Abstract
This paper presents a concurrent algorithm for computing a consistent approximation to a generalized pairwise comparisons matrix (i.e. it is assumed that the reciprocity property is not required). Like its sequential counterpart, it is based on the iterative strategy “find the worst case and fix it”. The conducted experiments confirmed that a significant increase in speed between the sequential and concurrent approach is achieved. Our results may be particularly important for the large decision support systems where the number of pairs considered is large and the sequential approach may not be fast enough.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Choo, E.U., Wedley, W.C.: A common framework for deriving preference values from pairwise comparison matrices. Computers and Operations Research 31(6), 893–908 (2004)
Crawford, R., Williams, C.: A note on the analysis of subjective judgement matrices. Journal of Mathematical Psychology 29, 387–405 (1985)
Ishizaka, A., Labib, A.: Review of the main developments in the analytic hierarchy process. Expert Systems with Applications 38(11), 14336–14345 (2011)
Janicki, R., Soudkhah, M.H.: On Classification with Pairwise Comparisons, Support Vector Machines and Feature Domain Overlapping. Computer Journal, bxu085 (September 2014)
Jensen, R.E.: An alternative scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 28(3), 317–332 (1984)
Kacprzyk, J., Zadrozny, S., Fedrizzi, M., Nurmi, H.: On Group Decision Making, Consensus Reaching, Voting and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and some Perspectives. In: Bustince, H., Herrera, F., Montero, J. (eds.) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. STUDFUZZ, vol. 220, pp. 263–295. Springer, Heidelberg (2008)
Koczkodaj, W.W.: A new definition of consistency of pairwise comparisons. Math. Comput. Model. 18(7), 79–84 (1993)
Koczkodaj, W.W., Kułakowski, K., Ligęza, A.: On the quality evaluation of scientific entities in Poland supported by consistency-driven pairwise comparisons method. Scientometrics 99(3), 911–926 (2014)
Koczkodaj, W.W., Szarek, S.J.: On distance-based inconsistency reduction algorithms for pairwise comparisons. Logic Journal of the IGPL 18(6), 859–869 (2010)
Koczkodaj, W.W., Szybowski, J., Kosiek, M., Xu, D.: Fast Convergence of Distance-based Inconsistency in Pairwise Comparisons. Fundamenta Informaticae, 1–13 (January 2015)
Kułakowski, K.: Heuristic Rating Estimation Approach to The Pairwise Comparisons Method. Fundamenta Informaticae 133, 367–386 (2014)
Kułakowski, K.: A heuristic rating estimation algorithm for the pairwise comparisons method. Central European Journal of Operations Research 23(1), 187–203 (2015)
Kułakowski, K., Grobler-Dębska, K., Wąs, J.: Heuristic rating estimation: geometric approach. Journal of Global Optimization (2014)
Kułakowski, K., Szybowski, J., Tadeusiewicz, R.: Tender with Success The Pairwise Comparisons Approach. Procedia Computer Science 35, 1122–1131 (2014)
Saaty, T.L.: A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15(3), 234–281 (1977)
Saaty, T.L., Vargas, L.G.: The possibility of group choice: pairwise comparisons and merging functions. Social Choice and Welfare 38(3), 481–496 (2011)
Subramanian, N., Ramanathan, R.: A review of applications of Analytic Hierarchy Process in operations management. International Journal of Production Economics 138(2), 215–241 (2012)
Thurstone, L.L.: A law of comparative judgment, reprint of an original work published in 1927. Psychological Review 101, 266–270 (1994)
Xu, D.: Improving the reduction of distance-based inconsistency of pairwise comparisons matrix. Master’s thesis, Laurentian University, Sudbury, Ontario (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Kułakowski, K., Juszczyk, R., Ernst, S. (2015). A Concurrent Inconsistency Reduction Algorithm for the Pairwise Comparisons Method. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9120. Springer, Cham. https://doi.org/10.1007/978-3-319-19369-4_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-19369-4_20
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19368-7
Online ISBN: 978-3-319-19369-4
eBook Packages: Computer ScienceComputer Science (R0)