Synopses & Reviews
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.
Table of Contents
: 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.