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New definition of the cross entropy based on the Dempster-Shafer theory and its application in a decision-making process

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  • Mehran Khalaj
  • Reza Tavakkoli-Moghaddam
  • Fereshteh Khalaj
  • Ali Siadat

Abstract

Cross entropy is an important index for determining the divergence between two sets or distributions. Most existing cross entropy are proposed in a fuzzy environment and undefined in some uncertain situations (e.g., Dempster–Shafer theory). This study proposes an extended cross entropy measure of belief values based on a belief degree using available evidence. Thus, a new aspect of belief functions represents in the name of a belief set. Then, a new cross entropy measure between two belief sets is defined. Furthermore, the application of the cross-entropy measure in multi-criteria decision making (MCDM) is provided with belief valued information.

Suggested Citation

  • Mehran Khalaj & Reza Tavakkoli-Moghaddam & Fereshteh Khalaj & Ali Siadat, 2020. "New definition of the cross entropy based on the Dempster-Shafer theory and its application in a decision-making process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(4), pages 909-923, February.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:4:p:909-923
    DOI: 10.1080/03610926.2018.1554123
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    Cited by:

    1. Peide Liu & Xiaoxiao Liu & Guiying Ma & Zhaolong Liang & Changhai Wang & Fawaz E. Alsaadi, 2020. "A Multi-Attribute Group Decision-Making Method Based on Linguistic Intuitionistic Fuzzy Numbers and Dempster–Shafer Evidence Theory," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 499-524, April.
    2. Xingyuan Chen & Yong Deng, 2022. "An Evidential Software Risk Evaluation Model," Mathematics, MDPI, vol. 10(13), pages 1-19, July.

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