Piecewise Linear Approximation of Fuzzy Numbers Preserving the Support and Core

  • Lucian Coroianu
  • Marek Gagolewski
  • Przemyslaw Grzegorzewski
  • M. Adabitabar Firozja
  • Tahereh Houlari
Part of the Communications in Computer and Information Science book series (CCIS, volume 443)

Abstract

A reasonable approximation of a fuzzy number should have a simple membership function, be close to the input fuzzy number, and should preserve some of its important characteristics. In this paper we suggest to approximate a fuzzy number by a piecewise linear 1-knot fuzzy number which is the closest one to the input fuzzy number among all piecewise linear 1-knot fuzzy numbers having the same core and the same support as the input. We discuss the existence of the approximation operator, show algorithms ready for the practical use and illustrate the considered concepts by examples. It turns out that such an approximation task may be problematic.

Keywords

Approximation of fuzzy numbers core fuzzy number piecewise linear approximation support 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lucian Coroianu
    • 1
  • Marek Gagolewski
    • 2
    • 3
  • Przemyslaw Grzegorzewski
    • 2
    • 3
  • M. Adabitabar Firozja
    • 4
  • Tahereh Houlari
    • 5
  1. 1.Department of Mathematics and InformaticsUniversity of OradeaOradeaRomania
  2. 2.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  3. 3.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland
  4. 4.Department of Mathematics, Qaemshahr BranchIslamic Azad UniversityIran
  5. 5.School of Mathematics and Computer SciencesDamghan UniversityIran

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