What is it about?
We define expected value of a basic probability assignment for a variable with numeric state space. We use this definition to define variance, covariance, correlation, and higher moments. We study properties of these definitions and compare with corresponding properties of probabilistic expectation, variance, covariance, correlation, and higher moments.
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Why is it important?
The concept of an expected value of Dempster-Shafer (D-S) belief functions is important in decision-making and information theory where uncertainty is represented by D-S belief functions.
Perspectives
We used this definition for defining entropy of D-S belief functions, which has the compound distributions property that characterizes Shannon's entropy of probability mass functions. Our definition of entropy is the only one in the literature that has such a compound distributions or decomposable property. This is crucial in the computation of entropy of large graphical D-S belief function models.
Distinguished Professor Emeritus Prakash Pundalik Shenoy
University of Kansas School of Business
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This page is a summary of: An expectation operator for belief functions in the Dempster–Shafer theory, International Journal of General Systems, September 2019, Taylor & Francis,
DOI: 10.1080/03081079.2019.1658756.
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