Ambiguous Criteria Weights in AHP: Consequences and Solutions*

Abstract

lkio related streams of criticism of the analytic hierarchy process (AHP) have not yet been satisk t o r i l y resolved, although both date from the early 1980s. The first relates to ambiguity in the meaning of the relative importance of one criterion as compared to another. The second is concerned with reversals of rank alleged to be possible when new options are introduced in an AHP problem. Both proponents and critics of AHP agree that rank reversals occur, but disagree on the legitimacy of such reversals. This paper shows that there is a necessary correspondence between the manner in which criteria importances are interpreted and computed and the manner in which the weights of the options under each criterion are normali7ed. In general, if this relationship is ignored, incorrect weights are generated f o r options under consideration regardless of whether new options are added or deleted. A rank reversal on the addition of an option is merely symptomatic of this fact, and such reversals do riot occur when the correspondence condition is met.

Regarding the Preliminary Feasibility Study of National R＆D Program : With Focus on the Applicability of Theory of Attractive Quality

“…반면 이러한 AHP 평가기법의 광범위한 활용과 더불어 이의 방법론적 타당성에 대한 학술적 논쟁 † † 이 학계에서 매우 활발하게 있어왔다 (Belton, 1982(Belton, , 1986(Belton, , 2002Dong et al, 2008;Finan & Hurley, 1999;Gass, 2005;Harker & Vargas, 1990;Salo & Hamalainen, 1997;Saaty, 1990Saaty, , 1994Saaty, , 1997Millet & Saaty, 2000;Forman & Gass, 2001;Schoner & Wedley, 1989, 1993, 1997Stewart, 1992 등) • 둘째, 일원적 품질(one-dimensional quality)은 성과요소와 같은 개념으로 품질이 좋아지면 좋아질수록 만족도 도 높아지고, 품질이 나빠지면 나빠질수록 불만족이 증대되는 품질요소를 의미한다.…”

Comparing Fundamentals of Additive and Multiplicative Aggregation in Ratio Scale Multi-Criteria Decision Making

“…The scaling factors 1 , 2 ,…, m and their relationship with the criteria weights have caused much ambiguity and confusion in Analytic Hierarchical Process (AHP) type models [4,5,11,12]. The local preference values in x p are represented as p u[y 1p ,y 2p ,…,y np ] but the role of unit is obscure because the unit of measure u used in measuring the local preference values is usually not explicitly specified and p is an arbitrary positive number.…”

“…In most AHP type models, 1 , 2 ,…, m are not explicitly shown as arbitrary positive numbers. This obscurity has led to some misunderstanding [12]. A common technique used to determine 1 , 2 ,…, m and hence fixing the numerical values of x p is to impose some artificial normalization constraint such as x 1p +x 2p +…+x np =1.…”

“…It is problematic when the generic term "criteria weight of importance" is used in questioning the DM without explaining its specific intended meaning. The criteria weights in w elicited from the DM may not be consistent with the associated mathematical operations used in the model [11,12]. The local preferences x 1 ,x 2 ,…,x m are subjective evaluations from the DM with reference to the performance of the alternatives under individual criteria.…”

“…If a different normalization constraint is used and p is changed to p ', then the criteria weight w p must be adjusted to w p '=w p p / p ' to maintain the same results generated from the original units. Otherwise, unwarranted rank reversals may occur [12]. on the right hand side of (2a) is a common factor which can be deleted in the ratios g j /g k , 1 j,k n. The relative ratios of g 1 ,g 2 ,…,g n are unchanged when the scaling factors 1 , 2 ,…, m and the normalization constraints are changed.…”