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On the Proper Interpretation and Impact of the AHP Axiom of Independence in Single‐Criterion and Multiple‐Criteria Problems
Author(s) -
Hauser David,
Peniwati Kirti
Publication year - 1996
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/(sici)1099-1360(199612)5:4<259::aid-mcda117>3.0.co;2-l
Subject(s) - analytic hierarchy process , pairwise comparison , axiom independence , independence (probability theory) , axiom , computer science , hierarchy , interpretation (philosophy) , mathematics , mathematical economics , mathematical optimization , artificial intelligence , statistics , economics , geometry , programming language , market economy
Some authors have proposed that the analytic hierarchy process (AHP) axiom of independence be relaxed to accommodate observations drawn from (a) examples of pairwise comparisons of alternatives in clusters in single‐criterion AHP problems and (b) examples of problems in which the criteria have the same underlying measurement and both the achievement of the goal and the alternatives are measured objectively. We show that the illustrations given are actually single‐criterion problems according to the AHP. Thus the AHP axiom of independence is inapplicable in both situations and therefore not violated. We also consider the consequence of failure to distinguish between a criterion as an attribute of alternatives and cluster of alternatives, the two being different in the hierarchic structure. Finally, we discuss transformable problems , which look like multicriteria problems but are actually single‐criterion problems, and how failure to recognize this fact may lead to incorrect syntheses and false conclusions.