23.2 Distances of fuzzy quantities
The so-called Hausdorff metric dH(·, ·) on the space of all nonempty compact and convex subsets of n is defined for A, B ∈ by
With this metric the space (, dH) is a metric space.
There is the following relationship between this metric and the difference of support functions [see Diamond and Kloeden (1990, page 243)]:
Based on the Hausdorff metric different metrics can be defined on the set (n). Frequently the following distances are used:
For x*, y* ∈ (n) and 1≤ p < ∞
For details on the spaces ((n), hp) and ((n), h∞) see Diamond and ...