Uncertainty-based information. Elements of generalized information theory
The aim of this book is to overview measures of uncertainty of different theories (namely, probability, fuzzy sets, possibility, and evidence theories), measures of information for these theories (whenever information is quantified as the uncertainty reduction, which is refereed to as uncertainty-based information), and some methodological principles based upon the preceding uncertainty measures. The name generalized information theory is understood in the book in the sense that the information is not limited to a probabilistic context, but rather to several different approaches. However, the book does not refer to generalized information theory in the Kampé de Fériet sense [\textit{J. Kampé de Fériet}, Lect. Notes Math. 398, 1-35 (1974; Zbl 0299.94020)] (that is, in the sense of the general axiomatic information theory [\textit{B. Forte}, Rev. Franc. Inform. Rech. Oper. 3, No. R-2, 63-90 (1969; Zbl 0192.56001)]). After a general introduction in Chapter 1, Chapter 2 includes the main concepts, ideas and conclusions of some relevant theories of uncertainty: Fuzzy set theory, Fuzzy measure theory, Evidence theory, Probability theory and Possibility theory. A clear relationship among the measures in these theories is also stated. In Chapter 3 three types of uncertainty in the five considered theories are analyzed: nonspecificity (or imprecision) and strife (or conflict) (which are often joined under the term `ambiguity'), and `fuzziness' (or vagueness). In Chapter 4 three principles of uncertainty using uncertainty measures to deal with system problems, as well as some of these problems, are examined. These principles are: a principle of minimum uncertainty, a principle of maximum uncertainty, and a principle of uncertainty invariance. Chapter 5 shows a summary of the conclusions obtained, some unresolved problems and some future directions in connection with the subject covered in the book.
scientific article; zbMATH DE number 1134727