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1999 | Buch | 2. Auflage

Uncertainty-Based Information

Elements of Generalized Information Theory

verfasst von: Professor George J. Klir, Professor Mark J. Wierman

Verlag: Physica-Verlag HD

Buchreihe : Studies in Fuzziness and Soft Computing

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Über dieses Buch

Information is precious. It reduces our uncertainty in making decisions. Knowledge about the outcome of an uncertain event gives the possessor an advantage. It changes the course of lives, nations, and history itself. Information is the food of Maxwell's demon. His power comes from know­ ing which particles are hot and which particles are cold. His existence was paradoxical to classical physics and only the realization that information too was a source of power led to his taming. Information has recently become a commodity, traded and sold like or­ ange juice or hog bellies. Colleges give degrees in information science and information management. Technology of the computer age has provided access to information in overwhelming quantity. Information has become something worth studying in its own right. The purpose of this volume is to introduce key developments and results in the area of generalized information theory, a theory that deals with uncertainty-based information within mathematical frameworks that are broader than classical set theory and probability theory. The volume is organized as follows.

Inhaltsverzeichnis

Frontmatter
1. Introduction
Abstract
For three hundred years (from about the mid-seventeenth century, when the formal concept of numerical probability emerged, until the 1960s), uncertainty was conceived solely in terms of probability theory. This seemingly unique connection between uncertainty and probability is now challenged. The challenge comes from several mathematical theories, distinct from probability theory, which are demonstrably capable of characterizing situations under uncertainty. The most visible of these theories, which began to emerge in the 1960s, are the theory of fuzzy sets [Zadeh, 1965], evidence theory [Dempster, 1967a,b; Shafer, 1976], possibility theory [Zadeh, 1978], and the theory of fuzzy measures [Sugeno, 1974, 1977].
George J. Klir, Mark J. Wierman
2. Uncertainty Formalizations
Abstract
Mathematical theories of uncertainty in which measures of uncertainty are now well established are fuzzy set theory, evidence theory, and possibility theory, in addition to classical set theory and probability theory. Some of these theories are connected. Classical set theory is subsumed under fuzzy set theory. Probability theory and possibility theory are branches of evidence theory, while evidence theory is, in turn, a branch of fuzzy measure theory. Although information aspects of fuzzy measure theory have not been investigated as yet, the theory is briefly introduced in this chapter because it represents a broad framework for future research.
George J. Klir, Mark J. Wierman
3. Uncertainty Measures
Abstract
When the seemingly unique connection between uncertainty and probability theory was broken, and uncertainty began to be conceived in terms of the much broader frameworks of fuzzy set theory and fuzzy measure theory, it soon became clear that uncertainty can manifest itself in different forms. These forms represent distinct types of uncertainty. In probability theory, uncertainty is manifested only in one form.
George J. Klir, Mark J. Wierman
4. Principles of Uncertainty
Abstract
Although measures of the various types of uncertainty-based information (Table 3.5) are not sufficient in human communication [Cherry, 1957], they are highly effective tools for dealing with systems problems of virtually any kind [Klir, 1985]. For the classical information measures (Hartley function and Shannon entropy), which were originally conceived solely as tools for analyzing and designing telecommunication systems, this broad utility is best demonstrated by Ashby [1958, 1965, 1969, 1972] and Conant [1969, 1974, 1976, 1981].
George J. Klir, Mark J. Wierman
5. Conclusions
Abstract
A turning point in our understanding of the concept of uncertainty was reached when it became clear that there are several types of uncertainty. This new insight was obtained by examining uncertainty emerging from mathematical theories more general than classical set theory and probability theory.
George J. Klir, Mark J. Wierman
Backmatter
Metadaten
Titel
Uncertainty-Based Information
verfasst von
Professor George J. Klir
Professor Mark J. Wierman
Copyright-Jahr
1999
Verlag
Physica-Verlag HD
Electronic ISBN
978-3-7908-1869-7
Print ISBN
978-3-7908-2464-3
DOI
https://doi.org/10.1007/978-3-7908-1869-7