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.
This work is supported partially by the Nature Science Foundation of China (Nos. 61771174 and 61433001) and Graduate Innovation Foundation of Hangzhou Dianzi University (Nos. CXJJ2019034).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Coroianu, L., Gagolewski, M., Grzegorzewski, P.: Nearest piecewise linear approximation of fuzzy numbers. Fuzzy Sets Syst. 233, 26–51 (2013). https://doi.org/10.1016/j.fss.2013.02.005
Drugowitsch, J., Barry, A.M.: A formal framework and extensions for function approximation in learning classifier systems. Mach. Learn. 70, 45–88 (2008). https://doi.org/10.1007/s10994-007-5024-8
Grzegorzewski, P.: Metrics and orders in space of fuzzy numbers. Fuzzy Sets Syst. 97(1), 83–94 (1998)
Nikolaev, G.N.: Renormalization group approach to function approximation and to improving subsequent approximations. Theoret. Math. Phys. 164(2), 1035–1050 (2010). https://doi.org/10.1007/s11232-010-0083-6
Pekarskii, A.A.: Approximation to the function \(z^\alpha \) by rational fractions in a domain with zero external angle. Math. Notes 91(5), 714–724 (2012). https://doi.org/10.1134/s0001434612050136
Wang, G., Li, J.: Approximations of fuzzy numbers by step type fuzzy numbers. Fuzzy Sets Syst. 310, 47–59 (2017). https://doi.org/10.1016/j.fss.2016.08.003
Yeh, C.T.: Weighted semi-trapezoidal approximations of fuzzy numbers. Fuzzy Sets Syst. 165, 61–80 (2011). https://doi.org/10.1016/j.fss.2010.11.001
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Shen, C., Wang, G., Xu, Y. (2020). Approximation of Fuzzy Numbers by Using \(\alpha \)-\(\beta \)-knots Piecewise Linear Fuzzy Numbers. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_75
Download citation
DOI: https://doi.org/10.1007/978-3-030-32456-8_75
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32455-1
Online ISBN: 978-3-030-32456-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)