Synthese 190 (3):353-378 (2013)

The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability function of traditional Bayesian theory. The Shannon entropy has been shown to uniquely capture certain highly intuitive properties of uncertainty, and can thus be considered a measure of that quantity. This article presents two measures developed with the purpose of generalizing the Shannon entropy for (1) unordered convex credal sets and (2) possibly non-convex credal sets ordered by second order probability, thereby providing uncertainty measures for such epistemic representations. There is also a comparison with the results of the measure AU developed within Dempster–Shafer theory in a few instances where unordered convex credal set theory and Dempster–Shafer theory overlap.
Keywords Uncertainty  Probability  Information  Credal set  Entropy
Categories (categorize this paper)
DOI 10.1007/s11229-011-0042-2
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 51,304
Through your library

References found in this work BETA

Humean Supervenience Debugged.David K. Lewis - 1994 - Mind 103 (412):473--490.
The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
Semantic Conceptions of Information.Luciano Floridi - 2008 - Stanford Encyclopedia of Philosophy.
On Indeterminate Probabilities.Isaac Levi - 1974 - Journal of Philosophy 71 (13):391-418.

View all 14 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles


Added to PP index

Total views
46 ( #203,444 of 2,330,230 )

Recent downloads (6 months)
2 ( #393,610 of 2,330,230 )

How can I increase my downloads?


My notes