Chapter 6. Measure of Uncertainty and Information
Published Online: 7 NOV 2005
DOI: 10.1002/0471755575.ch6
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) Measure of Uncertainty and Information, in Uncertainty and Information: Foundations of Generalized Information Theory, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471755575.ch6
Publication History
- Published Online: 7 NOV 2005
- Published Print: 4 NOV 2005
ISBN Information
Print ISBN: 9780471748670
Online ISBN: 9780471755579
- Summary
- Chapter
Keywords:
- generalized Hartley functional;
- generalized Shannon entropy;
- aggregated measure of uncertainty;
- disaggregated total measure of uncertainty
Summary
Requirements for measures of uncertainty and uncertainty-based information are introduced and discussed in generic terms. Generalizations of the Hartley measure of nonspecificity to the theory of graded possibilities and Dempster-Shafer theory are examined in detail, including the respective uniqueness proofs. A historical overview is presented of several unsuccessful attempts to generalize the Shannon entropy. An aggregated measure of uncertainty, which satisfies all the essential requirements, is introduced. It is shown that this measure is applicable to all uncertainty theories, but it is not sufficiently sensitive. Two ways of disaggregating this measure are introduced and compared.