The Random Permutation Set (RPS) is a new type of set proposed recently,
which can be regarded as the generalization of evidence theory. To measure the
uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy
have been proposed. Exploring the maximum entropy provides a possible way of
understanding the physical meaning of RPS. In this paper, a new concept, the
envelope of entropy function, is defined. In addition, the limit of the
envelope of RPS entropy is derived and proved. Compared with the existing
method, the computational complexity of the proposed method to calculate the
envelope of RPS entropy decreases greatly. The result shows that when $N \to
\infty$, the limit form of the envelope of the entropy of RPS converges to $e
\times (N!)^2$, which is highly connected to the constant $e$ and factorial.
Finally, numerical examples validate the efficiency and conciseness of the
proposed envelope, which provides a new insight into the maximum entropy
function.

RPS 的熵的包络是通过计算 RPS 熵的上限获得的，与常数 e 和阶乘高度相关，通过降低计算复杂度提供了一种理解 RPS 物理意义的新方法。

最大随机排列集熵的极限

Limit of the Maximum Random Permutation Set Entropy

While effective concentration inequalities for suprema of empirical processes
exist under boundedness or strict tail assumptions, no comparable results have
been available under considerably weaker assumptions. In this paper, we derive
concentration inequalities assuming only low moments for an envelope of the
empirical process. These concentration inequalities are beneficial even when
the envelope is much larger than the single functions under consideration.

本研究探讨了在仅具有低动量的情况下，对经验过程的包络推导浓度不等式的方法。这种推导非常有益，即使包络比单个函数的情况要大得多。