FUZZEKS [to Index]
Handling Kriging Result / Overview

Kriging is a method that interpolates values for all points in a 2-dimensional space. Each of these values, in the case of FUZZEKS, can be fuzzy as well.

The result at a point is a fuzzy number (as described in the kriging basics) that can be represented by a membership function, e.g.:

We need two dimensions in order to present this information. One more dimension could be used in order to show the kriging variance for this point.

The complete result of fuzzy kriging provides such a fuzzy number for each point (a mesh of points) in 2-dimensional space. So four dimensions (or even five dimensions if the variance should be shown additionally) are needed to present the result in full detail.

Because the computer screen (or paper) has only two dimenions, the difficulties in displaying this result are obvious and additional ways to present the result must be found.

• One method is to use greyshades and colors, a map of greyshades for the values can be used in FUZZEKS. But this method doesn't deliver very much information to the observer, because the human eye can not see where exactly specific values are. The rough distribution of the values can be seen, but this very good.
The same problems apply for colors, but using colors allows even to display values of more than one dimension, because the space of RGB-colors itself is 3-dimensional (RGB is the abbreviation for the cubic Red/Green/Blue color model, which is used for TV and computer monitors; the human eyes' color reception abilities are based on independant receptors for these three colors).
• Another method is to use isolines. Of course only one 1-dimensional parameter can be shown with this method without confusion, FUZZEKS allows e.g. to show the values with membership value 1, which is the most possible value. This would be the 4 in the above example.
• A third method is to reduce the dimensionality of the space that should be displayed. FUZZEKS allows to show the values for a cut (section) through the 2-dimensional space, which reduces the space dimensionality of the result by 1.
It is also possible to view the value for every single point. This function delivers a graphical representation similar to the example at the beginning of this page.

In order to control the display of the result various topics must be taken into account: