Maximum Entropy of Random Permutation Set. (arXiv:2203.11941v1 [cs.IT])

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.

Source: https://arxiv.org/abs/2203.11941

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