
A Mathematical Theory of Evidence
Glenn Shafer
Princeton University Press, 1976.
This book was published by the Princeton University Press in 1976.
The author was an assistant professor at Princeton University when the
book was written. The first paragraph of his preface reads as follows:
In the spring of 1971, I attended a course on statistical
inference taught by Arthur Dempster at Harvard. In the fall of that
same year Geoffrey Watson suggested I give a talk expositing Dempster's
work on upper and lower probabilities to the Department of Statistics
at Princeton. This essay is one of the results of the ensuing effort.
It offers a reinterpretation of Dempster's work, a reinterpretation
that identifies his "lower probabilities" as epistemic probabilities
or degrees of belief, takes the rule for combining such degrees of belief
as fundamental, and abandons the idea that they arise as lower bounds
over classes of Bayesian probabilities.
Jeff Barnet, one of the computer scientists who introduced the book's
theory to the artificial intelligence community in the late 1970s and
early 1980s, called the theory "the DempsterShafer theory,"
and this name has stuck.
Other Work on the
DempsterShafer Theory
A search on the web will reveal thousands of discussions, applications,
and extensions of the DempsterShafer theory. Here are a few references
that may be particularly useful.
 A Mathematical Theory of Evidence turns 40. International Journal of Approximate Reasoning 79 725. December 2016. PREPUBLICATION VERSION. The issue in which this article appears also includes some related articles and a bibliography of articles on the DempsterShafer theory that had previously appeared in the journal.
 Advances in the DempsterShafer Theory of Evidence, edited
by Ronald R. Yager, Mario Fedrizzi, and Janusz Kacprzyk. Wiley. 1994.
 Special Issue on DempsterShafer Theory, Methodology, and Applications.
International Journal of Approximate Reasoning. Volume 31, Numbers 12,
October 2002.
 Belief Functions in Business Decision: Studies in Fuzziness and
Soft Computing, Srivastava, R. J. and Mock, T.J.; PhysicaVerlag
Heidelberg: New York, 2002.
 Classic Works of the DempsterShafer Theory of Belief Functions, edited by Ronald Yager and Liping Liu, February, 2008, Springer. ISBN: 9783540253815.
 The Dempster–Shafer calculus for statisticians, by A. P. Dempster, International Journal of Approximate Reasoning, 2008.
