Abstract
In this paper, we discuss approximation spaces in a 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 that include 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, pp. 201–227. Physica-Verlag, Heidelberg (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)
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley & Sons, New York (2001)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, Heidelberg (2001)
Kloesgen, W., Żytkow, J. (eds.): Handbook of Knowledge Discovery and Data Mining. Oxford University Press, New York (2002)
Słowiński, R., Greco, S., Matarazzo, B.: Rough set analysis of preference-ordered data. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 44–59. Springer, Heidelberg (2002)
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Skowron, A., Świniarski, R., Synak, P. (2005). Approximation Spaces and Information Granulation. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets III. Lecture Notes in Computer Science, vol 3400. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427834_8
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DOI: https://doi.org/10.1007/11427834_8
Publisher Name: Springer, Berlin, Heidelberg
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