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Approximation Spaces in Rough–Granular Computing

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Języki publikacji
EN
Abstrakty
EN
We discuss some generalizations of the approximation space definition introduced in 1994 [24, 25]. These generalizations are motivated by real-life applications. Rough set based strategies for extension of such generalized approximation spaces from samples of objects onto their extensions are discussed. This enables us to present the uniform foundations for inducing approximations of different kinds of granules such as concepts, classifications, or functions. In particular, we emphasize the fundamental role of approximation spaces for inducing diverse kinds of classifiers used in machine learning or data mining.
Wydawca
Rocznik
Strony
141--157
Opis fizyczny
Bibliogr. 31 poz., tab., wykr.
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autor
autor
Bibliografia
  • [1] Bazan J.: Hierarchical classifiers for complex spatio-temporal concepts, Trans. Rough Sets IX LNCS 5390, 2008, 474-750.
  • [2] Bazan J., Osmólski A., Skowron A., Ślęzak D., Szczuka M., Wróblewski J.: Rough Set Approach to the Survival Analysis. In: James J. Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (Eds.), Proceedings of the Third International Conference Rough Sets and Current Trends in Computing (RSCTC 2002), Malvern, PA, USA, October 14-16, 2002, LNCS 2475, Springer, Heidelberg, 522-529.
  • [3] Bazan J., Skowron A., Swiniarski R.: Rough sets and vague concept approximation: From sample approximation to adaptive learning, Trans. Rough Sets V LNCS 4100, 2006, 39-62.
  • [4] Bianucci D., Cattaneo G.: Information entropy and granulation co-Entropy of partitions and coverings: A summary, Trans. Rough Sets X LNCS 5656, 2009, 15-66.
  • [5] Greco S., Matarazzo B., Słowiński R.: Dominance-based rough set approach and bipolar abstract rough approximation spaces, Chan Ch.-Ch., Grzymala-Busse J.W., ZiarkoW. (Eds.), 6th Int. Conf. Rough Sets and Current Trends in Computing (RSCTC 2008), Akron, OH, USA, October 23-25, 2008, LNCS 5306, Springer, Heidelberg, 31-40.
  • [6] Grünwald P. D.: The Minimum Description Length Principle, The MIT Press, Cambridge, MA 2007.
  • [7] Hastie T., Tibshirani R., Friedman J.H.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, Heidelberg, 2008 (second edition).
  • [8] Jankowski A., Skowron A.: A wistech paradigm for intelligent systems, Trans. Rough Sets VI LNCS 4374, 2007, 94-132.
  • [9] Jankowski A., Skowron A.: Logic for artificial intelligence: The Rasiowa-Pawlak school perspective, In: Ehrenfeucht, A., Marek V., Srebrny M. (Eds.) Andrzej Mostowski and Foundational Studies, IOS Press, Amsterdam, 2008, 106-143.
  • [10] Klir G.J: Uncertainty and Information: Foundations of Generalized Information Theory, JohnWiley & Sons, Hoboken, NJ, 2007.
  • [11] Łukasiewicz J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, 1913, In: Borkowski L. (Ed.), Jan Łukasiewicz - Selected Works, North Holland Publishing Company, Amsterdam, London, Polish Scientific Publishers,Warsaw, 1970, 16-63.
  • [12] Malyszko D., Stepaniuk J.: Adaptive Multilevel Rough Entropy Evolutionary Thresholding, Information Sciences 180(7), 2010, 1138-1158.
  • [13] Ng K.S., Lloyd J.W., Uther W.T.B.: Probabilistic modelling, inference and learning using logical theories, Annals of Mathematics and Artificial Intelligence 54(1-3), 2008, 159-205.
  • [14] Nguyen H.S.: Approximate Boolean Reasoning: Foundations and Applications in Data Mining, Trans. On Rough Sets V LNCS 4100, 2006, 344-523.
  • [15] Pal S. K., Shankar B. U., Mitra P.: Granular computing, rough entropy and object extraction, Pattern Recognition Letters, 26(16), 2005, 2509-2517.
  • [16] Pawlak Z.: Rough sets, International Journal of Computer and Information Sciences 11, 1982, 341-356.
  • [17] Pawlak Z.: Rough Sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, vol. 9, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
  • [18] Pawlak Z., Skowron, A.: Rudiments of rough sets; Rough sets: Some extensions; Rough sets and Boolean reasoning. Information Sciences 177(1), 2007, 3-27; 28-40; 41-73.
  • [19] Pedrycz W., Skowron, A., Kreinovich, V. (Eds.): Handbook of Granular Computing, John Wiley & Sons, New York 2008.
  • [20] Peters J., Skowron A., Stepaniuk J.: Nearness of objects: extension of the approximation space model. Fundamenta Informaticae 79 (3,4), 2007, 497-512.
  • [21] Polkowski L., Skowron A.: Rough mereology: A new paradigm for approximate reasoning. Int. J. Approximate Reasoning 51, 1996, 333-365.
  • [22] Ramsay J. O., Silverman B. W.: Applied Functional Data Analysis. Springer, Berlin, 2002.
  • [23] Rissanen J.: Minimum-description-length principle. In: Kotz, S., Johnson, N. (Eds.), Encyclopedia of Statistical Sciences, John Wiley & Sons, New York, 1985, 523-527.
  • [24] Skowron A., Stepaniuk J.: Generalized approximation spaces. Lin T.Y., Wildberger A.M. (Eds.), The Third Int. Workshop on Rough Sets and Soft Computing Proceedings (RSSC'94), San Jose State University, San Jose, CA, USA, November 10-12, 1994, 156-163.
  • [25] Skowron A., Stepaniuk J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 1996, 245-253.
  • [26] Skowron A.: Toward intelligent systems: Calculi of information granules, (keynote talk at RSTGC'01), Matsue, May 20-22, Japan, In: S. Hirano, M. Inuiguchi, and S. Tsumoto (eds.) Proc. Int. Workshop on Rough Set Theory and Granular Computing (RSTGC'2001), May 20-22, 2001, Matsue, Japan, Bull. Int. Rough Set Society 5(1-2), 2001, 9-30; see also: Terano T., Nishida T., Namatame A., Tsumoto S., Ohsawa Y., Washio T.(Eds.), New Frontiers in Artificial Intelligence, Joint JSAI Workshop Post Proceedings, LNAI 2253, Springer, Heidelberg, 2001, 251-260.
  • [27] Skowron A., Stepaniuk J., Peters J., Swiniarski R.: Calculi of approximation spaces, Fundamenta Informaticae 72(1-3), 2006, 363-378.
  • [28] Słowiński R., Vanderpooten D.: A generalized definition of rough approximations based on similarity. IEEE Trans. Knowledge and Data Engineering 12, 2000, 331-336.
  • [29] Stepaniuk J.: Rough-Granular Computing in Knowledge Discovery and Data Mining, Springer, 2008.
  • [30] Zhu W.: Relationship between generalized rough sets based on binary relation and covering, Information Sciences 179(3), 2009, 210-225.
  • [31] Ziarko W.: Variable precision rough set model, J. Computer and System Sciences 46, 1993, 39-59.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0010-0052
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