Entropy of Random Permutation Set

Recently, a new kind of set, named Random Permutation Set (RPS), has been presented. RPS takes the permutation of a certain set into consideration, which can be regarded as an ordered extension of evidence theory. Uncertainty is an important feature of RPS. A straightforward question is how to measure the uncertainty of RPS. To address this issue, the entropy of RPS (RPS entropy) is presented in this article. The proposed RPS entropy is compatible with Deng entropy and Shannon entropy. In addition, RPS entropy meets probability consistency, additivity, and subadditivity. Numerical examples are designed to illustrate the efficiency of the proposed RPS entropy. Besides, a comparative analysis of the choice of applying RPS entropy, Deng entropy, and Shannon entropy is also carried out.