I n recent years, many numerical methods have been proposed for solving fuzzy linear integral equations. For example, in [10], the authors used the divided differences and finite differences methods for solving a parametric of the fuzzy Fredholm integral equations of the second kind. Also, in [9], a numerical method is proposed for the approximate solution of fuzzy linear Fredholm functional in...

An adaptive fuzzy integral sliding mode controller for mismatched time-varying linear systems is presented in this paper. The proposed fuzzy integral sliding mode controller is designed to have zero steady state system error under step inputs and alleviate the undesired chattering around the sliding surface. The parameters in the fuzzy mechanism are adapted on-line to improve the performance of...

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formal...

in this paper, an optimal adaptive fuzzy integral sliding mode control is presented to control the robot manipulator position tracking in the presence of uncertainties and permanent magnet dc motor. in the proposed control, sliding surface of the sliding mode control is defined according to the information of position tracking error, derivatives, and error integral. in order to estimate bounds ...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this paper, the bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (iemtl) through expansion methods (collocation method, partition method, galerkin method). the method is discussed in detail and illustrated by solving some numerical examples. comparison between the exact and approximated results obtained from these methods is...

Fuzzy integrals as image lters provide a standard representational form which generalize linear lters such as the averaging lter, morphological lters such as at dilations and erosions, and order statistic lters such as the median lter. However, fuzzy integral lters are computationally intensive. Computing the output value obtained by fuzzy integral ltering at a point involves sorting all the pi...

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

The theory of fuzzy measures and fuzzy integrals was introduced by S u g e n o [16] and intensively studied. Monographs [15] and [18] are dedicated to this topic. Recently, several classical inequalities were generalized to fuzzy integral. F l o r e sF r a n u l i č and R o m á n-F l o r e s [11] provided a Chebyshev type inequality for fuzzy integral of continuous and strictly monotone functio...