Abstract
In the paper, algorithms are provided to check the consistency of pairwise comparison matrices and to build consistent matrices over abelian linearly ordered groups. A measure of consistency is also given; this measure improves a consistent index provided in a previous paper.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Barzilai, J.: Consistency measures for pairwise comparison matrices. J. MultiCrit. Decis. Anal. 7, 123–132 (1998)
Basile, L., D’Apuzzo, L.: Ranking and weak consistency in the a.h.p. context. Rivista di matematica per le scienze economiche e sociali 20(1), 99–110 (1997)
Basile, L., D’Apuzzo, L.: Weak consistency and quasi-linear means imply the actual ranking. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10(3), 227–239 (2002)
Basile, L., D’Apuzzo, L.: Transitive matrices, strict preference and intensity operators. Mathematical Methods in Economics and Finance 1, 21–36 (2006)
Basile, L., D’Apuzzo, L.: Transitive matrices, strict preference and ordinal evaluation operators. Soft Computing 10(10), 933–940 (2006)
Cavallo, B., D’Apuzzo, L.: A general unified framework for pairwise comparison matrices in multicriterial methods. International Journal of Intelligent Systems 24(4), 377–398 (2009)
Chiclana, F., Herera-Viedma, E., Alonso, S., Herera, F.: Cardinal Consistency of Reciprocal Preference Relations: A Characterization of Multiplicative Transitivity. IEEE Transaction on Fuzzy Systems 17(1), 14–23 (2009)
D’Apuzzo, L., Marcarelli, G., Squillante, M.: Generalized consistency and intensity vectors for comparison matrices. International Journal of Intelligent Systems 22(12), 1287–1300 (2007)
Fodor, J., Yager, R., Rybalov, A.: Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5(4), 411–427 (1997)
Herrera-Viedma, E., Herrera, F., Chiclana, F., Luque, M.: Some issue on consistency of fuzzy preferences relations. European Journal of Operational Research 154, 98–109 (2004)
Saaty, T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psychology 15, 234–281 (1977)
Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)
Saaty, T.L.: Axiomatic foundation of the analytic hierarchy process. Management Science 32(7), 841–855 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cavallo, B., D’Apuzzo, L., Squillante, M. (2009). Building Consistent Pairwise Comparison Matrices over Abelian Linearly Ordered Groups. In: Rossi, F., Tsoukias, A. (eds) Algorithmic Decision Theory. ADT 2009. Lecture Notes in Computer Science(), vol 5783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04428-1_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-04428-1_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04427-4
Online ISBN: 978-3-642-04428-1
eBook Packages: Computer ScienceComputer Science (R0)