Fuzzy Transform to Approximate Solution of Boundary Value Problems via Optimal Coefficients

In this study, we propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of fuzzy transform to solve a second-order ordinary differential equation with boundary conditions. To determine the optimal coefficients in expansion of a function, we minimize the integral squared error in 2-norm. Some examples are presented to illustrate the applicability of the method.

[1]  Wei Chen,et al.  Approximate solution for a class of second-order ordinary differential equations by the fuzzy transform , 2014, J. Intell. Fuzzy Syst..

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

[3]  Irina Perfilieva,et al.  F-TRANSFORM FOR NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM , 2017 .

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

[5]  Luigi Troiano.  Fuzzy co-transform and its application to time series , 2010, 2010 International Conference of Soft Computing and Pattern Recognition.

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

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

[8]  Luigi Troiano,et al.  Improving Approximation Properties of Fuzzy Transform Through Non-uniform Partitions , 2016, WILF.

[9]  Imre J. Rudas,et al.  Approximation properties of fuzzy transforms , 2011, Fuzzy Sets Syst..

[10]  Luigi Troiano,et al.  A mean-reverting strategy based on fuzzy transform residuals , 2012, 2012 IEEE Conference on Computational Intelligence for Financial Engineering & Economics (CIFEr).

[11]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[12]  Giuseppe Patanè,et al.  Fuzzy transform and least-squares approximation: Analogies, differences, and generalizations , 2011, Fuzzy Sets Syst..

[13]  Irina Perfilieva.  Fuzzy Transform: Application to the Reef Growth Problem , 2004 .