Recently, the existence and uniqueness of positive solution for multilinear systems with ${\mathcal{H}}^{+}$-tensor were proved by Wang et al. (2019). To expand the range of multilinear systems with positive solutions, a new class of tensors, called generalized strong $\mathcal{M}$-tensor, is proposed while the ${\mathcal{H}}^{+}$-tensor is a special case of the generalized strong $\mathcal{M}$-tensor. Under certain conditions, the existence and the uniqueness of positive (nonnegative) solutions are proved for multilinear systems with generalized strong $\mathcal{M}$-tensor. Finally, numerical examples are given to illustrate the theoretical results with Venn diagram for the relationship among generalized strong $\mathcal{M}$-tensor with certain conditions, ${\mathcal{H}}^{+}$-tensor, and strong $\mathcal{M}$-tensor.

最近，多线性系统正解的存在性和唯一性${\mathcal{H}}^{+}$-张量由Wang等人证明。（2019）。为了扩大具有正解的多线性系统的范围，一种新的张量类，称为广义强$\mathcal{米}$-张量，建议同时${\mathcal{H}}^{+}$-张量是广义强的一个特例$\mathcal{米}$-张量。在一定条件下，证明了具有广义强的多线性系统正（非负）解的存在性和唯一性$\mathcal{米}$-张量。最后通过数值例子说明了广义强之间关系的维恩图的理论结果。$\mathcal{米}$-具有特定条件的张量，${\mathcal{H}}^{+}$-张量，强$\mathcal{米}$-张量。