Abstract
In this article, we compare mappings of Pawlak’s lower and upper approximations of concepts with those proposed by Skowron and Stepaniuk. It is known that both approaches coincide for the standard rough inclusion, so we consider the case of an arbitrary rough inclusion function. Even if the approximation space investigated is based on an arbitrary non-empty binary relation, the lower approximation mappings are equal in both approaches. Nevertheless, the upper approximation mappings are different in general.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Pawlak, Z.: Rough sets. Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Information systems – Theoretical foundations. Information Systems 6, 205–218 (1981)
Pawlak, Z.: Rough sets. Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Information Systems. Theoretical Foundations (in Polish). Wydawnictwo Naukowo-Techniczne, Warsaw (1983)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)
Pomykała, J.A.: Approximation operations in approximation space. Bull. Polish Acad. Sci. Math. 35, 653–662 (1987)
Wybraniec-Skardowska, U.: On a generalization of approximation space. Bull. Polish Acad. Sci. Math. 37, 51–62 (1989)
Żakowski, W.: Approximations in the space (U,Π). Demonstratio Mathematica 16, 761–769 (1983)
Skowron, A., Stepaniuk, J.: Generalized approximation spaces. In: Proc. 3rd Int. Workshop Rough Sets and Soft Computing, San Jose, USA, November 10-12, pp. 156–163 (1994)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Gomolińska, A.: Variable-precision compatibility spaces. Electronical Notices in Theoretical Computer Science 82, 1–12 (2003), http://www.elsevier.nl/locate/entcs/volume82.html
Słowiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Wang, P.P. (ed.) Advances in Machine Intelligence and Soft Computing, vol. 4, pp. 17–33. Duke University Press, Durham (1997)
Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis of Imprecise Data, pp. 47–75. Kluwer, Dordrecht (1997)
Ziarko, W.: Variable precision rough set model. J. Computer and System Sciences 46, 39–59 (1993)
Ziarko, W.: Probabilistic decision tables in the variable precision rough set model. J. Comput. Intelligence 17, 593–603 (2001)
Peters, J.F.: Approximation space for intelligent system design patterns. Engineering Applications of Artificial Intelligence 17, 1–8 (2004)
Skowron, A.: Approximation spaces in rough neurocomputing. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.) Rough Set Theory and Granular Computing. Studies in Fuzziness and Soft Computing, vol. 125, pp. 13–22. Springer, Heidelberg (2003)
Skowron, A., Swiniarski, R., Synak, P.: Approximation spaces and information granulation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 175–189. Springer, Heidelberg (2005)
Polkowski, L., Skowron, A.: Rough mereology. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1994. LNCS, vol. 869, pp. 85–94. Springer, Heidelberg (1994)
Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. Int. J. Approximated Reasoning 15, 333–365 (1996)
Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung (First published in Kraków in 1913). In: Borkowski, L. (ed.) Jan Łukasiewicz – Selected Works, pp. 16–63. North Holland, Amsterdam (1970)
Zadeh, L.A.: Outline of a new approach to the analysis of complex system and decision processes. IEEE Trans. on Systems, Man, and Cybernetics 3, 28–44 (1973)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this chapter
Cite this chapter
Gomolińska, A. (2007). A Comparison of Pawlak’s and Skowron–Stepaniuk’s Approximation of Concepts. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds) Transactions on Rough Sets VI. Lecture Notes in Computer Science, vol 4374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71200-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-71200-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71198-8
Online ISBN: 978-3-540-71200-8
eBook Packages: Computer ScienceComputer Science (R0)