Skip to main content
SpringerLink
Log in

L-Fuzzy Databases in Arrow Categories

  • Conference paper
  • First Online:
Relational and Algebraic Methods in Computer Science (RAMICS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9348))

Abstract

In this paper we present a query language for lattice-based (or L-fuzzy) databases. These databases store L-fuzzy sets in their attributes instead of (crisp) values in order to handle imprecise or incomplete information. A semantics for the language is defined using the abstract notion of an arrow category.

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

Access this chapter

Log in via an institution
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. Adjei, E.: L-Fuzzy Structural Query Language. Brock University (M.Sc. Thesis), tbp (2015)

    Google Scholar 

  2. Birkhoff, G.: Lattice Theory, 3rd edn., vol. XXV. American Mathematical Society Colloquium Publications (1967)

    Google Scholar 

  3. Chowdhury, W.: An Abstract Algebraic Theory of L-Fuzzy Relations in Relational Databases. Brock University (M.Sc. Thesis), tbp (2015)

    Google Scholar 

  4. Freyd, P., Scedrov, A.: Categories, Allegories. North-Holland (1990)

    Google Scholar 

  5. Galindo, J., Medina, J.M., Pons, O., Cubero, J.C.: A Server for Fuzzy SQL Queries. In: Andreasen, T., Christiansen, H., Larsen, H.L. (eds.) FQAS 1998. LNCS (LNAI), vol. 1495, pp. 164–174. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  6. Galindo, J.: New Characteristics in FSQL, a Fuzzy SQL for Fuzzy Databases. WSEAS Transactions on Information Science and Applications 2(2), 161–169 (2005)

    MathSciNet  Google Scholar 

  7. Galindo, J., Urrutia, A., Piattini, M.: Fuzzy Databases: Modeling, Design and Implementation. Idea Group Publishing Hershey, USA (2006)

    Google Scholar 

  8. Goguen, J.A.: L-fuzzy Sets. J. Math. Anal. Appl. 18, 145–157 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jónsson, B., Tarski, A.: Boolean Algebras with Operators, I, II. Amer. J. Math. 73, 891–939 (1951); 74, 127–162 (1952)

    Google Scholar 

  10. Kawahara, Y., Furusawa, H.: Crispness and Representation Theorems in Dedekind Categories. DOI-TR 143, Kyushu University (1997)

    Google Scholar 

  11. Olivier, J.P., Serrato, D.: Catégories de Dedekind. Morphismes dans les Catégories de Schröder. C.R. Acad. Sci. Paris 290, 939–941 (1980)

    MathSciNet  MATH  Google Scholar 

  12. Olivier, J.P., Serrato, D.: Squares and Rectangles in Relational Categories - Three Cases: Semilattice, Distributive lattice and Boolean Non-unitary. Fuzzy Sets and Systems 72, 167–178 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. Schmidt, G., Hattensperger, C., Winter, M.: Heterogeneous Relation Algebras. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science. Advances in Computer Science. Springer, Vienna (1997)

    Google Scholar 

  14. Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer (1989); English version: Relations and Graphs. Discrete Mathematics for Computer Scientists, EATCS Monographs on Theoret. Comput. Sci., Springer (1993)

    Google Scholar 

  15. Schmidt, G.: Relational Mathematics. Encyplopedia of Mathematics and Its Applications 132 (2011)

    Google Scholar 

  16. Winter, M.: Strukturtheorie heterogener Relationenalgebren mit Anwendung auf Nichtdetermismus in Programmiersprachen. Dissertationsverlag NG Kopierladen GmbH, München (1998)

    Google Scholar 

  17. Winter, M.: A new Algebraic Approach to L-Fuzzy Relations Convenient to Study Crispness. INS Information Science 139, 233–252 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Winter, M.: Relational Constructions in Goguen Categories. In: de Swart, H. (ed.) RelMiCS 2001. LNCS, vol. 2561, pp. 212–227. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  19. Winter, M.: Derived Operations in Goguen Categories. TAC Theory and Applications of Categories 10(11), 220–247 (2002)

    MathSciNet  MATH  Google Scholar 

  20. Winter, M.: Goguen Categories - A Categorical Approach to L-fuzzy relations. Trends in Logic, vol. 25. Springer (2007)

    Google Scholar 

  21. Winter, M.: Arrow Categories. Fuzzy Sets and Systems 160, 2893–2909 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Brock University, St. Catharines, Ontario, Canada, L2S 3A1

    Evans Adjei, Wazed Chowdhury & Michael Winter

Authors
  1. Evans Adjei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wazed Chowdhury
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Winter
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Evans Adjei .

Editor information

Editors and Affiliations

  1. McMaster University, Hamilton, Ontario, Canada

    Wolfram Kahl

  2. Brock University, St. Catharines, Ontario, Canada

    Michael Winter

  3. Universidade do Minho, Braga, Portugal

    José Oliveira

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Adjei, E., Chowdhury, W., Winter, M. (2015). L-Fuzzy Databases in Arrow Categories. In: Kahl, W., Winter, M., Oliveira, J. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2015. Lecture Notes in Computer Science(), vol 9348. Springer, Cham. https://doi.org/10.1007/978-3-319-24704-5_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24704-5_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24703-8

  • Online ISBN: 978-3-319-24704-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation