An Improved Axiomatic Definition of Information Granulation

• Autorzy: Zhu P.
• Języki publikacji: EN

Abstrakty

EN

To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation have been introduced. In this paper, we try to improve these axiomatic definitions and give a universal construction of information granulation by relating information granulations with a class of functions of multiple variables. We show that the improved axiomatic definition has some concrete information granulations in the literature as instances.

Słowa kluczowe

EN

information systems; equivalence relation; information granulation; knowledge granulation; granulation measure

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 120, nr 1
• Strony: 93--109
• Opis fizyczny: Bibliogr. 43 poz.

Twórcy

autor

Zhu P.

• School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China,

Bibliografia

• [1] Bianucci, D., Cattaneo, G.: Information entropy and granulation co-entropy of partitions and coverings: A summary, in: Transactions on Rough Sets X (J. Peters, A. Skowron, M. Wolski, M. Chakraborty, W.-Z. Wu, Eds.), vol. 5656 of Lect. Notes Comput. Sci., Springer Berlin/Heidelberg, 2009, 15-66.
• [2] Codd, E. F.: A relational model of data for large shared data banks, Commun. ACM, 13(6), 1970, 377-387.
• [3] Dash, M., Liu, H.: Consistency-based search in feature selection, Artif. Intell., 151(1-2), 2003, 155-176.
• [4] Düntsch, I., Gediga, G.: Uncertainty measures of rough set prediction, Artif. Intell., 106(1), 1998, 109-137.
• [5] Grzymala-Busse, J. W.: Knowledge acquisition under uncertaintyłA rough set approach, J. Intel. Rob. Syst., 1(1), 1988, 3-16.
• [6] Grzymala-Busse, J. W.: LERS-A system for learning from examples based on rough sets, in: Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory (R. Słowiński, Ed.), Boston. MA: Kluwer Academic Publishers, 1992, 3-18.
• [7] Hu, Q., Xie, Z., Yu, D.: Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation, Pattern Recogn., 40, 2007, 3509-3521.
• [8] Kryszkiewicz, M.: Rough set approach to incomplete information systems, Inform. Sci., 112, 1998, 39-49.
• [9] Liang, J. Y., Li, D. Y.: Uncertainty and Knowledge Acquisition in Information Systems, Science Press, Beijing, 2005.
• [10] Liang, J. Y., Qian, Y. H.: Axiomatic approach of knowledge granulation in information system, vol. 4304 of Lect. Notes Artif. Intell., 2006, 1074-1078.
• [11] Liang, J. Y., Qian, Y. H.: Knowledge, knowledge granulation in information system, 2006, Sciencepaper online, available at http://www.paper.edu.cn /en/paper.php?serial􀀀number=200604-129.
• [12] Liang, J. Y., Qian, Y. H.: Information granules and entropy theory in information systems, Sci. China Ser. F-Inform. Sci., 51(10), 2008, 1427-1444.
• [13] Liang, J. Y., Shi, Z. Z.: The information entropy, rough entropy and knowledge granulation in rough set theory, Int. J. Uncert. Fuzz. Knowl. Syst., 12(1), 2004, 37-46.
• [14] Liang, J. Y., Shi, Z. Z., Li, D. Y., Wierman, M. J.: The information entropy, rough entropy and knowledge granulation in incomplete information systems, Int. J. Gen. Syst., 35(6), 2006, 641-654.
• [15] Liang, J. Y., Xu, Z. B.: The algorithm on knowledge reduction in incomplete information systems, Int. J. Uncert. Fuzz. Knowl. Syst., 24(1), 2002, 95-103.
• [16] Lipski, W.: On semantic issues connected with incomplete information databases, ACM Trans. Database Syst., 4, 1979, 262-296.
• [17] Molina, L. C., Belanche, L., Nebot, A` .: Feature selection algorithms: A survey and experimental evaluation, IEEE International Conference on Data Mining, ICDM 2002, IEEE, 2002.
• [18] Nguyen, H.: Approximate boolean reasoning: Foundations and applications in data mining, Trans. Rough Sets V, LNCS, 4100, 2006, 334-506.
