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Approximation of Fuzzy Numbers by Using \(\alpha \)-\(\beta \)-knots Piecewise Linear Fuzzy Numbers

  • Chenjie Shen
  • Guixiang WangEmail author
  • Yifeng Xu
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)

Abstract

In this paper, the problems of approximating general fuzzy number by using \(\alpha \)\(\beta \)–knots piecewise linear fuzzy number are studied. Firstly, \(\alpha \)\(\beta \)–knots piecewise linear fuzzy number are defined, and the conceptions of nearest \(\alpha -\beta -\)knots piecewise linear approximation and nearest \(\{0,\alpha ,1\}\)\(\{0,\beta ,1\}\)–knots piecewise linear approximation are introduced for a general fuzzy number. Then, it is also the most important work of this paper that for a general fuzzy number, we obtain a formula to get the nearest \(\alpha -\beta \)–knots piecewise linear approximation and the nearest \(\{0,\alpha ,1\}-\{0,\beta ,1\}\)–knots piecewise linear approximation using weighted metric as a criterion. And then, we give specific example to show more reasonable and effective of the methods proposed by us.

Keywords

Approximations Membership functions Fuzzy numbers \(\alpha \)\(\beta \)–knots piecewise linear fuzzy numbers 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Operations Research and CyberneticsHangzhou Dianzi UniversityHangzhouChina

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