Fuzzy differential and integral equations have been studied by many authors [1, 2, 5, 6, 7, 14]. Kaleva [5] discussed the properties of differentiable fuzzy set-valued mappings by means of the concept of H-differentiability introduced by Puri and Ralescu [9]. Seikkala [11] defined the fuzzy derivative which is a generalization of the Hukuhara derivative [9] and the fuzzy integral which is the s...

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...

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, ‎first we propose a new method to approximate the solution of two-dimensional linear fuzzy fredholm integral equations of the second kind based on the fuzzy wavelet like operator‎. ‎then‎, ‎we discuss and investigate the convergence and error analysis of the proposed method‎. ‎finally‎, ‎to show the accuracy of the proposed method‎, ‎we present two numerical ‎examples.‎

The fuzzy differential and integral equations are important part of the fuzzy analysis theory. Park et al. [8] have considered the existence of solution of fuzzy integral equation in Banach space and Subrahmaniam and Sudarsanam [12] proved the existence of solution of fuzzy functional equations. An integral equation is called singular if either the range of integration is infinite or the kernel...

T he concept of fuzzy integral was initiated by Dubois and Prade [11] and then investigated by Kaleva [21], Goetschel and Voxman [20], Nanda [23] and others. In [33], the Henstock integral of fuzzy-valued functions is defined, while the fuzzy Riemann integral and its numerical integration was investigated byWu in [34]. In [7], the authors introduced some quadrature rules for the integral of fuz...

Abstract In this paper, we use new parametic formof fuzzy numbers and convert a system of fuzzy integral equations to two system of integral equations in crisp. Then we solve a system of fuzzy integral equations by means of an analytic technique, namely the homotopy analysis method (HAM). Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. The res...

We study conditions under which the solutions of a fuzzy integral equation are bounded. 1. Introduction. The concept of set-valued functions and their calculus [2] were found useful in some problems in economics [3], as well as in control theory [17]. Later on, the notion of H-differentiability was introduced by Puri and Ralesku in order to extend the differential of set-valued functions to tha...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...