Research On Methods Of Interval Number Multiple Attribute Decision Making

Multi-attribute decision making (MADM) is very important in modern decision making analysis, and its main task is, based on the gathered information, how to determine the priority vector of the alternatives. Because of the complexity and uncertainty involved in real-world decision problems and the inherent subjective nature of human judgment, during practical decision process, decision information is sometimes expressed as interval number, triangular fuzzy number, trapezoidal fuzzy number and L-R fuzzy number, and so on. Furthermore, some studies on theories, methods and application of uncertain multi-attribute decision making have attracted much attention. In this thesis, some problems of interval number multi-attribute decision making have been investigated.Firstly, the possibility degree of interval number is studied. After pointing out the imperfection of a sort of possibility degree formula of interval number, a new definition of relative superiority degree describling big or small interval numbers is given from the viewpoint of two-dimensional area, and its properties are proven. Some simple and practical formulas for calculation are presented. A numerical example is computed to explain its feasibility and practicability.Secondly, we analyze a consistent interval number complementary judgment matrix (CINCJM). A new definition of CINCJM is given and its superior properties are investigated. A construction of CINCJM and a method of ranking of alternatives are also presented.Thirdly, a consistent interval number reciprocal judgment matrix (CINRJM) of interval number multi-attribute decision making is considered. A new definition of CINRJM as well as its superior properties are given, and a construction of CINRJM is proposed.Fourthly, the weights of interval number complementary judgment matrix generated in the analytic hierarchy process are investigated. By using convex combination, a family of real complementary judgment matrices are constructed from an interval number complementary judgment matrix. The aggregation of the weights of the family of real complementary judgment matrices is considered as the weight of interval number complementary judgment matrix. In order to make any weight vector of the family of real complementary judgment matrices reliable, the sufficient and necessary conditions of their consistency and weak transitivity are given. A numerical example is also presented to illustrate the validity and practicality of the developed methods.Finally, based on preference relation of decision maker, we illustrate the method and application of interval number multi-attribute decision making. By translating an interval number reciprocal judgment matrix (INRJM) into a real complementary judgment matrix, the weight vector of the INRJM is obtained to rank the alternatives and choose the best.