On reducing inconsistency of pairwise comparison matrices below an acceptance threshold

Central European Journal of Operations Research

Volumn 23, Issue 4, 2015, Pages 849-866

  Bozóki, Sándor ^a,b   Fülöp, János ^a   Poesz, Attila ^b  

^a INSTITUTE FOR COMPUTER SCIENCE AND CONTROL   (Hungary)

^b Institute of Data Analytics and Information Systems   (Hungary)

Author keywords

Inconsistency; Mixed 0 1 convex programming; Multi attribute decision making; Pairwise comparison matrix

Indexed keywords

EID: 84957953970     PISSN: 1435246X     EISSN: 16139178     Source Type: Journal    
DOI: 10.1007/s10100-014-0346-7     Document Type: Article

References (21)

1. Bozóki S, Rapcsák T (2008) On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. J Glob Optimiz 42(2):157–175
2. Bozóki S, Fülöp J, Rónyai L (2010) On optimal completions of incomplete pairwise comparison matrices. Math Comput Model 52(1–2):318–333
3. Bozóki S, Fülöp J, Koczkodaj WW (2011a) LP-based consistency-driven supervision for incomplete pairwise comparison matrices. Math Comput Model 54(1–2):789–793
4. Bozóki S, Fülöp J, Poesz A (2011b) On pairwise comparison matrices that can be made consistent by the modification of a few elements. Central Eur J Oper Res 19(2):157–175
5. Bozóki S, Fülöp J, Poesz A (2012) Convexity properties related to pairwise comparison matrices of acceptable inconsistency and applications (in Hungarian, Elfogadható inkonzisztenciájú páros összehasonlítás mátrixokkal kapcsolatos konvexitási tulajdonságok és azok alkalmazásai). In: Solymosi T, Temesi J (eds) Egyensúly és optimum: Tanulmányok Forgó Ferenc 70. születésnapjára, Aula Kiadó, pp 169–184.
6. Brunelli M, Fedrizzi M (2011) Characterizing properties for inconsistency indices in the AHP. In: Proceedings of the 11th international symposium on the AHP. Sorrento, Naples, Italy, June 15–18, 2011.
7. Brunelli M, Canal L, Fedrizzi M (2013a) Inconsistency indices for pairwise comparison matrices: a numerical study. Ann Oper Res 211(1):493–509
8. Brunelli M, Fedrizzi M (2013b) Axiomatic properties of inconsistency indices for pairwise comparisons. J Oper Res Soc, published online first on 4 Dec 2013. doi:10.1057/jors.2013.135.
9. Cao D, Leung LC, Law JS (2008) Modifying inconsistent comparison matrix in Analytic Hierarchy Process: a heuristic approach. Decis Support Syst 44(4):944–953
10. Chu MT (1997) On the optimal consistent approximation to pairwise comparison matrices. Linear Alg Appl 272(1–3):155–168
11. Duszak Z, Koczkodaj WW (1994) Generalization of a new definition of consistency for pairwise comparisons. Inf Process Lett 52(5):273–276
12. Harker PT (1987) Derivatives of the Perron root of a positive reciprocal matrix: with application to the Analytic Hierarchy Process. Appl Math Comput 22(2–3):217–232
13. Koczkodaj WW, Szwarc R (2013) On axiomatization of inconsistency indicators for pairwise comparisons. arXiv:1307.6272v4.
14. Koczkodaj WW (1993) A new definition of consistency of pairwise comparisons. Mathematical and Computer Modelling 18(7):79–84
15. Peláez JI, Lamata MT (2003) A new measure of consistency for positive reciprocal matrices. Comput Math Appl 46(12):1839–1845
16. Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15(3):234–281
17. Saaty TL (1980) The Analytic Hierarchy Process. McGraw-Hill, New York
18. Saaty TL (1994) Fundamentals of decision making. RSW Publications, Pittsburgh
19. Sekitani K, Yamaki N (1999) A logical interpretation for the eigenvalue method in AHP. J Oper Res Soc Japan 42(2):219–232
20. Vargas LG (1982) Reciprocal matrices with random coefficients. Math Model 3(1):69–81
21. Xu Z, Wei C (1999) A consistency improving method in the Analytic Hierarchy Process. Eur J Oper Res 116(2):443–449