Skip to main content

Advertisement

Springer Nature Link
Log in

Algebraic structures for fuzzy numbers from categorial point of view

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Using a classic algebraic construction additive and multiplicative structures (as commutative monoids) for fuzzy numbers are obtained. Moreover, we realize here an isomorphism between these structures.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  • Ban A, Bica A (2006) Solving linear systems of equivalences. J Appl Math Comput 20(1–2):97–118

    MATH  MathSciNet  Google Scholar 

  • Bica A (1998) Algebraic operations with fuzzy numbers. Analele Univ. Oradea, fasc. mat. 11–29

  • Bica A (2003) Categories and algebrical structures for real fuzzy numbers. PU.M.A Pure Math Appl 13(1–2):63–77

    MATH  MathSciNet  Google Scholar 

  • Buckley JJ (1989) On the algebra of interactive fuzzy numbers. Fuzzy Sets Syst 32(3):291–306

    Article  MATH  MathSciNet  Google Scholar 

  • Buckley JJ (1990) On the algebra of interactive fuzzy numbers. The continuous case. Fuzzy Sets Syst 37(3):317–326

    Article  MATH  MathSciNet  Google Scholar 

  • Chou ChCh (2003) The canonical representation of multiplication operation on triangular fuzzy numbers. Comput Math Appl 45(10–11):1601–1610

    Article  MATH  MathSciNet  Google Scholar 

  • Congxin W, Bokan Z (1999) Embedding problem of noncompact fuzzy number space E. Fuzzy Sets Syst 105:165–169

    Article  MATH  Google Scholar 

  • Congxin W, Gong Z (2001) On Henstock integral of fuzzy-number-valued functions (I). Fuzzy Sets Syst 120:523–532

    Article  MATH  Google Scholar 

  • Di Lascio L, Gisolfi A (2002) On the algebraic properties of some fuzzy numbers. J Fuzzy Math 10(1):151–168

    MATH  MathSciNet  Google Scholar 

  • Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9:613–626

    MATH  MathSciNet  Google Scholar 

  • Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic, New York

    MATH  Google Scholar 

  • Goetschel R, Voxman W (1986) Elementary fuzzy calculus. Fuzzy Sets Syst 18:31–43

    Article  MATH  MathSciNet  Google Scholar 

  • Heilpern S (1992) The expected value of a fuzzy number. Fuzzy Sets Syst 47:81–86

    Article  MATH  MathSciNet  Google Scholar 

  • Hong DH, Lee S (2002) Some algerbraic properties and a distance measure for interval-valued fuzzy numbers. Inf Sci 148(1–4):1–10

    Article  MATH  MathSciNet  Google Scholar 

  • Kovacs M (1992) A stable embedding of ill-posed linear systems into fuzzy systems. Fuzzy Sets Syst 45:305–312

    Article  MATH  MathSciNet  Google Scholar 

  • Kovacs M, Tran LH (1988) Algebraic structure of symmetrical M-fuzzy numbers. BUSEFAL 35:60–69

    MATH  Google Scholar 

  • Kovacs M, Tran LH (1991) Algebraic structure of centered M-fuzzy numbers. Fuzzy Sets Syst 39(1):91–99

    Article  MATH  MathSciNet  Google Scholar 

  • Mako Z (2002) Contributions to quasi-triangular fuzzy numbers theory with application in fuzzy linear programing. PHD Thesis, University of “Babeş-Bolyai”, Cluj-Napoca

    Google Scholar 

  • Mares M (1989) Addition of fuzzy quantities: disjunction-conjunction approach. Kybernetika 25(2):104–116

    MATH  MathSciNet  Google Scholar 

  • Mares M (1992) Multiplication of fuzzy quantities. Kybernetika 28(5):337–356

    MATH  MathSciNet  Google Scholar 

  • Mares M (1992/1993) Algebraic purism is expensive if it concerns fuzzy quantities. BUSEFAL 53:48–53

    Google Scholar 

  • Mares M (1993) Algebraic equivalences over fuzzy quantities. Kybernetika 29(2):122–132

    Google Scholar 

  • Mares M (1995a) Brief note on distributivity of triangular fuzzy numbers. Kybernetika 31(5): 451–457

    MATH  MathSciNet  Google Scholar 

  • Mares M (1995b) Equivalentions over fuzzy quantities. Tatra Mountains Math Publ 6:117–121

    MATH  MathSciNet  Google Scholar 

  • Mares M (1997) Weak arithmetics of fuzzy numbers. Fuzzy Sets Syst 91:143–153

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Oradea, Str. Armatei Romane no.5, 410087, Oradea, Romania

    Alexandru Mihai Bica

Authors
  1. Alexandru Mihai Bica
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Alexandru Mihai Bica.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bica, A.M. Algebraic structures for fuzzy numbers from categorial point of view. Soft Comput 11, 1099–1105 (2007). https://doi.org/10.1007/s00500-007-0167-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-007-0167-x

Keywords