Inconsistent and contradictory judgements in pairwise comparison method in the AHP. (English) Zbl 1048.90121

Summary: The aim of this paper is to show the relationship between inconsistent and contradictory matrices of data obtained as a result of the pairwise comparison of factors in the sense of the analytic hierarchy process. The consistency check is performed to ensure that judgements are neither random nor illogical. This paper shows that even if a matrix will pass a consistency test successfully, it can be contradictory. Moreover an algorithm of checking contradictions is proposed.


90B50 Management decision making, including multiple objectives
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[1] Saaty, T.L., The analytic hierarchy process, (1980), McGraw-Hill New York · Zbl 1176.90315
[2] Murphy, C.K., Limits on the analytic hierarchy process from its consistency index, European journal of operational research, 65, 138-139, (1993) · Zbl 0775.90009
[3] Finan, J.S.; Hurley, W.J., Transitive calibration of the AHP verbal scale, European journal of operational research, 112, 367-372, (1999) · Zbl 0939.91036
[4] Triantaphyllou, E., Multi-criteria decision making methods: a comparative study, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0980.90032
[5] Triantaphyllou, E.; Mann, S.H., Using the analytic hierarchy process for decision making in engineering applications: some challenges, International journal of industrial engineering: applications and practice, 2, 35-44, (1995)
[6] Saaty, T.L.; Vargas, L., Comparison of eigenvalue, logarithmic least-squares and least-squares methods in estimating ratios, Mathematical modelling, 5, 309-324, (1984) · Zbl 0584.62102
[7] Karpetrovic, S.; Rosenbloom, E.S., A quality control approach to consistency paradoxes in AHP, European journal of operational research, 119, 704-718, (1999) · Zbl 0938.91015
[8] Buckley, J.J., Fuzzy hierarchical analysis, Fuzzy sets and systems, 17, 233-247, (1985) · Zbl 0602.90002
[9] Buckley JJ. Fuzzy hierarchical analysis revisited. Proceedings of the Eighth International Fuzzy Systems Association World Congress, August 17-20, Taipei, Taiwan, ROC, 1999.
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