Relational Operations and Uncertainty Measure in Rough Relational Database

• Autorzy: Jiang F. , Sui Y. , Cao C. , Wan X. , Du J.
• Języki publikacji: EN

Abstrakty

EN

The traditional relational database model (RDM) is not effective for dealing with imprecise and uncertain data as it deals with precise and unambiguous data. Hence, Beaubouef et al. proposed the rough relational database model (RRDM) for the management of uncertainty in relational databases. Beaubouef et al. defined the corresponding rough relational operators in rough relational databases as in ordinary relational databases. And to give an effective measure of uncertainty in rough relational databases, they defined the rough relation entropy. In this paper, we further discuss the issues of relational operations and uncertainty measure in rough relational databases. We give some new definitions for rough relational operators and rough relation entropy in rough relational databases. Furthermore, we discuss the basic properties of rough relational operators and rough relation entropy, as well as the connections between rough relational operators and rough relation entropy.

Słowa kluczowe

EN

rough sets; relational database model (RDM); RDM; rough relational database model (RRDM); RRDM; rough relation entropy; relational operations

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 123, nr 4
• Strony: 401--416
• Opis fizyczny: Bibliogr. 47 poz., tab.

Twórcy

autor

Jiang F.

• College of Information Science and Technology, Qingdao University of Science and Technology, Qingdao 266061, P. R. China

autor

Sui Y.

• Institute of Computing Technology Chinese Academy of Sciences Beijing 100080, P. R. China

autor

Cao C.

• Institute of Computing Technology Chinese Academy of Sciences Beijing 100080, P. R. China

autor

Wan X.

• Qingdao Hismile College, Qingdao, Shandong Province 266100, P. R. China

autor

Du J.

• College of Information Science and Technology, Qingdao University of Science and Technology, Qingdao 266061, P. R. China

