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A new uncertainty measure via belief Rényi entropy in Dempster-Shafer theory and its application to decision making

Author

Listed:
  • Zhe Liu
  • Yu Cao
  • Xiangli Yang
  • Lusi Liu

Abstract

Dempster-Shafer theory (DST) has attracted wide attention in many fields thanks to its strong advantages over probability theory. Whereas the uncertainty measure of basic belief assignment (BBA) in DST is an open and essential problem. The main goal of this article is to propose a new belief Rényi entropy for the uncertainty measure of BBA, which is inspired by generalized Rényi entropy in DST. The proposed belief Rényi entropy satisfies some desirable properties of uncertainty measure. Furthermore, the proposed belief Rényi entropy can be degraded to Rényi entropy when BBA is transformed into a probability distribution. Finally, a new decision-making method is designed based on the proposed belief Rényi entropy. The validity of the proposed belief entropy is verified by some numerical examples and its application to decision-making.

Suggested Citation

  • Zhe Liu & Yu Cao & Xiangli Yang & Lusi Liu, 2024. "A new uncertainty measure via belief Rényi entropy in Dempster-Shafer theory and its application to decision making," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(19), pages 6852-6868, October.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:19:p:6852-6868
    DOI: 10.1080/03610926.2023.2253342
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