A Relational Algebra for Generalized Fuzzy Bipolar Conditions

  • Ludovic Liétard
  • Daniel  Rocacher
  • Nouredine Tamani
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 497)

Abstract

Flexible querying of regular databases consists in expressing user’s preferences (fuzzy conditions) inside queries instead of Boolean requirements. Fuzzy bipolar conditions are particular cases of fuzzy conditions which are made of two components, a mandatory fuzzy condition and an optional fuzzy condition. They define two different types of complex preferences which can be either of a conjunctive nature or of a disjunctive nature (both of them being interpreted in a hierarchical way). The first case leads to define fuzzy bipolar conditions of type and if possible, the second case leads to define fuzzy bipolar conditions of type or else. This chapter shows that a general form of fuzzy bipolar conditions having a hierarchical interpretation can be considered since these two forms are compatible. As a consequence, fuzzy bipolar conditions of both types can be used together in a single bipolar query and all the algebraic operators are extended to this generalization. The particular case (non algebraic) of the use of linguistic quantifiers is also studied.

References

  1. 1.
    Bosc, P., Pivert, O.: SQLf: A relational database langage for fuzzy querying. IEEE Trans. Fuzzy Syst. 3(1), 1–17 (Feb 1995)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bosc, P., Pivert, O.: A propos de la négation de conditions bipolaires floues. On the negation of fuzzy bipolar conditions. In: Rencontre francophone sur la logique floue et ses applications, pp. 21–28 (2010)Google Scholar
  3. 3.
    Bosc, P., Pivert, O., Liétard, L., Mokhtari, A.: Extending relational algebra to handle bipolarity. In: 25th ACM Symposium on Applied Computing, SAC’10, pp. 1717–1721 (2010)Google Scholar
  4. 4.
    de Tré, G., Zadrozny, S., Matthé, T., Kacprzyk, J., Bronselaer, A.: Dealing with positive and negative query criteria in fuzzy database quering bipolar satisfaction degrees. LNAI FQAS 5822, 593–604 (2009)Google Scholar
  5. 5.
    Dubois, D., Prade, H.: Bipolarité dans un processus d’interrogation flexible. In: Actes des Rencontres Francophones sur la Logique Floue et ses Applications (LFA’02), pp. 127–134 (2002)Google Scholar
  6. 6.
    Dubois, D., Prade, H.: Bipolarity in flexible querying. LNAI 2522, 174–182 (2002)Google Scholar
  7. 7.
    Dubois, D., Prade, H.: Handling bipolar queries in fuzzy information processing. In: Galindo, J. (ed.) Handbook of Research on Fuzzy Information Processing in Databases, pp. 97–114. Information Science Reference, Hershey (2008)CrossRefGoogle Scholar
  8. 8.
    Dubois, D., Prade, H.: An introduction to bipolar representations of information and preference. Int. J. Intell. Syst. 23, 866–877 (2008)CrossRefMATHGoogle Scholar
  9. 9.
    Liétard, L., Rocacher, D.: On the definition of extended norms and co-norms to aggregate fuzzy bipolar conditions. In: IFSA/EUSFLAT, pp. 513–518 (2009)Google Scholar
  10. 10.
    Liétard, L., Rocacher, D., Bosc, P.: On the extension of SQL to fuzzy bipolar conditions. In: The 28th North American Information Processing Society Annual Conference (NAFIPS’09) (2009)Google Scholar
  11. 11.
    Liétard, L., Tamani, N., Rocacher, N.: Fuzzy bipolar conditions of type “or else”. In: The 20th IEEE International Conference on Fuzzy Systems (FUZZZ-IEEE’11), pp. 2546–2551 (2011)Google Scholar
  12. 12.
    Tamani, N., Liétard, L., Rocacher, D.: Bipolar SQLf: A flexible querying language for relational databases. In: The 9th International Conference on Flexible Query Answering Systems (FQAS’11), LNAI, vol. 7022, Springer, pp. 472–484 (2011)Google Scholar
  13. 13.
    Yager, R.R.: Quantifiers in the formulation of multiple objective decision functions. Inf. Sci. 31, 107–139 (1983)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18, 183–190 (1988)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Zadeh, L.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl. 9, 149–184 (1983)Google Scholar
  17. 17.
    Zadrozny, S.: Bipolar queries revisited. LNAI MDAI 3558, 387–398 (2005)Google Scholar
  18. 18.
    Zadrozny, S., Kacprzyk, J.: Bipolar queries and queries with preferences (invited paper). In: DEXA’06: 17th International Conference on Database and Expert Systems Applications (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ludovic Liétard
    • 1
  • Daniel  Rocacher
    • 2
  • Nouredine Tamani
    • 2
  1. 1.IRISA/IUT/University Rennes 1Lannion CedexFrance
  2. 2.IRISA/ENSSAT/University Rennes 1Lannion CedexFrance

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