Cuzzolin F. The Geometry of Uncertainty: The Geometry of Imprecise Probabilities

Springer, 2021. — 864 p. — (Artificial Intelligence: Foundations, Theory, and Algorithms). — ISBN 978-3-030-63152-9.The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned.The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.Belief functions
Understanding belief functions
Reasoning with belief functions
A toolbox for the working scientist
The bigger picture
The geometry of belief functions
Geometry of Dempster’s rule
Three equivalent models
The geometry of possibility
Probability transforms: The affine family
Probability transforms: The epistemic family
Consonant approximation
Consistent approximation
Geometric conditioning
Decision making with epistemic transforms
An agenda for the future