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On the Z-Numbers

  • Tofigh AllahviranlooEmail author
  • Somayeh Ezadi
Chapter
  • 23 Downloads
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 391)

Abstract

In this chapter, first the Z-number is introduced then calculating operations are defined. Moreover several ranking methods are investigated to order the Z-numbers for using in other appropriate models. To points out one of the application, a regression method based on neural network technique is described in detail. Finally, the initial value problem with Z-number initial value (as a most applicable model) is introduced.

Keywords

Z-numbers Ranking Neural network Initial value problem Regression 

References

  1. 1.
    R.A. Aliev, O.H. Huseynov, R.R. Aliyev, A.A. Alizadeh, The Arithmetic of Z-Numbers (2015)Google Scholar
  2. 2.
    A.S.A. Bakar, A. Gegov, Multi-layer decision methodology for ranking Z-numbers. Int J Comput Intell Syst. 8, 395–406 (2015).CrossRefGoogle Scholar
  3. 3.
    S. Ezadi, T. Allahviranloo, New multi-layer method for Z-number ranking using hyperbolic tangent function and convex combination. Intell. Autom. Soft Comput. (2017)Google Scholar
  4. 4.
    S. Ezadi, T. Allahviranloo, Two new methods for ranking of Z-numbers based on sigmoid function and sign method. Int. J. Intell. Syst. 1–12 (2018)Google Scholar
  5. 5.
    S. Ezadi, T. Allahviranloo, Numerical solution of linear regression based on Z-numbers by improved neural network.Intell. Autom. Soft Comput. (2017)Google Scholar
  6. 6.
    M. Hukuhara, Integration des applications measurables dont lavaleur est un compact convexe. Funkcialaj Ekvacioj 10, 205223 (1967)Google Scholar
  7. 7.
    W. Jiang, Ch. Xie, Y. Luo, Y. Tang, Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers. J. Intell. Fuzzy Syst. 32(3), 1931–1943 (2017)CrossRefGoogle Scholar
  8. 8.
    B. Kang, D. Wei, Y. Li, & Y. Deng, Decision making using Z-numbers under uncertain environment. J. Comput. Inf. Syst. 8, 2807–2814 (2012)Google Scholar
  9. 9.
    D.C. Liu, J. Nocedal, On the limited memory BFGS method for large scale optimization. Math. Program. 45(3), 503–528 (1989)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D. Mohamada, S. Akma Shaharanib, N.H. Kamisc, in A Z-Number-Based Decision Making Procedure with Ranking Fuzzy Numbers method. International Conference on Quantitative Sciences and Its Applications, pp. 160–166 (2014)Google Scholar
  11. 11.
    S. Pirmuhammadi, T. Allahviranloo, M. Keshavarz, The parametric form of Z-number and its application in Z-number initial value Problem. Int. J. Intell. Syst. 32(10), 1030–1061 (2017)CrossRefGoogle Scholar
  12. 12.
    L.A. Zadeh, A note on Z-numbers. Inf. Sci. 181, 2923–2932 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Engineering and Natural SciencesBahcesehir UniversityIstanbulTurkey
  2. 2.Department of MathematicsTehran North Branch, Islamic Azad UniversityTehranIran

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