Statistics with Fuzzy Data
Besides stochastic variation of real data there is another kind of uncertainty in observations called imprecision and the corresponding measurement results are called non-precise data. Usually this kind of uncertainty is not described in statistics. Especially in environment statistics, where also very small quantities are measured, this imprecision cannot be neglected. Otherwise by extrapolations the precision of results is very misleading. Therefore statistical methods have to be generalized for non-precise data. The mathematical concept to describe non-precise data are so-called non-precise numbers and non-precise vectors. Situations are explained, where the characterizing functions of non-precise numbers can be given explicitly. Using the mathematical concept of non-precise numbers and vectors statistical procedures can be generalized to non-precise data. These generalizations are explained in the contribution.
KeywordsFuzzy Data Extension Principle Observation Space Predictive Density Stochastic Quantity
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