Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The approximation space definition has evolved in rough set theory over the last 15 years. The aim was to build a unified framework for concept approximations. We present an overview of this evolution together with some operations on approximation spaces that are used in searching for relevant approximation spaces. Among such operations are inductive extensions and granulations of approximation spaces. We emphasize important consequences of the paper for research on approximation of vague concepts and reasoning about them in the framework of adaptive learning. This requires developing new approach to vague concepts going beyond the traditional rough or fuzzy approaches.
Wydawca
Czasopismo
Rocznik
Tom
Strony
417--431
Opis fizyczny
Bibliogr. 34 poz., wykr.
Twórcy
autor
- Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland, skowron@mimuw.edu.pl
Bibliografia
- [1] M. Banerjee,M.K. Chakraborty (2004). Algebras from Rough Sets. In Pal, S.K., Polkowski, L., Skowron, A. (eds.), Rough-Neural Computing: Techniques for Computing with Words, Cognitive Technologies, Springer-Verlag, Heidelberg, 157-188.
- [2] G. Cattaneo (1998). Abstract Approximation Apaces for Rough Theories. In L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery 1: Methodology and Applications, Studies in Fuzziness and Soft Computing 18, Physica-Verlag, Heidelberg, 59–98.
- [3] J. Friedman, T. Hastie, R. Tibshirani (2001). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer-Verlag, Heidelberg.
- [4] R. Keefe (2000). Theories of Vagueness. Cambridge Studies in Philosophy, Cambridge, UK.
- [5] R. Keefe, P. Smith (eds.) (1997). Vagueness: A Reader. MIT Press, Massachusetts, MA.
- [6] E. Kloesgen, J. ˙Zytkow (eds.) (2002). Handbook of Knowledge Discovery and Data Mining. Oxford University Press, Oxford, UK.
- [7] T,Y, Lin (1998). The Discovery, Analysis and Representation of Data Dependencies in Databases. In L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery 1: Methodology and Applications, Studies in Fuzziness and Soft Computing 18, Physica-Verlag, Heidelberg, 107–121.
- [8] J. Łukasiewicz (1913). Die Logischen Grundlagen der Wahrscheinlichkeitsrechnung (1913). In Borkowski, L. (ed.), Jan Łukasiewicz - Selected Works, North Holland Publishing Company, Amsterdam, London, Polish Scientific Publishers, Warsaw.
- [9] S. Marcus (1994). Tolerance Rough Sets, Cech Topologies, Learning Processes. Bulletin of the Polish Academy of Sciences, Technical Sciences 42(3), 471–487.
- [10] S. Marcus (1998). The Paradox of the Heap of Grains, in Respect to Roughness, Fuzziness and Negligibility. In L.Polkowski, A. Skowron (eds.) First International Conference on Rough Sets and Current Trends in Computing (RSCTC’98), Warsaw, Poland, June 22-26, 1998, Lecture Notes in Artificial Intelligence 1424, Springer-Verlag, Heidelberg, 19–23.
- [11] J. Pavelka (1979). On Fuzzy Logic I-III. Zeit. Math Logik Grund. Math. 25, 45–52, 119-134, 447-464.
- [12] Z. Pawlak (1991). Rough Sets: Theoretical Aspects of Reasoning about Data. System Theory, Knowledge Engineering and Problem Solving 9, Kluwer Academic Publishers, Dordrecht.
- [13] Z. Pawlak, A. Skowron (1994). Rough Membership Functions. In R. R. Yager, M. Fedrizzi, J. Kacprzyk (eds.), Advances in the Dempster-Schafer Theory of Evidence, John Wiley and Sons, New York, 251–271.
- [14] Z. Pawlak, S.K.M.Wong,W. Ziarko (1990). Rough Sets: Probabilistic Versus Deterministic Approach. In B. Gaines, J. Boose (eds.), Machine Learning and Uncertain Reasoning 3, Academic Press, London, 227–242.
