Uncertainty and Information / Wiley - IEEE (PDF)

Deal with information and uncertainty properly and efficiently
using tools emerging from generalized information theory

Uncertainty and Information: Foundations of Generalized Information
Theory contains comprehensive and up-to-date coverage of results
that have emerged from a research program begun by the author in
the early 1990s under the name "generalized information theory"
(GIT). This ongoing research program aims to develop a formal
mathematical treatment of the interrelated concepts of uncertainty
and information in all their varieties. In GIT, as in classical
information theory, uncertainty (predictive, retrodictive,
diagnostic, prescriptive, and the like) is viewed as a
manifestation of information deficiency, while information is
viewed as anything capable of reducing the uncertainty. A broad
conceptual framework for GIT is obtained by expanding the
formalized language of classical set theory to include more
expressive formalized languages based on fuzzy sets of various
types, and by expanding classical theory of additive measures to
include more expressive non-additive measures of various
types.

This landmark book examines each of several theories for dealing
with particular types of uncertainty at the following four
levels:

* Mathematical formalization of the conceived type of
uncertainty

* Calculus for manipulating this particular type of
uncertainty

* Justifiable ways of measuring the amount of uncertainty in any
situation formalizable in the theory

* Methodological aspects of the theory

With extensive use of examples and illustrations to clarify complex
material and demonstrate practical applications, generous
historical and bibliographical notes, end-of-chapter exercises to
test readers' newfound knowledge, glossaries, and an Instructor's
Manual, this is an excellent graduate-level textbook, as well as an
outstanding reference for researchers and practitioners who deal
with the various problems involving uncertainty and information. An
Instructor's Manual presenting detailed solutions to all the
problems in the book is available from the Wiley editorial
department.