New methods for computing fuzzy eigenvalues and fuzzy eigenvectors of fuzzy matrices using nonlinear programming approach

In this paper, we propose a new method to obtain the eigenvalues and fuzzy triangular eigenvectors of matrix $$\left( {\tilde{A}} \right)$$ , where elements are given. For purpose, solve 1-cut eigenvectors. Considering interval system $$\left[ \right]_{\alpha } \left[ {\tilde{X}} = {\tilde{\lambda }} 0 \le \alpha 1$$ as α-cut $$\tilde{A}\tilde{X} \tilde{\lambda }\tilde{X}$$ determine left right width }$$ eigenvector make linear nonlinear equations inequalities. And programming models inequalities calculate . Furthermore, define three other (namely, escribed eigenvalue, peripheral approximate eigenvalue) for (Ã) that eigenvalue cannot be obtained based on calculations. Therefore, which is placed in tolerable set, controllable an set defined paper. Finally, numerical examples presented illustrate proposed method.