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...

Many nonlinear systems can be modeled by uncertain linear-in-parameter models. In this paper, the uncertainty parameters are the Z number coe¢ cients. We use dual fuzzy equations as the models for the uncertain nonlinear systems. The solutions of these fuzzy equations are the controllers when the desired references are regarded as the outputs. The conditions of controllability are proposed. Two...

In the literature, some studies have shown that determining the consistency of bipolar fuzzy relational equations is NP-complete. Namely, the solution procedure for solving a system of bipolar fuzzy relational equations with max-product composition contains a high computational complexity. In this study, some sufficient conditions for consistency of bipolar fuzzy relational equations are propos...

A method to solve linear fuzzy equations with a symmetric matrix is proposed. Ignoring the symmetry leads to an overestimation of the solution. Our method to find the solution of a system of linear fuzzy equations takes the symmetry of the matrix into account and is based on parametric functions. It is a practical algorithm using parametric functions in which the variables are given by elements...