Abstract
Granular structure is one of the fundamental concepts in granular computing. Different granular structures reflect multiple aspects of knowledge and information, and depict the different characteristics of data. This paper investigates a family of set-theoretic models of different granular structures. The proposed models are particularly useful for concept formulation and learning. Some of them can be used in formal concept analysis, rough set analysis and knowledge spaces. This unified study of granular structures provides a common framework integrating these theories of granular computing.
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References
Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Boston (2002)
Caspard, N., Monjardet, B.: Some lattices of closure systems on a finite set. Discrete Mathematics and Theoretical Computer Science 6, 163–190 (2004)
Doignon, J.P., Falmagne, J.C.: Knowledge Spaces. Springer, Berlin (1999)
Hobbs, J.R.: Granularity. In: Joshi, A. (ed.) Proceedings of the 9th International Joint Conference on Artificial Intelligence, pp. 432–453. IEEE Computer Society Press, Los Angeles (1985)
Keet, C.M.: A Formal Theory of Granularity, PhD Thesis, KRDB Research Centre, Faculty of Computer Science, Free University of Bozen-Bolzano, Italy (2008), http://www.meteck.org/files/AFormalTheoryOfGranularity_CMK08.pdf (accessed June 8, 2008)
Lin, T.Y., Yao, Y.Y., Zedah, L.A. (eds.): Data Mining, Rough Set and Granular Computing. Physica-Verlag, Heidelberg (2002)
Miao, D.Q., Fan, S.D.: The calculation of knowledge granulation and its application. System Engeering-Theory and Practice 1, 48–56 (2002)
Miao, D.Q., Wang, G.Y., Liu, Q., Lin, T.Y., Yao, Y.Y. (eds.): Granular Computing: Past, Present and Prospect. Tsinghua University Press, Beijing (2007)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough Sets-Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Boston (1991)
Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley Interscience, New York (2008)
Shiu, L.P., Sin, C.Y.: Top-down, middle-out, and bottom-up processes: a cognitive perspective of teaching and learning economics. International Review of Economics Education 5, 60–72 (2006)
Wille, R.: Concept lattices and conceptual knowledge systems. Computers Mathematics with Applications 23, 493–515 (1992)
Xu, F.F., Yao, Y.Y., Miao, D.Q.: Rough set approximations in formal concept analysis and knowledge spaces. In: An, A., Matwin, S., Raś, Z.W., Ślęzak, D. (eds.) ISMIS 2008. LNCS (LNAI), vol. 4994, pp. 319–328. Springer, Heidelberg (2008)
Yao, Y.Y.: On generalizing Pawlak approximation operators. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 298–307. Springer, Heidelberg (1998)
Yao, Y.Y.: A comparative study of formal concept analysis and rough set theory in data analysis. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 59–68. Springer, Heidelberg (2004)
Yao, Y.Y.: Perspectives of granular computing. In: Hu, X.H., Liu, Q., Skowron, A., Lin, T.Y., Yager, R.R., Zhang, B. (eds.) Proceedings of 2005 IEEE International Conference on Granular Computing (GrC 2005), pp. 85–90. IEEE Computer Society Press, Los Angles (2005)
Yao, Y.Y.: Three perspectives of granular computing. Journal of Nanchang Institute of Technology 25, 16–21 (2006)
Yao, Y.Y.: Granular computing: past, present and future. In: Hu, X.H., Hata, Y., Slowinski, R., Liu, Q. (eds.) Proceedings of 2008 IEEE International Conference on Granular Computing (GrC 2008), pp. 80–85. IEEE Computer Society Press, Los Angles (2008)
Yao, Y.Y.: Interpreting concept learning in cognitive informatics and granular computing. IEEE Transactions on Systems, Man, and Cybernetics (Part B) 4, 855–866 (2009)
Yao, Y.Y., Miao, D.Q., Xu, F.F.: Granular Structures and Approximations in Rough Sets and Knowledge Spaces. In: Ajith, A., Rafael, F., Rafael, B. (eds.) Rough Set Theory: A True Landmark in Data Analysis. Springer, Berlin (2009)
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Yao, Y., Miao, D., Zhang, N., Xu, F. (2010). Set-Theoretic Models of Granular Structures. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds) Rough Set and Knowledge Technology. RSKT 2010. Lecture Notes in Computer Science(), vol 6401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16248-0_18
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DOI: https://doi.org/10.1007/978-3-642-16248-0_18
Publisher Name: Springer, Berlin, Heidelberg
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