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Deal with information and uncertainty properly and efficiently using tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized Information Theory contains comprehensive and up-to-date coverage of results that have emerged from a research program begun by the author in the early 1990s under the name "generalized information theory" (GIT). This ongoing research program aims to develop a formal mathematical treatment of the interrelated concepts of uncertainty and information in all their varieties. In GIT, as in classical information theory, uncertainty (predictive, retrodictive, diagnostic, prescriptive, and the like) is viewed as a manifestation of information deficiency, while information is viewed as anything capable of reducing the uncertainty. A broad conceptual framework for GIT is obtained by expanding the formalized language of classical set theory to include more expressive formalized languages based on fuzzy sets of various types, and by expanding classical theory of additive measures to include more expressive non-additive measures of various types. This landmark book examines each of several theories for dealing with particular types of uncertainty at the following four levels: * Mathematical formalization of the conceived type of uncertainty * Calculus for manipulating this particular type of uncertainty * Justifiable ways of measuring the amount of uncertainty in any situation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complex material and demonstrate practical applications, generous historical and bibliographical notes, end-of-chapter exercises to test readers' newfound knowledge, glossaries, and an Instructor's Manual, this is an excellent graduate-level textbook, as well as an outstanding reference for researchers and practitioners who deal with the various problems involving uncertainty and information. An Instructor's

Deal with information and uncertainty properly and efficiently using tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized Information Theory contains comprehensive and up-to-date coverage of results that have emerged from a research program begun by the author in the early 1990s under the name "generalized information theory" (GIT). This ongoing research program aims to develop a formal mathematical treatment of the interrelated concepts of uncertainty and information in all their varieties. In GIT, as in classical information theory, uncertainty (predictive, retrodictive, diagnostic, prescriptive, and the like) is viewed as a manifestation of information deficiency, while information is viewed as anything capable of reducing the uncertainty. A broad conceptual framework for GIT is obtained by expanding the formalized language of classical set theory to include more expressive formalized languages based on fuzzy sets of various types, and by expanding classical theory of additive measures to include more expressive non-additive measures of various types. This landmark book examines each of several theories for dealing with particular types of uncertainty at the following four levels: * Mathematical formalization of the conceived type of uncertainty * Calculus for manipulating this particular type of uncertainty * Justifiable ways of measuring the amount of uncertainty in any situation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complex material and demonstrate practical applications, generous historical and bibliographical notes, end-of-chapter exercises to test readers' newfound knowledge, glossaries, and an Instructor's Manual, this is an excellent graduate-level textbook, as well as an outstanding reference for researchers and practitioners who deal with the various problems involving uncertainty and information. An Instructor's

Deal with information and uncertainty properly and efficiently using tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized Information Theory contains comprehensive and up-to-date coverage of results that have emerged from a research program begun by the author in the early 1990s under the name "generalized information theory" (GIT). This ongoing research program aims to develop a formal mathematical treatment of the interrelated concepts of uncertainty and information in all their varieties. In GIT, as in classical information theory, uncertainty (predictive, retrodictive, diagnostic, prescriptive, and the like) is viewed as a manifestation of information deficiency, while information is viewed as anything capable of reducing the uncertainty. A broad conceptual framework for GIT is obtained by expanding the formalized language of classical set theory to include more expressive formalized languages based on fuzzy sets of various types, and by expanding classical theory of additive measures to include more expressive non-additive measures of various types. This landmark book examines each of several theories for dealing with particular types of uncertainty at the following four levels: * Mathematical formalization of the conceived type of uncertainty * Calculus for manipulating this particular type of uncertainty * Justifiable ways of measuring the amount of uncertainty in any situation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complex material and demonstrate practical applications, generous historical and bibliographical notes, end-of-chapter exercises to test readers' newfound knowledge, glossaries, and an Instructor's Manual, this is an excellent graduate-level textbook, as well as an outstanding reference for researchers and practitioners who deal with the various problems involving uncertainty and information. An Instructor's

A new entropy-like measure as well as a new measure of total uncertainty pertaining to the Dempster-Shafer theory are introduced. It is argued that these measures are better justified than any of the previously proposed candidates., Comment: Appears in Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI1992)

The objective of this project is to develop theoretical foundations, based upon the broad framework of the theory of fuzzy measures, and methodology, supported by appropriate computer software, for systems modeling with imprecise probabilities of various kinds. This objective is motivated by the recognition that the assumption that relevant probabilities can be assessed precisely is highly unrealistic. The results are loosely classified into the following seven areas: (1) Complete methodology for Bayesian inference based upon interval valued or fuzzy probabilities and likelihoods; (2) Well justified information measure in Dempster Shafer theory; (3) Relevant theoretical results in fuzzy measure theory, a theory that is connected with imprecise probabilities in a similar way as classical measure theory is connected with classical probabilities; (4) Procedures for constructing imprecise probabilities and fuzzy measures by various methods, including the use of neural networks and genetic algorithms; (5) Various other theoretical results that emerged from the work on the project, including (a) Complete representations of Dempster Shafer theory and possibility theory in terms of the usual semantics of propositional modal logic, (b) Basic ideas of mathematics of finite resolution, (c) Constrained fuzzy arithmetic, (d) A method for identifying key variables in systems modeling via fuzzy c-means clustering based on varying distance function, and (e) A thorough mathematical analysis of the well known Cox's proof, by which it is shown that the proof does not demonstrate the inevitability of the rules of classical Bayesian inference, as often claimed; (6) Applications of the Bayesian inference with fuzzy probabilities to the problem of military unit identification and to statistical decision making; and (7) Computer programs for some algorithms that emerged from the work on this project.