Earticle

초록

한국어

본 연구는 기존연구의 잘못된 주장 - 계층분석과정(Analytic Hierarchy Process: AHP)은 그 적용과정에서 무차별 기준(대안간 차이가 없는 기준)의 추가/삭제로 인하여 대안들간 기존 순위의 변경(순위 역전 현상)이 발생하는 문제점이 있음 – 을 바로 잡는데 그 목적이 있다. 이는 결과적으로 대안평가에서 기준의 중요도와 기준에 따른 각 대안의 성과를 종합하는 과정에서 잘못된 결론에 도달하는 사태를 피하고자 함이다. 본 연구의 논리 전개는 AHP 공리에 그 기초를 두고 있는데 관련된 공리는 첫째, 올바른 결과를 기대하기 위해서는 관련된 사항들이 모두 고려되어야 한다는 점(고려사항의 완전성)과 둘째, 계층 구성에서 동일 계층의 구성인자들은 상호 독립적이어야 한다는 점이다. 본 연구가 밝히고자 하는 바는 새로 추가 또는 삭제되는 무차별 기준에 따라 계층적으로 이들과 연계되는 상위 요소들은 그 개념이 변하는 것이 논리적으로 타당하며 따라서 이에 대한 중요도 또한 계층적으로 변해야 한다는 사실이다. 이를 통하여 순위역전 현상은 발생하지 않음을 보인다. 동시에 계층보다 보다 보편적인 관계를 포함하여 분석할 수 있는 네트워크분석과정(Analytic Network Process: ANP)을 이용해서도 순위역전 현상은 발생하지 않는다는 사실을 보인다. 본 연구의 ANP 모형에서 고려한 종속성은 계층모형에서의 피드백 즉, 각 대안의 특징이 기준의 중요도 결정에 미치는 효과이다. 마지막으로 본 연구는 무차별 기준의 추가 또는 삭제에 따른 다양한 종속성을 가정한 일반적인 접근에 ANP가 대안이 됨을 논한다.

영어

This study deals with addition of indifferent or wash criteria on which the alternatives have equal performance in the Analytic Hierarchy Process (AHP) against the misguided argument as shortcoming of the AHP. In such case, it is noted that careful attention and a correct approach are required in order not to lead towards the wrong decision of rank reversal when composing priorities of criteria and performances of alternatives according to the criteria. It is proposed that prioritizing effect of added or deleted indifferent criteria requires consistency with the change of conceptual definition in regards to the related elements as well as that of the hierarchical structure if needed. Corresponding to such importance in ranking alternatives, two principles of the AHP need to be considered simultaneously: the completeness for expectation and the outer dependence of a hierarchy on which the argument of rank reversal focuses only. The completeness implies all criteria are represented in the hierarchy or the network. Then the decision makers make sure that their ideas are adequately represented for the outcome to match their expectations. The outer dependence is concerned with hierarchical decomposition, which implies containment of the small elements by large clusters or levels. If one is to omit this axiom, the principle of hierarchic composition would no longer be applied. Through simply adding a new criterion or deleting a criterion in a given hierarchy with no other dependency except outer-dependency, we can show how to adjust the current global priorities by the addition or deletion corresponding to the hierarchic level. This is based on the fact that the conceptual/substantial definition of corresponding higher criterion needs to change as well. As a result, this study shows the wrong example in the previous study overlooked the correct meaning of expectation. This approach coincides with the outcome by supermatrix approach as a general matrix form dealing with a hierarchy. Logically, the adding or deleting of subcriterion in a level of criterion requires the change of the related criteria definition in upper levels and impacts on their priorities according to the related equation which is accompanying with its local priority matrix. When the meaning of completeness is considered to change global vector, not only changing local vector but also changing the else is required. Therefore, it is required to consider the outer-dependency and completeness principles for expectation simultaneously when using hierarchical approach. This study also show that the Analytic Network Process (ANP) as a general approach can cover the case of adding feedback from alternatives to the given hierarchic criteria or subcriteria, where the input and output can be represented in the supermatrix. At first, we show the necessary calculation of feedback from the assumption that the new criterion is indifferent between the two alternatives. Finally, we also show that there is no rank reversal between the two given alternatives, and total priorities with regards to the alternative coincide with those before adding a new but indifferent criterion with the same values to alternatives. Additionally, we find out a feedback characteristic that the priorities of criteria are transferred to the lower subcriteria, which is from the assumption of bidirectional dependency between the criteria and two alternatives in the limiting supermatrix. The other is from the assumption of cycle, the direction of feedback to criteria and subcriteria. We can find the same result as that of the hierarchic approach in this example, and there is no rank reversal. Finally, this paper discusses the way in which there is no irrational/unreasonable rank reversal with simple addition of indifferent criteria in addition to the deletion of the indifferent criteria, which helps AHP/ANP application.

목차

Abstract
 Ⅰ. Introduction
 Ⅱ. Independence, Completeness and Feedback
  2.1 Characteristics and Principles of Application
  2.2 Addition or Deletion of Criteria in a Hierarchy
  2.3 Addition or Deletion of Criteria in Network
 Ⅲ. Addition of Indifferent Criteria
  3.1 Incorrect Argument
  3.2 Correction under Hierarchy Assumption
  3.3 Correction under Network Assumption
 Ⅳ. Discussion and Final Remarks
 Acknowledgements
 
 국문요약

저자

• Min-Suk Yoon [ 윤민석 | Professor, Electronic Commerce, Chonnam National University ]

참고문헌