A note on fuzzy power relations (Q1311886)

The extension principle of fuzzy set theory provides a method to extend an operation on elements of a set \(Y\) to a power operation on fuzzy subsets of \(Y\). The authors generalize this idea to obtain for any fuzzy relation \(\rho\) over \(Y\) a fuzzy power relation \(\rho^ +\) over the fuzzy power set of \(Y\). If \(\rho\) is a metric, \(\rho^ +\) generalizes the Hausdorff metric on the crisp power set of \(Y\).