article

On the Possibilistic-Based Decision Model: Characterization of Preference Relations Under Partial Inconsistency

Authors:

Adriana ZapicoAuthors Info & Claims

Applied Intelligence, Volume 14, Issue 3

Pages 319 - 333

https://doi.org/10.1023/A:1011203021670

Published: 09 May 2001 Publication History

Abstract

A qualitative counterpart to Von Neumann and Morgenstern's Expected Utility Theory of decision under uncertainty was recently proposed by Dubois and Prade. In this model, belief states are represented by normalised possibility distributions over an ordinal scale of plausibility, and the utility (or preference) of consequences of decisions are also measured in an ordinal scale. In this paper we extend the original Dubois and Prade's decision model to cope with partially inconsistent descriptions of belief states, represented by non-normalised possibility distributions. Subnormal possibility distributions frequently arise when adopting the possibilistic model for case-based decision problems. We consider two qualitative utility functions, formally similar to the original ones up to modifying factors coping with the inconsistency degree of belief states. We provide axiomatic characterizations of the preference orderings induced by these utility functions.

References

[1]

1. J. von Neumann and O. Morgenstern, Theory of Games and Economic Behaviour, Princeton Univ. Press: Princeton, NJ, 1944.

[2]

2. A. Zapico and L. Godo, "On the possibilistic-based decision model: Preferences under partially inconsistent belief states," in Proc of the Workshop on Decision Theory Meets Artificial Intelligence: Qualitative and Quantitative Approaches. ECAI'98. Brighton 1998, pp. 99-109.

[3]

3. D. Schmeidler, "Subjective probability and expected utility without additivity," in Econometrica, vol. 57, pp. 571-587, 1989.

[4]

4. I. Gilboa, "Expected utility with purely subjective nonadditive probabilities," Journal of Mathematical Economics, vol. 16, pp. 65-88, 1987.

[5]

5. R. Sarin and P.P. Wakker, "A simple axiomatization of nonadditive expected utility," Econometrica, vol. 60, no 6, pp. 1255-1272, 1992.

[6]

6. R.R. Yager, "Possibilistic decision making," IEEE Trans. on Systems, Man and Cybernetics, vol. 9, pp. 388-392, 1979.

[7]

7. J. Doyle and R. Thomason, "Background to qualitative decision theory". AI Magazine, vol. 20, no. 2, pp. 55-68, 1999.

Digital Library

[8]

8. B. Bonet and H. Geffner, "Arguing for decisions: A qualitative model of decision making," in Proc. of the 12th Conf. on Uncertainty in Artificial Intelligence, Portland, OR, edited by E. Horwitz and F. Jensen, pp. 98-105, 1996.

Digital Library

[9]

9. R.I. Brafman and M. Tennenholtz, "On the axiomatization of qualitative decision criteria," in Proc. 14th Nat. Conf. on A.I. (AAI'97), 1997, pp. 76-81.

Digital Library

[10]

10. J. Pearl, "From qualitative utility to conditional "ought to"," in Proc. of the 9th Inter. Conf. on Uncertainty in Artificial Intelligence, edited by D. Heckerman, H. Mamdani, pp. 12-20, 1993.

[11]

11. D. Dubois and H. Prade, "A fuzzy set approach to case-based decision," in Proc. of the Second European Workshop on Fuzzy Decision Analysis and Neural networks for Management, Planning and Optimization (EFDAN97), Dortmund, 1997, pp. 1-9.

[12]

12. D. Dubois, L. Godo, H. Prade, and A. Zapico, "Making decision in a qualitative setting: From decision under uncertainty to case-based decision," in Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR'98). Trento, 1998, pp. 594-605.

[13]

13. I. Gilboa and D. Schmeidler, "Case-based decision theory," The Quarterly Journal of Economics, vol. 110, pp. 607-639, 1995.

[14]

14. D. dubois and Prade H. "Possibility theory as a basis for qulitative decision theory," in Proc. of the 14th Int. Joint Conf. on Artificial Intellignce (IJCAI '95), Montreal, 1995, pp. 1924- 1930.

[15]

15. T. Whalen, "Decision making under uncertainty with various assumptions about available information." IEEE Trans. on Systems, Man and Cybernetics, vol. 14, pp. 888-900, 1984.

[16]

16. D. Dubois, J.C. Fodor, H. Prade, and M. Roubens "Aggregation of decomposable measures with application to utility theory," in Theory and Decision, vol. 41, pp. 59-95, 1996.

[17]

17. D. Dubois, F. Esteva, P. Garcia, L. Godo, R.L. de Màntaras, and H. Prade, "Fuzzy set modelling in case-based reasoning," International Journal of Intelligent Systems, vol. 13, pp. 345- 373, 1998.

