Study On Approximate Consistency Of Interval Additive Reciprocal Matrices And Its Related Problems

With the rapid development of social economy,the environments of decision-making are becoming more and more complex.The study of decision-making problems has increasingly become the focus of modern science.When using the analytic hierarchy process to solve decision problems,decision-makers(experts)usually need to give a preference relation by comparing of alternatives in pairs.However,with the complexity and uncertainty of the considered problems,the decision-making information in the actual decision-making process is expressed more reasonable by fuzzy numbers such as interval numbers and others.Moreover,in the decision-making process,decision-makers may not be able to provide complete entries of interval-valued preference relations due to the lack of experience or expertise.Therefore,it is very important how to deal with the lack of information in interval-valued preference relations.This thesis mainly analyzes the consistency of interval additive reciprocal matrices and its related problems.The main conclusions are summarized as follows:(1)The definition of additive consistency is discussed.Based on the study of the additive consistency of interval additive reciprocal matrices,three axiomatic properties are proposed to characterize the consistency of interval additive reciprocal matrices.The existing definitions of interval additive reciprocal matrices with additive consistency has been reviewed based on this three axiomatic properties.A new concept of additive approximate consistency of interval additive reciprocal matrices is proposed and some properties are studied.(2)The method of obtaining weight is studied.In order to reduce the number of test consistency,a novel exchange method is proposed to enumerate all permutations of alternatives,and a new method of obtaining interval weight is given by considering the permutations of alternatives.A new algorithm is given to solving the decision-making problem with interval additive reciprocal matrices.This new algorithm is illustrated by two numerical examples.(3)The method of complementing the incomplete information is considered.Based on the additive approximation-consistency of the interval additive reciprocal matrices,a goal programming model is proposed to estimate the missing values of the,incomplete interval additive reciprocal matrices.And a new algorithm is given to solve the decision-making problem with incomplete interval additive reciprocal matrices.The obtained results have overcome the shortcoming of the consistency definitions of interval additive reciprocal matrices.Some new definitions and decision making models have been made.The observations have enriched the theory and methodology of decision making.