Abstract
We study estimations of similarity of query results in a similarity-based database model. The model results as extension of Codd’s model of data in which domains are additionally equipped with similarity relations and tuples in data tables have ranks indicating degrees to which tuples match similarity-based queries. We present ranked-based and tuple-based similarity of data tables, similarity closures, prove that relational operations in our model preserve similarity, and provide formulas for estimating similarity of query results based on similarity of input data. Most of the proofs are only sketched or omitted because of the limited scope of the paper.
Supported by grant no. P103/11/1456 of the Czech Science Foundation.
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References
Abiteboul, S., et al.: The Lowell database research self-assessment. Communications of the ACM 48(5), 111–118 (2005)
Belohlavek, R.: Fuzzy closure operators. Journal of Mathematical Analysis and Appl. 262, 473–489 (2001)
Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, Academic/Plenum Publishers, New York (2002)
Belohlavek, R.: Fuzzy closure operators induced by similarity. Fundamenta Informaticae 58(2), 79–91 (2003)
Belohlavek, R., Vychodil, V.: Logical foundations for similarity-based databases. In: Chen, L., Liu, C., Liu, Q., Deng, K. (eds.) DASFAA 2009. LNCS, vol. 5667, pp. 137–151. Springer, Heidelberg (2009)
Belohlavek, R., Vychodil, V.: Query systems in similarity-based databases: logical foundations, expressive power, and completeness. In: ACM SAC 2010, pp. 1648–1655 (2010)
Belohlavek, R., Vychodil, V.: Codd’s relational model from the point of view of fuzzy logic. J. Logic and Computation (to appear), doi:10.1093/logcom/exp056
Buckles, B.: P., Petry F.E.: Fuzzy databases in the new era. In: ACM SAC 1995, Nashville, TN, pp. 497–502 (1995)
Codd, E.F.: A relational model of data for large shared data banks. Communications of the ACM 13(6), 377–387 (1970)
Fagin, R.: Combining fuzzy information: an overview. ACM SIGMOD Record 31(2), 109–118 (2002)
Gottwald, S.: A Treatise on Many-Valued Logics. Research Studies Press, Beldock (2001)
Gottwald, S.: Mathematical fuzzy logics. Bull. Symbolic Logic 14(2), 210–239 (2008)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)
Hájek, P.: On very true. Fuzzy Sets and Syst. 124, 329–333 (2001)
Klawonn, F., Castro, J.L.: Similarity in fuzzy reasoning. Mathware & Soft Computing 2, 197–228 (1995)
Li, C., Chang, K.C.-C., Ilyas I.F., Song, S.: RankSQL: Query Algebra and Optimization for Relational top-k queries. In: ACM SIGMOD 2005, pp. 131–142 (2005)
Maier, D.: The Theory of Relational Databases. Comp. Sci. Press, Rockville (1983)
Prade, H., Testemale, C.: Generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries. Inf. Sci. 34, 115–143 (1984)
Raju, K.V.S.V.N., Majumdar, A.K.: Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems. ACM Trans. Database Systems 13(2), 129–166 (1988)
Takahashi, Y.: Fuzzy database query languages and their relational completeness theorem. IEEE Trans. Knowledge and Data Engineering 5, 122–125 (1993)
Shenoi, S., Melton, A.: Proximity relations in the fuzzy relational database model. Fuzzy Sets and Syst. 100, 51–62 (1999)
Valverde, L.: On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17, 313–328 (1985)
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Belohlavek, R., Urbanova, L., Vychodil, V. (2011). Similarity of Query Results in Similarity-Based Databases. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_35
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DOI: https://doi.org/10.1007/978-3-642-24425-4_35
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