Research On Inconsistency Index Of Interval Comparison Matrix And Its Application In Group Decision Making

In daily lives,one is always faced with many decision-making(DM)problems.With the development of society and economy,the decision-making environment becomes more and more complicated.The decision-making problems under complex environment have attracted much attention.Analyt-ic Hierarchy Process(AHP)provides a feasible theory framework to simulate and solve the problem of complex decision-making problems.The processes of DM include information collection,analysis,synthesis and selection of the best alternative.The consistency of judgment matrix is one of the importan-t topics of AHP and an important reference index of information synthesis.This thesis mainly studies the inconsistency indexes of interval multiplicative and additive reciprocal comparison matrices and their application in group decision-making(GDM).The main work and novelties are summarized as follows:(1)The research on inconsistency index of interval multiplicative recip-rocal matrices and its application in GDM.The inconsistency index of the interval multiplicative reciprocal comparison matrix is analyzed,and check whether they remain variant under different permutations of alternatives when compared in pairs.Based on the concept of approximate consistency of in-terval multiplicative reciprocal matrices,a new inconsistency index which re-mains invariant under permutations of alternati'ves is proposed and its prop-erties are studied.Based on the new inconsistency index,a new aggrega-tion operator is formed.Furthermore,the relation between the approximate consistency of the individual matrix and the synthesis matrix is investigated.A novel GDM arithmetic with interval multiplicative reciprocal comparison matrices is established.(2)The research on inconsistency index of interval additive reciprocal matrices and its application in GDM are studied.The existing inconsistency index of interval additive reciprocal matrices is analyzed.Considering the permutations of alternatives,a novel inconsistency index is proposed and it-s properties are studied in detail.Based on the new inconsistency index,a new aggregation operator and algorithm are proposed and its properties are studied in detail.A new GDM arithmetic with interval additive reciprocal matrices is constructed.The above works are involving of the new inconsistency indexes,over-coming the shortcoming of the existing inconsistency indexes of interval mul-tiplicative and additive reciprocal matrices.Novel aggregation operators and GDM arithmetics are proposed,which can enrich and develop decision mak-ing theory and methods under complex environments.