
## References

[1] Beaubouef, T., Petry, F. E., Arora, G., 1998. Information-theoretic measures of uncertainty for rough sets and rough relational databases.

Inform. Sci. 109, 185–195.

[2] Bianucci, D., Cattaneo, G., 2009. Information entropy and granulation co-entropy of partitions and coverings: A summary. In: Peters, J.,
Skowron, A., Wolski, M., Chakraborty, M., Wu, W.-Z. (Eds.), Transactions on Rough Sets X. Vol. 5656 of Lect. Notes Comput. Sci. Springer Berlin/Heidelberg, pp. 15–66.

[3] Bianucci, D., Cattaneo, G., Ciucci, D., 2007. Entropies and co-entropies of coverings with application to incomplete information systems.

Fund. Inform. 75, 77–105.

[4] Bryniarski, E., 1989. A calculus of rough sets of the first order. Bull. Pol. Acad. Sci. 36 (16), 71–77.

[5] Dubois, D., Prade, H., 1990. Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–208.

[6] D¨untsch, I., Gediga, G., 1998. Uncertainty measures of rough set prediction. Artif. Intell. 106 (1), 109–137. [7] Hartley, R. V. L., 1928. Transmission of information. Bell Syst. Tech. J. 7, 535–564. [8] Liang, J., Shi, Z., Li, D., Wierman, M. J., 2006. Information entropy, rough entropy and knowledge granulation in incomplete information systems. Int. J. Gen. Syst. 35 (6), 641–654.

[9] Liang, J. Y., Chin, K. S., Dang, C. Y., Yam, R. C. M., 2002. A new method for measuring uncertainty and fuzziness in rough set theory. Int.

J. Gen. Syst. 31, 331–342.

[10] Liang, J. Y., Qian, Y. H., 2008. Information granules and entropy theory in information systems. Sci. China Ser. F: Inform. Sci. 51 (10),
1427–1444.

[11] Liang, J. Y., Shi, Z. Z., 2004. The information entropy, rough entropy and knowledge granulation in rough set theory. Int. J. Uncert. Fuzz.

Knowl. Syst. 12 (1), 37–46.

[12] Lin, T. Y., Cercone, N. (Eds.), 1997. Rough Sets and Data Mining. Kluwer Academic Publishers, Boston. [13] Miao, D. Q., Wang, J., 1998. On the relationships between information entropy and roughness of knowledge in rough set theory (in Chinese).

Pattern Recognit. Artif. Intell. 11 (1), 34–40.

[14] Pawlak, Z., 1982. Rough sets. Int. J. Comput. Inform. Sci. 11 (5), 341–356.

[15] Pawlak, Z., 1991. Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston. [16] Pawlak, Z., 1992. Rough sets: a new approach to vagueness. In: Zadeh, L. A., Kacprzyc, J. (Eds.), Fuzzy Logic for the Management of Uncertainty. John Wiley & Sons, Inc, New York, pp. 105–118.

[17] Polkowski, L., Skowron, A. (Eds.), 1998. Rough Sets and Current Trends in Computing. Vol. 1424. Springer, Berlin.

[18] Polkowski, L., Skowron, A. (Eds.), 1998. Rough Sets in Knowledge Discovery. Vol. 1 and 2. Physica-Verlag, Heidelberg. [19] Pomykala, J. A., 1987. Approximation operations in approximation space. Bull. Pol. Acad. Sci. 35 (9-10), 653–662. [20] Qian, Y. H., Liang, J. Y., 2008. Combination entropy and combination granulation in rough set theory. Int. J. Uncert. Fuzz. Knowl. Syst.

16 (2), 179–193.

[21] Sen, D., Pal, S. K., 2009. Generalized rough sets, entropy, and image ambiguity measures. IEEE Trans. Syst., Man, Cybern. B, Cybern.

39 (1), 117–128.

[22] Shannon, C. E., 1948. A mathematical theory of communication, I, II. Bell Syst. Techn. J. 27, 379–423, 623–656.

[23] Wierman, M., 1999. Measuring uncertainty in rough set theory. Int. J. Gen. Syst. 28, 283–297. [24] Xu, W. H., Zhang, X. Y., Zhang, W. X., 2009. Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems. Appl. Soft Comput. 9 (4), 1244–1251.

[25] Yao, Y. Y., 2003. Information-theoretic measures for knowledge discovery and data mining. In: Karmeshu (Ed.), Entropy Measures, Maximum Entropy and Emerging Applications. Springer, Berlin, pp. 115–136.

[26] Yao, Y. Y., 2003. Probabilistic approaches to rough sets. Expert Syst. 20 (5), 287–297.

[27] Yao, Y. Y., 2010. Notes on rough set approximations and associated measures. J. Zhejiang Ocean Univ. (Natur. Sci.) 29, 399–410. [28] Yao, Y. Y., Zhao, L. Q., 2009. Granularity of partitions, (private communication).

[29] Zakowski, W., 1983. Approximations in the space (u, π). Demonstr. Math. 16, 761–769.

[30] Zhong, N., Yao, Y., Ohshima, M., 2003. Peculiarity oriented multidatabase mining. IEEE Trans. Knowl. Data Eng. 15 (4), 952–960. [31] Zhu, P., 2009. An axiomatic approach to the roughness measure of rough sets. Fund. Inform.To appear, available at: Arxiv preprint arXiv:0911.5395.

[32] Zhu, P., 2009. An improved axiomatic definition of information granulation. Arxiv preprint arXiv:0908.3999.

[33] Zhu, P., Wen, Q., 2010. Some improved results on communication between information systems. Inform. Sci. 180 (18), 3521–3531. [34] Zhu, W., Wang, F. Y., 2006. Covering based granular computing for conflict analysis. Vol. 3975 of Lect. Notes Comput. Sci. pp. 566–571, IEEE Int. Conf. Intell. Secur. Inform. (ISI 2006), San Diego, CA, May 23-24, 2006.

[35] Ziarko, W. (Ed.), 1994. Rough Sets, Fuzzy Sets, and Knowledge Discovery. Springer-Verlag, Berlin.