Study On The Ranking Algorithms Of Weight Vectors, Consistency And Compatibility Of Judgement Matrices

The Analytic Hierarchy Process (AHP) was proposed in the 1970's by Dr Thomas Saaty, who is an Operations Research professor in American. AHP is an approach of multi-objective decision making systems, which can deal with the problems of transforming complex correlative relations to quantitative analysis in economy and society. This approach is highly regarded for its characters, such as system, flexible, terseness and practicality, and is widely used in economy and society.There are five chapters work on it.In the first chapter,we mainly introduce the origin and current research situations of ranking algorithm,consistency and compatibility of judgement matrices.Furthermore,the main contribution of this paper is also listed.In the second chapter,first,we introduce a ranking algorithm of interval judgement matrix proposed by L.Mikhailov(2003),then verify that the algorithm has a defect in theory. We can prove that the upper and the lower triangular judgments will lead to distinctive priorities if this algorithm is used. An improved method is proposed. At last, a new method of consistent correction for interval judgment matrix and two number examples are given.In the third chapter,on the base of minimizing the maximum of the judgment deviation, a priority model of a positive reciprocal matrix is presented, and the properties of the model are explored. Then an aggregation model of group decision included positive reciprocal matrices (positive complementary matrices) is given. As a result, a integrate aggregation model of group decision with two preference information is proposed.In the fourth chapter, we first propose a compatibility index of measuring interval numbers, and generalize the index to measure compatibility of two numbers among triangular fuzzy number, interval number and certain number. On the base of the index, we propose an index of measuring compatibility of two matrices with same or different style of judgement numbers. A criterion to measure the compatibility of judgement matrices is provided and an numerical example is also given.In the last chapter, we present two approaches to determine the weights of experts. The first one is to make use of the correlation of interval judgment matrices, and the second one is to make use of the consistence of the interval judgment matrices. Then the two results are integrated by means of the convex combination.