SOME NUMERICAL TECHNIQUES FOR SOLVING FUZZY NONLINEAR INTEGRAL EQUATION OF A FUZZIFYING FUNCTION OVER A NON-FUZZY INTERVAL

In this paper, the basic principle and definitions for fuzzy nonlinear integral equation of a fuzzy function over a crisp interval have been discussed. The numerical technique method and some algorithmfor solving fuzzy non-linear of a fuzzy function including fuzzifying function, bunch function and LR-Type of fuzzy function over crisp domain by a computational and illustration have been developed and presented . The fuzzy nonlinear integral of fuzzy function over a crisp interval can be divided into two subsections in this paper . Some numerical examples are prepared to show the efficiency and simplicity of the method

Numerical Solution for Solving Nonlinear Fuzzy Fractional Integral Equation by Using Approximate Method

In this paper, we discus fractional order for fuzzy non-linear integral equation . The fractional integral is consider in the sense Riemann-liouville  and establish the exists solution  of nonlinear fuzzy fractional  integral equation. Finally, Numerical  examples are given to  illustrate the results

Numerical and analytic method for solvingproposal New Type for fuzzy nonlinear volterra integral equation

In this paper, we proved the existence and uniqueness and convergence of the solution of new type for nonlinear fuzzy volterra integral equation . The homotopy analysis method are proposed to solve the new type fuzzy nonlinear Volterra integral equation . We convert a fuzzy volterra integral equation for new type of kernel for integral equation, to a system of crisp function nonlinear volterra integral equation . We use the homotopy analysis method to find the approximate solution of the system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy volterra integral equation . Some numerical examples is given and results reveal that homotopy analysis method is very effective and compared with the exact solution and calculate the absolute error between the exact and AHM .Finally using the MAPLE program to solve our problem

Fuzzy ϑ –BFGS Update for Numerical Optimization

In this paper, we develop a quasi-Newton method for unconstrained optimization problems with fuzzy functions. Also, we Propose  the -BFGS method to fuzzy optimization problems. The generalized Hukuhara differentiability for fuzzy functions is employed. By using a Hessian approximation, we resolve the high computational cost of finding the Hessian in Newton method for fuzzy optimization problems. We will find the solutions of a fuzzy optimization problem. Finally, some numerical results support this claim and also indicate that the -BFGS update may be competitive with the BFGS update in genera