Skip to main content
SpringerLink
Log in

Bounded Linear Transformations Between Probabilistic Normed Vector Spaces

  • Chapter
Fuzzy Logic

Part of the book series: Theory and Decision Library ((TDLD,volume 12))

Abstract

We denote by R*(I) the set of all nonnegative fuzzy real numbers; that is functions n from R*=[0,∞[ to the unit interval I which are left continuous and nonascending, and satisfy η(0) = 1 and η(+∞-) = 0. This set R*(I) canonically includes R* in the obvious way. It is ordered by the usual pointwise order of real functions.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover 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. T.M.G. Ahsanullah and N.N. Morsi, Invariant probabilistic metrizability of fuzzy neighbourhood groups, Fuzzy Sets and Systems 47 (1992) 233–245.

    Article  MathSciNet  MATH  Google Scholar 

  2. M.A. Amer and N.N. Morsi, Characterizations of some fuzzy topological notions in probabilistic metric spaces, Fuzzy Sets and Systems (1993) (to appear).

    Google Scholar 

  3. A.M. El-Abyad and H.M. El-Hamouly, Fuzzy inner product spaces, Fuzzy Sets and Systems 44 (1991) 309–326.

    Article  MathSciNet  MATH  Google Scholar 

  4. U. Höhle, Probabilistic metrization of fuzzy uniformities, Fuzzy Sets and Systems 8 (1982) 63–69.

    Article  MathSciNet  MATH  Google Scholar 

  5. A.K. Katsaras, Linear fuzzy neighbourhood spaces, Fuzzy Sets and Systems 16 (1985) 25–40. Part II: J. Math. Anal. Appl. 115 (1986) 560-573

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56 (1976) 621–633.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Lowen, Fuzzy uniform spaces, J. Math. Anal. Appl. 82 (1981) 370–385.

    Article  MathSciNet  Google Scholar 

  8. R. Lowen, Fuzzy neighborhood spaces, Fuzzy Sets and Systems 7 (1982) 165–189.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Lowen, On ( R(L), ⊕), Fuzzy Sets and Systems 10 (1983) 203–209.

    Article  MathSciNet  MATH  Google Scholar 

  10. A.S. Mashhour and N.N. Morsi, Fuzzy metric neighbourhood spaces, Fuzzy Sets and Systems 45 (1992) 367–388.

    Article  MathSciNet  MATH  Google Scholar 

  11. N.N. Morsi, On fuzzy pseudo-normed vector spaces, Fuzzy Sets and Systems 27 (1988) 351–372.

    Article  MathSciNet  MATH  Google Scholar 

  12. N.N. Morsi, Dual fuzzy neighbourhood spaces I, Fuzzy Sets and Systems 44 (1991) 245–263

    Article  MathSciNet  MATH  Google Scholar 

  13. N.N. Morsi, The Urysohn Lemma for fuzzy neighbourhood spaces, Fuzzy Sets and Systems 39 (1991) 347–360.

    Article  MathSciNet  MATH  Google Scholar 

  14. N.N. Morsi and S.E. Yehia, Continuity of fuzzy multiplication in the N-Euclidean space, Fuzzy Sets and Systems 46 (1992) 97–106.

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Schweizer and A. Sklar, Probabilistic Metric Spaces (North-Holland, Amsterdam, 1983).

    Google Scholar 

  16. H.-J. Zimmermann, Fuzzy Set Theory and Its Applications (Kluwer-Nijhoff Publishing Co., Norwell MA, 1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Physical Sciences, Faculty of Engineering Mansura University, Egypt

    Mustafa A. Amer

  2. Dept. of Mathematics, Military Technical College, Cairo, Egypt

    Nehad N. Morsi

Authors
  1. Mustafa A. Amer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nehad N. Morsi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Antwerp, Antwerp, Belgium

    R. Lowen

  2. Université de Liège, Liège, Belgium

    M. Roubens

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Amer, M.A., Morsi, N.N. (1993). Bounded Linear Transformations Between Probabilistic Normed Vector Spaces. In: Lowen, R., Roubens, M. (eds) Fuzzy Logic. Theory and Decision Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2014-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2014-2_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4890-3

  • Online ISBN: 978-94-011-2014-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation