Abstract
Rough set theory offers new perspective on Bayes’ theorem. The look on Bayes’ theorem offered by rough set theory reveals that any data set (decision table) satisfies total probability theorem and Bayes’ theorem. These properties can be used directly to draw conclusions from objective data without referring to subjective prior knowledge and its revision if new evidence is available.
Thus the rough set view on Bayes’ theorem is rather objective in contrast to subjective “classical” interpretation of the theorem .
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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; 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.: Bayesian 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. Springer-Verlag, Berlin, Heidelberg, New York (1999)
Łukasiewicz, J.: Die logishen Grundlagen der Wahrscheinilchkeitsrechnung. Kraków, 1913. In: L. Borkowski (ed.), Jan Łukasiewicz— 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. Proceeding of International Workshop on Rough Set Theory and Granular Computing (RSTGC-2001), Matsue, Shimane, Japan, May 20–22, S. Hirano, M. Inuiguchi and S. Tsumoto(eds.), Bull. of Int. Rough Set Society vol. 5 no. 1/2 2001 1–8
Z. Pawlak, A. Skowron, 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
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Pawlak, Z. (2002). The Rough Set View on Bayes’ Theorem. In: Pal, N.R., Sugeno, M. (eds) Advances in Soft Computing — AFSS 2002. AFSS 2002. Lecture Notes in Computer Science(), vol 2275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45631-7_15
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DOI: https://doi.org/10.1007/3-540-45631-7_15
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