Abstract
Rough set theory offers new insight into Bayes’ theorem. It does not refer either to prior or posterior probabilities, inherently associated with Bayesian reasoning, but reveals some probabilistic structure of the data being analyzed. This property can be used directly to draw conclusions from data.
It is also worth mentioning the relationship between Bayes’ theorem and flow graphs.
“I had come to an entirely erroneus conclusions, which shows, my dear Watson, how dangerous it always is to reason from insufficient data”
Sherlock Holmes In: “The speckled band”
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adams, E. W.: The logic of conditionals, an application of probability to deductive Logic. D. Reidel Publishing Company, Dordrecht, Boston (1975)
Bayes, T.: An essay toward solving a problem in the doctrine of chances, Phil. Trans. Roy. Soc. 53 (1763) 370–418;
Bayes, T.: An essay toward solving a problem in the doctrine of chances, Reprint Biometrika 45 (1958) 296–315
Bernardo, J. M., Smith, A. F. M.: Baysian theory, Wiley series in probability and mathematical statistics. John Wiley & Sons, Chichester, New York, Brisbane, Toronto, Singapore (1994)
Box, G.E.P., Tiao, G.C.: Bayesiaon inference in statistical analysis. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1992)
Berthold, M., Hand, D.J.: Intelligent data analysis, an introduction. SpringerVerlag, Berlin , Heidelberg, New York (1999)
Ford, L.R., Fulkerson, D. R.: Flows in Networks. Princeton University Press, Princeton, New Yersy (1962)
Lukasiewicz, J.: Die logishen Grundlagen der Wahrscheinilchkeitsrechnung. Krakow (1913). In: L. Borkowski (ed.), Jan Lukasiewicz — Selected Works, North Holland Publishing Company, Amsterdam, London, Polish Scientific Publishers, Warsaw (1970)
Pawlak, Z.: Rough sets — theoretical aspect of reasoning about data, Kluwer Academic Publishers, Boston, Dordrech, London (1991)
Pawlak, Z.: New Look on Bayes’ Theorem — the Rough Set Outlook. Proceedings of the International Workshop on Rough Set Theory and Granular Computing (RSTGC-2001), S. Hirano, M. Inuiguichi and S. Tsumoto (eds.), Bull. of International Rough Set Society, Vol. 5. No. 1/2, Matsue, Shimane, Japan, May 20–22, (2001) 1–8
Pawlak, Z., Skowron, A.: Rough membership functions. Advances in the Dempster-Shafer Theory of Evidence, R, Yager, M. Fedrizzi, J. Kacprzyk (eds.), John Wiley & Sons, Inc. New York (1994) 251–271
Skowron, A.: Rough Sets in KDD (plenary talk); 16-th World Computer Congress (IFFIP’2000), Beijing, August 19–25, 2000, In:Zhongzhi Shi, Boi Faltings, Mark Musem (eds.) Proceedings of the Conference on Intelligent Information Processing (IIP2000), Publishing Hous of Electronic Industry, Beijing (2000) 1–17
Tsumoto, S., Tanaka, H.: Discovery of functional components of proteins based on PRIMEROSE and domain knowledge hierarchy. Proceedings of the Workshop on Rough Sets and Soft Computing (RSSC-94) (1994): Lin, T.Y., and Wildberger, A.M.(eds.) Soft Computing (1995) 280–285
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Pawlak, Z. (2003). Bayes’ Theorem — the Rough Set Perspective. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds) Rough Set Theory and Granular Computing. Studies in Fuzziness and Soft Computing, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36473-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-36473-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05614-7
Online ISBN: 978-3-540-36473-3
eBook Packages: Springer Book Archive