Abstract
The concept of (crisp) set is now extended to fuzzy set and rough set. The key notion of rough set is the two boundaries, the lower and upper approximations, and the lower approximation must be inside of the upper approximation. This inclusive condition makes the inference using rough sets complex: each approximation can not be determined independently. In this paper, the probabilistic inferences on rough sets based on two types of interpretation of If-Then rules, conditional probability and logical implication, are discussed. There are some interesting correlation between the lower and upper approximation after probabilistic inference.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
N. J. Nilsson, “Probabilistic Logic”, Artificial Intelligence, Vol.28, No.1, 71–78, (1986).
Z. Pawlak, “Decision Rules, Bayes' Rule and Rough Sets”, N. Zhong, A. Skowron, S. Ohsuga (eds.) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing LNAI 1711, 1–9, Springer-Verlag (1999).
Z. Pawlak, “Rough Sets”, International Journal of Computer and Information Sciences, 11, 341–356, (1982).
Y. Yamauchi, M. Mukaidono, “Interval and Paired Probabilities for Treating Uncertain Events,” IEICE Transactions of Information and Systems, Vol.E82-D, No.5, 955–961, (1999).
Y. Yamauchi, M. Mukaidono, “Probabilistic Inference and Bayesian Theorem Based on Logical Implication” N. Zhong, A. Skowron, S. Ohsuga (eds) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing LNAI 1711, 334–342, Springer-Verlag (1999).
Y. Y. Yao, “A Comparison of Two Interval-valued Probabilistic Reasoning Methods”, Proceedings of the 6th International Conference on Computing and Information, special issue of Journal of Computing and Information, 1, 1090–1105, (1995).
Y. Y. Yao, X. Li, “Comparison of Rough-Set and Interval-Set Models for Uncertain Reasoning”, Fundamenta Informaticae, 27, 289–298, (1996).
Y. Y. Yao, Q. Liu, “A Generalized Decision Logic in Interval-Set-Valued Information Tables” N. Zhong, A. Skowron, S. Ohsuga (eds) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing LNAI 1711, 285–293, Springer-Verlag (1999).
Y. Y. Yao, S. K. M. Wong, “Interval Approaches for Uncertain Reasoning”, Z. W. Ras and A. Skowron (eds.) Foundations of Intelligent Systems, LNAI 1325, 381–390, (1997).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yamauchi, Y., Mukaidono, M. (2001). Probabilistic Inference and Bayesian Theorem on Rough Sets. In: Ziarko, W., Yao, Y. (eds) Rough Sets and Current Trends in Computing. RSCTC 2000. Lecture Notes in Computer Science(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45554-X_8
Download citation
DOI: https://doi.org/10.1007/3-540-45554-X_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43074-2
Online ISBN: 978-3-540-45554-7
eBook Packages: Springer Book Archive