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"They Can't Expect to be Treated Like Normal Americans so Soon": Reconceptualizing Latinx Immigrants in Social Studies Education
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In: Journal of Critical Thought and Praxis (2018)
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Translation: Rights and Agency - A Public Policy Perspective for Knowledge, Technology and Globalization
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Sadek, Gaafar. - : Université d'Ottawa / University of Ottawa, 2018
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A new definition of entropy of belief functions in the Dempster–Shafer theory
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Abstract:
We 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.
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Keyword:
Dempster's rule of combination; Dempster–Shafer theory of belief functions; Dempster–Shafer theory semantics; Maximum entropy property; Plausibility transform of a belief function
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URL: https://doi.org/10.1016/j.ijar.2017.10.010
http://hdl.handle.net/1808/26087
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The Holographic Principle: Typological Analysis Using Lower Dimensions
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In: Proceedings of the Annual Meetings on Phonology; Proceedings of the 2017 Annual Meeting on Phonology ; 2377-3324 (2018)
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