Fuzzy Information and Stochastics

In applications there occur different forms of uncertainty. The two most important types are randomness (stochastic variability) and imprecision (fuzziness). In modelling, the dominating concept to describe uncertainty is using stochastic models which are based on probability. However, fuzziness is not stochastic in nature and therefore it is not considered in probabilistic models. Since many years the description and analysis of fuzziness is subject of intensive research. These research activities do not only deal with the fuzziness of observed data, but also with imprecision of informations. Especially methods of standard statistical analysis were generalized to the situation of fuzzy observations. The present paper contains an overview about the presentation of fuzzy information and the generalization of some basic classical statistical concepts to the situation of fuzzy data.