A $t/s$-diagnosable system refers to such a system that all the faulty nodes of the system can be isolated within a set of size at most s in the presence of at most t faulty nodes. Moreover, it increases the allowed faulty nodes, hence enhancing the diagnosability of the system. We can find that the $t/s$-diagnosability of n-dimensional folded hypercube $F{Q}_n$ has not been studied under the PMC model and MM* model. In this paper, we determine the $t/s$-diagnosability of $F{Q}_n$ under the PMC model and MM* model. First, we propose some new fault tolerant properties of $F{Q}_n$. Then we prove that the $t/s$-diagnosability of n-dimensional folded hypercube $F{Q}_n$ is $(n+1)g-\frac{1}{2}(g-1)(g+2)$ for $2\le g\le \frac{1}{2}(n-1)$ where $s=(n+1)g-\frac{1}{2}(g-1)(g+2)+g-2$ under both the PMC model and MM* model. In addition, we establish two $t/s$-diagnosis algorithms of complexity $O(Nlo{g}_{2}N)$ and complexity $O(N{(lo{g}_{2}N)}^2)$ to isolate the faulty nodes in a node subset of the system under the PMC model and MM* model, respectively. The comparison analysis results showed that the $t/s$-diagnosability of $F{Q}_n$ is the largest, and it increases faster than the other types of diagnosability as n increases.

一种 $吨/秒$-可诊断系统是指在最多存在t个故障节点的情况下，可以在最多s个大小的集合内隔离系统所有故障节点的系统。此外，它增加了允许的故障节点，从而增强了系统的可诊断性。我们可以发现，$吨/秒$-n维折叠超立方体的可诊断性$F{问}_n$尚未在 PMC 模型和 MM* 模型下进行研究。在本文中，我们确定$吨/秒$- 可诊断性 $F{问}_n$在 PMC 模型和 MM* 模型下。首先，我们提出了一些新的容错特性$F{问}_n$. 然后我们证明$吨/秒$-n维折叠超立方体的可诊断性$F{问}_n$ 是 $(n+1)G-\frac{1}{2}(G-1)(G+2)$ 为了 $2\le G\le \frac{1}{2}(n-1)$ 在哪里 $秒=(n+1)G-\frac{1}{2}(G-1)(G+2)+G-2$在 PMC 模型和 MM* 模型下。此外，我们建立了两个$吨/秒$- 复杂度诊断算法 $哦(N升○G_{2}N)$ 和复杂性 $哦(N{(升○G_{2}N)}^2)$分别在PMC模型和MM*模型下隔离系统节点子集中的故障节点。对比分析结果表明，$吨/秒$- 可诊断性 $F{问}_n$是最大的，并且随着n 的增加，它比其他类型的可诊断性增加得更快。