The Comparison of Approaches Used for Estimating Uncertain Probabilities

Oleg Uzhga-Rebrov, Galina Kuleshova

Abstract


Probabilistic estimates are numerical representations of chances of random event occurrence. The classical theory of probability is based on the assumption that probabilistic estimates are deterministic. If available initial data are sufficient, this kind of estimates can be really obtained. However, when such data are not available, probabilistic estimates become uncertain. This paper analyses and compares three widespread approaches to modelling uncertain estimates and provides practical recommendations on their use.


Keywords:
Choquet capacities; interval probabilities; lower and upper probabilities; -measures; monotone measures; Möbius representation

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References


P. Billingsley, Probability and Measure. John Wiley, New York 1986.

L.M. De Campos, J.F. Huete and S.Moral, “Probability intervals: a tool for uncertain reasoning”, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 2, No. 2, pp. 167 – 196, 1994.

G.J. Klir, Uncertainty and Information: Foundations of Generalized Information Theory, New Jersey, John Wiley & Sons, 2006.

D.H. Krantz, R.D. Luce, P. Suppes and A.Tversky, Foundations of Measurement, New York and London, Academic Press, 1971.

M. Sugeno, “Fuzzy measures and fuzzy integrals: a survey,” in Fuzzy Automata and Decision Processes. North Holland, Amsterdam and New York, 1977, pp. 89-102.

Z. Wang and G. J. Klir, Fuzzy Measure Theory, New York, Plenum Press, 1992.


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Copyright (c) 2013 Oleg Uzhga-Rebrov, Galina Kuleshova

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