Summary
The main aim of this brief note is to explain relations between the classic approach to set approximations and recent proposals appearing in the literature on rough sets. In particular, relations between the standard topological concepts and basic concepts of rough set theory are considered.
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
Alexandroff, P.: Discrete Räume. Mat. Sb. 2, 501–518 (1937)
Gniłka, S.: On extended topologies. I: Closure operators. Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 34, 81–94 (1994)
Halmos, P.R.: Naive Set Theory. Springer, New York (1987)
Hammer, P.C.: Extended topology and systems. Math. Systems Theory 1, 135–142 (1967)
Järvinen, J.: Approximations and rough sets based on tolerances. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 182–189. Springer, Heidelberg (2001)
Järvinen, J., Kortelainen, J.: A note on definability in rough set theory. In: De Baets, B., et al. (eds.) Current Issues in Data and Knowledge Engineering, Problemy Współczesnej Nauki, Teoria i Zastosowania, Informatyka, Warsaw, Poland, pp. 272–277 (2004)
Kelley, J.L.: General Topology. D. Van Nostrand Company, London (1967)
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 (1997)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Stopher Jr., E.C.: Point set operators and their interrelations. Bull. Amer. Math. Soc. 45, 758–762 (1939)
Vlach, M.: Approximation Operators in Optimization Theory. Zeitschrift für Operations Research 25, 15–23 (1981)
Vlach, M.: On nonenlarging closures in affine spaces. In: Novak, J. (ed.) General Topology and its Relations to Modern Analysis and Algebra V, pp. 653–656. Helderman-Verlag, Berlin (1982)
Vlach, M.: Closures and neighbourhoods induced by tangential approximations. In: Hammer, G., Pallaschke, D. (eds.) Selected Topics in Operations Research and Mathematical Economics, pp. 119–127. Springer, Berlin (1984)
Vlach, M.: Rough sets, neighborhoods, and set approximations. In: Noguchi, H., Ishii, H., Inuiguchi, M. (eds.) Proceedings of 7th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty, Japan, pp. 155–157 (2004)
Wybraniec-Skardovska, U.: On a generalization of approximation space. Bulletin of The Polish Academy of Sciences: Mathematics 37, 51–62 (1989)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Vlach, M. (2008). Topologies of Approximation Spaces of Rough Set Theory. In: Huynh, VN., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H.T. (eds) Interval / Probabilistic Uncertainty and Non-Classical Logics. Advances in Soft Computing, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77664-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-77664-2_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77663-5
Online ISBN: 978-3-540-77664-2
eBook Packages: EngineeringEngineering (R0)