Journal
FUZZY SETS AND SYSTEMS
Volume 288, Issue -, Pages 75-95Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.fss.2015.01.001
Keywords
F-transform; Higher degree F-transform; Cauchy problem; Fuzzy initial value problem; Mid-point rule
Funding
- European Regional Development Fund in the IT4Innovations Centre of Excellence project [CZ.1.05/1.1.00/02.0070]
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We present new numeric methods based on the first and second degree F-transform for solving the Cauchy problem. We show that they outperform the second order Runge-Kutta method especially when a right-hand function is oscillating and/or a solution is requested on a long interval. Moreover, a new numeric method to solve fuzzy initial value problem using the F-transform is presented. The suitability of the presented new methods is theoretically justified and illustrated on various examples. (C) 2015 Elsevier B.V. All rights reserved.
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