Abstract
Decision-theoretic rough set models are a probabilistic extension of the algebraic rough set model. The required parameters for defining probabilistic lower and upper approximations are calculated based on more familiar notions of costs (risks) through the well-known Bayesian decision procedure. We review and revisit the decision-theoretic models and present new results. It is shown that we need to consider additional issues in probabilistic rough set models.
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References
Abd El-Monsef, M.M.E., Kilany, N.M.: Decision analysis via granulation based on general binary relation. International Journal of Mathematics and Mathematical Sciences, Article ID 12714 (2007)
Greco, S., Matarazzo, B., Slowinski, R.: Rough membership and bayesian confirmation measures for parameterized rough sets. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 314–324. Springer, Heidelberg (2005)
Deogun, J.S., et al.: Data mining: trends in research and development. In: Lin, T.Y. (ed.) Rough Sets and Data Mining, pp. 9–45. Kluwer Academic Publishers, Boston (1997)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. Wiley, New York (1973)
Grzymala-Busse, J.W.: LERS – a system for learning from examples based on rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Apllications and Advances of the Rough Sets Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)
Katzberg, J.D., Ziarko, W.: Variable precision rough sets with asymmetric bounds. In: Ziarko, W. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 167–177. Springer, Heidelberg (1994)
Kitchener, M., Beynon, M., Harrington, C.: Explaining the diffusion of medicaid home care waiver programs using VPRS decision rules. Health Care Management Science 7, 237–244 (2004)
Li, Y., Zhang, C., Swanb, J.R.: Rough set based model in information retrieval and filtering. In: Proceeding of the 5th International Conference on Information Systems Analysis and Synthesis, pp. 398–403 (1999)
Li, Y., Zhang, C., Swanb, J.R.: An information fltering model on the Web and its application in JobAgent. Knowledge-Based Systems 13, 285–296 (2000)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academatic Publishers, Boston (1991)
Pawlak, Z., Skowron, A.: Rough membership functions. In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 251–271. John Wiley and Sons, New York (1994)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177, 3–27 (2007)
Pawlak, Z., Skowron, A.: Rough sets: some extensions. Information Sciences 177, 28–40 (2007)
Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29, 81–95 (1988)
Qiu, G.F., Zhang, W.X., Wu, W.Z.: Characterizations of attributes in generalized approximation representation spaces. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 84–93. Springer, Heidelberg (2005)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Slezak, D.: Rough sets and Bayes factor. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 202–229. Springer, Heidelberg (2005)
Slezak, D., Ziarko, W.: Attribute reduction in the Bayesian version of variable precision rough set model. Electronic Notes in Theoretical Computer Science 82, 263–273 (2003)
Srinivasan, P., et al.: Vocabulary mining for information retrieval: rough sets and fuzzy sets. Information Processing and Management 37, 15–38 (2001)
Tsumoto, S.: Accuracy and coverage in rough set rule induction. In: Alpigini, J.J., et al. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 373–380. Springer, Heidelberg (2002)
Tsumoto, S.: Statistical independence from the viewpoint of linear algebra. In: Hacid, M.-S., et al. (eds.) ISMIS 2005. LNCS (LNAI), vol. 3488, pp. 56–64. Springer, Heidelberg (2005)
Wei, L.L., Zhang, W.X.: Probabilistic rough sets characterized by fuzzy sets. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems 12, 47–60 (2004)
Wong, S.K.M., Ziarko, W.: Comparison of the probabilistic approximate classification and the fuzzy set model. Fuzzy Sets and Systems 21, 357–362 (1987)
Wu, W.Z.: Upper and lower probabilities of fuzzy events induced by a fuzzy set-valued mapping. In: Urzyczyn, P. (ed.) TLCA 2005. LNCS, vol. 3461, pp. 345–353. Springer, Heidelberg (2005)
Yao, J.T., Herbert, J.P.: Web-based Support Systems based on Rough Set Analysis. Manuscript (2007)
Yao, J.T., Zhang, M.: Feature selection with adjustable criteria. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 204–213. Springer, Heidelberg (2005)
Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximation Reasoning 15, 291–317 (1996)
Yao, Y.Y.: Information granulation and approximation in a decision-theoretical model of rough sets. In: Polkowski, L., Pal, S.K., Skowron, A. (eds.) Rough-neuro Computing: Techniques for Computing with Words, pp. 491–516. Springer, Berlin (2003)
Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20, 287–297 (2003)
Yao, Y.Y.: Probabilistic rough set approximations. Manuscript (2006)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. International Journal of Man-machine Studies 37, 793–809 (1992)
Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems, vol. 5, pp. 17–24. North-Holland, New York (1990)
Zhang, W.X., et al.: Rough Set Theory and Methodology (in Chinese). Xi’an Jiaotong University Press, Xi’an (2001)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)
Ziarko, W.: Acquisition of hierarchy-structured probabilistic decision tables and rules from data. Expert Systems 20, 305–310 (2003)
Ziarko, W.: Probabilistic rough sets. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 283–293. Springer, Heidelberg (2005)
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Yao, Y. (2007). Decision-Theoretic Rough Set Models. In: Yao, J., Lingras, P., Wu, WZ., Szczuka, M., Cercone, N.J., Ślȩzak, D. (eds) Rough Sets and Knowledge Technology. RSKT 2007. Lecture Notes in Computer Science(), vol 4481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72458-2_1
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DOI: https://doi.org/10.1007/978-3-540-72458-2_1
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