Abstract
The aim of this paper is to improve the F-transform technique based on B-splines. A modification of the F-transform of higher degree with respect to fuzzy partitions based on B-splines is done to extend the good approximation properties from the interval where the Ruspini condition is fulfilled to the whole interval under consideration. The effect of the proposed modification is characterized theoretically and illustrated numerically.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bede, B., Rudas, I.J.: Approximation properties of fuzzy transforms. Fuzzy Sets Syst. 180(1), 20–40 (2011)
Demanet, L., Townsend, A.: Stable extrapolation of analytic functions. arXiv preprint (2016). arXiv:1605.09601
Holčapek, M., Tichý, T.: Discrete fuzzy transform of higher degree. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2014, 6–11 July 2014, Beijing, China, pp. 604–611. IEEE (2014)
Kodorane, I., Asmuss, S.: On approximation properties of spline based F-transform with respect to fuzzy m-partition. In: Montero, J., Pasi, G., Ciucci, D. (eds.) Proceedings of EUSFLAT 2013, Advances in Intelligent Systems Research, Milan, Italy, vol. 32, pp. 772–779. Atlantis Press (2013)
Kokainis, M., Asmuss, S.: Approximation properties of higher degree F-transforms based on B-splines. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2015, 2–5 August 2015, Istanbul, Turkey. IEEE (2015)
Kokainis, M., Asmuss, S.: Discrete higher degree F-transforms based on bivariate B-splains. In: Proceedings of the 12th International FLINS Conference on Uncertainty Modelling in Knowledge Engineering and Decision Making, 24–26 August 2016, Roubaix, France, pp. 264–269. World Scientific (2016)
Kokainis, M., Asmuss, S.: Higher degree F-transforms based on B-splines of two variables. In: Carvalho, J.P., Lesot, M.-J., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2016. CCIS, vol. 610, pp. 648–659. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40596-4_54
Kokainis, M., Asmuss, S.: Approximation by multivariate higher degree F-transform based on B-splines. Soft Comput. 21(13), 3587–3614 (2017)
Kokainis, M., Asmuss, S.: Continuous and discrete higher-degree F-transforms based on B-splines. Soft Comput. 21(13), 3615–3639 (2017)
Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157(8), 993–1023 (2006)
Perfilieva, I.: F-Transform. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 113–130. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-43505-2
Perfilieva, I., Dan̆ková, M., Bede, B.: Towards a higher degree F-transform. Fuzzy Sets Syst. 180(1), 3–19 (2011)
Perfilieva, I., Haldeeva, E.: Fuzzy transformation and its applications. In: 2001 Proceedings of the 4th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty, Czech Republic, pp. 116–124 (2001)
Schoenberg, I.J.: Cardinal spline interpolation. In: CBMS, vol. 12. SIAM (1973)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Kokainis, M., Asmuss, S. (2018). Modified F-transform Based on B-splines. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 854. Springer, Cham. https://doi.org/10.1007/978-3-319-91476-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-91476-3_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91475-6
Online ISBN: 978-3-319-91476-3
eBook Packages: Computer ScienceComputer Science (R0)