Weighted trapezoidal approximation-preserving cores of a fuzzy number

  • Authors:

  • S. Abbasbandy;T. Hajjari

  • Affiliations:

  • Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778, Iran;Department of Mathematics, Firuz-Kuh Branch, Islamic Azad University, Firuz-Kuh, 132, Iran

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

Recently, various researchers have proved that approximations of fuzzy numbers may fail to be fuzzy numbers. In this contribution, we suggest a new weighted trapezoidal approximation of an arbitrary fuzzy number, which preserves its cores. We prove that the weighted trapezoidal approximation-preserving core is always a fuzzy number. We then discuss properties of the approximation strategy including translation invariance, scale invariance identity and continuity. The advantage is that the method presented here is simpler than other methods computationally.