On improving trapezoidal and triangular approximations of fuzzy numbers

  • Authors:

  • Chi-Tsuen Yeh

  • Affiliations:

  • Department of Mathematics Education, National University of Tainan, 33, Sec. 2, Shu-Lin Street, 70005 Tainan, Taiwan

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2008

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Abstract

Recently, various researchers have proved that the approximations of fuzzy numbers may fail to be fuzzy numbers, such as the trapezoidal approximations of fuzzy numbers. In this paper, we show by an example that the weighted triangular approximation of fuzzy numbers, proposed by Zeng and Li, may lead to the same result. For filling the gap, improvements of trapezoidal and triangular approximations are proposed. The formulas for computing the two improved approximations are provided. Some properties of the two improved approximations are also proved.