The typical procedure for working with FUZZEKS

If you are additionally interested in aggregating parameters, you should go through this page first and then read about

• the membership functions (overview, a required preparation for composing parameters),
• opening membership function windows and
• adding compositions (the compositions yield the aggregation function).

1. Preparing a data file

• A "region" section (the bottom left, bottom right and top left corner of the area where fuzzy kriging should be performed), e.g.:
  

  region
      0    0
   1800    0
      0 1800
  

  
  
• A "cuts" section. Determination of the representation of fuzzy data in the form of fuzzy numbers. In FUZZEKS fuzzy numbers are represented by so-called level-cuts (for FUZZEKS intervals of values where the membership function value is greater the level (or equal the level if the level is 1)). As example the cuts section
  "cuts 1 0.75 0.5 0.25 0" leads to a representation of the fuzzy numbers with 5 level-cuts as can also be seen in the display of the membership function for such a fuzzy number:
  
  At least you have to choose the levels 1 and 0 as in the following example:
  

  cuts
      1    0
  

  
  
• A "parameters" section (a list of the parameters in this file, each of them occupies a single line), e.g.:
  

  parameters
      Cl_concentration
  

  
  
• A "table" section (contains the data itself, Cl_concentration entries explained below), e.g.:
  

  table
    X    Y   Cl_concentration
  
   165 1630    20
   460 1690    30
   435 1500    40
   105 1265    40
   300 1080    75
   560 1240    80/0:50-130
  1010 1600    65
  1400 1600    85
  1350 1260   130
  1510  950   175
  1710  650   150
   540  530   145/0:95-195
   225  755    90
    70  590    70
   210  130    65
   435  130   100
   930   45   105/0:55-155
  1010  275   160
  1135  175   130
  1185  360   170
  1705  415   125
  1625  160    85
   915 1270   101
  1000 1165   130
   860 1100   130
  1770 1545    85
  1135 1070   155
   705  870   145
  1190  750   220
  1055  545   210

  
  The entry 80/0:50-130 means the value is most possibly 80, but it can not be smaller than 50 or greater than 130 (which is the simplest representation of a fuzzy number in FUZZEKS and which corresponds to the levels 1 and 0 - if more levels of cuts have been defined in the cuts section, the other level-cuts would be interpolated (linear)).
  
• And at last the word end.

2. Loading the data file

As only visible result of loading an input data file (as e.g. the file that consists of the example sections above), the following contents in the management window will appear.

3. Preparing the fuzzy kriging process (and perform fuzzy kriging)

The meaning of the variogram is explained in Kriging Basics / Theoretical concepts. A description of the variogram graphics is found in Handling Variograms.
The facilities to diplay the kriging result are described in Result Display Options.

The preparation of the fuzzy kriging process must be done in two steps:

• Setting of the experimental variogram's calculation options.
• Selection of a theoretical variogram that fits the experimental variogram.

To find a proper theoretical variogram (a variogram function - described by the parameters in the edit and listbox fields - that fits the experimental variogram) should be done with care, because its quality determines the quality of the kriging results.
A detailed description for fitting the theoretical variogram can be found on the page Theoretical variogram fitting (Function types and parameters).

If you do not use the above example data you must fix a different theoretical variogram, of course.
For simple testing purposes, where the quality of the kriging result is not important, a 100% linear theoretical variogram should do (instead of this 50% gaussian and 50% spherical theoretical variogram in the above example). This variogram type has the advantage that the kriging result is independant of range, sill and nugget effect, so the values of these parameters are always sufficient. As warning there must be said that it is not a common variogram type, it is only easy to handle!

You need not to start the kriging process; it is started automatically everytime when a recalculation is needed, which guarantees that all displayed information in the kriging window fits together anytime (the status of the calculations can be seen at the top of the screen).

4. Viewing and exporting the fuzzy kriging result

The size of the result graphics (at the right side) can be changed by the buttons at the bottom right of the window (the "all"-button usually should change it to a good size).

The lettering of the isolines can be achieved by dragging an arrow in the display with the mouse and then pressing "L" (at the intersections of isolines with the arrow an inscription is placed). The dialog window "Options"/"Lettering" can change the format and size of the numbers.

After following the above instructions the display shows isolines for the most possible values (in this case, with respect to these isolines, there is no difference between the usual crisp and fuzzy kriging results). The data points are small squares for crisp input values and small triangles for the fuzzy values (and small "u"s indicate undefined values (positions where other parameters have a value or where an "undef" has been assigned in the input data file)). The fuzziness of the result (possible deviations of the results) is displayed as density of the small dots. More detailed information at Result basics / Overview and Result Display Options / Overview, where other types of result-display are also described.

The graphical result can be exported to the clipboard by selecting "Edit"/"Copy result to clipboard", an ASCII representation can be obtained by "File"/"Krige values for raster and save to ascii-file", which needs an additional inputfile, described at Export of results .