The computation of eigenvalues and eigenvectors under uncertainty is a fundamental problem in fuzzy linear algebra and decision analysis. When matrix elements are represented by fuzzy numbers, classical spectral methods cannot be directly applied due to nonlinearity, ambiguity in ordering, and the propagation of uncertainty. Moreover, in many practical applications, particularly those involving pairwise comparison matrices, the reliability of eigenvalue-based results strongly depends on the consistency of the underlying data. This paper proposes a consistency-based framework for computing fuzzy eigenvalues and fuzzy eigenvectors that explicitly integrates consistency analysis into the spectral derivation process. The proposed method preserves the fuzzy structure of the matrix without premature defuzzification and systematically adjusts the computation according to consistency measures, thereby improving stability and interpretability. A structured algorithm is developed to obtain fuzzy spectral components while maintaining coherence between uncertainty modeling and matrix structure. The effectiveness of the approach is demonstrated through an application example, and comparative analysis highlights its computational reliability and theoretical advantages over conventional techniques. The proposed framework provides a robust foundation for eigenvalue-based fuzzy modeling in decision-making and related engineering applications.
Aliyeva et al. (Thu,) studied this question.
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