Recently, a new type of set, named as random permutation set (RPS), is
proposed by considering all the permutations of elements in a certain set. For
measuring the uncertainty of RPS, the entropy of RPS is presented. However, the
maximum entropy principle of RPS entropy has not been discussed. To address
this issue, in this paper, the maximum entropy of RPS is presented. The
analytical solution for maximum entropy of RPS and its corresponding PMF
condition are respectively proofed and discussed. Numerical examples are used
to illustrate the maximum entropy RPS. The results show that the maximum
entropy RPS is compatible with the maximum Deng entropy and the maximum Shannon
entropy. When the order of the element in the permutation event is ignored, the
maximum entropy of RPS will degenerate into the maximum Deng entropy. When each
permutation event is limited to containing just one element, the maximum
entropy of RPS will degenerate into the maximum Shannon entropy.

本研究提出了随机置换集（RPS）的最大熵原理，并通过数值实验验证，结果表明最大熵的 RPS 与最大邓（Deng）熵和最大香农熵相容。当排列事件中元素的顺序被忽略时，RPS 的最大熵将退化为最大邓熵；当每个排列事件被限制为仅包含一个元素时，RPS 的最大熵会退化为最大香农熵。