Define Fuzzy Membership

Membership of data in a fuzzy set is defined using values in the range [0,1]. A value of 1 indicates full membership in the set. In Arc-SDM, fuzzy membership values are written to the attribute table of the data set they are defining.

  1. If you want to use data contained in other tables to guide the process of defining membership values, join the table(s) to the grid attribute theme.
  2. Select 'Define Fuzzy Membership...' from the SDM menu. This displays a wizard dialog box. You can return to previous panels of the dialog at any time to verify and/or revise entries.


  1. Select the integer grid theme for which you want to define fuzzy membership values. The first active grid theme will be selected by default.
  2. Select the field that contains the (class) values for which you want to define fuzzy membership.
  3. Optionally, select a field to label numeric values in the field selected in the previous step.
  4. Click 'Next'.
  5. Specify a name for the new field that the fuzzy membership values will be written to. The default name is FMemshp#.
  6. Click 'Next'.
  7. Specify an integer value that defines areas of missing data. You need to define this value even if there is no missing data within the study area. Any areas of missing data will not be determined and handled until the fuzzy membership values are written to the attribute table. The fuzzy membership value for areas where data is missing is determined by taking an area weighted average of the fuzzy membership values assigned to areas of known data within the study area.

If you want to explicitly define the fuzzy membership value for areas of missing data yourself, you can edit the calculated value in the theme attribute table once the fuzzy memberships have been applied. An alternate technique is to specify a dummy value for the missing data class, that is some value that does not occur in the evidential theme. In this case, the missing data value will be available for the assignment of a fuzzy membership value.

  1. Click 'Next'.
  2. Select any additional fields containing data that may be useful as a guide to determining fuzzy membership values. Select a field by clicking on its name in the list. Select additional field by holding down the shift-key while clicking on their names. Clear the selection by clicking 'Unselect'. The values in these fields will be displayed in the interface used to define fuzzy membership.
  3. Click 'Next'.
  4. Select either 'Define values by table' or 'Define values by graph and table'. If there are more than 64 values for which you need to define fuzzy membership, the 'Define values by graph and table' option will be disabled.
  5. Click 'Next'.

Define values by table

What's in the table:

Column Heading Description
1 Value The values for which you want to define a fuzzy membership.
2 FMemshp<#> The column where fuzzy membership values are entered.
3 - n   Remaining columns are user specified, to guide the selection of fuzzy memberships.

 

To...

  
...edit a single membership value:
  1. Double-click the value in the column that you want to edit. This displays an edit dialog.
  2. Enter the new value.
  3. Click 'OK'.
...make a linear interpolation between two fuzzy membership values:
  1. Select the first value by clicking on it.
  2. Hold down the shift-key and drag the mouse to select the cells contiguous to the first value until the second value defining the interpolation is selected.
  3. Click the 'Interpolate' button.

When definition of fuzzy membership values is complete, click 'Finish'.

The values will be written to the grid theme attribute table.

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Define values by graph and table

This option allows all of the same functionality as the "table only" option, but also allows users to graphically define a relationship between the values and their fuzzy memberships.

  1. Optionally, select a field containing values to be displayed in the graph interface as a guide to defining fuzzy membership values.
  2. Click 'Next' to display the interface.

To...

  
...edit a single fuzzy membership value in the table:
  1. Double-click on the value to display an edit dialog.
  2. Enter the new value in the text entry line of the dialog.
  3. Click 'OK'. Both the table and chart will be updated.
...edit a single fuzzy membership value in the chart:
  1. Select the point to edit by:
    Clicking on or near it.
    OR
    Right-clicking on or near the point and selecting 'Select Point' from the pop-up menu.
  2. Right-click and select 'Edit point position' from the pop-up menu. The point will turn green to indicate that it is in edit mode.
  3. Left-click at the new position for the point. The point will move to the new position and the value displayed in the table will be updated.

NOTE: The points can only vary along the y-axis so even if you select a position to the right or left of the point it will maintain its position along the x-axis.

  1. Right-click and select 'Stop editing'.
...unselect one selected point: If there is only one point selected:

Right-click and select 'Unselect point' from the pop-up menu.
OR
Click on another point. This will select this point and unselect the one previously selected.

If there are two points selected:

Selecting 'Unselect point' from the pop-up menu will unselect the first of the two points that was selected.
...unselect two selected points: Right-click and select 'Unselect all' from the pop-up menu.
OR
Click on a third point. This will select that points and unselect the two previously selected points.
...select a second point: Right-click near the second point and select 'Select second point' from the pop-up menu.
OR
Hold down the shift-key and click the second point.
...apply a linear interpolation of values between two selected values: Select the points defining the minimum and maximum values of the interpolation function.

Right-click and select 'Align points between selected' from the pop-up menu. This will adjust the graph and update the values in the table.

When the definition of fuzzy memberships is complete, click 'Finish'. The values will be written to the theme's attribute table.

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