An Approximation of Fuzzy Numbers Based on Polynomial Form Fuzzy Numbers

Main Article Content

Sh. Yeganehmanesh, M. Amirfakhrian


In this paper, we approximate an arbitrary fuzzy number by a polynomial fuzzy number through minimizing the distance between them. Throughout this work, we used a distance that is a meter on the set of all fuzzy numbers with continuous left and right spread functions. To support our claims analytically, we have proven some theorems and given supplementary corollaries.

Article Details


  1. S. Abbasbandy, M. Amirfakhrian, The nearest trapezoidal form of a generalized left right fuzzy number, Int. J. Approx. Reason. 43 (2006), 166-178.
  2. S. Abbasbandy, B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity, Appl. Math. Comput. 156 (2004), 381-386.
  3. M. Amirfakhrian, Numerical Solution of a System of Polynomial Parametric form Fuzzy Linear Equations, Book Chapter of Ferroelectrics, INTECH Publisher, Austria, (2010).
  4. A. I. Ban, L. Coroianu, Existence, uniqueness and continuity of trapezoidal approximations of fuzzy numbers under a general condition, Fuzzy Sets Syst. 3 (2014) 3-22.
  5. D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Application, Academic Press, New York, (1980).
  6. L. Coroianu, M. Gagolewski, P. Grzegorzewski, Nearest piecewise linear approximation of fuzzy numbers, Fuzzy Sets Syst. 233 (2013), 26-51.
  7. P. Grzegorzewski, Metrics and orders in space of fuzzy numbers, Fuzzy Sets Syst. 97 (1998), 83-94.
  8. P. Grzegorzewski, Nearest interval approximation of a fuzzy number, Fuzzy Sets Syst. 130 (2002), 321-330.
  9. P. Grzegorzewski, P. Mró wka, Trapezoidal approximations of fuzzy numbers, Fuzzy Sets Syst. 153 (2005), 115-135.
  10. P. Grzegorzewski, K. Pasternak-Winiarska,Natural trapezoidal approximations of fuzzy numbers, Fuzzy Sets Syst. 250 (2014), 90-109.
  11. M. Ma and A. Kandel and M. Friedman, Correction to ”A new approach for defuzzification”, Fuzzy Sets Syst. 128 (2002), 133-134.
  12. V. Powers, B. Reznick, Polynomials that are positive on an interval, Trans. Amer. Math. Soc. 352 (10) (2000), 4677C4692.
  13. J. Stolfi, M.V.A. Andrade, J.L.D. Comba, and R.Van Iwaarden. Affine arithmetic: a correlation-sensitive variant of interval arithmetic, accessed January 17, (2008).
  14. W. Voxman, Some remarks on distance between fuzzy numbers, Fuzzy Sets Syst. 100 (1998), 353-365.
  15. H. J. Zimmermann, Fuzzy Set Theory and Its Applications, 2 nd Edition, Kluwer Academic, Boston, (1991).