A Method for Finding LR Fuzzy Eigenvectors of Real Symmetric Matrix

Subject Areas : Transactions on Fuzzy Sets and Systems

Xinyi Duan ¹ , Hangru Lin ² , Xiaobin Guo ³

1 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
2 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
3 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.

Received: 2024-08-08 Accepted : 2024-10-10 Published : 2024-11-05

Keywords: Fuzzy eigenvector, Fuzzy number, Fuzzy linear system, Matrix computation.,

Abstract :

In this paper, the calculation methods of the real eigenvalues and LR fuzzy eigenvectors of clear real symmetry matrices are deeply considered. The original fuzzy feature problem is extended by using the arithmetic algorithm of LR fuzzy numbers into a simple feature problem with a high-order clear real symmetry matrix. We discuss two cases: (a) λ is a non-negative unknown eigenvalue; (b) λ is a negative unknown eigenvalue. We established two computational models and proposed an algorithm for finding the fuzzy eigenvectors of the true symmetry matrix. Some numerical examples are used to illustrate our proposed method.

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