تقرير
Limit of the Maximum Random Permutation Set Entropy
| العنوان: | Limit of the Maximum Random Permutation Set Entropy |
|---|---|
| المؤلفون: | Zhou, Jiefeng, Li, Zhen, Cheong, Kang Hao, Deng, Yong |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Information Theory, Computer Science - Artificial Intelligence |
| الوصف: | 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 $N \to \infty$, the limit form of the envelope of the entropy of RPS converges to $e \times (N!)^2$, 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. Comment: 22 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.06206 |
| رقم الأكسشن: | edsarx.2403.06206 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |