What is it about?
We define entropy of Dempster-Shafer belief functions so that given a joint belief function for two variables, Say X and Y, the joint entropy of belief for (X, Y) is equal to the marginal entropy of the belief for X and the conditional entropy for belief for Y given X.
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Why is it important?
A decomposable entropy means we can compute the entropy of a large graphical belief function model, and use the entropy of a model to decide when to stop the learning process in a data-rich domain. Our definition is the only one in the literature that is decomposable.
Perspectives
Shannon's definition of entropy of probability mass functions is characterized by its decomposability property. Yet none of the many definitions of entropy of Dempster-Shafer belief functions satisfy such a property. Ours is the only one. Our definition of entropy of a belief function measures the dissonance in the belief function, it is not a measure of uncertainty.
Distinguished Professor Emeritus Prakash Pundalik Shenoy
University of Kansas School of Business
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This page is a summary of: A Decomposable Entropy of Belief Functions in the Dempster-Shafer Theory, January 2018, Springer Science + Business Media,
DOI: 10.1007/978-3-319-99383-6_19.
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