Comparative Performance of Contradictory and Non-Contradictory Judgement Matrices in AHP Under Qualitative and Quantitative Metrics

Abstract

Over the years, although AHP has proved its success in various diverse fields, many authors in the literature have also shown its shortcomings, often called as criticisms of AHP. One such criticism is allowing the consideration of contradictory judgement matrices. Such matrices violate the principle of ordinal transitivity and thus there does not exist any ranking of corresponding decision elements which satisfy all the judgements. In this paper, the results of our investigation towards measuring this criticism are further explored and discussed by comparing the quality of priority vector of contradictory judgement matrices and non-contradictory judgement matrices under Rank Reversals and the common frame work of “aggregated deviation”. The results further strengthen the notion of contradictory judgement matrices as a strong criticism of AHP for higher order judgement matrices and necessitate some proper avoidance (if not elimination) procedure for them.