Research The Priority Theory Of Interval Numbers, Triangular Fuzzy Numbers And Their Judgment Matrices

The analytic hierarchy process (AHP) was introduced in middle 1970s by American professor T.L.Saaty, who made researches on Operations Analysis in Pittsburgh University. It is a very practical multi-criterion decision making method which combines the quality and the quantity and is widely applied in society, economics and lives etc. During the decision making, the experts usually give fuzzy and uncertain judgment since the complexity, vagueness of the real decision problems and the influence of people's knowledge structure and information master situation. In 1965, L.A. Zadeh professor proposed the fuzzy set notion, created the research theory methods of fuzzy or uncertainty problems, which has been widely used in application, decision making, management science and has become a matured branch of mathematics. It is an important research direction of model decision problems that fuzzy set theory is applied in the analytic hierarchy process, which composed the fuzzy analytic hierarchy process. The theory and method of the fuzzy analytic hierarchy process decision is an important decision branch in model decision area, which is more reality and effectiveness. The usual theory and method of fuzzy analytic hierarchy process decision main about the weighted vector priority problems of judgment matrix, which elements are interval numbers and triangular fuzzy numbers.In this paper, the theory and the priority method of interval numbers, triangular fuzzy numbers and their judgment matrices are analyzed and studied. The main research works are as follows:The home and abroad recent researches and existence problems of interval numbers, triangular fuzzy numbers and their judgment matrices are roughly stated and analyzed, and the main research contents are involved.On the theory of possibility degree, a new priority method of interval numbers is proposed; On the basis of the consistency of interval numbers complementary judgment matrix, two new priority methods of its complementary judgment matrix are proposed; Which are compared with the existence methods, the advantage of the new methods is given by discussion and analysis of examplesOn the theory of possibility degree, a new priority method of triangular fuzzy numbers is proposed; On the thought of ideal point; two new priority methods of triangular fuzzy numbers are proposed; On the theory ofα- cut set, two new priority methods of triangular fuzzy numbers are proposed; On the basis of distance formula, two new priority methods of triangular fuzzy numbers are proposed. All the above methods are discussed or given examples.The priority theory and method of triangular fuzzy numbers of reciprocal, complementary judgment matrix and multiple attribute group decision making are discussed, a new priority method is given respectively which is compared with the existence methods, the advantage of the new methods is given by comparison and analysis of examplesIn the end, the research works are summarized, and some new ideas about the research on interval numbers, triangular fuzzy numbers and their complementary judgment matrices are proposed.