Abstract
This paper presents some functional dependency relations defined on the attribute set of an information system. We establish some basic relationships between functional dependency relations, attribute reduction, and closure operators. We use the partial order for dependencies to show that reducts of an information system can be obtained from the maximal elements of a functional dependency relation.
This work was supported by Universidad Militar Nueva Granada’s VICEIN Special Research Fund, under project CIAS 3144-2020, and by the Odysseus program of the Research Foundation-Flanders.
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References
Armstrong, W.: Dependency structures of database relationships. In: Information Processing, pp. 580–583. North Holland Publishing (1974)
Blyth, T.S.: Lattices and Ordered Algebraic Structures. Universitext. Springer, London (2005). https://doi.org/10.1007/b139095
Chiaselotti, G., Infusino, F., Notions from rough sets theory in a generalized dependency relation context. Int. J. Approx. Reason. 98, 25–61 (2018)
Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129, 1–47 (2001)
Järvinen, J.: Lattice theory for rough sets. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400–498. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71200-8_22
Matús, F.: Abstract functional dependency structures. Theor. Comput. Sci. 81, 117–126 (1991)
Pawlak Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)
Pawlak Z.: Information systems theoretical foundations. Inf. Syst. 6(3), 205–218 (1981)
Qu, Y., Fu, X.: Rough set based algorithm of discovering functional dependencies for relation database. In: 4th International Conference on Wireless Communications, Networking and Mobile Computing, Dalian, 2008, pp. 1–4 (2008). https://doi.org/10.1109/WiCom.2008.2526
Novotný, M., Pawlak, Z.: Independence of attributes. Bull. Polish Acad. Sci. Math. 36, 459–465 (1988)
Novotný, M.: Dependence spaces of information systems. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis. Studies in Fuzziness and Soft Computing, vol. 13, pp. 193-246. Physica, Heidelberg (1998). https://doi.org/10.1007/978-3-7908-1888-8_7
Rauszer, C.M.: An equivalence between indiscernibility relations in information systems and a fragment of intuitionistic logic. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 298–317. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-16066-3_25
Restrepo M., Cornelis C., Attribute reduction from closure operators and matroids in Rough Set Theory. In: Bello, R., Miao, D., Falcon, R., Nakata, M., Rosete, A., Ciucci, D. (eds.) IJCRS 2020. LNAI, vol. 11499, pp. 183–192. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-52705-1_13
Ślezak, D.: Rough sets and functional dependencies in data: foundations of association reducts. In: Gavrilova, M.L., Tan, C.J.K., Wang, Y., Chan, K.C.C. (eds.) Transactions on Computational Science V. LNCS, vol. 5540, pp. 182–205. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02097-1_10
Yang T., Li Q.: Reduction about approximation spaces of covering generalized rough sets. Int. J. Approx. Reason. 51, 335–345 (2010)
Zhang, B., Qian, S., Wei, C.: Research of reduct algorithm based on functional dependency. In: International Conference on Computer and Communication Technologies in Agriculture Engineering, Chengdu, 2010, pp. 312–315 (2010). https://doi.org/10.1109/CCTAE.2010.5543312
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Restrepo, M., Cornelis, C. (2021). Attribute Reduction Using Functional Dependency Relations in Rough Set Theory. In: Ramanna, S., Cornelis, C., Ciucci, D. (eds) Rough Sets. IJCRS 2021. Lecture Notes in Computer Science(), vol 12872. Springer, Cham. https://doi.org/10.1007/978-3-030-87334-9_8
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