Linear statistical inference for fuzzy data

The paper presents some steps towards linear statistical inference for fuzzy data. In establishing best linear unbiased estimators (BLUE) it is necessary to consider a suitable notion of expectation and variance for random fuzzy sets. As methodological guide, the authors use the Frechet-approach which leads for a given metric to an associated expectation and variance. Especially the well known Aumann expectation appears as Frechet-expectation and the associated variance has the advantage, that at least special fuzzy number data can formally be handled like Euclidean vectors. Application to linear regression shows that only in special cases the fuzzified version of classical BLUE keeps their optimality