# Maximum Entropy of Random Permutation Set

arXiv: https://arxiv.org/abs/2203.11941 · HTML: https://mlsanity.com/paper/2203.11941/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 64 references that are in the map.
- First posted on arXiv 16 Dec 2021.

## Builds on (most cited first, 2 of 2)

- [The Learning of Fuzzy Cognitive Maps With Noisy Data: A Rapid and Robust Learning Method With Maximum Entropy](https://mlsanity.com/paper/1908.08339/) (2019)
- [Exponential Negation of a Probability Distribution](https://mlsanity.com/paper/2010.11533/) (2020)

## Built on by (most cited first, 4 of 4)

- [Limit of the Maximum Random Permutation Set Entropy](https://mlsanity.com/paper/2403.06206/) (2024)
- [Random Graph Set and Evidence Pattern Reasoning Model](https://mlsanity.com/paper/2402.13058/) (2024)
- [Random Walk in Random Permutation Set Theory](https://mlsanity.com/paper/2404.03978/) (2024)
- [Repeatable Random Permutation Set](https://mlsanity.com/paper/2211.01676/) (2022)

## Abstract (arXiv)

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.