A generalization of Rényi entropy for basic probability assignment

Ran Yu and Yong Deng

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 19, 6991-7008

Abstract: To measure the uncertainty of basic probability assignment (BPA) in the field of evidence theory is an open issue. The Rényi entropy, a continuous family of entropy measures, is extended from the Shannon entropy and has been widely applied in many fields. In this paper, the generalized Rényi entropy for basic probability assignments is proposed. The proposed entropy can degenerate into the Rényi entropy under the condition that the BPA degenerates to probability distributions. Additionally, some desirable properties of the proposed entropy are explored. Finally, the numerical examples are given to show the feasibility and effectiveness of the proposed entropy. Compared with the Shannon entropy and other existing measures, the entropy is efficient to measure the uncertainty of BPA.

Date: 2023
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DOI: 10.1080/03610926.2022.2037646

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