To locate the eigenvalues of a given tensor, we present two classes of new Ky Fan type eigenvalue inclusion sets for tensors, which are tighter than those in Yang et al. (SIAM J Matrix Anal Appl 31:2517–2530, 2010) and He et al. (J Inequal Appl 114:1-9, 2014), respectively. Under certain conditions, the theoretical comparisons of the new proposed Ky Fan type eigenvalue inclusion sets for tensors are established. As applications, some sufficient conditions for identifying strong \(\mathcal {M}\)-tensors, the non-singularity and positive definiteness of tensors are obtained. Some numerical examples are given to verify the validity of our theoretical results.

为了找到给定张量的特征值，我们提出了两类新的张量的Ky Fan型特征值包含集，它们比Yang等人的方法更严格。（SIAM J Matrix Anal Appl 31：2517–2530，2010）和He等人。（J Inequal Appl 114：1-9，2014）。在特定条件下，建立了新的张量Ky Fan型特征值包含集的理论比较。作为应用，获得了确定强\（\ mathcal {M} \） -张量，张量的非奇异性和正定性的一些充分条件。通过数值算例，验证了本文理论结果的正确性。