Limit of the Maximum Random Permutation Set Entropy
CoRR(2024)
摘要
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.
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