Skip to main content

Similarity of Query Results in Similarity-Based Databases

  • Conference paper
Rough Sets and Knowledge Technology (RSKT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6954))

Included in the following conference series:

  • 1872 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abiteboul, S., et al.: The Lowell database research self-assessment. Communications of the ACM 48(5), 111–118 (2005)

    Article  Google Scholar 

  2. Belohlavek, R.: Fuzzy closure operators. Journal of Mathematical Analysis and Appl. 262, 473–489 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, Academic/Plenum Publishers, New York (2002)

    Book  MATH  Google Scholar 

  4. Belohlavek, R.: Fuzzy closure operators induced by similarity. Fundamenta Informaticae 58(2), 79–91 (2003)

    MathSciNet  MATH  Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. Belohlavek, R., Vychodil, V.: Query systems in similarity-based databases: logical foundations, expressive power, and completeness. In: ACM SAC 2010, pp. 1648–1655 (2010)

    Google Scholar 

  7. 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

    Google Scholar 

  8. Buckles, B.: P., Petry F.E.: Fuzzy databases in the new era. In: ACM SAC 1995, Nashville, TN, pp. 497–502 (1995)

    Google Scholar 

  9. Codd, E.F.: A relational model of data for large shared data banks. Communications of the ACM 13(6), 377–387 (1970)

    Article  MATH  Google Scholar 

  10. Fagin, R.: Combining fuzzy information: an overview. ACM SIGMOD Record 31(2), 109–118 (2002)

    Article  Google Scholar 

  11. Gottwald, S.: A Treatise on Many-Valued Logics. Research Studies Press, Beldock (2001)

    MATH  Google Scholar 

  12. Gottwald, S.: Mathematical fuzzy logics. Bull. Symbolic Logic 14(2), 210–239 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    Book  MATH  Google Scholar 

  14. Hájek, P.: On very true. Fuzzy Sets and Syst. 124, 329–333 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Klawonn, F., Castro, J.L.: Similarity in fuzzy reasoning. Mathware & Soft Computing 2, 197–228 (1995)

    MathSciNet  MATH  Google Scholar 

  16. 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)

    Google Scholar 

  17. Maier, D.: The Theory of Relational Databases. Comp. Sci. Press, Rockville (1983)

    MATH  Google Scholar 

  18. 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)

    Article  MathSciNet  MATH  Google Scholar 

  19. 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)

    Google Scholar 

  20. Takahashi, Y.: Fuzzy database query languages and their relational completeness theorem. IEEE Trans. Knowledge and Data Engineering 5, 122–125 (1993)

    Article  Google Scholar 

  21. Shenoi, S., Melton, A.: Proximity relations in the fuzzy relational database model. Fuzzy Sets and Syst. 100, 51–62 (1999)

    Article  MATH  Google Scholar 

  22. Valverde, L.: On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17, 313–328 (1985)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24425-4_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24424-7

  • Online ISBN: 978-3-642-24425-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics