Let ( ) [ ] { } t G G t T = ∈ ω , 0, be a fuzzy stochastic process and ( ) [ ] { } t A t T ∈ ω , 0, be a real valued finite variation process. We define the Lebesgue-Stieltjes integral denoted by ( ) ( ) ∫ t s s G A ω ω 0 d for each t > 0 by using the selection method, which is direct, nature and different from the indirect definition appearing in some references. We shall show that this kind o...

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

in this paper a linear fuzzy fredholm integral equation(ffie) with arbitrary fuzzy function input and symmetric triangular (fuzzy interval) output is considered. for each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (ffie).

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

In this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear Fredholm integral equations of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.

Considering some unmeasurable states, a fuzzy static output control problem of nonlinear stochastic systems is discussed in this paper. Based on modelling approach, Takagi–Sugeno (T–S) system, constructed by family differential equations and membership functions, applied to represent systems. Parallel distributed compensation (PDC) technology used construct the controller. A line-integral Lyapu...

Since the 2-DOF rehabilitation robot actuated by pneumatic muscle actuators (PMAs) has highly nonlinear and time-varying behavior due to gas compression and nonlinear elasticity of bladder containers, it is difficult to achieve excellent control performance using classical control methods. Here, this study proposes a novel Takagi-Sugeno(T-S) fuzzy approach to improve tracking performance. The T...

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples. Keywor...