FUZZY INFORMATION AND STOCHASTICS

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

Keywords:

Fuzzy numbers , Fuzzy Probability Distributions , Fuzzy Random Variables , Fuzzy Stochastic Processes , Decision on Fuzzy Information