Approximation Space and LEM2-like Algorithms for Computing Local Coverings

• Autorzy: Grzymała-Busse J.W. , Rząsa W.
• Języki publikacji: EN

Abstrakty

EN

In this paper we discuss approximation spaces that are useful for studying local lower and upper approximations. Set definability and properties of the approximation space, including best approximations, are considered as well. Finding best approximations is a NP-hard problem. Finally, we present LEM2-like algorithms for determining local lower and upper coverings for a given incomplete data set. Lower and upper approximations, associated with these coverings, are sub-optimal.

Słowa kluczowe

EN

approximate space

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 85, nr 1-4
• Strony: 205--217
• Opis fizyczny: bibliogr. 23 poz.

Twórcy

autor

Grzymała-Busse J.W.

autor

Rząsa W.

• Department of Electrical Engineering and Computer Sciences, University of Kansas, Lawrence, KS 66045, USA,

Bibliografia

• [1] Grzymala-Busse, J.: A new version of the rule induction system LERS. Fundamenta Informaticae 31 (1997) 27-39.
• [2] Grzymala-Busse., J.W.: MLEM2: A new algorithm for rule induction from imperfect data. Proceedings of the 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2002, July 1-5, Annecy, France, 243-250.
• [3] Grzymala-Busse., J.W.: Data with missing attribute values: Generalization of indiscernibility relation and rule induction. Transactions on Rough Sets, Lecture Notes in Computer Science Journal Subline, Springer-Verlag, 1 (2004), 78-95.
• [4] Grzymala-Busse, J.W.: Incomplete data and generalization of indiscernibility relation, definability and approximations. Proceedings of the RSFDGrC'2005, the Tenth International Conference on Rough Sets, Fuzzy Sets, data Mining, and Granular Computing, Lecture Notes in Artificial Intelligence 3641, Springer Verlag, Berlin, Heidelberg, 2005, 244-253.
• [5] Grzymala-Busse, J.W., Rzasa, W.: Local and global approximations for incomplete data. Proceedings of the RSCTC 2006, the Fifth International Conference on Rough Sets and Current Trends in Computing, Kobe, Japan. Lecture Notes in AI, 4259, Springer Verlag, Berlin, Heidelberg, 2006, 244-253.
• [6] Grzymala-Busse, J., Rzasa, W.: Definability of approximations for a generalization of the indiscernibility relation, Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (FOCI'2007), Honolulu, Hawaii, April 1-5, 2007, 65-72.
• [7] Grzymala-Busse, J., Rzasa, W.: Approximation space and LEM2-like algorithms for local approximations. Proceedings of the Concurrency, Specification and ProgrammingWorkshop, Lagow, Poland, September 27-29, 2007, 279-289.
• [8] Grzymala-Busse, J.W., Siddhaye, S.: Rough set approaches to rule induction from incomplete data. Proceedings of the IPMU'2004, the 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Perugia, Italy, 2004, vol. 2, 923-930.
• [9] Johnstone, P.T.: Stone Spaces. Cambridge University Press, Cambridge (1982).
• [10] Kryszkiewicz,M.: Rough set approach to incomplete information systems. Proc. of the Second Annual Joint Conference on Information Sciences, Wrightsville Beach, NC, 1995, 194-197.
• [11] Lin, T.Y., Yao, Y.Y.: Mining soft rules using rough sets and neighborhoods, in: Proceedings of the Symposium on Modeling, Analysis and Simulation, Computational Engineering in Systems Applications (CESA'96), IMASCS Multiconference, Lille, France, July 9-12, 1996, Vol. 2, 1095-1100.
• [12] Marek, V.W., Truszczynski, M.: Rough Sets and Approximation Schemes, in: Rough Sets and Intelligent Systems Paradigms. International Conference, RSEISP 2007,Warsaw, Poland, June 2007, 22 - 28.
• [13] Pawlak, Z: Rough sets, International Journal of Computer and Information Science 11 (1982) 341-356.
• [14] Pomykała, J.A.: On definability in the nondeterministic information system, Bulletin of the Polish Academy of Science Mathematics 36 (1988) 193-210.
• [15] Skowron, A., Pawlak, Z.: Rough sets: Some extensions, Information Sciences 177(1) (2007), 28 - 40.
• [16] Skowron, A., Pawlak, Z.: Rudiments of rough sets, Information Sciences 177(1) (2007), 3 - 27.
• [17] Skowron, A., Pawlak, Z.: Rough sets and Boolean reasoning, Information Sciences 177(1) (2007), 41 - 73.
• [18] Skowron, A., Stepaniuk, J.: Tolerance approximation spaces.Fundamenta Informaticae 27 (1996) 245 - 253.
• [19] Słowi´nski, R. and Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12 (2000) 331-336.
• [20] Stefanowski, J. and Tsoukias, A.: On the extension of rough sets under incomplete information. Proc. Of the Seventh Int. Workshop on Rough Sets, Fuzzy Sets, Data Mining and Granular-Soft Computing (RSFDGrC'99), Ube, Yamaguchi, Japan, November 810, 1999. Lecture Notes in Artificial Intelligence, No. 1711, Springer Verlag, Berlin, Heidelberg1999, 73-81.
• [21] Wybraniec-Skardowska, U.: On a generalization of approximation space, Bulletin of the Polish Academy of Science Mathematics, 37 (1989) 51-62.
• [22] Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111 (1998) 239-259.
• [23] Żakowski,W.: Approximations in the space (U,II), Demonstratio Mathematica, 16 (1983) 761-769.