Metric Fuzziness and Eigenvalue Theory

This article is dedicated to the exploration of fuzzy eigenvalues and fuzzy eigenvectors within the context of a fuzzy metric space. To facilitate this discussion, we introduce a specific metric for this space. Furthermore, we provide comprehensive definitions for fuzzy eigenvalues and fuzzy eigenvectors, focusing on their application to fuzzy square matrices. In the course of our exploration, we establish a series of theorems pertaining to fuzzy eigenvalues and eigenvectors within a fuzzy metric space. To enhance understanding, we illustrate these theorems with practical examples.