We show that the size reduction problem for fuzzy automata is related to the problem of solving a particular system of fuzzy relation equations. This system consists of infinitely many equations, and finding its general solution is a very difficult task, so we first consider one of its special cases, a finite system whose solutions, called right invariant fuzzy equivalences, are common generali...

In this paper, we introduce a computational method to find an approximate analytical solution for fuzzy differential equations. At first, variational iteration method (VIM) is used to solve the crisp problem then with the extension principle we find the fuzzy approximation solution. Examples are given , including linear and nonlinear fuzzy firstorder differential equations.

In this paper, the variational iteration method (VIM) and Buckley-Feuring method (BFM) are applied to find the exact fuzzy solution of the fuzzy heat-like equations in one and two dimensions with variable coefficients. Further a comparison between VIM-BFM and Seikkala solutions is provided. [Hamid Rouhparvar, Saeid Abbasbandy, Tofigh Allahviranloo. Journal of American Science 2011; 7(2):338-345...

Fuzzy differential equations are used in modeling problems in science and engineering. For instance, it is known that the knowledge of dynamical systems modeled by ordinary differential equations is often incomplete or vague. While, fuzzy differential equations represent a proper way to model dynamical systems under uncertainty and vagueness. In this paper, two methods for solving first order l...

In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional integral equations by employing the fixed point technique.

The uncertain nonlinear systems can bemodeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations.We use the neural networks to approximate the coefficients of the fuzzy equations.The approximation theory for ...

From the algorithm procedure presented in section 4 and the examples in this section, we can nd out it is easy to solve interval valued fuzzy relation equations by using fuzzy relation inequality system (8). The computation complexity of this algorithm is as same as that of the more commonly used algorithm 5] for fuzzy relation equations (1). So, the problem is more complicated than constant fu...

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

In this paper we study numerical methods for hybrid fuzzy differential equations by an application of the Adams fifth order predictor-corrector method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.

‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