Abstract
There are multiple kinds of data in information systems, e.g., categorical data, numerical data, set-valued data, interval-valued data and missing data. Such information systems are called as composite information systems in this paper. To process such data, composite rough sets are introduced, composite relation is defined and composite classes are used to drive approximations from composite information systems. Lower and upper approximations of a concept are the basis for rule acquisition and attribute reduction in rough set theory. To intuitively compute the approximations, positive, boundary and negative regions, matrix-based method is presented in composite rough sets. A case study validates the feasibility of the proposed method.
This work is supported by the National Science Foundation of China (Nos. 60873108, 61175047, 61100117), the Fundamental Research Funds for the Central Universities (No. SWJTU11ZT08), the Doctoral Innovation Foundation of Southwest Jiaotong University (No. 2012ZJB), and the Young Software Innovation Foundation of Sichuan Province (No. 2011-017), China.
This is a preview of subscription content, log in via an institution to check access.
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
Dubois, D., Prade, H.: Putting fuzzy sets and rough sets together. In: Slowiniski, R. (ed.) Intelligent Decision Support, pp. 203–232. Kluwer Academic, Dordrecht (1992)
Grzymała-Busse, J.W.: Characteristic Relations for Incomplete Data: A Generalization of the Indiscernibility Relation. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 244–253. Springer, Heidelberg (2004)
Guan, Y., Wang, H.: Set-valued information systems. Information Sciences 176(17), 2507–2525 (2006)
Abu-Donia, H.M.: Multi knowledge based rough approximations and applications. Knowledge-Based Systems 26, 20–29 (2012)
Hu, Q., Xie, Z., Yu, D.: Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recognition 40, 3509–3521 (2007)
Hu, Q., Yu, D., Liu, J., Wu, C.: Neighborhood rough set based heterogeneous feature subset selection. Information Sciences 178(18), 3577–3594 (2008)
Kryszkiewicz, M.: Rough set approach to incomplete information systems. Information Sciences 112(1-4), 39–49 (1998)
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. International Journal of Approximate Reasoning 47(2), 233–246 (2008)
Li, T., Ruan, D., Wets, G., Song, J., Xu, Y.: A rough sets based characteristic relation approach for dynamic attribute generalization in data mining. Knowledge-Based Systems 20(5), 485–494 (2007)
Liu, G.: The axiomatization of the rough set upper approximation operations. Fundamenta Informaticae 69(3), 331–342 (2006)
Liu, G.: Axiomatic systems for rough sets and fuzzy rough sets. International Journal of Approximate Reasoning 48(3), 857–867 (2008)
Mi, J.S., Zhang, W.X.: An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences 160(1-4), 235–249 (2004)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, vol, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177(1), 28–40 (2007)
Qian, Y., Dang, C., Liang, J., Tang, D.: Set-valued ordered information systems. Information Sciences 179(16), 2809–2832 (2009)
Qian, Y., Liang, J., Pedrycz, W., Dang, C.: Positive approximation: An accelerator for attribute reduction in rough set theory. Artificial Intelligence 174(9-10), 597–618 (2010)
Wilson, D.R., Martinez, T.R.: Improved heterogeneous distance functions. Journal of Artificial Intelligence Research 6, 1–34 (1997)
Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111(1-4), 239–259 (1998)
Zhang, J., Li, T., Ruan, D., Gao, Z., Zhao, C.: A parallel method for computing rough set approximations. Information Sciences 194(1), 209–223 (2012)
Zhang, J., Li, T., Ruan, D., Liu, D.: Neighborhood Rough Sets for Dynamic Data Mining. International Journal of Intelligent Systems 27(4), 317–342 (2012)
Zhang, J., Li, T., Ruan, D., Liu, D.: Rough sets based matrix approaches with dynamic attribute variation in set-valued information systems. International Journal of Approximate Reasoning 53(4), 620–635 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, J., Li, T., Chen, H. (2012). Composite Rough Sets. In: Lei, J., Wang, F.L., Deng, H., Miao, D. (eds) Artificial Intelligence and Computational Intelligence. AICI 2012. Lecture Notes in Computer Science(), vol 7530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33478-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-33478-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33477-1
Online ISBN: 978-3-642-33478-8
eBook Packages: Computer ScienceComputer Science (R0)