The Study Of Several Types Of Uncertain Multiple Attribute Decision Making Problems

The multiple attribute decision making(MADM) problem is an important part of modern decision making science. Its theory and methods have been widely applied in engineering, economics, management, military and others, such as, investment decision making, item evaluation, optimizing alternatives, selecting the address of factory, comprehensive evaluating on economic results and so on. MADM is using the available information to rank the alternatives and select the optimal one. Because of the complexity, uncertainty and the fuzziness of man's thinking, uncertain MADM problems attract more and more scholars and researchers. Many problems remained to be solved, there are needed to research MADM problem in broad fields.Several types of MADM problems are studied in this paper. The main content and achievement are following.1 MADM background and recent research achievements are introduced.2 Some operational laws of linguistic variables are defined. Some new aggregation operators are proposed. We introduce linguistic induced ordered weighted geometric averaging (LIOWG) operator, uncertain linguistic induced ordered weighted averaging (ULIOWA) operator, generalizing linguistic ordered weighted averaging (GLOWA) operator, generalizing uncertain ordered weighted averaging (GUOWA) operator and uncertain induced ordered weighted geometric averaging(UIOWGA) operator. The properties of the operators are studied. We also give the ranking methods based on these operators.3 By making use of fuzzy numbers and analytic hierarchy process, we propose a fuzzy AHP method. With the possibility of triangular fuzzy number comparing, we can compute the importance of element to its upper level element. We can rank the alternatives according to the overall attributes values.4 We analyze the shortcoming of the computation of triangular fuzzy numbers. It does not use all the information available. We propose a method to compute triangular fuzzy number by using the equality constraints. We combine the method with AHP to giv a constrained fuzzy analytic hierarchy process method.5 The numerical examples are to demonstrate the effectiveness and the feasibility of the algorithm.