## Main parameters

### The border

The border is a polygon used to limit the processed area. Only data points within the border are processed.

If `NULL`

the Convex Hull polygon of the input dataset
will be used (computed with st_convex_hull
function of the sf R
package).

An object of class SpatialPolygons can be used as border:

### The neighborhood

The neighborhood relation can be filtered by a minimal common edge length.

If `NULL`

all contiguous Voronoi polygons are considered
as neighbors:

The user can define the minimum edge length (in the same unit as the input dataset coordinate system) shared by two Voronoi polygons for being considered as neighbors:

#### Show the neighborhood relations

The red lines shows the pairs of Voronoi polygons that are no longer considered as neighbors.

### Attribute distance

This distance function is used for a given attribute. It computes the
distance between two data points in the monodimensional attribute space.
As many distance functions as there are attributes in the zonable
dataset are needed (in a list if multiple attributes).

Two
univariate distances are available: `EuclideanDistance`

(the
default) or `FuzzyDistance`

. Or `NULL`

if the
attribute should not be used in the zoning process.

The fuzzy distance function is based on a fuzzy partition that allows
for integrating expert knowledge into distance calculations (Guillaume, Charnomordic, and Loisel 2013; Guillaume
and Charnomordic 2013). The partition must be a standardized
fuzzy partition based on a `FisIn`

object of the FisPro R
package.

The following command-line sets the fuzzy distance based on 3
Mfs-partition defined by the following breakpoints: 20, 30, 100. The
range of the `conduct`

attribute is [12, 116]:

The default value, used in this example, is the euclidean distance:

### Zone distance aggregation

To compute the distance between two zones, all the data points included in the two zones are considered and the aggregation is done using the aggreg parameter:

\[ d(z_i,z_j) = (Aggreg) d(x,y), \forall x
\in z_i, y \in z_j\] Three aggreg operators are available:
`MinimumDistance`

, `MaximumDistance`

(the default)
or `MeanDistance`

.

The two zones to be merged at a given
iteration are the ones for which the zone distance is minimum.

### Combine distance

The combination function distance is needed when the zoning is done
according to several attributes. In this case, each univariate or
elementary distance is computed and normalized in a unit interval. These
partial distances are then aggregated to yield the distance between two
data points in the multidimensional attribute space. The distance
combination is done before computing the between-zones distance.

Two
combinations are proposed: `EuclideanDistance`

(the default)
or `MinkowskiDistance`

.

### Smallest zone

This criterion is used to determine the smallest size for a zone
(number of points or area) to be kept in the final map. The zones with a
size less than the threshold are included in the most compatible
neighboring zone.

The two available parameters are:
`ZoneSize`

or `ZoneArea`

.

The default value is
`ZoneSize`

with 1 point.