-preferences.Chapter five defines the Risk Ordered Weighted Averaging (R-OWA) operator and the Risk Ordered Weighted Geometric Averaging (R-OWGA) operator and their properties are discussed. At the same time, it studies a new method of the risk multi-attribute decision making based on ordered information integration operator.Chapter six gives the new concepts of the preference dominating relational index and the preference be dominated relational index in preference structure based on the distance between the preference relations and on this basis this chapter studies multi-attribute decision making method with the only ordinal information.Chapter seven studies the rank preference optimal ordering method in the multi-attribute decision making. This chapter first describes the optimal ordering method and puts forward the concept of rank preferences correlation coefficient, then proposes the rank preference optimal ordering method by using rank preferences dominating correlation coefficient instead of the precedence order number in optimal ordering method. The rank preference optimal ordering method was achieved on the computer, therefore makes the method to play a significant role in solving practical decision problems. Finally, the studies on the expansion of the rank preference optimal ordering method are carried out.Chapter eight sets up a lectotype decision model of retaining & protecting structures for deep foundation pit by use of the rank preference optimal ordering method. Using the rank preference optimal ordering method, the base case indexing model is proposed. In the model, the degree of similarity between the base case and the target case of deep foundation pit is obtained by the Hamming distance in order to find the deep foundation pit base case which is the most similar to the target case in the base cases of deep foundation pit. The retaining & protecting structure of the deep foundation pit base case which is the most similar to the target case in the base cases of deep foundation pit shall be the priority structure that can be considered for the terget case. The engineering example presented in this chapter proves that the lectotype decision model of retaining & protecting structures is reliable and applicable.Chapter nine sums up the main content in this dissertation and the main conclusions then puts forward the need for further refinement and in-depth research directions in the future.