In this work, the homotopy perturbation method is developed and formulated to find an approximate-analytical solution of fuzzy initial value problems involving a nonlinear first order ordinary differential equation. HPM allows for the solution of FIVPs to be calculated in the form of an infinite series in which the components can be easily computed. An efficient algorithm is proposed of HPM on ...

Fuzzy integral equations play major roles in various areas, therefore a new method for finding a solution of the Fredholm fuzzy integral equation is presented. This method converts the fuzzy integral equation into linear system by using the Taylor series. For this scope, first the Taylor expansion of unknown function is substituted in parametric form of the given equation. Then we differentiate...

The fuzzy set theory introduced by Zadeh has emerged as an interesting and fascinating branch of pure and applied sciences. The applications of fuzzy set theory can be found in many branches of regional, physical, mathematical, differential equations andengineering sciences. Recently, the authors have made important research results in the theory of fuzzy differentialequations, integrodifferent...

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...

We present a new approach to multi-dimensional parsing using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is developed, motivated by the two-dimensional structure of written mathematics. Our approach makes no hard decisions; recognized math expressions are reported to the user in ranked order. A flexible correction mechanism enables users to quickly choose the corre...

In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. ...

In the paper a distance based operators based approximate reasoning method is represented, applying fuzzy measure. Distance based operators satisfy most of properties as generally defined parametrical operators. Based on this the possible relationship with the integrals based on fuzzy measures is introduced. It can be shown, that the reason used for fuzzy integral introduction is similar to the...

on the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional linear and nonlinear schrödinger equations is presented. the analytical solution is shown in a series form in the reproducing kernel space and the approximate solution is constructed by truncating the series. the convergence of the approximate solution to the analytical solution is also proved. th...