Abstract
This paper concerns a relationship between Bayes’ inference rule and decision rules from the rough set perspective.
In statistical inference based on the Bayes’ rule it is assumed that some prior knowledge (prior probability) about some parameters without knowledge about the data is given first. Next the posterior probability is computed by employing the available data. The posterior probability is then used to verify the prior probability.
In the rough set philosophy with every decision rule two conditional probabilities, called certainty and coverage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic notions of rough set theory. Besides, it is revealed that these two factors satisfy the Bayes’ rule. That means that we can use to data analysis the Bayes’ rule of inference without referring to Bayesian philosophy of prior and posterior probabilities.
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References
Adams, E.W.: The logic of conditionals, an application of probability to deductive logic. D. Reidel Publishing Company, Dordrechtz (1975)
Grzymała-Busse, J.: Managing Uncertainty in Expert Systems. Kluwer Academic Publishers, Dordrecht (1991)
Łukasiewicz, J.: Die logishen Grundlagen der Wahrscheinilchkeitsrechnung. Krakow (1913); Borkowski, L. (ed.): Jan Łukasiewicz - Selected Works. North Holland Publishing Company/Polish Scientific Publishers, Amsterdam/Warazawa (1970)
Pawlak, Z.: Rough Sets - Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston (1991)
Pawlak, Z.: Reasoning about data- a rough set perspective. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 25–34. Springer, Heidelberg (1998)
Pawlak, Z.: Rough Modus Ponens. In: Proceedings of Seventh International Conference, International Processing and Management of Uncertainty in Knowledge-Based (IPMU), Paris, France, July 6-10, pp. 1162–1166 (1998)
Pawlak, Z.: Logic, probability and rough sets (to appear)
Pawlak, Z.: Inference rules, decision rules and rough sets (to appear)
Pawlak, Z., Skowron, A.: Rough membership functions. In: Yaeger, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster Shafer Theory of Evidence, pp. 251–271. John Wiley & Sons, Inc., NewYork (1994)
Polkowski, L., Skowron, A. (eds.): RSCTC 1998. LNCS (LNAI), vol. 1424. Springer, Heidelberg (1998)
Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery, vol. 1(2). Physica-Verlag, New York (1998)
Skowron, A.: Menagement of uncertainty in AI: A rough set approach. In: Proceedings of the conference SOFTEKS, pp. 69–86. Springer, British Computer Society (1994)
Tsumoto, S., Kobayashi, S., Yokomori, T., Tanaka, H., Nakamura, A. (eds.): Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery (RSFD 1996), November 6-8. The University of Tokyo (1996)
Tsumoto, S.: Modelling medical diagnostic rules based on rough sets. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 475–482. Springer, Heidelberg (1998)
Ziarko, W.: Approximation Region -Based Decision Tables. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, vol. 1(2), pp. 178–185. Physica-Verlag, New York (1998)
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Pawlak, Z. (1999). Decision Rules, Bayes’ Rule and Rough Sets. In: Zhong, N., Skowron, A., Ohsuga, S. (eds) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing. RSFDGrC 1999. Lecture Notes in Computer Science(), vol 1711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48061-7_1
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DOI: https://doi.org/10.1007/978-3-540-48061-7_1
Publisher Name: Springer, Berlin, Heidelberg
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