Summary
The paper addresses the problem of dealing with real numbers for scores or utilities in decision making, that is, with numbers being positive or negative. The use of non-additive models, as the Choquet integral, entails the possibility of having (at least) two choices when defining the Choquet integral for real-valued integrand, which can be named, after Denneberg, symmetric or asymmetric. The problem is examined in the frameworks of multicriteria decision making and decision under risk and uncertainty.
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References
F.J. Anscombe and R.J. Aumann. A definition of subjective probability. The Annals of Mathematical Statistic, 34: 199–205, 1963.
S.J. Chen and C.L. Hwang. Fuzzy Multiple Attribute Decision Making. Springer-Verlag, 1992.
G. Choquet. Theory of capacities. Annales de l’Institut Fourier, 5: 131–295, 1953.
D. Denneberg. Non-Additive Measure and Integral. Kluwer Academic, 1994.
D. Denneberg and M. Grabisch. Interaction transform of set functions over a finite set. Information Sciences,to appear.
P. Fishburn and P. Wakker. The invention of the independence condition for preferences. Management Sciences, 41 (7): 1130–1144, 1995.
M. Grabisch. The application of fuzzy integrals in multicriteria decision making. European J. of Operational Research, 89: 445–456, 1996.
M. Grabisch. k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems, 92: 167–189, 1997.
M. Grabisch. Fuzzy integral for classification and feature extraction. In M. Grabisch, T. Murofushi, and M. Sugeno, editors, Fuzzy Measures and Integrals-Theory and Applications. Physica Verlag, to appear.
M. Grabisch, Ch. Labreuche, and J.C. Vansnick. On the extension of pseudoboolean functions for the aggregation of interacting bipolar criteria. European J. of Operational Research,submitted.
M. Grabisch and M. Roubens. Application of the choquet integral in multicriteria decision making. In M. Grabisch, T. Murofushi, and M. Sugeno, editors, Fuzzy Measures and Integrals-Theory and Applications. Physica Verlag, 2000.
M. Grabisch and M. Roubens. An axiomatic approach to the concept of interaction among players in cooperative games. Int. Journal of Game Theory,to appear.
D. Kahneman and A. Tversky. Prospect theory: an analysis of decision under risk. Econometrica, 47: 263–291, 1979.
R.L. Keeney and H. Raiffa. Decision with Multiple Objectives. Wiley, New York, 1976.
J.L. Marichal. Aggregation operators for multicriteria decision aid. PhD thesis, University of Liège, 1998.
T. Murofushi and S. Soneda. Techniques for reading fuzzy measures (III): interaction index. In 9th Fuzzy System Symposium,pages 693–696, Sapporo, Japan, May 1993. In Japanese.
G.C. Rota. On the foundations of combinatorial theory I. Theory of Möbius functions. Zeitschrift fiir Wahrscheinlichkeitstheorie and Verwandte Gebiete, 2: 340–368, 1964.
L. J. Savage. The Foundations of Statistics. Dover, 2nd edition, 1972.
D. Schmeidler. Subjective probability and expected utility without additivity. Econometrica,57(3):571–587, 1989
L.S. Shapley. A value for n-person games. In H.W. Kuhn and A.W. Tucker, editors, Contributions to the Theory of Games, Vol. II, number 28 in Annals of Mathematics Studies, pages 307–317. Princeton University Press, 1953.
M. Sugeno. Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology, 1974.
M. Sugeno and T. Murofushi. Fuzzy measure theory,volume 3 of Course on fuzzy theory. Nikkan Kógyo, 1993. In Japanese.
A. Tversky and D. Kahneman. Advances in prospect theory: cumulative representation of uncertainty. J. of Risk and Uncertainty, 1992.
J. ipos. Integral with respect to a pre-measure. Math. Slovaca, 29: 141–155, 1979.
H. Zank. Risk and Uncertainty: Classical and Modern Models for Individual Decision Making. PhD thesis, Universiteit Maastricht, 1999.
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Grabisch, M., Labreuche, C. (2000). To be Symmetric or Asymmetric? A Dilemma in Decision Making. In: Fodor, J., De Baets, B., Perny, P. (eds) Preferences and Decisions under Incomplete Knowledge. Studies in Fuzziness and Soft Computing, vol 51. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1848-2_10
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DOI: https://doi.org/10.1007/978-3-7908-1848-2_10
Publisher Name: Physica, Heidelberg
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