# Limit of the Maximum Random Permutation Set Entropy

arXiv: https://arxiv.org/abs/2403.06206 · HTML: https://mlsanity.com/paper/2403.06206/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 43 references that are in the map.
- First posted on arXiv 10 Mar 2024.

## Builds on (most cited first, 5 of 5)

- [MMGET: A Markov model for generalized evidence theory](https://mlsanity.com/paper/2105.07952/) (2021)
- [A generalized intelligent quality-based approach for fusing multi-source information](https://mlsanity.com/paper/1910.06150/) (2019)
- [Maximum Entropy of Random Permutation Set](https://mlsanity.com/paper/2203.11941/) (2021)
- [On the negation of a Dempster-Shafer belief structure based on maximum uncertainty allocation](https://mlsanity.com/paper/1901.10072/) (2019)
- [A betweenness structure entropy of complex networks](https://mlsanity.com/paper/1407.0097/) (2014)

## Built on by (most cited first, 3 of 3)

- [Random Walk in Random Permutation Set Theory](https://mlsanity.com/paper/2404.03978/) (2024)
- [A Distance Measure for Random Permutation Set: From the Layer-2 Belief Structure Perspective](https://mlsanity.com/paper/2510.10596/) (2025)
- [An Order-Sensitive Conflict Measure for Random Permutation Sets](https://mlsanity.com/paper/2510.16001/) (2025)

## Abstract (arXiv)

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been proposed. Exploring the maximum entropy provides a possible way of understanding the physical meaning of RPS. In this paper, a new concept, the envelope of entropy function, is defined. In addition, the limit of the envelope of RPS entropy is derived and proved. Compared with the existing method, the computational complexity of the proposed method to calculate the envelope of RPS entropy decreases greatly. The result shows that when N → ∞, the limit form of the envelope of the entropy of RPS converges to e × (N!)2, which is highly connected to the constant e and factorial. Finally, numerical examples validate the efficiency and conciseness of the proposed envelope, which provides a new insight into the maximum entropy function.