Abstract
We present a new interactive algorithm allowing to solve the inconsistencies problem, when the preferences of a decision maker cannot be representable by a numerical function. This algorithm is based on technics of linear programming and the type of preferences we use are cardinal information.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bana e Costa, C.A., De Corte, J.-M., Vansnick, J.-C.: On the mathematical foundations of MACBETH. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys, pp. 409–437. Springer, Heidelberg (2005)
Chinneck, J.W.: Computer codes for the analysis of infeasible linear programs. Journal of the Operational Research Society 47 (1996)
Chinneck, J.W.: An effective polynomial-time heuristic for the minimum cardinality IIS set-covering problem. Annals of Mathematics and Artificial Intelligence 17 (1996)
De Corte, J.M.: Un logiciel d’Exploitation d’Information Préférentielles pour l’Aide à la Décision. Bases Mathématiques et Algorithmiques. PhD thesis, University of Mons-Hainaut, Mons (2002)
Doignon, J.P.: Thresholds representation of multiple semiorders. SIAM Journal on Algebraic and Discrete Methods 8, 77–84 (1987)
Figueira, J.R., Greco, S., Slowinski, R.: Building a set of additive value functions representing a reference preorder and intensities of preference: Grip method. European Journal of Operational Research 195(2), 460–486 (2009)
Mayag, B., Grabisch, M., Labreuche, C.: A characterization of the 2-additive Choquet integral through cardinal information. In: Proceedings of EUROFUSE 2009 Workshop Preference Modelling and Decision Analysis (CD), Pamplona, Spain, September 16-18 (2009)
Mousseau, V., Dias, L., Figueira, J.R.: Dealing with inconsistent judgments in multiple criteria sorting models. 4OR, 4 (2006)
Mousseau, V., Figueira, J.R., Dias, L., Da Silva, C.G., Climaco, J.: Resolving inconsistencies among constraints on the parameters of an MCDA model. European Journal of Operational Research 147 (2003)
Mousset, C.: Familles de structures de préférence non complètes. PhD thesis, University of Mons-Hainaut, Belgium (2004)
Mousset, C.: Families of relations modelling preferences under incomplete information. European journal of operational research 192(2), 538–548 (2009)
Mousset, C., Vansnick, J.-C.: About the representation of a precardinal information. Documents d’Economie et de Gestion de l’Université de Mons-Hainaut (2005)
Pirlot, M., Vincke, P.: Semiorders — Properties, Representations, Applications. Kluwer Academic Publishers, Dordrecht (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mayag, B., Grabisch, M., Labreuche, C. (2010). An Interactive Algorithm to Deal with Inconsistencies in the Representation of Cardinal Information. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-14055-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14054-9
Online ISBN: 978-3-642-14055-6
eBook Packages: Computer ScienceComputer Science (R0)