[18]

18. D. Dubois, H. Lang, and H. Prade, "Possibilistic logic," Handbook of Logic in Artificial Intelligence and Logic Programming, edited by D.M. Gabbay, C.J. Hopper, J.A. Robinson, Oxford University Press, Oxford, UK, vol. 3, pp. 439-513, 1994.

Digital Library

[19]

19. A. Zapico, "Axiomatic foundations for qualitative/ordinal decisions with partial preferences," in Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI'99), Stockholm, 1999, pp. 132-137.

Digital Library

[20]

20. L. Godo and A. Zapico, "Generalised qualitative utility functions for representing partial preference relations," Proc. of EUSFLAT'99, Palma de Mallorca, Sept. 22-25, Spain, 1999, pp. 343-346.

[21]

21. C. Boutilier, "Toward a logic for qualitative decision theory," in Proc. 4th. Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR'94), Bonn, 1994, pp. 75-86.

[22]

22. L.J. Savage, The Foundations of Statistics. Dover: New York.

[23]

23. D. Schmeidler, "Integral representation without additivity", in Proc. Amer. Math. Soc., vol. 9, 1986, pp. 255-261.

Cited By

Torra VNarukawa Y(2019)On network analysis using non-additive integralsSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-018-03710-923:7(2321-2329)Online publication date: 1-Apr-2019
https://dl.acm.org/doi/10.1007/s00500-018-03710-9
Das STripathi S(2018)Adaptive and intelligent energy efficient routing for transparent heterogeneous ad-hoc network by fusion of game theory and linear programmingApplied Intelligence10.1007/s10489-017-1061-648:7(1825-1845)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s10489-017-1061-6
Liao SChen Y(2018)A rough set-based association rule approach implemented on exploring beverages product spectrumApplied Intelligence10.1007/s10489-013-0465-140:3(464-478)Online publication date: 28-Dec-2018
https://dl.acm.org/doi/10.1007/s10489-013-0465-1
Show More Cited By

Index Terms

On the Possibilistic-Based Decision Model: Characterization of Preference Relations Under Partial Inconsistency

Index terms have been assigned to the content through auto-classification.

Recommendations

On the possibilistic decision model: from decision under uncertainty to case-based decision
A special issue on fuzzy measures
Qualitative decision theory with preference relations and comparative uncertainty

This paper investigates a purely qualitative approach to decision making under uncertainty. Since the pioneering work of Savage, most models of decision under uncertainty rely on a numerical representation where utility and uncertainty are commensurate. ...
Qualitative decision under uncertainty: back to expected utility

Different qualitative models have been proposed for decision under uncertainty in Artificial Intelligence, but they generally fail to satisfy the principle of strict Pareto dominance or principle of ''efficiency'', in contrast to the classical numerical ...

Comments

Information & Contributors

Information

Published In

Copyright © Copyright © 2001 Kluwer Academic Publishers.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 09 May 2001

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 10 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Torra VNarukawa Y(2019)On network analysis using non-additive integralsSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-018-03710-923:7(2321-2329)Online publication date: 1-Apr-2019
https://dl.acm.org/doi/10.1007/s00500-018-03710-9
Das STripathi S(2018)Adaptive and intelligent energy efficient routing for transparent heterogeneous ad-hoc network by fusion of game theory and linear programmingApplied Intelligence10.1007/s10489-017-1061-648:7(1825-1845)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s10489-017-1061-6
Liao SChen Y(2018)A rough set-based association rule approach implemented on exploring beverages product spectrumApplied Intelligence10.1007/s10489-013-0465-140:3(464-478)Online publication date: 28-Dec-2018
https://dl.acm.org/doi/10.1007/s10489-013-0465-1
Amor NKhalfi ZFargier HSabbadin R(2016)Lexicographic refinements in possibilistic decision treesProceedings of the Twenty-second European Conference on Artificial Intelligence10.3233/978-1-61499-672-9-202(202-208)Online publication date: 29-Aug-2016
https://dl.acm.org/doi/10.3233/978-1-61499-672-9-202
Brzostowski JKowalczyk RPechoucek MSteiner DThompson S(2005)On possibilistic case-based reasoning for selecting partners for multi-attribute agent negotiationProceedings of the fourth international joint conference on Autonomous agents and multiagent systems10.1145/1082473.1082515(273-279)Online publication date: 25-Jul-2005
https://dl.acm.org/doi/10.1145/1082473.1082515
Brzostowski JKowalczyk R(2004)On possibilistic case-based reasoning for selecting partners in multi-agent negotiationProceedings of the 17th Australian joint conference on Advances in Artificial Intelligence10.1007/978-3-540-30549-1_60(694-705)Online publication date: 4-Dec-2004
https://dl.acm.org/doi/10.1007/978-3-540-30549-1_60

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents