Abstract
Let us assume that we observe a class of objects and have some well-defined features with which an observed object possesses or not. In real life, two relevant groups of objects can be established determined by our current and necessarily constrained knowledge. In particular, a group whose elements really possess a feature in question, and another group whose elements substantially do not possess the same feature. In practice, as a rule, we can observe a feature of objects via only tools with which we are able to judge easily whether an object possesses a property or not. Of course, a property ascertained by tools does not coincide with a feature completely. To manage this problem, we propose a general tool-based approximation framework based on partial approximation of sets in which a positive feature and its negative one of any proportion of the observed objects can simultaneously be approximated.
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
Csajbók, Z.: Partial approximative set theory: A generalization of the rough set theory. In: Martin, T., Muda, A.K., Abraham, A., Prade, H., Laurent, A., Laurent, D., Sans, V. (eds.) Proceedings of SoCPaR 2010, Cergy Pontoise / Paris, France, December 7-10, pp. 51–56. IEEE, Los Alamitos (2010)
Csajbók, Z.: A security model for personal information security management based on partial approximative set theory. In: Ganzha, M., Paprzycki, M. (eds.) Proceedings of IMCSIT 2010, Wisła, Poland, October 18-20, vol. 5, pp. 839–845. PTI – IEEE Computer Society Press, Katowice, Poland – Los Alamitos, USA (2010)
Csajbók, Z.: Simultaneous anomaly and misuse intrusion detections based on partial approximative set theory. In: Cotronis, Y., Danelutto, M., Papadopoulos, G.A. (eds.) Proceedings of PDP 2011, Ayia Napa, Cyprus, February 9-11, pp. 651–655. IEEE Computer Society Press, Los Alamitos (2011)
Denning, D.E.: An intrusion-detection model. IEEE Transactions on Software Engineering SE 13(2), 222–232 (1987)
Järvinen, J.: Lattice theory for rough sets. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400–498. Springer, Heidelberg (2007)
Keefe, R.: Theories of Vagueness. Cambridge Studies in Philosophy. Cambridge University Press, Cambridge (2000)
Lavrač, N., Džeroski, S.: Inductive Logic Programming: Techniques and Applications. Ellis Horwood, New York (1994)
Marek, V.W., Truszczyński, M.: Approximation schemes in logic and artificial intelligence. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 135–144. Springer, Heidelberg (2008)
Mihálydeák, T.: On tarskian models of general type-theoretical languages. In: Drossos, C., Peppas, P., Tsinakis, C. (eds.) Proceedings of the 7th Panhellenic Logic Symposium, pp. 127–131. Patras University Press, Patras (2009)
Odifreddi, P.: Classical Recursion Theory. In: The Theory of Functions and Sets of Natural Numbers. Studies in Logic and the Foundations of Mathematics, vol. 125. Elsevier, Amsterdam (1989)
Pawlak, Z.: Rough sets. International Journal of Information and Computer Science 11(5), 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: An approach to vagueness. In: Rivero, L.C., Doorn, J., Ferraggine, V. (eds.) Encyclopedia of Database Technologies and Applications, pp. 575–580. Idea Group Inc., Hershey (2005)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177(1), 3–27 (2007)
Russell, B.: Vagueness. Australasian Journal of Philosophy and Psychology 1, 84–92 (1923)
Skowron, A.: Vague concepts: A rough-set approach. In: Beats, B.D., Caluwe, R.D., Tré, G.D., Fodor, J., Kacprzyk, J., Zadrożny, S. (eds.) Proceedings of EUROFUSE 2004, Warszawa, Poland, September 22-25, pp. 480–493. Akademicka Oficyna Wydawnicza EXIT, Warszawa (2004)
Yao, Y.Y.: On generalizing rough set theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 44–51. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Csajbók, Z., Mihálydeák, T. (2011). General Tool-Based Approximation Framework Based on Partial Approximation of Sets. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2011. Lecture Notes in Computer Science(), vol 6743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21881-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-21881-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21880-4
Online ISBN: 978-3-642-21881-1
eBook Packages: Computer ScienceComputer Science (R0)