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Clustering, dependence and ratio scales in AHP: Rank reversals and incorrect priorities with a single criterion
Author(s) -
Wedley William C.,
Schoner Bertram,
Choo Eng Ung
Publication year - 1993
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.4020020304
Subject(s) - analytic hierarchy process , rank (graph theory) , cluster analysis , cluster (spacecraft) , hierarchy , scale (ratio) , statistics , mathematics , mode (computer interface) , econometrics , computer science , mathematical economics , economics , physics , combinatorics , quantum mechanics , market economy , programming language , operating system
In the analytic hierarchy process, it is often thought that rank reversals cannot occur in a single‐criterion problem. This paper demonstrates that if it is necessary to cluster items under a single criterion, such reversals are possible. The reversals occur prior to aggregating across clusters and are caused by a failure to make reference to the alternatives when performing criteria comparisons. Rank reversals, however, are only a symptom of the problem. The real problem is a failure to calibrate global weights to a common scale which spans different clusters. Even in the absence of reversals, aggregated weights from the AHP's relative mode of measurement can fail to maintain composite ratio relationships.