### GIS and decision support (3): a tool to create fuzzy criteria with ArcMap

In the two previous articles ( GIS
and decision support (2): the crossing of two
fuzzy criteria
, and GIS
and decision support (1): ranking with fuzzy numbers
), we have discussed examples for using fuzzy
logic to process geographic information .
It is time to get your hands dirty. This is why we put, here, at your
disposal an ArcGIS command to create a fuzzy criterion.

In a second stage (the next
article) we will discuss how to perform the
aggregation of two fuzzy criteria with another command, which we will put at

As
we have seen in the examples discussed in previous articles, the first step to
process the information as fuzzy is to transform the values of a classic attribute into a fuzzy number:

The core
is the set of elements
that wholly belong to the criterion, that is to say,
the degree of membership is worth 1.
The support is
the set of elements belonging, even very little, to the criterion,
that is to say, the degree of membership is different from 0.
The height of a fuzzy set is defined by the maximum degree
of membership. We will use 1 as default value,
but it is clear that there are situations where the maximum value of a criterion is not synonymous of maximum satisfaction (1).

ArcMap command to create a new attribute, from an existing attribute, and meeting the
criteria of a fuzzy number.

The command Fuzzy Criterion

A criterion is a numeric field of a
layer belonging to a
class of entities. The
content of this field will be transformed in
another field, numerical too, but depicting values between 0 and
1. This transformation is carried out to match
the values of the original field with a degree of satisfaction of the
criterion: 1 corresponds to total satisfaction, 0 to total dissatisfaction, the others values
being partial satisfactions.

Once
the command is installed, the button

displays the following interface:

The command works on
shapefiles (shapefiles) and geodatabases files. It
does not work on personal geodatabases (.
Mdb), the Enterprise geodatabases, and SpatiaLite
bases. This is
due to the fact that the command writes a metadata file
in the layer Workspace . This is possible with
shapefiles and geodatabases file (directory. gdb). There is no integrated protection in the command! If you try to
work with a personal geodatabase, it will work
… until crashing! (sorry …).

Transformation
methods

The window proposes five transformations of a field with
fuzzy criterion (fuzzy
number): Type1: The first corresponds, in fact, to a non-fuzzy
number, but allows the aggregation of a non-fuzzy criterion with fuzzy criteria.

The criterion is defined in an exact way. All values
different from the one input in the ” a: “
window will be set to 0.

Type2: The second allows to define a fuzzy number where only an exact value (“b:”) delivers full satisfaction. Values below “a:” and above “c:” will have zero satisfaction, while values between “a:” and “b:” and between “b:” and “c:” will correspond to values between 0 and 1. These values correspond to the value of the curve. This corresponds to an exact number with a given uncertainty.

Type3: The third allows establishing a fuzzy “threshold “. All values below ” a: ” will be zero, all values above “b:” will be equal to 1, while the values between “a:” and “b:” will have values between 0 and 1. This corresponds to the larger set than the set with a given uncertainty.

Type4: The fourth is a reversed threshold. All values below “a:” will be equal to 1, all the values above “b:” will be null , while the values between “a:” and “b:” will have values between 0 and 1. This corresponds to a smaller set than the set including some uncertainty.

Type5: The fifth method allows creating a classic fuzzy criterion. The range of values between “b:” and “c:” delivers total satisfaction and have a value equal to 1.
Values below ” a: ” and above “d:” will be excluded and will have a value equal to 0. Values between ” a: ” and “b:” as well as those between “b:” and “d:” will have values between 0 and 1. This corresponds to the typical fuzzy number, with its core and support. As we have indicated above, the default height is 1

Processing aids:
field
statistics

The
button

displays a window with the description of the fuzzy criteria included in the data layers.
The following window shows an example of metadata for a fuzzy criterion:

displays a window with the description of the fuzzy criteria included in the data layers.
The following window shows an example of metadata for a fuzzy criterion:

stored in a separate file ( .fzy ),
managed by the command .
The management of these files
is automatic. For example,
the elimination of metadata corresponding to a fuzzy
criterion if being
erased manually from the
entities class table.
On the other side, if you
move the layers in different directories or geodatabases, you will have
to move the file . FZY manually.

Available languages
+A drop
down list selects the
language to use.

Available languages:
• French ( default )
• English
• Spanish
• Vietnamese

Even if the command
is supposed to go from
one language to another without any problem , depending on the Windows version used
, it is safer to close and reopen the order
after selecting another language in the drop-down menu .

ArcGis
versions

The command can be
used with ArcGis versions between 9.2 and 10.3, and
with Windows XP , Vista W7 and W8.

(version
10.3.0.6)

The

dllcriterenombre

Tools installation

The tools are provided as . dll file together with an Access database . Copy and unzip the command file in a
permanent directory of your disc .

To
install you must go through the Customize menu -> Customize Mode
of ArcMap.
The customization window opens:

In the Commands tab , click the Add from a file button. Select the fuzzy_numberV92_103ML.dll file that you will have, beforehand, copied in a permanent directory of your local disk WITH the Text.mdb file delivered in same time. This file contains the different language versions used. It’s not very elegant, but it allows the command to operate without special adaptation with Xp , Vista, W7 and w8.
Click OK. The following message must appear indicating the installation has been completed without any problem.

Click OK. In the available Commands window you will be positioned automatically in the category NASCAcommands and you will find the available tool: Fuzzy Criterion.

In order to use it , click-drag on the command icon and drop it in an open ArcMap toolbar.

In the next article we will discuss the second
tool , which allows the
aggregation of two fuzzy criteria

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