Show simple item record

dc.contributor.authorJiroušek, Radim
dc.contributor.authorShenoy, Prakash P.
dc.date.accessioned2018-03-08T21:45:49Z
dc.date.available2018-03-08T21:45:49Z
dc.date.issued2017-10-10
dc.identifier.citationRadim Jiroušek, Prakash P. Shenoy, A new definition of entropy of belief functions in the Dempster–Shafer theory, International Journal of Approximate Reasoning, Volume 92, 2018, Pages 49-65. https://doi.org/10.1016/j.ijar.2017.10.010en_US
dc.identifier.urihttp://hdl.handle.net/1808/26087
dc.description.abstractWe propose a new definition of entropy of basic probability assignments (BPAs) in the Dempster–Shafer (DS) theory of belief functions, which is interpreted as a measure of total uncertainty in the BPA. Our definition is different from those proposed by Höhle, Smets, Yager, Nguyen, Dubois–Prade, Lamata–Moral, Klir–Ramer, Klir–Parviz, Pal et al., Maeda–Ichihashi, Harmanec–Klir, Abellán–Moral, Jousselme et al., Pouly et al., and Deng. We state a list of six desired properties of entropy for DS belief functions theory, four of which are motivated by Shannon's definition of entropy of probability functions, and the remaining two are requirements that adapt this measure to the philosophy of the DS theory. Three of our six desired properties are different from the five properties proposed by Klir and Wierman. We demonstrate that our definition satisfies all six properties in our list, whereas none of the existing definitions do. Our new definition has two components. The first component is Shannon's entropy of an equivalent probability mass function obtained using the plausibility transform, which constitutes the conflict measure of entropy. The second component is Dubois–Prade's definition of entropy of basic probability assignments in the DS theory, which constitutes the non-specificity measure of entropy. Our new definition is the sum of these two components. Our definition does not satisfy the subadditivity property. Whether there exists a definition that satisfies our six properties plus subadditivity remains an open question.en_US
dc.publisherElsevieren_US
dc.rightsThis paper is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.subjectDempster–Shafer theory of belief functionsen_US
dc.subjectPlausibility transform of a belief functionen_US
dc.subjectDempster–Shafer theory semanticsen_US
dc.subjectDempster's rule of combinationen_US
dc.subjectMaximum entropy propertyen_US
dc.titleA new definition of entropy of belief functions in the Dempster–Shafer theoryen_US
dc.typeArticleen_US
kusw.kuauthorShenoy, Prakash P.
kusw.kudepartmentBusinessen_US
dc.identifier.doi10.1016/j.ijar.2017.10.010en_US
dc.identifier.orcidhttp://orcid.org/0000-0002-8425-896Xen_US
kusw.oaversionScholarly/refereed, author accepted manuscripten_US
kusw.oapolicyThis item meets KU Open Access policy criteria.en_US
dc.rights.accessrightsopenAccessen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

This  paper  is  licensed  under  a  Creative  Commons  Attribution-NonCommercial-NoDerivatives  4.0  International  License.
Except where otherwise noted, this item's license is described as: This paper is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.