Abstract
Rule induction based on indiscernible classes from neighborhood rough sets is described in information tables with continuous values. An indiscernible range that a value has in an attribute is determined by a threshold on that attribute. The indiscernible class of every object is derived from using the indiscernible range. First, lower and upper approximations are described in complete information tables by using indiscernible classes. Rules are obtained from the approximations. A rule that an object supports, which is called a single rule, is short of applicability. To improve the applicability of rules, a series of single rules is put into one rule expressed in an interval value, which is called a combined rule. Second, these are addressed in incomplete information tables. Incomplete information is expressed in a set of values or an interval value. Two types of indiscernible classes; namely, certainly and possibly indiscernible ones, are obtained from in an information table. The actual indiscernibility class is between the certainly and possibly indiscernible classes. The family of indiscernible classes of an object has a lattice structure. The minimal element is the certainly indiscernible class while the maximal one is the possibly indiscernible class. By using certainly and possibly indiscernible classes, we obtain four types of approximations: certain lower, certain upper, possible lower, and possible upper approximations. From these approximations we obtain four types of combined rules: certain and consistent, certain and inconsistent, possible and consistent, and possible and inconsistent ones. These combined rules have greater applicability than single rules that individual objects support.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
For the sake of simplicity and space limitation, We describe the case of an attribute, although our approach can be easily extended to the case of more than one attribute.
- 2.
Hu and Yao also say that approximations describes by using an interval set in information tables with incomplete information [2].
References
Grzymala-Busse, J.W.: Mining numerical data – a rough set approach. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XI. LNCS, vol. 5946, pp. 1–13. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11479-3_1
Hu, M.J., Yao, Y.Y.: Rough set approximations in an incomplete information table. In: Polkowski, L., et al. (eds.) IJCRS 2017. LNCS (LNAI), vol. 10314, pp. 200–215. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60840-2_14
Jing, S., She, K., Ali, S.: A universal neighborhood rough sets model for knowledge discovering from incomplete hetergeneous data. Expert Syst. 30(1), 89–96 (2013). https://doi.org/10.1111/j.1468-0394.2012.00633_x
Kryszkiewicz, M.: Rules in incomplete information systems. Inf. Sci. 113, 271–292 (1999)
Lipski, W.: On semantics issues connected with incomplete information databases. ACM Trans. Database Syst. 4, 262–296 (1979)
Lipski, W.: On databases with incomplete information. J. ACM 28, 41–70 (1981)
Lin, T.Y.: Neighborhood systems: a qualitative theory for fuzzy and rough sets. In: Wang, P. (ed.) Advances in Machine Intelligence and Soft Computing, vol. IV, pp. 132–155. Duke University (1997)
Nakata, M., Sakai, H.: Rough sets handling missing values probabilistically interpreted. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 325–334. Springer, Heidelberg (2005). https://doi.org/10.1007/11548669_34
Nakata, M., Sakai, H.: Applying rough sets to information tables containing missing values. In: Proceedings of 39th International Symposium on Multiple-Valued Logic, pp. 286–291. IEEE Press (2009). https://doi.org/10.1109/ISMVL.2009.1
Nakata, M., Sakai, H.: Twofold rough approximations under incomplete information. Int. J. Gener. Syst. 42, 546–571 (2013). https://doi.org/10.1080/17451000.2013.798898
Nakata, M., Sakai, H.: Describing rough approximations by indiscernibility relations in information tables with incomplete information. In: Carvalho, J.P., Lesot, M.-J., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2016. CCIS, vol. 611, pp. 355–366. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40581-0_29
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991). https://doi.org/10.1007/978-94-011-3534-4
Sikora, M.: Decision rule-based data models using TRS and NetTRS – methods and algorithms. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XI. LNCS, vol. 5946, pp. 130–160. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11479-3_8
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Stefanowski, J., Tsoukiàs, A.: Incomplete information tables and rough classification. Comput. Intell. 17, 545–566 (2001)
Yang, X., Zhang, M., Dou, H., Yang, Y.: Neighborhood systems-based rough sets in incomplete information system. Inf. Sci. 24, 858–867 (2011). https://doi.org/10.1016/j.knosys.2011.03.007
Zenga, A., Lia, T., Liuc, D., Zhanga, J., Chena, H.: A fuzzy rough set approach for incremental feature selection on hybrid information systems. Fuzzy Sets Syst. 258, 39–60 (2015). https://doi.org/10.1016/j.fss.2014.08.014
Zhao, B., Chen, X., Zeng, Q.: Incomplete hybrid attributes reduction based on neighborhood granulation and approximation. In: 2009 International Conference on Mechatronics and Automation, pp. 2066–2071. IEEE Press (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Nakata, M., Sakai, H., Hara, K. (2018). Rule Induction Based on Indiscernible Classes from Rough Sets in Information Tables with Continuous Values. In: Nguyen, H., Ha, QT., Li, T., Przybyła-Kasperek, M. (eds) Rough Sets. IJCRS 2018. Lecture Notes in Computer Science(), vol 11103. Springer, Cham. https://doi.org/10.1007/978-3-319-99368-3_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-99368-3_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99367-6
Online ISBN: 978-3-319-99368-3
eBook Packages: Computer ScienceComputer Science (R0)