Abstract
Rough sets based rule generation from tables with uncertain numerical values is presented. We have already focused on two topics, i.e., rule generation from tables with non-deterministic information and rule generation from tables with numerical values. For non-deterministic information, we have extended the typical rough sets to rough sets based on uncertain information. For numerical values, we have defined numerical patterns with two symbols ’@’ and ’#’, and have introduced the equivalence classes depending upon the figures. This paper employs intervals for uncertain numerical values, as well as rules with intervals. By using a real example, we show that it is possible to handle such rules according to the same method as the one already developed for non-deterministic information.
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
Agrawal, R., Srikant, R.: Fast Algorithms for Mining Association Rules. In: Proc. the 20th Very Large Data Base, pp. 487–499 (1994)
Ceglar, A., Roddick, J.F.: Association mining. ACM Comput. Surv. 38(2) (2006)
Chmielewski, M., Grzymala-Busse, J.: Global Discretization of Continuous Attributes as Preprocessing for Machine Learning. Int’l. J. Approximate Reasoning 15, 319–331 (1996)
Cluster Analysis, http://en.wikipedia.org/wiki/Cluster_analysis
Confidence Interval, http://en.wikipedia.org/wiki/Confidence_interval
Grzymala-Busse, J.: Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction. Transactions on Rough Sets 1, 78–95 (2004)
Grzymala-Busse, J., Stefanowski, J.: Three Discretization Methods for Rule Induction. Int’l. Journal of Intelligent Systems 16, 29–38 (2001)
Infobright.org Forums, http://www.infobright.org/Forums/viewthread/288/ , http://www.infobright.org/Forums/viewthread/621/
Kryszkiewicz, M.: Rules in Incomplete Information Systems. Information Sciences 113, 271–292 (1999)
Leung, Y., Fischer, M.M., Wu, W.Z., Mi, J.S.: A Rough Set Approach for the Discovery of Classification Rules in Interval-valued Information Systems. Int’l. J. Approximate Reasoning 47(2), 233–246 (2008)
Lipski, W.: On Semantic Issues Connected with Incomplete Information Data Base. ACM Trans. DBS 4, 269–296 (1979)
Murai, T., Resconi, G., Nakata, M., Sato, Y.: Operations of Zooming In and Out on Possible Worlds for Semantic Fields. In: Knowledge-Based Intelligent Information Engineering Systems and Allied Technologies, pp. 1083–1087. IOS Press, Amsterdam (2002)
Orłowska, E., Pawlak, Z.: Representation of Nondeterministic Information. Theoretical Computer Science 29, 27–39 (1984)
Pawlak, Z.: Rough Sets. Kluwer Academic Publishers, Dordrecht (1991)
Quinlan, J.R.: Improved Use of Continuous Attributes in C4.5. Journal of Artificial Intelligence Research 4, 77–90 (1996)
Sakai, H., Okuma, A.: Basic Algorithms and Tools for Rough Non-deterministic Information Analysis. Transactions on Rough Sets 1, 209–231 (2004)
Sakai, H., Ishibashi, R., Nakata, M.: On Rules and Apriori Algorithm in Non-deterministic Information Systems. Transactions on Rough Sets 9, 328–350 (2008)
Sakai, H., Ishibashi, R., Nakata, M.: Lower and Upper Approximations of Rules in Non-deterministic Information Systems. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 299–309. Springer, Heidelberg (2008)
Sakai, H., Koba, K., Nakata, M.: Rough Sets Based Rule Generation from Data with Categorical and Numerical Values. Journal of Advanced Computational Intelligence and Intelligent Informatics 12(5), 426–434 (2008)
Skowron, A., Rauszer, C.: The Discernibility Matrices and Functions in Information Systems. In: Intelligent Decision Support - Handbook of Advances and Applications of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)
Ślȩzak, D., Sakai, H.: Automatic Extraction of Decision Rules from Non-deterministic Data Systems: Theoretical Foundations and SQL-Based Implementation. In: Proc. of DTA 2009. CCIS, vol. 64, pp. 151–162 (2009)
UCI Machine Learning Repository, http://mlearn.ics.uci.edu/MLRepository.html
Van-Nam, H., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H. (eds.): Interval / Probabilistic Uncertainty and Non-Classical Logics. Advances in Soft Computing, vol. 46. Springer, Heidelberg (2008)
Van-Nam, H., Nakamori, Y., Hu, C., Kreinovich, V.: On Decision Making under Interval Uncertainty. In: Proc.39th International Symposium on Multiple-Valued Logic, pp. 214–220. IEEE Society, Los Alamitos (2009)
Yang, X., Yu, D., Jingyu, Y., Wei, L.: Dominance-based Rough Set Approach to Incomplete Interval-valued Information System. Data and Knowledge Engineering 68(11), 1331–1347 (2009)
Yao, Y., Liau, C., Zhong, N.: Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions. In: Zhong, N., Raś, Z.W., Tsumoto, S., Suzuki, E. (eds.) ISMIS 2003. LNCS (LNAI), vol. 2871, pp. 152–159. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sakai, H., Nakata, M., Ślȩzak, D. (2010). Toward Rough Sets Based Rule Generation from Tables with Uncertain Numerical Values. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-11960-6_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11959-0
Online ISBN: 978-3-642-11960-6
eBook Packages: EngineeringEngineering (R0)