Journals Articles

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https://hdl.handle.net/20.500.14170/1995

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Analytical and numerical solutions of fuzzy differential equations

( 2013-02-26)
Muhammad Zaini Ahmad
;
M.K. Hasan
;
B. De Baets

In this paper, we study analytical and numerical solutions of fuzzy differential equations based on the extension principle. For linear fuzzy differential equations, we state some results on the behaviour of the solutions and study their relationship with the generalised Hukuhara derivative. In order to approximate the solutions of linear and non-linear fuzzy differential equations, we propose a new fuzzification of the classical Euler method and then incorporate an unconstrained optimisation technique. This combination offers a powerful tool to tackle uncertainty in any numerical method. An efficient computational algorithm is also provided to guarantee the convexity of fuzzy solutions on the time domain. Several illustrative examples are given.
Applications of the fuzzy sumudu transform for the solution of first order fuzzy differential equations

( 2015)
Norazrizal Rahman
;
Muhammad Zaini Ahmad

In this paper, we study the classical Sumudu transform in fuzzy environment, referred to as the fuzzy Sumudu transform (FST). We also propose some results on the properties of the FST, such as linearity, preserving, fuzzy derivative, shifting and convolution theorem. In order to show the capability of the FST, we provide a detailed procedure to solve fuzzy differential equations (FDEs). A numerical example is provided to illustrate the usage of the FST.