The Similar-Consistency Of The Judgment Matrix In Uncertain AHP And The Modified IEM Arithmetic

The Analytic Hierarchy Process (AHP) presented by T.L.Saaty in 1970s has been applied widely in various fields for decision-making for its 30 years development. In recent years with more and more research about it the theory of AHP has been proved to have some limitation as well as its application. The AHP in uncertain condition and group AHP are hot topics in research field interesting scholars.In this paper, we put forward the concept of similar-consistency of the judgment matrix in uncertain AHP and based on the similar-consistency modify the IEM arithmetic that has been applied widely, and then a new method of calculating the interval number eigenvalue is provided. After the proven by a numeric example we can obviously find the rationality and simpleness of the method. In the last part of the paper, the theory of group decision is combined with AHP that we apply the aggregation method of Hadamard convex-combination in interval number judgment matrices that can be proved theoretically to make the integration interval number judgment matrix have the property of satisfying consistency.The research combined the uncertain AHP and the theory of group decision has not been given much attention. The paper will accelerate the combination of these two research fields from a new point of view as well as provide the theory foundation for the development of AHP applying to other science fields.