O'Reilly logo

Statistical Methods for Fuzzy Data by Reinhard Viertl

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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

Unnumbered Display Equation

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)]:

(23.2) Numbered Display Equation

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 < ∞

(23.3)

and

(23.4)

For details on the spaces ((n), hp) and ((n), h) see Diamond and ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required