Dissertation > Mathematical sciences and chemical > Mathematics > Operations Research > An integrated approach

Consistent Problem about Linguistic Judgement Matrix

Author ZhangZhiGang
Tutor LiJiQian
School Qufu Normal University
Course Operational Research and Cybernetics
Keywords Analytic Hierarchy Process Linguistic Judgment Matrix Fuzzy Judgment Matrix Consistency Satisfying Consistency Priority
CLC O223
Type Master's thesis
Year 2009
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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 American.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 satisfying consistency of the judgment matrices,there are three 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 this paper is also listed.In the second chapter,I have studied the consistency of addition and ranking problem based on linguistic judgment matrix.Based on the related concepts of fuzzy judgment matrix and linguistic judgment matrix,it puts forward the concepts of the addition consistency about linguistic judgment matrix.Then,transforming judgment matrix with linguistic assessment information into digital matrix through introducing the educed matrix,we can judge the consistency of the linguistic matrix according to the way of judging the educed matrices.At the same time,group decision-making can also apply this method.Finally,some numerical example was given to illustrate the use of the proposed in this paper.In the third chapter,firstly,a concept called ordinal linguistic judgment matrix is presented and it is proven that any satisfying consistency linguistic judgment matrix.Then,the properties of the shadow matrix of ordinal linguistic judgment matrix are analyzed and the priority method is proposed based on these properties.In the end,illustrative examples are given to show that this method is not only simple and practical,but also more coincident with experts.

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