On Multiplicative, Additive and Qualitative Pairwise Comparisons

• Autorzy: Janicki Ryszard , Mahmoud Mahmoud

Identyfikatory

DOI

10.15439/2022F57

• Konferencja: Federated Conference on Computer Science and Information Systems (17 ; 04-07.09.2022 ; Sofia, Bulgaria)
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

pairwise comparisons; consistency; weight; calculation; qualitative judgement

PL

porównania parami; spójność; obliczanie; waga; ocena jakościowa

• Wydawca: Polskie Towarzystwo Informatyczne
• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2022
• Tom: Vol. 30
• Strony: 247--251
• Opis fizyczny: Bibliogr. 18 poz., tab., wz.

Twórcy

autor

Janicki Ryszard

• Department of Computing and Software McMaster University Hamilton, ON, L8S 4K1, Canada

autor

Mahmoud Mahmoud

• IBM Canada Markham, Ontario, L6G 1C7, Canada

Bibliografia

• 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.

Uwagi

1. Short article

2. Track 5: 4th International Symposium on Rough Sets: Theory and Applications

3. Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).