Part III

FOUNDATIONS OF STATISTICAL INFERENCE WITH FUZZY DATA

Statistical inference is based on stochastic models like probability distributions, parametric families of probability distributions, cumulative distribution functions, expectations, dependence structures, and others.

In this part the basic mathematical concepts for statistical inference in the case of fuzzy data as well as fuzzy probabilities are explained.

In standard statistical inference the combination of observations of a classical random variable to form an element of the sample space is trivial. Different from that for fuzzy data the combination is nontrivial because a vector of fuzzy numbers is not a fuzzy vector.

Therefore it is important to distinguish between observation space and sample space.

There are survey papers on different concepts concerned with statistical inference for fuzzy data by Gebhardt et al. (1997) and Taheri (2003).