<p>A new approach for solving fuzzy Fredholm integral equations of the second kind has been proposed here. Typically, it can be seen from the literature that integral equations of this type use the parametric form to transform the problem into a system of crisp integral equations. This system is then solved to obtain the final solution. In general, these techniques are computationally expensive, as they involve solving a system of equations rather than a single equation. Accordingly, by keeping this fact in mind, a new method based on double parametric form of fuzzy numbers has been developed and applied to derive an equivalent crisp form of the original problem. Subsequently, the well-known Adomian decomposition method is used to solve this crisp equation, yielding a semi-analytic solution in double parametric form. Notably, this approach requires solving only one equation. Several numerical examples have been solved and compared with the existing results for the validation.</p>

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Double parametric based solution of fuzzy Fredholm integral equation of the second kind using Adomian decomposition method: a new approach

  • Diptiranjan Behera

摘要

A new approach for solving fuzzy Fredholm integral equations of the second kind has been proposed here. Typically, it can be seen from the literature that integral equations of this type use the parametric form to transform the problem into a system of crisp integral equations. This system is then solved to obtain the final solution. In general, these techniques are computationally expensive, as they involve solving a system of equations rather than a single equation. Accordingly, by keeping this fact in mind, a new method based on double parametric form of fuzzy numbers has been developed and applied to derive an equivalent crisp form of the original problem. Subsequently, the well-known Adomian decomposition method is used to solve this crisp equation, yielding a semi-analytic solution in double parametric form. Notably, this approach requires solving only one equation. Several numerical examples have been solved and compared with the existing results for the validation.