Measures of uncertainty and information (Q2702364)

This handbook chapter brings a state-of-the-art overview of several types of measures of uncertainty. Three main uncertainty measure types discussed here involve the imprecision (nonspecifity) linked to the classical set theory, the entropy-like uncertainty originating in probability theory, and the fuzziness measures connected with fuzzy sets (see also chapter 9 of this handbook [\textit{N. R. Pal} and \textit{J. C. Bezdek}, ibid. 459-480 (2000; Zbl 0986.94056)]). Note that the information measures in the spirit of Kampé de Fériet are not discussed here.NEWLINENEWLINENEWLINEFive sections of this chapter bring the introduction, conclusions, and overview of the three above mentioned types of measures of uncertainty. Among the measures of nonspecifity, recall e.g. the Hartley function \(U(A)= \log\text{ card}(A)\) and its several generalizations, especially in the possibility theory and the evidence theory. Entropy-like measures come up from the probabilistic Shannon entropy. In the framework of Dempster-Shafer theory, several related types of measures are introduced, such as measure of dissonance, confusion, discord, strife, etc. Finally, measures of fuzziness, especially those proposed by DeLuca and Termini are discussed. All presented measures and results are properly quoted, indicating the original sources. The chapter gives a good impression about several types of measures of uncertainty, however, for their deeper understanding it is necessary to study the indicated original sources or monographs mentioned in the text, especially [\textit{G. J. Klir} and \textit{M. J. Wierman}, Uncertainty-based information: Elements of generalized information theory, Studies in Fuzziness and Soft Computing 15 (Physica-Verlag, Heidelberg) (1998; Zbl 0902.68061)].NEWLINENEWLINEFor the entire collection see [Zbl 0942.00007].