Calculation of fuzzy eigenvalues of fuzzy matrix using algorithms and non-linear optimization models

Subject Areas : Numeric Analyze

somayehh khosravi ¹ , Ali Hosseinzadeh ² , Armin Ghane Kanafi ³ , Amir Hosein Refahi Sheikhani ⁴

1 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
2 - Department of mathematics, Lahijan, Branch, Islamic Azad University, Lahijan, Iran
3 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
4 - Department of Applied Mathematics,Faculty of Mathematical Sciences,Lahidjan Branch,Islamic Azad University,Lahijan,Iran

Received: 2023-02-25 Accepted : 2024-05-13 Published : 2025-09-23

Keywords: Fuzzy number, fuzzy matrix, fuzzy eigenvalues,

Abstract :

In this article, the fuzzy eigenvalues ​​of a fuzzy matrix are investigated based on the α-cut point of view of fuzzy numbers and also based on the point of view of interval calculations. It is clear that the degree of ambiguity of a fuzzy eigenvalue of a fuzzy matrix, considering different points of view, according to the degree of ambiguity in the elements of the fuzzy matrix, has different values, and these values ​​are directly related to the definition of a fuzzy eigenvalue of the fuzzy matrix. Based on the α-cut approach of fuzzy numbers, several definitions for the fuzzy eigenvalue of a fuzzy matrix have been stated and calculated using nonlinear optimization models of fuzzy eigenvalues. In the next section, the value of the fuzzy feature for a fuzzy matrix is ​​calculated using basic algorithms, where the effect of the ambiguity value of the elements of the fuzzy matrix on the ambiguity of the fuzzy eigenvalue, in each cut, is considered. At the end, the methods presented in a practical example have been used to check the stable population situation according to the fuzzy migration rate matrix.