Uncertainty-Based Information: Elements of Generalized Information Theory / Edition 2

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Overview

The book is an overview of the development of basic ideas and mathematical results regarding measures and principles of uncertainty-based information formalized within the framework of classical set theory, probability theory, fuzzy set theory, possibility theory, and the Dempster-Shafer theory of evidence.
The book contains many new results, which had until now not been available in a single monograph. The book is very useful for researchers, but it can also be used as a graduate text.

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Product Details

  • ISBN-13: 9783790824643
  • Publisher: Physica-Verlag HD
  • Publication date: 12/15/2010
  • Series: Studies in Fuzziness and Soft Computing Series , #15
  • Edition description: Softcover reprint of hardcover 2nd ed. 1999
  • Edition number: 2
  • Pages: 170
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.40 (d)

Table of Contents

Introduction: Significance of Uncertainty; Uncertainty and Information.- Uncertainty Formalizations: Classical Sets: Terminology and Notation; Fuzzy Set Theory. Fuzzy Operations. Fuzzy Subsethood. Cylindric Extensions. Types of Fuzzy Sets; Fuzzy Measure Theory; Evidence Theory. Upper and Lower Probabilities; Probability Theory; Possibility Theory; Overview of Uncertainty Theories.- Uncertainty Measures: Nonspecifity. Hartley Function. U-uncertainty. Nonspecifity in Evidence Theory. Nonspecifity of Sets in n-Dimensional Euclidean Space. Generalized Hartley-Like Measures of Nonspecifity ; Conflict. Shannon Entropy. Entropy-Like Measure in Evidence Theory. Conflict in Possibility Theory; Aggregate Uncertainty in Evidence Theory. General Algorithm. for Computing Function AU. Computing Function AU in Possibility Theory; Fuzziness; Summary of Uncertainty Measures.- Principles of Uncertainty: Principle of Minimum Uncertainty; Principle of Maximum Uncertainty; Principle of Uncertainty Invariance. Probability-Possibility Transformations. Approximations of Fuzzy Sets. Approximations in Evidence Theory. Revised Probability-Possibility Transformations; Summary of Uncertainty Principles.- Conclusions: Appraisal of Current Results; Unresolved Problems; Future Directions.

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