r.fuzzy.set - GRASS GIS manual

NAME

r.fuzzy.set - Calculate membership value of any raster map according to a user's rules.

KEYWORDS

SYNOPSIS

r.fuzzy.set

r.fuzzy.set --help

r.fuzzy.set input=name output=name points=string[,string,...] [side=string] [boundary=string] [shape=float] [height=float] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

Flags:

--overwrite: Allow output files to overwrite existing files
--help: Print usage summary
--verbose: Verbose module output
--quiet: Quiet module output
--ui: Force launching GUI dialog

Parameters:

input=name [required]: Raster map to be fuzzified
output=name [required]: Membership map
points=string[,string,...] [required]: Inflection points: a,b[,c,d]; Default: a,b[,c,d]
side=string: Fuzzy range; Options: both, left, right; Default: both
boundary=string: Type of fuzzy boundaries; Options: Linear, S-shaped, J-shaped, G-shaped; Default: S-shaped
shape=float: Shape modifier: -1 to 1; Options: -1-1; Default: 0.
height=float: Membership height: 0 to 1; Options: 0-1; Default: 1.

OPTIONS
OUTPUTS
FUZZY SET PARAMETERS
DESCRIPTION
NOTES
SEE ALSO
REFERENCES
AUTHOR

OPTIONS

input: Name of input raster map to be fuzzified. This map may be of any type and may require null values.
points: A list containing 4 (A,B,C,D) or 2 (A,B) points defining set boundaries as defined in Figure 1. Points do not have to be in map range, but this may lead to only 0 or 1 membership for the whole map. For side parameter "both", range between A and D defines base, and the range between B and C defines the core of the fuzzy set. Between A and B and between C and D are the set's boundaries. If side is "both", points requires 4 points, or else 2 points.

Figure 1: Fuzzy set definition
side: This option indicates if set is fuzzified of both sides (both), left or right side. See description for details.

OUTPUTS

output: Map containing membership value of original map. Map is always of type FCELLS and contains values from 0 (no membership) to 1 (full membership). Values between 0 and 1 indicate partial membership

FUZZY SET PARAMETERS

boundary: Defines the shape of the fuzzy boundary. The default and most popular is S-shaped. Linear, J-shaped and G-shaped boundaries are also available. The same boundaries are applied to the both sides. The available options are illustrated in Figure 2.

Figure 2: Boundary definition for boundary parameter values "Linear", "S-shaped", "G-shaped", and "J-shaped".
shape: Optional shape modifier. Range from -1 to 1. The default value is 0 and should not be changed in most of the time. The negative values indicate more dilatant set, the positive values more concentrate set. See NOTES for details.

Figure 3: Impact of shape parameter on shape boundary
height: Optional height modifier. Range from 0 to 1. The default value is 1 and indicates full membership. If height is less than one, the maximum membership is equal to height. See Figure 1: Fuzzy set definition.

DESCRIPTION

Definition of fuzzy set

Fuzzy sets are sets whose elements have degrees of membership. Zadeh (1965) introduced fuzzy sets as an extension of the classical notion of sets. Classical membership of elements in a set are binary terms: an element either belongs or does not belong to the set. Fuzzy set theory use the gradual assessment of the membership of elements in a set. A membership function is valued in the real unit interval [0, 1]. Classical sets are special cases of the membership functions of fuzzy sets, if the latter only takes values 0 or 1. Classical sets are in fuzzy set theory usually called crisp sets. Fuzzy set theory can be used in a wide range of domains in which information is imprecise, including many GIS operations.

NOTES

Calculation of boundary shape

Depending on type of the boundary, different equations are used to determine its shape:

Linear: the membership is calculated according following equation:


value  <=  A -> x = 0
A < value > B -> x = (value-A)/(B-A)
B <= value >= C -> x = 1
C < value > D -> x = (D-value)/(D-C)
value >= D -> x = 0

where x: membership

S-shaped: the membership is calculated according following equation:


sin(x * Pi/2)^m (for positive shape parameter)
1-cos(x * Pi/2)^m (for negative shape parameter)

where x: membership, and
m = 2^exp(2 * |shape|)
For default shape=0, m = 2 (most common parameter for that equation).

G-shaped: the membership is calculated according following equation:


tan(x * Pi/4)^1/m

where x: membership, and
m = 2^exp(-2 * shape) (for negative shape parameter)
m = 2^(1-shape) (for positive shape parameter)
For default shape=0, m = 2 (most common parameter for that equation).

J shaped: it uses following equations:


tan(x * Pi/4)^m

where x: membership, and
m = 2^exp(2 * shape) (for positive shape parameter)
m = 2^(1+shape) (for negative shape parameter)
For default shape=0, m = 2 (most common parameter for that equation).

REFERENCES

Jasiewicz, J. (2011). A new GRASS GIS fuzzy inference system for massive data analysis. Computers & Geosciences (37) 1525-1531. DOI https://doi.org/10.1016/j.cageo.2010.09.008
Zadeh, L.A. (1965). "Fuzzy sets". Information and Control 8 (3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.
Novák, Vilém (1989). Fuzzy Sets and Their Applications. Bristol: Adam Hilger. ISBN 0-85274-583-4.
Klir, George J.; Yuan, Bo (1995). Fuzzy sets and fuzzy logic: theory and applications. Upper Saddle River, NJ: Prentice Hall PTR. ISBN 0-13-101171-5.
Klir, George J.; St Clair, Ute H.; Yuan, Bo (1997). Fuzzy set theory: foundations and applications. Englewood Cliffs, NJ: Prentice Hall. ISBN 0133410587.
Meyer D, Hornik K (2009a). Generalized and Customizable Sets in R. Journal of Statistical Software, 31(2), 1-27. DOI https://doi.org/10.18637/jss.v031.i02
Meyer D, Hornik K (2009b). sets: Sets, Generalized Sets, and Customizable Sets. R~package version~1.0, URL https://cran.r-project.org/package=sets.

AUTHOR

Jarek Jasiewicz

SOURCE CODE

Available at: r.fuzzy.set source code (history)

Latest change: Sunday Aug 17 09:42:07 2025 in commit: aaa98676c0950081a9d07c628b519a4300fedd44