Case study on a multi-sample problem in AHP

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  • AHPにおける多標本問題に関する研究
  • AHP ニ ヨル タヒョウホン モンダイ ニ カンスル ケンキュウ
  • AHP ニ オケル タヒョウホン モンダイ ニ カンスル ケンキュウ

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Abstract

AHP (Analytic Hierarchy Process) is a tool for making a decision of one group or a project team that has several alternative plans on some particular subject. Usually, in applying AHP, a data set is given as a paired comparison matrix, and a decision is made through one weight vector coming from the first eigenvector of the given paired comparison matrix. However, when we have a lot of decisions with respect to many groups or many individuals on the same subject, we need to classify those decisions, that is, relevant weight vectors into small classes that have similar tendencies. In other words, this is a classification problem of weight vectors in a simplex. Our concern is to study a notion of closeness or similarity between weight vectors. In the present paper, using real data sets of weight vectors on some subject, we define various distances between weight vectors and examine classifications given by distances of different kinds. We also use directly real paired comparison matrices to define several distances between paired comparison matrices and give classification results. Finally, we compare classifications based on weight vectors with those based on paired comparison matrices

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