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First order linear fuzzy differential equations under generalized differentiability

First order linear fuzzy differential equations under generalized differentiability,10.1016/j.ins.2006.08.021,Information Sciences,Barnabás Bede,Imre

First order linear fuzzy differential equations under generalized differentiability   (Citations: 39)
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We provide solution of flrst order linear fuzzy difierential equations by varia- tion of constant formula. The difierentiability concept used in this paper is the strongly generalized difierentiability since a fuzzy difierential equation under this difierentiabil- ity can have decreasing legth of support function. Under some conditions we provide solution with decreasing support and so the behaviour of the solution better re∞ects the behaviour of real-world systems.
Journal: Information Sciences - ISCI , vol. 177, no. 7, pp. 1648-1662, 2007
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    • ...We consider the following definition which was introduced by Bede and Gal in [9]...
    • ...(13)–(14) in the sense of (2)-differentiability, since we seek the asymptotically stable solutions of fuzzy linear differential equations (for more detail see [9]).Since, the deterministicsolutions of Eqs.(13)–(14) tendtozerowhen x −→ ∞,i.e., diam{y(x) }− →0,weshouldchooseanappropriate kind of differentiability in order to solve fuzzy linear equations both first and second order fuzzy linear differential equations, whose behavior of the ...

    Tofigh Allahviranlooet al. A new method for solving fuzzy linear differential equations

    • ...The FDE and the fuzzy initial value problem (Cauchy problem) were rigorously treated by Kaleva (1987, 1990), Seikkala (1987), He and Yi (1989), Kloeden (1991) and Menda (1988), and by other researchers (see Bede et al. 2006; Buckley 2006; Buckley and Feuring 1999, 2003; Congxin and Shiji 1998; Ding et al. 1997; Jowers et al. 2007)...
    • ...Strongly generalized differentiability was introduced in Bede and Gal (2005) and studied in Bede et al. (2006)...
    • ...In this paper we consider the following definition which was introduced by Bede and Gal (2005) and Bede et al. (2006)...

    Tofigh Allahviranlooet al. Fuzzy Laplace transforms

    • ...Bede et.al in [2,3] have introduced a more general definition of the derivative for fuzzy mappings, enlarging the class of differentiable...

    S. Hajighasemiet al. Existence and Uniqueness of Solutions of Fuzzy Volterra Integro-differ...

    • ...First order linear fuzzy differential equations are investigated by the author’s research group [5]...

    Imre J. Rudaset al. Computational intelligence for problem solving in engineering

    • ...Fuzzy Calculus and Fuzzy Differential Equations are also two very important related fields [8], [9], [13], [14], [19]...
    • ...New alternatives of derivatives for set-valued functions and its applications for solving fuzzy differential equations have been introduced by Bede et al. [8], [9] and by Chalco-Cano et al. [13], [14] (also see [15])...

    Y. Chalco-Canoet al. On difference of intervals and differentiability of interval-valued fu...

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