- [15] J.F. Peters, A, Skowron, P. Synak, S. Ramanna (2003). Rough Sets and InformationGranulation. In Bilgic, T., Baets, D., Kaynak, O. (eds.), Tenth International Fuzzy Systems Association World Congress IFSA, Istanbul, Turkey, June 30-July 2, 2003, Lecture Notes in Artificial Intelligence 2715, Springer-Verlag, Heidelberg, 370–377.
- [16] L. Polkowski (2002). Rough Sets: Mathematical Foundations. Physica-Verlag, Heidelberg.
- [17] L. Polkowski (2004). A Note on 3-valued Rough Logic Accepting Decision Rules. Fundamenta Informaticae 61(1), 37–45.
- [18] L. Polkowski, A. Skowron, J. ˙Zytkow (1994). Rough Foundations for Rough Sets. In T.Y. Lin, A.M. Wildberger (eds.), Soft Computing. Simulation Councils, Inc., San Diego, CA, 55–58.
- [19] L. Polkowski, A. Skowron (1996). Rough Mereology: A New Paradigm for Approximate Reasoning. International Journal of Approximate Reasoning 15, 333–365.
- [20] L. Polkowski, A. Skowron (2001). Rough Mereological Calculi of Granules: A Rough Set Approach to Computation. Computational Intelligence 17, 472–492.
- [21] S. Read (1995). Thinking about Logic. An Introduction to the Philosophy of Logic. Oxford University Press, Oxford, New York.
- [22] A. Skowron, J. Stepaniuk (1996). Tolerance Approximation Spaces. Fundamenta Informaticae 27, 245–253.
- [23] A. Skowron, J. Stepaniuk (2004). Information Granules and Rough-Neural Computing. In S.K. Pal, L. Polkowski, A. Skowron (eds.), Rough-Neural Computing: Techniques for Computing with Words, Cognitive Technologies, Springer-Verlag, Heidelberg, 43–84.
- [24] A. Skowron, P. Synak (2004). Complex Patterns, Fundamenta Informaticae 60, 351–366.
- [25] A. Skowron, R. Swiniarski, P. Synak (2004). Approximation Spaces and Information Granulation. In Tsumoto, S., Slowinski, R., Komorowski, J., Grzymala-Busse, J. (eds.), Fourth International Conference on Rough Sets and Current Trends in Computing (RSCTC 2004), June 1-5, 2004, Uppsala, Sweden, Lecture Notes in Artificial Intelligence 3066, Springer-Verlag, Heidelberg, 114–123.
- [26] R. Słowiński, D. Vanderpooten (1997). Smilarity Relation as a Basis for Rough Set Approximations. In Wang, P.P. (ed.), Advances in Machine Intelligence & Soft-Computing, Bookwrights, Raleigh, NC, 17–33.
- [27] P. Stone (2000). Layered Learning in Multi-Agent Systems: A Winning Approach to Robotic Soccer. TheMIT Press, Cambridge, MA.
- [28] R.S. Sutton, A.G. Barto (1998). Reinforcement Learning: An Introduction.MIT Press, Cambridge,MA.
- [29] Y.Y. Yao (1998). Generalized Rough Set Models. In L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery 1: Methodology and Applications, Studies in Fuzziness and Soft Computing 18, Physica-Verlag, Heidelberg, 286–318.
- [30] V. Vapnik (1998). Statistical Learning Theory. John Wiley & Sons, New York, NY.
- [31] A. Wojna (2001). Constraint Based Incremental Learning of Classification Rules. In W. Ziarko, Y.Y. Yao (eds.), Second International Conference on Rough Sets and Current Trends in Computing (RSCTC 2001), Banff, Canada, October 16-19, 2001, Lecture Notes in Artificial Intelligence 2005, 428-435, Springer-Verlag, Heidelberg.
- [32] W. Ziarko (1993). Variable Precision Rough SetModel. Journal of Computer and System Sciences 46, 39–59.
- [33] L.A. Zadeh (1965). Fuzzy sets. Information and Control 8, 333–353.
- [34] L.A. Zadeh (1996). Fuzzy Logic = Computing withWords. IEEE Transactions on Fuzzy Systems 2, 103–111
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0005-0140