Study On The Consistency And The Solving Method For Weight Vector Of The Judgment Matrices

The Analytic Hierarchy Process (AHP) was proposed in the 1970's by Dr Thomas Saaty, who is an Operations Research professor of the University of Pittsburgh in America. AHP is an approach of multi-criteria decision making systems, for its combination of qualitative and quantitative factors to deal with the characteristics of the decision-making, as well as the advantage of system, simple, flexible, practicality, it has been widely used in the socio-economic fields. In the decision-making process, the decision-makers need to analyze the alternatives and express their pairwise comparison information in the judgment matrices.The paper mainly study on the consistency and the solving method for weight vector of the judgment matrices, there are four chapters work on it.In the first chapter, we mainly introduce the development of AHP history, application steps, the development and research situation of the consistency and the solving method for weight vector of the judgment matrices at home and abroad. Furthermore, the main contribution of thispaper is also listed.In the second chapter, we mainly discuss the consistency of the crisp preference relations(including multiplicative preference relations and fuzzy reciprocal preference relations).first, we introduce the concepts and properties as well as the test method of consistency of the crisp preference relations, then, the transformation relations between the multiplicative preference relations and fuzzy Reciprocal preference relations is given, at last, we design a method for improving the consistence of the judgment matrix based on the property of the fuzzy consistent judgment matrix. A numerical example is shown to illustrate the proposed method.In the third chapter, we first introduce the solving method of the fuzzy reciprocal judgment matrix, then we discuss the properties of the interval reciprocal matrix, a theorem of transforming a interval reciprocal judgment matrix into a fuzzy consistent matrix is given, based on this theorem, a new method on solving the weight vector of the interval reciprocal matrix is given.In the last chapter, We first introduce current research on group decision making, mainly focus on the aggregation method when decision makers give different types of preference relations, then We extend the OWA operator and the OWG operator to the C-OWA and the C-OWG operator respectively, using the C-OWA and the C-OWG operator as tools, We conform the interval fuzzy preference relation and the interval multiplicative preference relation into fuzzy preference relation and the multiplicative preference relation, then the ranking vector on alternatives of every decision maker can be obtained, at last, We aggregate the decision makers' ranking vector into a ranking vector as result of group decision making, in the approach ,We fully considered the decision maker's risk attitude. A numerical example is given to illustrate the feasible and practicability of the approach.