Introduction: Significance of Uncertainty; Uncertainty and Information -- Uncertainty Formalizations: Classical Sets: Terminology and Notation; Fuzzy Set Theory; Fuzzy Measure Theory; Evidence Theory; Probability Theory; Possibility Theory; Overview of Uncertainty Theories -- Uncertainty Measures: Nonspecifity; Conflict; Aggregate Uncertainty in Evidence Theory; Fuzziness; Summary of Uncertainty Measures -- Principles of Uncertainty: Principle of Minimum Uncertainty; Principle of Maximum Uncertainty; Principle of Uncertainty Invariance; Summary of Uncertainty Principles -- Conclusions.
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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.