Entropy of Random Permutation Set

Subjects: Mathematics >> Mathematics （General） submitted time 2021-12-24

Chen, Luyuan Deng, Yong

Abstract： Recently, a new kind of set, named as Random Permutation Set (RPS), is proposed. RPS takes the permutation of a certain set into consideration, which can be regarded as a generalization of evidence theory. Uncertainty is an important feature of RPS. A straightforward question is how to measure the uncertainty of RPS. To address this problem, the entropy of RPS is presented in this paper. When the order of elements in permutation event is ignored, the proposed RPS entropy degenerates into Deng entropy in evidence theory. When each permutation event is limited to containing just one element, the proposed RPS entropy degenerates into Shannon entropy in probability theory. Hence the RPS entropy can be regarded as the generalization of Deng entropy and Shannon entropy. Numerical examples are illustrated the efficiency of the proposed RPS entropy.

Peer Review Status:Awaiting Review

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