Abstract
We study in this paper the notion of conditional relative importance in a quantitative framework. Bi-capacities are shown to be suitable to represent such a notion. We restrict ourself to the case when the relative importance of two criteria are conditional on a third being attractive or repulsive. We give two algorithms that enable to construct the neutral level from the preference relation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Boutilier, C., Brafman, R. I., Domshlak, C., Hoos, H. H., & Poole, D. (2004). CP-nets: a tool for representing and reasoning with conditional Ceteris Paribus preference statements. Journal of Artificial Intelligence Research, 21, 135–191.
Bouyssou, D., & Pirlot, M. (2004). Preferences for multi-attributed alternatives: traces, dominance, and numerical representations. Journal of Mathematical Psychology, 48, 167–185.
Brafman, R., & Domshlak, C. (2002). Introducing variable importance tradeoffs into CP-nets. AIPS’02 workshop on planning and scheduling with multiple criteria.
Choquet, G. (1953). Theory of capacities. Annales de l’Institut Fourier, 5, 131–295.
De Finetti, F. (1974). Theory of probability. London: Wiley.
Fodor, J. C., & Roubens, M. (1994). Fuzzy preferences modeling and multicriteria decision aid. Dordrecht: Kluwer Academic.
Grabisch, M., & Labreuche, Ch. (2002). Bi-Capacities for decision making on bipolar scales. EUROFUSE workshop on information systems, Varenna, Italy, September 2002.
Grabisch, M., & Labreuche, Ch. (2005). Fuzzy measures and integrals in MCDA. In J. Figueira, S. Greco & M. Ehrgott (Eds.), Multiple criteria decision analysis: state of the art surveys (pp. 563–608). New York: Springer.
Grabisch, M., Murofushi, T., & Sugeno, M. (2000). Fuzzy measures and integrals. Heidelberg: Physica-Verlag.
Kahneman, D., & Tversky, D. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47, 263–291.
Keeney, R. L., & Raiffa, H. (1976). Decision with multiple objectives. New York: Wiley.
Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Additive and polynomial representations: Vol. 1. Foundations of measurement. San Diego: Academic.
Labreuche, Ch., & Grabisch, M. (2003). The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets and Systems, 137, 11–26.
Labreuche, Ch., & Grabisch, M. (2007). Generalized Choquet-like aggregation functions for handling bipolar scales. European Journal of Operational Research, to appear.
Pennings, J., & Smidts, A. (2000). Assessing the construct validity of risk attitude. Management Science, 46, 1337–1348.
Rescher, N. (1969). An introduction to value theory. New York: Prentice Hall.
Simon, H. (1956). Rational choice and the structure of the environment. Psychological Review, 63(2), 129–138.
Slovic, P., Finucane, M., Peters, E., & MacGregor, D. G. (2002). The affect heuristic. In T. Gilovitch, D. Griffin & D. Kahneman (Eds.), Heuristics and biases: the psychology of intuitive judgment (pp. 397–420). Cambridge: Cambridge University Press.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Labreuche, C., Grabisch, M. The representation of conditional relative importance between criteria. Ann Oper Res 154, 93–122 (2007). https://doi.org/10.1007/s10479-007-0184-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-007-0184-2