Uncertainty and Fuzziness
There are different mathematical frameworks dealing with uncertainty, vagueness and ambiguity: the probabilistic concept, the concept of a fuzzy set, and the concept of a fuzzy measure. The corresponding measures for the amount of relevant information lead to three types of uncertainty measures: Entropies or measures of information, measures of fuzziness and the uncertainty measures in the mathematical theory of evidence.
One purpose of this paper is to focus on recent results of measures of fuzziness and to give a survey on characterizations of these measures. Moreover, we want to show that certain “total entropies” which consist of a “random part” and a “fuzzy part”, are special cases of a more general information theory, where the entropies are dependent upon the events and the probabilities.
Unable to display preview. Download preview PDF.
- [Aczél 1984]J. Aczél: Measuring information beyond communication theory-Why some generalized information measures may be useful, others not.Aequationes Math. 27, 1–19 (1984)Google Scholar
- [Aczél, Daróczy 1975]
- [Aczél, Daróczy 1978]
- [Aczél, Kannappan 1978]J. Aczél, PL. Kannappan: A mixed theory of information-III: Inset entropies of degree β, Information and Control 1978, 312–322 (1978)Google Scholar
- [De Luca, Termini 1972]
- [Dubois, Prade 1980]
- [Ebanks 1983]B. R. Ebanks: On measures of fuzziness and their representations, J.Math. Anal. Appl., 24–37 (1983)Google Scholar
- [Groß 1993]H. Groß: Inset-Informationsmaße, Dissertation. Braunschweig 1993Google Scholar
- [Klir, Folger]
- [Sander 1987]
- [Sander 1989]