On the Accuracy of Fm-transform Approximation in Boundary Subintervals

Fm-transform approximation loses its accuracy near the boundaries of the function domain. This is because of the truncated basic functions in the first and last subintervals. In this paper, we impose some effective techniques on Fm-transform to overcome this defect. Throughout various examples, it is shown that the utilized techniques can significantly improve the accuracy of the Fm-transform approximation on the boundary subintervals.

[1]  Alfredo Vaccaro,et al.  Using fuzzy transform in multi-agent based monitoring of smart grids , 2017, Inf. Sci..

[2]  Martina Danková,et al.  Towards a higher degree F-transform , 2011, Fuzzy Sets Syst..

[3]  Stefania Tomasiello,et al.  An alternative use of fuzzy transform with application to a class of delay differential equations , 2017, Int. J. Comput. Math..

[4]  Vilém Novák,et al.  Mining pure linguistic associations from numerical data , 2008, Int. J. Approx. Reason..

[5]  Matteo Gaeta,et al.  Multisignal 1-D compression by F-transform for wireless sensor networks applications , 2015, Appl. Soft Comput..

[6]  Alfredo Vaccaro,et al.  Fuzzy Transform Based Compression of Electric Signal Waveforms for Smart Grids , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[7]  Irina Perfilieva,et al.  A new fuzzy approximation method to Cauchy problems by fuzzy transform , 2016, Fuzzy Sets Syst..

[8]  Matteo Gaeta,et al.  Cubic B-spline fuzzy transforms for an efficient and secure compression in wireless sensor networks , 2016, Inf. Sci..

[9]  Matteo Gaeta,et al.  Quasi–consensus in second–order multi–agent systems with sampled data through fuzzy transform , 2016 .

[10]  Irina Perfilieva,et al.  Fuzzy transforms: Theory and applications , 2006, Fuzzy Sets Syst..

[11]  Irina Perfilieva,et al.  Fuzzy Transforms: A Challenge to Conventional Transforms , 2007 .

[12]  Salvatore Sessa,et al.  An image coding/decoding method based on direct and inverse fuzzy transforms , 2008, Int. J. Approx. Reason..

[13]  Irina Perfilieva,et al.  Fuzzy transform to approximate solution of two‐point boundary value problems , 2017 .