Document Zbl 07736127

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Stat., Theory Methods</a> <a href="/?q=in%3A501910" title="Articles in this Issue">52, No. 19, 6991-7008 (2023)</a>. </div> <div class="abstract">Summary: 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.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7736127">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-XX" title="MSC2020">62-XX</a> </td> <td class="space"> Statistics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ADempster-Shafer+theory">Dempster-Shafer theory</a>; <a href="/?q=ut%3AR%C3%A9nyi+entropy">Rényi entropy</a>; <a href="/?q=ut%3Abasic+probability+assignment">basic probability assignment</a>; <a href="/?q=ut%3Auncertainty+measure">uncertainty measure</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07736127" data-ciurl="/ci/07736127" data-biburl="/bibtex/07736127.bib" data-amsurl="/amsrefs/07736127.bib" data-xmlurl="/xml/07736127.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07736127.pdf" title="Zbl 07736127 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1080/03610926.2022.2037646" aria-label="DOI for “A generalization of Rényi entropy for basic probability assignment”" title="10.1080/03610926.2022.2037646">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bosyk, G. 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