Maximum Entropy of Random Permutation Set
This work addresses a theoretical gap in uncertainty measurement for RPS, which is incremental as it extends existing entropy concepts to a new set type.
The paper tackles the problem of deriving the maximum entropy principle for random permutation sets (RPS), presenting an analytical solution and probability mass function condition, with results showing compatibility and degeneration to maximum Deng and Shannon entropies under specific conditions.
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.