On the Monoexistence of Hausdorff-like Metrics for Fuzzy Sets

Peter Braß
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin
email: brass@inf.fu-berlin.de

Report B 00-02
January 2000

There has been a number of papers proposing different extensions of the Hausdorff metric for fuzzy sets. None of these proposals behaves as one would intuitively expect. It is the aim of this paper to show that under a reasonable set of axioms, like triangle inequality, invariance under motions, and independence of the length unit, there is no metric on the nonempty bounded fuzzy subsets of an euclidean space.

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