Bibliografia

• [1] Shannon, C. E.: The mathematical theory of communication, Bell System Technical Journal, 27(3–4), 1948, 373–423.
• [2] Beaubouef, T., Petry, F. E., Buckles, B. P.: Extension of the relational database and its algebra with rough set techniques. Computational Intelligence, 11, 1995, 233–245.
• [3] Beaubouef, T., Petry, F. E., Arora, G.: Information-theoretic measures of uncertainty for rough sets and rough relational databases. Information Sciences, 109, 1998, 185–195.
• [4] Maji, P., Pal, S. K.: RFCM: A Hybrid Clustering Algorithm Using Rough and Fuzzy Sets. Fundamenta Informaticae, 80(4), 2007, 475–496.
• [5] Codd, E. F.: A relational model of data for large shared databases. Communications of the ACM, 13, 1970, 377–387.
• [6] Hsieh, N. C., Chiang, D. A., Wang, T. S.: Answers to Database Queries Concerning Imprecise Information in Logical Fuzzy Relational Databases. Tamkang Journal of Science and Engineering, 7(3), 2004, 149–160.
• [7] Jiang, F., Sui, Y. F., Cao, C. G.: Rough Contexts and Rough-Valued Contexts. Proc. of the First Int. Conf. on Rough Set and Knowledge Technology, LNAI 4062, China, 2006, 176–183.
• [8] Jiang, F., Sui, Y. F., Cao, C. G.: Formal Concept Analysis in Relational Database and Rough Relational Database. Fundamenta Informaticae, 80(4), 2007, 435–451.
• [9] Pawlak, Z.: “Rough sets”, International Journal of Computer and Information Sciences, 11, 1982, 341–356.
• [10] Pawlak, Z.: Rough sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.
• [11] Sui, Y. F., Wang, J., Jiang, Y. C.: Rough Relational Database: the Basic Definitions, Computer Science, 28(5), 2001, 122–124.
• [12] Sui, Y. F., Xia, Y. M., Wang, J.: The Information Entropy of Rough Relational Databases, Proc. of the 9th Int. Conf. on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, China, 2003, 320–324.
• [13] Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer-Verlag, Berlin, 1999.
• [14] D¨untsch, I., Gediga, G.: Uncertainty measures of rough set prediction, Artificial Intelligence, 106, 1998, 109–137.
• [15] Wierman, M. J.: Measuring uncertainty in rough set theory. International Journal of General Systems, 28(4), 1999, 283–297.
• [16] Liang, J. Y., Shi, Z. Z.: The information entropy, rough entropy and knowledge granulation in rough set theory, International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, 12(1), 2004, 37–46.
• [17] Petry, F. E.: Fuzzy Databases: Principles and Applications, Kluwer Academic, Boston, MA, 1996.
• [18] Zadeh, L. A.: Fuzzy Sets, Information and Control, 8, 1965, 338–353.
• [19] Pawlak, Z., Skowron, A.: Rough membership functions. In: Yager, R., et al., Eds., Advances in the Dempster-Shafer Theory of Evidence. John Wiley & Sons, New York, 1994, 251–271.
• [20] Pawlak, Z., Grzymala-Busse, J. W., Slowinski, R., Ziarko, W.: Rough sets. Communications of the ACM, 38(11), 1995, 89–95.
• [21] Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems, Handbook of applications and advances of rough set theory, Kluwer Academic Publishers, Dordrecht, 11, 1992, 331–362.
• [22] Buckles, B. P., Petry, F. E.: A fuzzy representation of data for relational databases. Fuzzy Sets and Systems, 7, 1982, 213–226.
• [23] Galindo, J., Urrutia, A., Piattini, M.: Fuzzy Databases, Modelling Design and Implementation, Hershey, USA, IDEA Group, 2006.
• [24] Jiang, F., Liu, G. Z.: Rough Relational Operators and Rough Entropy in Rough Relational Database. In: Proceedings of the Second International Workshop on Knowledge Discovery and Data Mining, 2009, 761–764.
• [25] Jiang, F., Sui, Y. F., Cao, C. G.: Relational Contexts and Relational Concepts. Fundamenta Informaticae, 99(3), 2010, 293–314.
• [26] Kent, R. E.: Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundamenta Informaticae, 27(2), 1996, 169–181.
• [27] Pagliani, P.: From concept lattices to approximation spaces: algebraic structures of some spaces of partial objects. Fundamenta Informaticae, 18, 1993, 1–25.
• [28] Pagliani, P.: Modalizing Relations by means of Relations: a general framework for two basic approaches to Knowledge Discovery in Database. In: Gevers, M. (Ed.), Proc. of the 7th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU ’98), Paris, France, 1998, 1175–1182.
• [29] Pagliani, P.: Transforming Information Systems. In: Proc. of the Tenth International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, University of Regina, Canada, 2005, 660–670.
• [30] Hońko, P.: Similarity-Based Classification in Relational Databases. Fundamenta Informaticae, 101(3), 2010, 187–213.
• [31] Lipski,W.: On Semantic Issues Connected with Incomplete Information Data Base. ACM Trans. on Database Systems, 4(3), 1979, 262–296.
• [32] Lipski, W.: On Databases with Incomplete Information. Journal of the ACM, 28(1), 1981, 41–70.
• [33] Orlowska, E., Pawlak, Z.: Representation of Nondeterministic Information. Theoretical Computer Science, 29, 1984, 27–39.
• [34] Orlowska, E. (ed.): Incomplete Information: Rough Set Analysis. Springer, Physica-Verlag, 1998.
• [35] Sakai, H.: Effective Procedures for Handling Possible Equivalence Relations in Non-deterministic Information Systems. Fundamenta Informaticae, 48(4), 2001, 343–362.
• [36] Sakai, H., Ishibashi, R., Nakata, M.: Lower and Upper Approximations of Rules in Non-deterministic Information Systems. Springer LNCS 5306, RSCTC 2008, 299–309.
• [37] Sakai, H., Ishibashi, R., Koba, K., Nakata, M.: Rules and Apriori Algorithm in Non-deterministic Information Systems. Transactions on Rough Sets IX, 2008, 328–350.
• [38] Sakai, H., Hayashi, K., Nakata, M., Slezak, D.: The Lower System, the Upper System and Rules with Stability Factor in Non-deterministic Information Systems. RSFDGrC 2009, 313–320.
• [39] Sakai, H., Nakata, M., Slezak, D.: Rule Generation in Lipski’s Incomplete Information Databases. RSCTC 2010, 376–385.
• [40] Okuma, H., Nakata, M., Slezak, D., Sakai, H.: An overview of decision making in Rough Non-deterministic Information Analysis. NaBIC 2010, 345–350.
• [41] Slezak, D.: Association Reducts: A Framework for Mining Multi-attribute Dependencies. ISMIS 2005, 354–363.
• [42] Slezak, D.: Degrees of conditional (in)dependence: A framework for approximate Bayesian networks and examples related to the rough set-based feature selection. Information Science, 179(3), 2009, 197–209.
• [43] Slezak, D.: Compound Analytics of Compound Data within RDBMS Framework - Infobright’s Perspective. FGIT 2010, 39–40.
• [44] Slezak, D., Toppin, G.: Injecting domain knowledge into a granular database engine: a position paper. CIKM 2010, 1913–1916.
• [45] Slezak, D., Synak, P., Wroblewski, J., Toppin, G.: Infobright Analytic Database Engine Using Rough Sets and Granular Computing. GrC 2010, 432–437.
• [46] Slezak, D., Kowalski, M.: Towards Approximate SQL - Infobright’s Approach. RSCTC 2010, 630–639.
• [47] An, A. J., Slezak, D.: Introduction to the special issue on advanced information retrieval and databases. Journal of Intelligent Information Systems, 34(3), 2010, 223–225.