Abstract
We present a novel approach to understanding the concepts of the theory of rough sets in terms of the inverse probabilities derivable from data. It is related to the Bayes factor known from the Bayesian hypothesis testing methods. The proposed Rough Bayesian model (RB) does not require information about the prior and posterior probabilities in case they are not provided in a confirmable way. We discuss RB with respect to its correspondence to the original Rough Set model (RS) introduced by Pawlak and Variable Precision Rough Set model (VPRS) introduced by Ziarko. We pay a special attention on RB’s capability to deal with multi-decision problems. We also propose a method for distributed data storage relevant to computational needs of our approach.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Box, G.E.P., Tiao, G.C.: Bayesian Inference in Statistical Analysis. Wiley, Chichester (1992)
Duentsch, I., Gediga, G.: Uncertainty measures of rough set prediction. Artificial Intelligence 106, 77–107 (1998)
Greco, S., Pawlak, Z., Słowiński, R.: Can Bayesian confirmation measures be useful for the rough set decision rules? Engineering Application of Artificial Intelligence 17, 345–361 (2004)
Good, I.J.: The Interface Between Statistics and Philosophy of Science. Statistical Science 3, 386–397 (1988)
Hilderman, R.J., Hamilton, H.J.: Knowledge Discovery and Measures of Interest. Kluwer, Dordrecht (2002)
Jeffreys, H.: Theory of Probability. Clarendon Press, Oxford (1961)
Kamber, M., Shingal, R.: Evaluating the interestingness of characteristic rules. In: Proc. of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD 1996), Portland, Oregon, pp. 263–266 (1996)
Kloesgen, W., Żytkow, J.M. (eds.): Handbook of Data Mining and Knowledge Discovery. Oxford University Press, Oxford (2002)
Mitchell, T.: Machine Learning. Mc Graw Hill, New York (1998)
Pawlak, Z.: Rough sets – Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z.: New Look on Bayes’ Theorem – The Rough Set Outlook. In: Proc. Of JSAI RSTGC 2001, pp. 1–8 (2001)
Pawlak, Z.: Decision Tables and Decision Spaces. In: Proc. of the 6th International Conference on Soft Computing and Distributed Processing (SCDP 2002), Rzeszów, Poland, June 24-25 (2002)
Pawlak, Z., Skowron, A.: Rough membership functions. In: Advances in the Dempster Shafer Theory of Evidence, pp. 251–271. Wiley, Chichester (1994)
Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.): Rough Set Methods and Applications. Physica Verlag, Heidelberg (2000)
Raftery, A.E.: Hypothesis testing and model selection. In: Gilks, W.R., Richardson, S., Spiegelhalter, D.J. (eds.) Markov Chain Monte Carlo in Practice, pp. 163–187. Chapman and Hall, London (1996)
Ślez̨ak, D.: Approximate Entropy Reducts. Fundamenta Informaticae 53/3-4, 365–390 (2002)
Ślez̨ak, D.: The Rough Bayesian Model For Distributed Decision Systems. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 384–393. Springer, Heidelberg (2004)
Ślez̨ak, D., Ziarko, W.: Bayesian Rough Set Model. In: Proc. of FDM 2002, pp. 131–135 (2002)
Ślez̨ak, D., Ziarko, W.: The Investigation of the Bayesian Rough Set Model. International Journal of Approximate Reasoning (2005) (to appear)
Swinburne, R. (ed.): Bayes’s Theorem. Proc. of the British Academy 113 (2003)
Tsumoto, S.: Accuracy and Coverage in Rough Set Rule Induction. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 373–380. Springer, Heidelberg (2002)
Wong, S.K.M., Ziarko, W.: Comparison of the probabilistic approximate classification and the fuzzy set model. International Journal for Fuzzy Sets and Systems 21, 357–362 (1986)
Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20(5), 287–297 (2003)
Ziarko, W.: Variable precision rough sets model. Journal of Computer and Systems Sciences 46(1), 39–59 (1993)
Ziarko, W.: Set approximation quality measures in the variable precision rough set model. In: Soft Computing Systems, Management and Applications, pp. 442–452. IOS Press, Amsterdam (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ślęzak, D. (2005). Rough Sets and Bayes Factor. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets III. Lecture Notes in Computer Science, vol 3400. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427834_10
Download citation
DOI: https://doi.org/10.1007/11427834_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25998-5
Online ISBN: 978-3-540-31850-7
eBook Packages: Computer ScienceComputer Science (R0)