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A Statistical Testing of the Consistency Index in Analytic Hierarchy Process

계층적 의사결정론에서 일관성 지수에 대한 통계적 검정

  • Received : 2013.11.15
  • Accepted : 2013.12.02
  • Published : 2014.02.28

Abstract

Significant research has been devoted to the consistency index of the Analytic Hierarchy Process(AHP) from several perspectives. Critics of the consistency index in AHP state that the critical value of consistency index depends on an average of the random index based simulation study using a 9 scale comparison matrix. We found that the distribution of the consistency index followed the skew distribution according to the dimension of the comparison matrix based on a simulation study with a 9 scale comparison matrix. From the simulation study, we suggest a consistency index quantile table to assist the decision-making process in AHP; in addition, we can approximate the distribution of the consistency index to the gamma distribution under the limited assumptions.

계층적 의사결정론(AHP)에서 응답자의 신뢰성을 평가하기 위해 일관성 지수가 활용된다. 일반적으로 일관성 지수값이 0에 근접할 수록 신뢰성이 있다고 판단되나, 신뢰성에 대한 임계값은 9점 척도의 비교행렬로 부터 모의실험 된 무작위 지수의 평균에 의존한다. 본 연구에서는 9점 척도 비교행렬에 의한 모의실험 분포가 차원별로 치우침이 심한 분포라는 점에 기초하여, 차원별 일관성 지수의 분위수에 기초한 통계적 가설검정 방법을 소개하기로 한다. 그리고, 모의실험으로 계산된 일관성 지수의 분포에 따라 적절한 임계 분위값을 제공하였다. 또한, 쌍대비교행렬의 각 원소에 오차를 고려한 모형을 적용하여, 일관성 지수의 분포를 감마분포로 특수한 경우 근사시킬 수 있음을 제시하였다.

Keywords

Acknowledgement

Supported by : 한국연구재단

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