Skip to main content
SpringerLink
Log in

About Zf, the Set of Fuzzy Relative Integers, and the Definition of Fuzzy Bags on Zf

  • Conference paper
  • First Online:
Fuzzy Sets and Systems — IFSA 2003 (IFSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2715))

Included in the following conference series:

Abstract

A characterization of fuzzy bags with fuzzy integers (ℕf) provides a general framework in which sets, bags, fuzzy sets and fuzzy bags are treated in a uniform way. In bag theory, the difference between two bags A and B is the relative complement of A intersection B to A. With fuzzy bags defined on ℕf, this difference does not always exist and, in such a case, only approximations of the exact result can be defined. The problem comes from the fact that the fuzzy bag model considered so far is based on positive fuzzy integers. In this paper, we show that fuzzy relative integers (ℤf) offer a well-founded framework in which the difference of two fuzzy bags is always defined.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Bosc P., Rocacher D., “About difference operations on fuzzy bags”, 9 th Inter. Conf. IPMU, pp 1441–1546, 2002.

    Google Scholar 

  2. Dubois D., Prade H., “Inverse operations for fuzzy numbers”, Proc. IFAC symp. On fuzzy information, knowledge representation and decision analysis, Marseille, pp 391–396, 1983.

    Google Scholar 

  3. Dubois D., Prade H., “Fuzzy set theoretic differences and inclusions and their use in the analysis of fuzzy equations”, Control and Cybernetics, vol 13, n° 3, 1984.

    Google Scholar 

  4. Dubois D., Prade H., “Fuzzy cardinality and modeling of imprecise quantification”, Fuzzy Sets and Systems, 16,3, pp 199–230, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  5. Miyamoto S., “Fuzzy Multisets and Fuzzy Clustering of Documents”, 10 th Inter. Conf. on Fuzzy Systems, (FUZZ IEEE’01), 2001.

    Google Scholar 

  6. Sanchez E., “Solutions of fuzzy equations with extended operations”, Fuzzy Set and Systems, 12, pp 237–248, 1984.

    Article  MATH  Google Scholar 

  7. Rocacher D., “On the use of fuzzy numbers in flexible querying”, 9 th IFSA World Cong. and 20 th NAFIPS Inter. Conf., pp 2440–2445, 2001.

    Google Scholar 

  8. Yager R., “On the Theory of Bags”, Inter. J. of General Systems, vol. 13, pp 23–27, 1986.

    Article  MathSciNet  Google Scholar 

  9. Zadeh L. A., “A computational approach to fuzzy quantifiers in natural languages”, Comp. Math. App., vol. 9, pp 149–184, 1983.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRISA/ENSSAT, BP 447, 22305, LANNION Cédex, France

    Patrick Bosc & Daniel Rocacher

Authors
  1. Patrick Bosc
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Rocacher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Taner Bilgiç

  2. Dept. of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, 9000, Gent, Belgium

    Bernard De Baets

  3. Department of Electrical and Electronics Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Okyay Kaynak

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bosc, P., Rocacher, D. (2003). About Zf, the Set of Fuzzy Relative Integers, and the Definition of Fuzzy Bags on Zf . In: Bilgiç, T., De Baets, B., Kaynak, O. (eds) Fuzzy Sets and Systems — IFSA 2003. IFSA 2003. Lecture Notes in Computer Science, vol 2715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44967-1_10

Download citation

  • DOI: https://doi.org/10.1007/3-540-44967-1_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40383-8

  • Online ISBN: 978-3-540-44967-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation