Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value

  • Authors:

  • A. Ban;A. Bríndaş;L. Coroianu;C. Negruiu;O. Nica

  • Affiliations:

  • Department of Mathematics and Informatics, University of Oradea, 410087 Oradea, Romania;Mihai Veliciu High School, 315100 Chişineu-Criş, Romania;Department of Mathematics and Informatics, University of Oradea, 410087 Oradea, Romania and Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania;Traian Vuia High School, 410191 Oradea, Romania;Oşorhei School, 417360 Oşorhei, Romania and Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2011

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Abstract

Value and ambiguity are two parameters which were introduced to represent fuzzy numbers. In this paper, we find the nearest trapezoidal approximation and the nearest symmetric trapezoidal approximation to a given fuzzy number, with respect to the average Euclidean distance, preserving the value and ambiguity. To avoid the laborious calculus associated with the Karush-Kuhn-Tucker theorem, the working tool in some recent papers, a less sophisticated method is proposed. Algorithms for computing the approximations, many examples, proofs of continuity and two applications to ranking of fuzzy numbers and estimations of the defect of additivity for approximations are given.