Abstract
We study probability intervals as a interesting tool to represent uncertain information. Basic concepts for the management of uncertain information, as combination, marginalization, conditioning and integration are considered for probability intervals. Moreover, the relationships of this theory with some others, as lower and upper probabilities and Choquet capacities of order two are also clarified. The advantages of probability intervals with respect to these formalisms in computational efficiency are highlighted too.
This work has been supported by the DGICYT under Project n. PB92-0939
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
L.M. de Campos, M.T. Lamata, S. Moral, Logical connectives for combining fuzzy measures, in Methodologies for Intelligent Systems 3, Z.W. Ras, L. Saitta (Eds.) North-Holland, 11–18 (1988).
L.M. de Campos, M.J. Bolaños, Representation of fuzzy measures through probabilities, Fuzzy Sets and Systems 31, 23–36 (1989).
L.M. de Campos, M.T. Lamata, S. Moral, The concept of conditional fuzzy measure, International Journal of Intelligent Systems 5, 237–246 (1990).
L.M. de Campos, M.J. Bolaños, Characterization and comparison of Sugeno and Choquet integrals, Fuzzy Sets and Systems 52, 61–67 (1992).
L.M. de Campos, J.F. Huete, Independence concepts in upper and lower probabilities, in Uncertainty in Intelligent Systems, B. Bouchon-Meunier, L. Valverde, R.R. Yager (Eds.), North-Holland, 85–96 (1993).
L.M. de Campos, J.F. Huete, S. Moral, Probability intervals: a tool for uncertain reasoning, DECSAI Technical Report 93205, Universidad de Granada (1993).
J.E. Cano, S. Moral, J.F. Verdegay, Propagation of convex sets of probabilities in directed acyclic networks, in Uncertainty in Intelligent Systems, B. Bouchon-Meunier, L. Valverde, R.R. Yager (Eds.), North-Holland, 15–26 (1993)
G. Choquet, Theory of capacities, Ann. Inst. Fourier 5, 131–295 (1953).
D. Dubois, H. Prade, A set-theoretic view of belief functions, International Journal of General Systems 12, 193–226 (1986).
H.E. Kyburg, Bayesian and non-bayesian evidential updating, Artificial Intelligence 31, 271–293 (1987).
S. Moral, L.M. de Campos, Updating uncertain information, in Uncertainty in Knowledge Bases, Lecture Notes in Computer Science 521, B. Bouchon-Meunier, R.R. Yager, L.A. Zadeh (Eds.), Springer Verlag, 58–67 (1991).
J. Pearl, Probabilistic reasoning in intelligent systems: networks of plausible inference, Morgan and Kaufmann, San Mateo (1988).
M. Sugeno, Theory of fuzzy integrals and its application, Ph.D. Thesis, Tokio Inst. of Technology (1974).
B. Tessem, Interval representation on uncertainty in Artificial Intelligence, Ph.D. Thesis, Department of Informatics, University of Bergen, Norway (1989).
L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, 3–28 (1978).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Campos, L.M., Huete, J.F., Moral, S. (1995). Uncertainty management using probability intervals. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Advances in Intelligent Computing — IPMU '94. IPMU 1994. Lecture Notes in Computer Science, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035950
Download citation
DOI: https://doi.org/10.1007/BFb0035950
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60116-6
Online ISBN: 978-3-540-49443-0
eBook Packages: Springer Book Archive