Abstract
We discuss approximation spaces in the granular computing framework. Such approximation spaces generalise the approaches to concept approximation existing in rough set theory. Approximation spaces are constructed as higher level information granules and are obtained as the result of complex modelling. We present illustrative examples of modelling approximation spaces including approximation spaces for function approximation, inducing concept approximation, and some other information granule approximations. In modelling of such approximation spaces we use an important assumption that not only objects but also more complex information granules involved in approximations are perceived using only partial information about them.
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References
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Polkowski, L., Skowron, A.: Rough mereology:A new paradigm for approximate reasoning. International Journal of Approximate Reasoning 15, 333–365 (1996)
Polkowski, L., Skowron, A.: Towards adaptive calculus of granules. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words in Information/Intelligent Systems, Heidelberg, Germany, pp. 201–227. Physica-Verlag (1999)
Skowron, A., Stepaniuk, J.: Information granules and rough-neural computing. In: [10], pp. 43–84
Lin, T.Y.: The discovery, analysis and representation of data dependencies in databases. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1: Methodology and Applications. Studies in Fuzziness and Soft Computing, vol. 18, pp. 107–121. Physica-Verlag, Heidelberg (1998)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)
Peters, J.F., Skowron, A., Synak, P., Ramanna, S.: Rough sets and information granulation. In: De Baets, B., Kaynak, O., Bilgiç, T. (eds.) IFSA 2003. LNCS, vol. 2715, pp. 370–377. Springer, Heidelberg (2003)
Skowron, A.: Toward intelligent systems: Calculi of information granules. Bulletin of the International Rough Set Society 5, 9–30 (2001)
Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Cognitive Technologies. Springer, Heidelberg (2003)
Zadeh, L.A.: A new direction in AI: Toward a computational theory of perceptions. AI Magazine 22, 73–84 (2001)
Kloesgen, W., Zytkow, J. (eds.): Handbook of Knowledge Discovery and Data Mining. Oxford University Press, Oxford (2002)
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Skowron, A., Swiniarski, R., Synak, P. (2004). Approximation Spaces and Information Granulation. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science(), vol 3066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25929-9_13
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DOI: https://doi.org/10.1007/978-3-540-25929-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22117-3
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