Abstract
This paper summarizes various formulations of the standard rough set theory. It demonstrates how those formulations can be adopted to develop different generalized rough set theories. The relationships between rough set theory and other theories are discussed.
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
Cattaneo, G. Abstract approximation spaces for rough theories, in: Rough Sets in Knowledge Discovery, Polkowski, L. and Skowron, A. (Eds.), Physica-Verlag, Heidelberg, 59–98, 1998.
Chellas, B.F. Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.
Cohn, P.M. Universal Algebra, Harper and Row Publishers, New York, 1965.
Järvinen, J. On the structure of rough approximations, Proceedings of the Third International Conference on Rough Sets and Current Trends in Computing, LNAI 2475, 123–130, 2002.
Lin, T.Y. and Liu, Q. Rough approximate operators: axiomatic rough set theory, in Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko (Ed.), Springer-Verlag, London, 256–260, 1994.
Pawlak, Z. Rough sets, International Journal of Computer and Information Sciences, 11, 341–356, 1982.
Pawlak, Z. Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Boston, 1991.
Pawlak, Z. and Skowron, A. Rough membership functions, in: Advances in the Dempster-Shafer Theory of Evidence, Yager, R.R., Fedrizzi, M. and Kacprzyk, J. (Eds.), John Wiley and Sons, New York, 251–271, 1994.
Pomykala, J.A. Approximation operations in approximation space, Bulletin of Polish Academy of Sciences, Mathematics, 35, 653–662, 1987.
Rasiowa, H. An Algebraic Approach to Non-classical Logics, North-Holland, Amsterdam, 1974.
Skowron, A. and Grzymala-Busse, J. From rough set theory to evidence theory, in: Advances in the Dempster-Shafer Theory of Evidence, Yager, R.R., Fedrizzi, M. and Kacprzyk, J. (Eds.), Wiley, New York, 193–236, 1994.
Wiweger, A. On topological rough sets, Bulletin of the Polish Academy of Sciences, Mathematics, 37, 89–93, 1989.
Wong, S.K.M. and Ziarko, W. Comparison of the probabilistic approximate classification and the fuzzy set model, Fuzzy Sets and Systems, 21, 357–362, 1987.
Wybraniec-Skardowska, U. On a generalization of approximation space, Bulletin of the Polish Academy of Sciences, Mathematics, 37, 51–61, 1989.
Wybraniec-Skardowska, U. Unit Operations, ZeszytyNaukowe Wyzszej Szkoly Pedagogicznej im Powstancow Slaskich w Opolu, Matematyka, XXVII, 113–129, 1992.
Yao, Y.Y. Two views of the theory of rough sets in finite universes, International Journal of Approximation Reasoning, 15, 291–317, 1996.
Yao, Y.Y. Constructive and algebraic methods of the theory of rough sets, Information Sciences, 109, 21–47, 1998.
Yao, Y.Y. Generalized rough set models, in: Rough Sets in Knowledge Discovery, Polkowski, L. and Skowron, A. (Eds.), Physica-Verlag, Heidelberg, 286–318, 1998.
Yao, Y.Y. Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 111, 239–259, 1998.
Yao, Y.Y. On generalizing Pawlak approximation operators, Proceedings of the First International Conference, RSCTC’98, LNAI 1424, 298–307, 1998.
Yao, Y.Y. Information granulation and rough set approximation, International Journal of Intelligent Systems, 16, 87–104, 2001.
Yao, Y.Y. Information granulation and approximation in a decision-theoretic model of rough sets, manuscript, 2002.
Yao, Y.Y. Probabilistic approaches to rough sets, manuscript, 2002.
Yao, Y.Y. Semantics of fuzzy sets in rough set theory, manuscript, 2002.
Yao, Y.Y. and Lin, T.Y. Generalization of rough sets using modal logic, Intelligent Automation and Soft Computing, An International Journal, 2, 103–120, 1996.
Yao, Y.Y. and Lingras, P.J. Interpretations of belief functions in the theory of rough sets, Information Sciences, 104, 81–106, 1998.
Yao, Y.Y. and Wang, T. On rough relations: an alternative formulation, Proceedings of The Seventh International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, LNAI 1711, 82–90, 1999.
Yao, Y.Y. and Wong, S.K.M. A decision theoretic framework for approximating concepts, International Journal of Man-machine Studies, 37, 793–809, 1992.
Yao, Y.Y., Wong, S.K.M. and Lin, T.Y. A review of rough set models, in: Rough Sets and Data Mining: Analysis for Imprecise Data, Lin, T.Y. and Cercone, N. (Eds.), Kluwer Academic Publishers, Boston, 47–75, 1997.
Zakowski, W. Approximations in the space (U, II), Demonstratio Mathematica, XVI, 761–769, 1983.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yao, Y.Y. (2003). On Generalizing Rough Set Theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2003. Lecture Notes in Computer Science(), vol 2639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39205-X_6
Download citation
DOI: https://doi.org/10.1007/3-540-39205-X_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-14040-5
Online ISBN: 978-3-540-39205-7
eBook Packages: Springer Book Archive