Abstract
A family of overlapping granules can be formed by granulating a finite universe under a binary relation in a set-theoretic setting. In this paper, we granulate a universe by a binary relation and obtain a granular universe. And then we define two kinds of operators between these two universes, study properties of them. By combining these two kinds of operators, we get two pairs of approximation operators. It is proved that one kind of combination operators is just the approximation operators under a generalized approximation space defined according to Pawlak’s rough set theory.
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Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–208 (1990)
Hobbs, J.R.: Granularity. In: Proc. of IJCAI, Los Angeles, pp. 432–435 (1985)
Lin, T.Y.: Granular computing on binary relations I: data mining and neighborhood systems, II: rough set representations and belief functions. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1, pp. 107–140. Physica-Verlag, Heidelberg (1998)
Lin, T.Y.: Generating concept hierarchies/networks:mining additional semantics in relational data. In: Cheung, D., Williams, G.J., Li, Q. (eds.) PAKDD 2001. LNCS (LNAI), vol. 2035, pp. 174–185. Springer, Heidelberg (2001)
Lin, T.Y.: Granular computing. In: Wang, G., et al. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 16–24. Springer, Heidelberg (2003)
Ma, J.-M., Zhang, W.-X., Li, T.-J.: A covering model of granular computing. In: Proceedings of 2005 International Conference in Machine Learning and Cybernetics, pp. 1625–1630 (2005)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)
Pawlak, Z.: Rough sets. Kluwer Academic Publishers, Dordrecht (1991)
Skowron, A., Stepaniuk, J.: Information granules: towards foundations of granular computing. International Journal of Intelligent Systems 16, 57–85 (2001)
Yao, Y.Y.: Granular computing: basic issues and possible solutions. In: Proceedings of the 5th joint conference on information sciences, pp. 186–189 (2000)
Yao, Y.Y.: Information granulation and rough set approximation. International Journal of Intelligent systems 16, 87–104 (2001)
Yao, Y.Y.: A partition model of granular computing. In: Peters, J.F., et al. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 232–253. Springer, Heidelberg (2004)
Yao, J.T., Yao, Y.Y.: Introduction of classification rules by granular computing. In: Alpigini, J.J., et al. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 331–338. Springer, Heidelberg (2002)
Zadeh, L.A.: Fuzzy sets and information granularity. In: Gupta, M.M., Ragade, R.K., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North-Holland, Amsterdam (1979)
Zadeh, L.A.: Fuzzy logic-computing with words. IEEE Transactions on Fuzzy Systems 4, 103–111 (1996)
Zadeh, L.A.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 19, 111–127 (1997)
Zhang, W.-X., et al.: Theory and Methods of Rough Sets. Science Press, Beijing (2001)
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Ma, JM., Zhang, WX., Wu, WZ., Li, TJ. (2007). Granular Computing Based on a Generalized Approximation Space. In: Yao, J., Lingras, P., Wu, WZ., Szczuka, M., Cercone, N.J., Ślȩzak, D. (eds) Rough Sets and Knowledge Technology. RSKT 2007. Lecture Notes in Computer Science(), vol 4481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72458-2_11
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DOI: https://doi.org/10.1007/978-3-540-72458-2_11
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