• [19] Pal, S. K., Uma Shankar, B., Mitra, P.: Granular computing, rough entropy and object extraction, Pattern Recogn. Lett., 26(16), 2005, 2509-2517.
• [20] Pawlak, Z.: Information systems − theoretical foundations, Inform. Syst., 6(3), 1981, 205-218.
• [21] Pawlak, Z.: Rough sets, Int. J. Comput. Inform. Sci., 11(5), 1982, 341-356.
• [22] Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Boston, 1991.
• [23] Qian, Y. H., Liang, J. Y.: Combination entropy and combination granulation in incomplete information system, vol. 4062 of Lect. Notes Artif. Intell., 2006, 184-190.
• [24] Qian, Y. H., Liang, J. Y.: Combination entropy and combination granulation in rough set theory, Int. J. Uncert. Fuzz. Knowl. Syst., 16(2), 2008, 179-193.
• [25] Qian, Y. H., Liang, J. Y., Dang, C. Y.: Knowledge structure, knowledge granulation and knowledge distance in a knowledge base, Int. J. Approx. Reasoning, 50(1), 2009, 174-188.
• [26] Qian, Y. H., Liang, J. Y., Wang, F.: A new method for measuring the uncertainty in incomplete information systems, Int. J. Uncert. Fuzz. Knowl. Syst., 17(6), 2009, 855-880.
• [27] Sakai, H.: Effective procedures for handling possible equivalence relation in non-deterministic information systems, Fund. Inform., 48, 2001, 343-362.
• [28] Sakai, H., Okuma, H., Nakata, M., Ślęzak, D.: Stable rule extraction and decision making in rough nondeterministic information analysis, Int. J. Hybr. Intell. Syst., 8, 2011, 41-57.
• [29] Shannon, C. E.: A mathematical theory of communication, I, II, Bell Syst. Techn. J., 27, 1948, 379-423, 623-656.
• [30] Skowron, A., Grzymala-Busse, J. W.: From rough set theory to evidence theory, in: Advances in the Dempster-Shafer Theory of Evidence (R. Yager, M. Fedrizzi, J. Kacprzyk, Eds.), John Wiley & Sons, New York, NY, 1994, 193-236.
• [31] Ślęzak, D.: Approximate entropy reducts, Fund. Inform., 53(3-4), 2002, 365-390.
• [32] Ślęzak, D.: Degrees of conditional (in) dependence: a framework for approximate Bayesian networks and examples related to the rough set-based feature selection, Inform. Sci., 179(3), 2009, 197-209.
• [33] Słowiński, R., Stefanowski, J.: Rough classification in incomplete information systems, Math. Computer Modell., 12(10-11), 1989, 1347-1357.
• [34] Słowiński, R., Zopounidis, C., Dimitras, A. I.: Prediction of company acquisition in Greece by means of the rough set approach, Eur. J. Oper. Res., 100(1), 1997, 1-15.
• [35] Yao, Y. Y.: The art of granular computing, vol. 4585 of Lect. Notes Artif. Intell., 2007, 101-112.
• [36] Yao, Y. Y.: Notes on rough set approximations and associated measures, J. Zhejiang Ocean Univ. (Natur. Sci.), 29, 2010, 399-410, Available at: http://www2.cs.uregina.ca/∼yyao/PAPERS/rst2010􀀀notes.pdf.
• [37] Yao, Y. Y., Zhao, L. Q.: Granularity of partitions, 2009, (private communication).
• [38] Zadeh, L. A.: Fuzzy Logic = computing with words, IEEE Trans. Fuzzy Syst., 4, 1996, 103-111.
• [39] Zadeh, L. A.: From computing with numbers to computing with words - From manipulation of measurements to manipulation of perceptions, IEEE Trans. Circuits Syst. I: Fund. Theory Appl., 45, 1999, 105-119.
• [40] Zeng, Y., Zhong, N., Wang, Y., Qin, Y., Huang, Z., Zhou, H., Yao, Y., van Harmelen, F.: User-centric query refinement and processing using granularity-based strategies, Knowl. Inf. Syst., 27, 2011, 419-450.
• [41] Zhao, M. Q., Yang, Q., Gao, D. Z.: Axiomatic definition of knowledge granularity and its constructive method, vol. 5009 of Lect. Notes Artif. Intell., 2008, 348-354.
• [42] Zhu, P.: An axiomatic approach to the roughness measure of rough sets, Fund. Inform., 109(4), 2011, 463-480.
• [43] Zhu, P., Wen, Q. Y.: Entropy and co-entropy of a covering approximation space, Int. J. Approx. Reason., 53(4), 2012, 528-540.