Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem

Pederson, S.; Sambandham, M.

doi:10.1016/j.ins.2008.09.023

Cited by 35 publications

(24 citation statements)

References 15 publications

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“…Proof In fact, this theorem attempts to extend and generalize the earlier results due to S. Pederson, M. Sambandham (Theorem 3.1 in [20]). Take into account the hypothesis, suppose that…”

Section: Hybrid Fuzzy Differential Equationsupporting

confidence: 61%

Solving hybrid fuzzy differential equations by Chebyshev wavelet

Fard

Bidgoli

2015

SeMA

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“…Proof In fact, this theorem attempts to extend and generalize the earlier results due to S. Pederson, M. Sambandham (Theorem 3.1 in [20]). Take into account the hypothesis, suppose that…”

Section: Hybrid Fuzzy Differential Equationsupporting

confidence: 61%

Solving hybrid fuzzy differential equations by Chebyshev wavelet

Fard

Bidgoli

2015

SeMA

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“…Also, the contribution of this paper is to extend Pederson's characterization theorem (Pederson and Sambandham 2009) to hybrid fuzzy differential equations under generalized Hukuhara differentiability.…”

Section: Preliminariesmentioning

confidence: 99%

“…However, we will extend the Euler method based on the generalized Hukuhara differentiability. Pederson et al (Pederson and Sambandham 2009) have extended Bede's characterization theorem (2008) to hybrid fuzzy differential equations. However, they performed such approaches based on the Hukuhara differentiability.…”

Section: Introductionmentioning

confidence: 99%

Euler method for solving hybrid fuzzy differential equation

Allahviranloo

Salahshour

2010

Soft Comput

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In this paper, we study the numerical method for solving hybrid fuzzy differential using Euler method under generalized Hukuhara differentiability. To this end, we determine the Euler method for both cases of H-differentiability. Also, the convergence of the proposed method is studied and the characteristic theorem is given for both cases. Finally, some numerical examples are given to illustrate the efficiency of the proposed method under generalized Hukuhara differentiability instead of suing Hukuhara differentiability.

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“…Also for each a 2 ½0; 1; f ðt; aÞ f ðt; aÞ: Definition 2.9 [29] A fuzzy function f : ða; bÞ ! E 1 is differentiable att 2 ða; bÞ, if there exists f 0 ðtÞ 2 E 1 such that the limits: …”

Section: Preliminariesmentioning

confidence: 99%

A new fuzzy neural network model for solving fuzzy linear programming problems and its applications

Effati

Pakdaman

Ranjbar

2010

Neural Comput & Applic

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This paper is concentrated on two types of fuzzy linear programming problems. First type with fuzzy coefficients in the objective function and the second type with fuzzy right-hand side values and fuzzy variables. Considering fuzzy derivative and fuzzy differential equations, these kinds of problems are solved using a fuzzy neural network model. To show the applicability of the method, it is applied to solve the fuzzy shortest path problem and the fuzzy maximum flow problem. Numerical results illustrate the method accuracy and it's simple implementation.

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Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem

Cited by 35 publications

References 15 publications

Solving hybrid fuzzy differential equations by Chebyshev wavelet

Solving hybrid fuzzy differential equations by Chebyshev wavelet

Euler method for solving hybrid fuzzy differential equation

A new fuzzy neural network model for solving fuzzy linear programming problems and its applications

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