Abstract
In this paper, we present a measure of Information Content (IC) of Basic Belief Assignments (BBAs), and we show how it can be easily calculated. This new IC measure is interpreted as the dual of the effective measure of uncertainty (i.e. generalized entropy) of BBAs developed recently.
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Notes
- 1.
However, we will keep \(m^\varTheta (\cdot )\) notation when very necessary.
- 2.
\(\triangleq \) means equal by definition.
- 3.
This terminology is not used by Shannon in his original paper but it has been introduced by Tribus in [10] in the probabilistic context, and by analogy we adopt Tribus’ terminology also for BBAs.
- 4.
Once the binary values are converted into their digit value with the most significant bit on the left (i.e. the least significant bit on the right).
- 5.
aside of the value of N of course.
- 6.
That is why it is better, we think, to use the notation \(IC(m^\varTheta )\) instead of IC(m).
- 7.
We suppose for convenience that the elements \(X \in 2^\varTheta \) are listed in increasing order using the classical \(|\varTheta |\)-bits representation with the least significant bit on the right.
- 8.
Similarly, we can define \(\varDelta _{IC}(m_1|m_2)\triangleq IC(m_1^\varTheta )-IC(m_2^\varTheta )=-\varDelta _{IC}(m_2|m_1)\).
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Dezert, J., Tchamova, A., Han, D. (2022). Measure of Information Content of Basic Belief Assignments. In: Le Hégarat-Mascle, S., Bloch, I., Aldea, E. (eds) Belief Functions: Theory and Applications. BELIEF 2022. Lecture Notes in Computer Science(), vol 13506. Springer, Cham. https://doi.org/10.1007/978-3-031-17801-6_12
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