Abstract
The aim of this contribution is to develop, following the pattern applied in the theory of statistical decision functions, an analogous mathematical tool for decision making under uncertainty supposing that probabilistic measures are replaced by the possibilistic ones and expected values are defined by Sugeno integrals with the minimum taken as the conjunctive t-seminorm function. The model is illustrated by possibilistic decision functions for the case of sequences of coin tosses.
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References
S. Benferhat, C. Sossai: Mergind Uncertain Knowledge Bases in a Possibilistic Logic Framework. In: UAI 98-Proceedings of the 14th Annual Conference (Gregory F. Cooper and Serafim Morales, Eds.), Morgan Kaufmann Publishers, Inc., San Francisco, 1998, pp. 8–15.
D. Blackwell, N.A. Girshick: Theory of Games and Statistical Decisions. John Wiley and Sons, New York, 1954.
G. De Cooman: Possibility Theory-Part I, II, III. Int. J. General Systems 25 (1997), No. 4, pp. 291–323 (Part I), 325-351 (Part II), 353-371 (Part III).
D. Dubois, H. Prade: Théorie des Possibilités. Masson, Paris, 1985.
D. Dubois, H. Fargier, H. Prade: Decision-Making under Ordinal Preferences and Comparative Uncertainty. In: UAI 97-Proceedings of the 13th Annual Conference (Dan Geiger and Prakash Shenoy, Eds.). 1997, pp. 157–164.
D. Dubois, H. Prade, R. Sabbadin: Decision under Qualitative Uncertainty with Sugeno Integrals-an Axiomatic Approach. In: IFSA’97-Proceedings, Vol. I, pp. 441–446.
D. Dubois, H. Prade, R. Sabbadin: Qualitative Decision Theory with Sugeno Integral. In: UAI 98-Proceedings of the 14th Annual Conference (Gregory F. Cooper and Serafim Morales, Eds.), Morgan Kaufmann Publishers, Inc., San Francisco, 1998, pp. 121–128.
I. Kramosil: Boolean-Like Interpretation of Sugeno Integral. In: ECSQARU99-Proceedings (Anthony Hunter and Simon Parsons, Eds.). LNAI 1638, Springer Verlag 1999, pp. 245–255.
I. Kramosil: On Statistical and Possibilistic Independence. Submitted for publication.
E. L. Lehman: Testing Statistical Hypotheses. John Wiley and Sons, New York, 1947.
L.A. Zadeh: Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems 1 (1978), no. 1, pp. 3–28.
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Kramosil, I. (1999). Towards Possibilistic Decision Functions with Minimum-Based Sugeno Integrals. In: Pavelka, J., Tel, G., Bartošek, M. (eds) SOFSEM’99: Theory and Practice of Informatics. SOFSEM 1999. Lecture Notes in Computer Science, vol 1725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47849-3_30
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DOI: https://doi.org/10.1007/3-540-47849-3_30
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