The Research On Scale Systems Of AHP

The analytic hierarchy process (AHP) was put forward by professor T.L.Saaty in 1970s. AHP is simple and effective, so it is applied more and more widely. The scale system is one of the core issues in AHP. The new scale system's proposition and the relation between the scale system and the ranking method are studied in this thesis.The main work and innovations of this thesis are as follows:Firstly, from the psychological perspective, the mathematical expression of psychological space corresponding to the existing reciprocal scale system is discussed through an example. At the same time the process of forming scale system according to the psychophysics law is given. Furthermore a new reciprocal scale system and a new multiplicative complementary scale system according to S.S.Steven's power law are proposed as examples.Secondly, according to the multiplicative consistency, the expression of the element of multiplicative fuzzy complementary judgment matrix is obtained from the functional relation between the subjective judgment and the relative weightiness of the objects. In addition the feasibility to generate the relative weightiness of elements by multiplicative consistency fuzzy complementary judgment matrix is demonstrated.Thirdly, the existing scale systems and ranking methods are classified. In addition a method for ranking based on multiplicative consistency fuzzy complementary judgment matrix and a ranking method to the judgment matrix constructed with the new interval scale system are put forward.The main significances of the results of this thesis are as follows:Firstly, the study on the new scale systems standardizes the steps proposed scale systems, and will help the scientific scale systems proposition.Secondly, the classification of the scale system and the ranking method makes them applied consistently, which facilitates the decision-makers on the use of the scale system and the ranking method.