22.1 Fuzzy estimators of regression parameters
Based on the fuzzy a posteriori density π*(·|z*) on the parameter space Θ ⊆r generalized point estimators for the parameter θ = (θ1,…,θr) can be calculated.
Without any loss function the most popular method is to calculate the generalized expectation of j with respect to π*(·|z*); i.e.
where πj*(·|z*) is the fuzzy marginal density
The characterizing function ψj(·) of j* is obtained via the construction lemma for characterizing functions. The nested family of subsets of is given by
Then ψj(·) of j* is given by its values
Another possibility ...