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Proceedings of the 17th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 30

On Multiplicative, Additive and Qualitative Pairwise Comparisons


DOI: http://dx.doi.org/10.15439/2022F57

Citation: Proceedings of the 17th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 30, pages 247251 ()

Full text

Abstract. A relationship between the classical multiplicative pairwise comparisons that are based on aijaji = 1, the additive model based on bij+bji = 1, and qualitative pairwise comparisons that uses the relations ≈ (indifferent), ⊏ (slightly in favour of), ⊂ (in favour of), < ( strongly better) and ≺ (extremely better), is discussed in detail. A special attention is paid to the concept of consistency and weights calculations. An on-line tool is also discussed.


  1. J. Barzilai, Deriving weights for pairwise comparison matrices, Journal of the Operational Research Society, 48, 1226-1232, 1997.
  2. Bozóki S., Rapcsák T., On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices, Journal of Global Optimization, 42, 2 (2008), 157-175.
  3. Bradley R. M., Terry M. E., The rank analysis of incomplete block designs. I. The method of paired comparisons, Biometrika 39, 324-345 (1952)
  4. Cowan N., The magical number four in short-term memory. A reconsideration of mental storage capacity, Behavioural and Brain Sciences, 24 (2001) 87-185
  5. Janicki R., Pairwise Comparisons Based Non-Numerical Ranking, Fundamenta Informaticae 94 (2009), 197-217.
  6. Janicki R., Finding Consistent Weights Assignments with Combined Pairwise Comparisons, International Journal of Management and Decision Making, 17, 3 (2018) 322-347.
  7. Janicki R., Soudkhah M. H., On Classification with Pairwise Comparisons, Support Vector Machines and Feature Domain Overlapping, The Computer Journal 58, 3 (2015), 416-431
  8. Janicki R., Zhai Y., On a Pairwise Comparison Based Consistent Non-Numerical Ranking, Logic Journal of IGPL, 20, 4, 667-676 (2012)
  9. Janicki R., Zhai Y., Remarks on Pairwise Comparison Numerical and Non-Numerical Rankings, Lecture Notes in Artificial Intelligence 6954, Springer 2011, pp. 290-300.
  10. Koczkodaj W. W., A new definition of consistency of pairwise comparisons, Mathematical and Computer Modelling, 18 (1993) 79-84.
  11. Koczkodaj, W.W., Kosiek, M., Szybowski, J. and Xu D., Fast convergence of distance-based inconsistency in pairwise comparisons’, Fundamenta Informaticae, 137,3 (2015) 355–367
  12. Koczkodaj W. W., Szarek S. J., On distance-based inconsistency reduction algorithms for pairwise comparisons, Logic Journal of the IGPL 18, 6 (2009) 859-869.
  13. Kong F., Liu H., Applying fuzzy Analytic Hierarchy Process to evaluate success factors of e-commerce, International Journal of Information and Systems Sciences, 1, 3-4 (2005) 406-412.
  14. Mahmoud M., PiXR: Pairwise Matrix Inconsistency Reduction Tool, https://pixr-tool.github.io/
  15. Miller G. A., The Magical Number Seven, Plus or Minus Two, The Psychological Review, 63, 2 (1956) 81-97.
  16. Mirdad A., Janicki R., Applications of Mixed Pairwise Comparisons, Proc. of ICAI’2015 (International Conference on Artificial Intelligence), Las Vegas, Nevada, USA, July 27-30, 2015, pp. 414-420, CSREA Press
  17. Saaty T. L., A Scaling Methods for Priorities in Hierarchical Structure, Journal of Mathematical Psychology, 15 (1977) 234-281.
  18. Saaty T. L., Theory and Applications of the Analytic Network Process, RWS Publications, Pittsburgh 2005.