On the nonexistence of Hausdorff-like metrics for fuzzy sets

There has been a number of papers proposing different extensions of the Hau sdorff metric to fuzzy sets. None of these proposals behave as one would in tuitively expect. It is the aim of this paper to start a systematic study o f the possible behaviour of metrics on fuzzy sets, and to show that under a reasonable set of axioms, like the metric space axioms and additionally in variance under motions and independence of the length unit, there is no met ric on the fuzzy subsets of a Euclidean space. (C) 2002 Elsevier Science B. V. All rights reserved.