Skip to main content
SpringerLink
Log in

Triangular approximations of fuzzy numbers using α-weighted valuations

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

Abstract

In this paper, a fuzzy triangular approximation using α-weighted valuations is introduced and the nearest approximation by the minimization technique is obtained, such that the computational complexity is less than that in Abbasbandy and Amirfakhrian 2006. Moreover, we investigate some reasonable properties of the α-weighted triangular approximation.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Abbasbandy S, Amirfakhrian M (2006) The nearest approximation of a fuzzy quantity in parametric form. Appl Math Comput 172:624–632

    Article  MATH  MathSciNet  Google Scholar 

  • Abbasbandy S, Asady B (2004) The nearest trapezodial fuzzy number to a fuzzy quantity. Appl Math Comput 156:381–386

    Article  MATH  MathSciNet  Google Scholar 

  • Allahviranloo T, Adabitabar Firozja M (2007) Note on “Trapezodial approximation of fuzzy numbers”. Fuzzy Sets Syst 158:755–756

    Article  MATH  MathSciNet  Google Scholar 

  • Ban A (2008) Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval. Fuzzy Sets Syst 159:1327–1344

    Article  MathSciNet  Google Scholar 

  • Chanas S (2001) On the interval approximation of a fuzzy number. Fuzzy Sets Syst 122:353–356

    Article  MATH  MathSciNet  Google Scholar 

  • Delgado M, Vila MA, Voxman W (1998) On a canonical representation of fuzzy numbers. Fuzzy Sets Syst 93:125–135

    Article  MATH  MathSciNet  Google Scholar 

  • Detyniecki M, Yager R (2000) Ranking fuzzy numbers using α-weighted valuations. Internat J Uncert Fuzziness Knowl Based Syst 8:573–591

    Article  MATH  MathSciNet  Google Scholar 

  • Filev DP, Yager RR (1991) A generalized defuzzification method via Bad distribution. Int J Intell Syst 6:687–697

    Article  MATH  Google Scholar 

  • Grzegorzewski P (2002) Nearest interval approximation of a fuzzy number. Fuzzy Sets Syst 130:321–330

    Article  MATH  MathSciNet  Google Scholar 

  • Grzegorzewski P (2003) Approximation of a fuzzy number preserving entropy-like nonspcifity. Oper Res Decis 4:49–59

    MathSciNet  Google Scholar 

  • Grzegorzewski P, Mrowka E (2005) Trapezoidal approximations of fuzzy numbers. Fuzzy Sets Syst 153:115–135

    Article  MATH  MathSciNet  Google Scholar 

  • Grzegorzewski P, Mrowka E (2007) Trapezoidal approximations of fuzzy numbers-revisited. Fuzzy Sets Syst 158:757–768

    Article  MATH  MathSciNet  Google Scholar 

  • Kandel A (1986) Fuzzy mathematical techniques with application. Addison-Wesley, New York

    Google Scholar 

  • Ma M, Kandel A, Friedman M (2000) A new approach for defuzzification. Fuzzy Sets Syst 111:351–356

    Article  MATH  MathSciNet  Google Scholar 

  • Roventa E, Spircu T (2003) Averaging procedures in defuzzification processes. Fuzzy Sets Syst 136:375–385

    Article  MATH  MathSciNet  Google Scholar 

  • Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inform Sci 24:143–161

    Article  MATH  MathSciNet  Google Scholar 

  • Yager RR (1999) On ranking fuzzy numbers using valuations. Int J Intell Syst 14:1249–1268

    Article  MATH  Google Scholar 

  • Yager RR, Filev DP (1998) On the instantiation of possibility distributions. Technical report MII-1817, Machine Intelligence Institute, Iona College, New Rochelle

Download references

Acknowledgments

The authors would like to thank the anonymous referees for their useful suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, 14778, Tehran, Iran

    S. Abbasbandy

  2. Shahryar-shahr-e-Qods-Branch, Islamic Azad University, Tehran, Iran

    E. Ahmady

  3. Department of Mathematics, Pishva-Varamin Branch, Islamic Azad University, Tehran, Iran

    N. Ahmady

  4. Department of Mathematics, Imam Khomeini International University, 34149-16818, Ghazvin, Iran

    S. Abbasbandy

Authors
  1. S. Abbasbandy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Ahmady
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Ahmady
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Abbasbandy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abbasbandy, S., Ahmady, E. & Ahmady, N. Triangular approximations of fuzzy numbers using α-weighted valuations. Soft Comput 14, 71–79 (2010). https://doi.org/10.1007/s00500-008-0390-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-008-0390-0

Keywords

Search

Navigation