Abstract
In this paper we consider a generalization of the indiscernibility relation, i.e., a relation R that is not necessarily reflexive, symmetric, or transitive. There exist 36 basic definitions of lower and upper approximations based on such relation R. Additionally, there are six probabilistic approximations, generalizations of 12 corresponding lower and upper approximations. How to convert remaining 24 lower and upper approximations to 12 respective probabilistic approximations is an open problem.
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Clark, P.G., Grzymala-Busse, J.W.: Experiments on probabilistic approximations. In: Proceedings of the 2011 IEEE International Conference on Granular Computing, pp. 144–149 (2011)
Clark, P.G., Grzymala-Busse, J.W.: Experiments on rule induction from incomplete data using three probabilistic approximations. In: Proceedings of the 2012 IEEE International Conference on Granular Computing, pp. 90–95 (2012)
Clark, P.G., Grzymala-Busse, J.W.: Experiments using three probabilistic approximations for rule induction from incomplete data sets. In: Proceeedings of the MCCSIS 2012, IADIS European Conference on Data Mining, ECDM 2012, pp. 72–78 (2012)
Clark, P.G., Grzymala-Busse, J.W.: Rule induction using probabilistic approximations and data with missing attribute values. In: Proceedings of the 15th IASTED International Conference on Artificial Intelligence and Soft Computing, ASC 2012, pp. 235–242 (2012)
Clark, P.G., Grzymala-Busse, J.W., Hippe, Z.S.: How good are probabilistic approximations for rule induction from data with missing attribute values? In: Yao, J., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 46–55. Springer, Heidelberg (2012)
Clark, P.G., Grzymala-Busse, J.W., Kuehnhausen, M.: Local probabilistic approximations for incomplete data. In: Chen, L., Felfernig, A., Liu, J., Raś, Z.W. (eds.) ISMIS 2012. LNCS, vol. 7661, pp. 93–98. Springer, Heidelberg (2012)
Clark, P.G., Grzymala-Busse, J.W., Kuehnhausen, M.: Mining incomplete data with many missing attribute values. a comparison of probabilistic and roug set approaches. In: Proceedings of the INTELLI 2013, the Second International Conference on Intelligent Systems and Applications, pp. 12–17 (2013)
Grzymala-Busse, J.W.: Rough set strategies to data with missing attribute values. In: Workshop Notes, Foundations and New Directions of Data Mining, in Conjunction with the 3rd International Conference on Data Mining, pp. 56–63 (2003)
Grzymala-Busse, J.W.: Data with missing attribute values: Generalization of indiscernibility relation and rule induction. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Swiniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 78–95. Springer, Heidelberg (2004)
Grzymala-Busse, J.W.: Three approaches to missing attribute values—a rough set perspective. In: Proceedings of the Workshop on Foundation of Data Mining, in conjunction with the Fourth IEEE International Conference on Data Mining, pp. 55–62 (2004)
Grzymala-Busse, J.W.: Generalized parameterized approximations. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 136–145. Springer, Heidelberg (2011)
Grzymala-Busse, J.W., Marepally, S.R., Yao, Y.: An empirical comparison of rule sets induced by LERS and probabilistic rough classification. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS, vol. 6086, pp. 590–599. Springer, Heidelberg (2010)
Grzymala-Busse, J.W., Rząsa, W.: Local and global approximations for incomplete data. In: Greco, S., et al. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 244–253. Springer, Heidelberg (2006)
Grzymala-Busse, J.W., Rząsa, W.: Definability of approximations for a generalization of the indiscernibility relation. In: Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (IEEE FOCI 2007), pp. 65–72 (2007)
Grzymala-Busse, J.W., Rząsa, W.: Local and global approximations for incomplete data. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 21–34. Springer, Heidelberg (2008)
Grzymala-Busse, J.W., Rząsa, W.: Definability and other properties of approximations for generalized indiscernibility relations. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XI. LNCS, vol. 5946, pp. 14–39. Springer, Heidelberg (2010)
Grzymala-Busse, J.W., Yao, Y.: A comparison of the LERS classification system and rule management in PRSM. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 202–210. Springer, Heidelberg (2008)
Grzymala-Busse, J.W., Yao, Y.: Probabilistic rule induction with the LERS data mining system. International Journal of Intelligent Systems 26, 518–539 (2011)
Grzymala-Busse, J.W., Ziarko, W.: Data mining based on rough sets. In: Wang, J. (ed.) Data Mining: Opportunities and Challenges, pp. 142–173. Idea Group Publ., Hershey (2003)
Kryszkiewicz, M.: Rough set approach to incomplete information systems. In: Proceedings of the Second Annual Joint Conference on Information Sciences, pp. 194–197 (1995)
Kryszkiewicz, M.: Rules in incomplete information systems. Information Sciences 113(3-4), 271–292 (1999)
Lin, T.Y.: Neighborhood systems and approximation in database and knowledge base systems. In: Proceedings of the ISMIS 1989, the Fourth International Symposium on Methodologies of Intelligent Systems, pp. 75–86 (1989)
Lin, T.Y.: Topological and fuzzy rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 287–304. Kluwer Academic Publishers, Dordrecht (1992)
Liu, G., Zhu, W.: Approximations in rough sets vs granluar computing for coverings. International Journal of Cognitive Informatics and Natural Intelligence 4, 63–76 (2010)
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 Academic Publishers, Dordrecht (1991)
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)
Ślęzak, D., Ziarko, W.: The investigation of the bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)
Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12, 331–336 (2000)
Stefanowski, J.: Algorithms of Decision Rule Induction in Data Mining. Poznan University of Technology Press, Poznan (2001)
Stefanowski, J., Tsoukiàs, A.: On the extension of rough sets under incomplete information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–82. Springer, Heidelberg (1999)
Stefanowski, J., Tsoukias, A.: Incomplete information tables and rough classification. Computational Intelligence 17(3), 545–566 (2001)
Tsumoto, S., Tanaka, H.: PRIMEROSE: probabilistic rule induction method based on rough sets and resampling methods. Computational Intelligence 11, 389–405 (1995)
Wang, G.: Extension of rough set under incomplete information systems. In: Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1098–1103 (2002)
Wong, S.K.M., Ziarko, W.: INFER—an adaptive decision support system based on the probabilistic approximate classification. In: Proceedings of the 6th International Workshop on Expert Systems and their Applications, pp. 713–726 (1986)
Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15, 291–317 (1996)
Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111, 239–259 (1998)
Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20, 287–297 (2003)
Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49, 255–271 (2008)
Yao, Y.Y., Lin, T.Y.: Generalization of rough sets using modal logics. Intelligent Automation and Soft Computing 2, 103–120 (1996)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximate 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: Proceedings of the 5th International Symposium on Methodologies for Intelligent Systems, pp. 388–395 (1990)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46(1), 39–59 (1993)
Ziarko, W.: Probabilistic approach to rough sets. International Journal of Approximate Reasoning 49, 272–284 (2008)
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Clark, P.G., Grzymała-Busse, J.W., Rząsa, W. (2013). Generalizations of Approximations. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds) Rough Sets and Knowledge Technology. RSKT 2013. Lecture Notes in Computer Science(), vol 8171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41299-8_5
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DOI: https://doi.org/10.1007/978-3-642-41299-8_5
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