Chapter 4. Generalized Measures and Imprecise Probabilities
Published Online: 7 NOV 2005
DOI: 10.1002/0471755575.ch4
Copyright © 2006 John Wiley & Sons, Inc.
Book Title
Uncertainty and Information: Foundations of Generalized Information Theory
Additional Information
How to Cite
Klir, G. J. (2005) Generalized Measures and Imprecise Probabilities, in Uncertainty and Information: Foundations of Generalized Information Theory, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471755575.ch4
Publication History
- Published Online: 7 NOV 2005
- Published Print: 4 NOV 2005
ISBN Information
Print ISBN: 9780471748670
Online ISBN: 9780471755579
- Summary
- Chapter
Keywords:
- monotone measures;
- Choquet capacities;
- Möbius transform;
- imprecise probabilities;
- lower probabilities;
- upper probabilities;
- interaction representation;
- Choquet integral;
- closed convex sets of probability distributions
Summary
Monotone measures and Choquet capacities are introduced as a framework for formalizing imprecise probabilities. Arguments for using imprecise probabilities are presented and five representations of imprecise probabilities are introduced: lower probability functions, upper probability functions, close convex sets of probability distributions, Möbius representations, and interactive representations. It is also shown that the classical notion of expected value can be generalized via the Choquet integral. The emphasis of this chapter is on the various unifying features of imprecise probabilities.