Uncertainty and Information: Foundations of Generalized Information Theory

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John Wiley & Sons, Nov 22, 2005 - Technology & Engineering - 499 pages
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Deal with information and uncertainty properly and efficientlyusing tools emerging from generalized information theory

Uncertainty and Information: Foundations of Generalized InformationTheory contains comprehensive and up-to-date coverage of resultsthat have emerged from a research program begun by the author inthe early 1990s under the name "generalized information theory"(GIT). This ongoing research program aims to develop a formalmathematical treatment of the interrelated concepts of uncertaintyand information in all their varieties. In GIT, as in classicalinformation theory, uncertainty (predictive, retrodictive,diagnostic, prescriptive, and the like) is viewed as amanifestation of information deficiency, while information isviewed as anything capable of reducing the uncertainty. A broadconceptual framework for GIT is obtained by expanding theformalized language of classical set theory to include moreexpressive formalized languages based on fuzzy sets of varioustypes, and by expanding classical theory of additive measures toinclude more expressive non-additive measures of varioustypes.

This landmark book examines each of several theories for dealingwith particular types of uncertainty at the following fourlevels:
* Mathematical formalization of the conceived type ofuncertainty
* Calculus for manipulating this particular type ofuncertainty
* Justifiable ways of measuring the amount of uncertainty in anysituation formalizable in the theory
* Methodological aspects of the theory

With extensive use of examples and illustrations to clarify complexmaterial and demonstrate practical applications, generoushistorical and bibliographical notes, end-of-chapter exercises totest readers' newfound knowledge, glossaries, and an Instructor'sManual, this is an excellent graduate-level textbook, as well as anoutstanding reference for researchers and practitioners who dealwith the various problems involving uncertainty and information. AnInstructor's Manual presenting detailed solutions to all theproblems in the book is available from the Wiley editorialdepartment.

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1 Introduction
2 Classical PossibilityBased Uncertainty Theory
3 Classical ProbabilityBased Uncertainty Theory
4 Generalized Measures and Imprecise Probabilities
5 Special Theories of Imprecise Probabilities
6 Measures of Uncertainty and Information
7 Fuzzy Set Theory
8 Fuzzification of Uncertainty Theories
Appendix B Uniqueness of Generalized Hartley Measure in the DempsterShafer Theory
Appendix C Correctness of Algorithm 61
Appendix D Proper Range of Generalized Shannon Entropy
Appendix E Maximum of GSa in Section 69
Appendix F Glossary of Key Concepts
Appendix G Glossary of Symbols
Subject Index

9 Methodological Issues
10 Conclusions
Appendix A Uniqueness of the UUncertainty

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Page 1 - I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.
Page 3 - ... conquered lies in the fact that these problems, as contrasted with the disorganized situations with which statistics can cope, show the essential feature of organization. We will therefore refer to this group of problems as those of organized complexity.
Page 1 - In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and methods for practically measuring some quality connected with it. I often say that when you can measure what you are speaking about and express it in numbers, you know something about it ; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory...
Page 18 - Membership in a fuzzy set is not a matter of affirmation or denial, but rather a matter of degree.
Page 3 - ... and left untouched a great middle region. The importance of this middle region, moreover, does not depend primarily on the fact that the number of variables involved is moderate — large compared to two, but small compared to the number of atoms in a pinch of salt. The problems in this middle region, in fact, will often involve a considerable number of variables.
Page 10 - A is contained in B, then A is said to be a subset of B, and B is said to be a superset of A.

About the author (2005)

GEORGE J. KLIR, PhD, is currently Distinguished Professor of Systems Science at Binghamton University, SUNY. Since immigrating to the U.S. in 1966, he has held positions at UCLA, Fairleigh Dickinson University, and Binghamton University. He is a Life Fellow of IEEE, IFSA, and the Netherlands Institute for Advanced Studies. He has served as president of SGSR, IFSR, NAFIPS, and IFSA. He has published over 300 research papers and sixteen books, and has edited ten books. He has also served as Editor in Chief of the International Journal of General Systems since 1974 and of the IFSR International Book Series on Systems Science and Engineering since 1985. He has received numerous professional awards, including five honorary doctoral degrees, Bernard Bolzano's Gold Medal, Arnold Kaufmann's Gold Medal, and the SUNY Chancellor's Award for "Exemplary Contributions to Research and Scholarship." He is listed in Who's Who in America and Who's Who in the World. His current research interests include intelligent systems, soft computing, generalized information theory, systems modeling and design, fuzzy systems, and the theory of generalized measures. He has guided twenty-nine successful doctoral dissertations in these areas. Some of his research has been funded by grants from NSF, ONR, the United States Air Force, NASA, Sandia Labs, NATO, and various industries.

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