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Appl. Syst. Innov. 2018, 1(3), 30; https://doi.org/10.3390/asi1030030

New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

1
Institute of Engineering Mathematics, Universiti Malaysia Perlis, Kampus Tetap Pauh Putra, Arau, Perlis 02600, Malaysia
2
Institute for Research and Applications of Fuzzy Modelling, University of Ostrava, NSC IT4Innovations, 30. Dubna 22, 701 03 Ostrava, Czech Republic
*
Author to whom correspondence should be addressed.
Received: 17 June 2018 / Revised: 11 August 2018 / Accepted: 14 August 2018 / Published: 23 August 2018
(This article belongs to the Special Issue Fuzzy Decision Making and Soft Computing Applications)
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Abstract

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods. View Full-Text
Keywords: fuzzy partition; fuzzy transform; numerical methods; NIM; systems of ordinary differential equations fuzzy partition; fuzzy transform; numerical methods; NIM; systems of ordinary differential equations
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ALKasasbeh, H.; Perfilieva, I.; Ahmad, M.Z.; Yahya, Z.R. New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II. Appl. Syst. Innov. 2018, 1, 30.

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