论文标题
随机置换集的最大熵
Maximum Entropy of Random Permutation Set
论文作者
论文摘要
最近，通过考虑特定集合中的所有元素排列提出了一种新型的集合，称为随机排列集（RPS）。为了测量RPS的不确定性，提出了RPS的熵。但是，尚未讨论RPS熵的最大熵原理。为了解决此问题，在本文中，提出了RPS的最大熵。分别对RP的最大熵及其相应的PMF条件的分析解决方案进行了证明和讨论。数值示例用于说明最大熵RP。结果表明，最大熵RPS与最大Deng熵和最大香农熵兼容。当置换事件中元素的顺序被忽略时，RPS的最大熵将退化为最大deng熵。当每个排列事件仅限于一个元素时，RPS的最大熵将退化为最大的香农熵。
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.
