Note: This addon document is for an older version of GRASS GIS that will be discontinued soon. You should upgrade your GRASS GIS installation, and read the current addon manual page.

**--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

**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.*

**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.
Points do not have to be in map range, but this may lead to only 0 o 1 membership for
the whole map. For side parameter "both", range between A and D defines base,
but range between B and C core of the fuzzy set. Between A and B and C and D are
set's boundaries. If side is "both" it require 4 points, else 2 points.
### Fuzzy set definition:

**side**- Option indicates if set is fuzzified of both sides (both), left or right
side. See description for details.
### Boundary definition:

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

**boundary**- Parameter defined 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.
**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.
### 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 image: Fuzzy set definition.

**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:** it use 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 positive shape parameter)
m = 2^(1+shape) (for negative shape parameter)
where m: shape parameter.
```

For default shape parameter = 0 m is = 2 which is most common parameter for
that equation.
**G-shaped and J shaped:** it use following equations:

```
tan(x * Pi/4)^m (for J-shaped)
tan(x * Pi/4)^1/m (for G-shaped)
where x: membership, and
m = 2^exp(2,shape) (for positive shape parameter)
m = 2^(1+shape) (for negative shape parameter)
where m: shape parameter.
```

- 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): 338â353. .
- NovÃ¡k, VilÃ©m (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 http://CRAN.R-project.org/package=sets.

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

Latest change: Mon Jun 28 07:54:09 2021 in commit: 1cfc0af029a35a5d6c7dae5ca7204d0eb85dbc55

Note: This addon document is for an older version of GRASS GIS that will be discontinued soon. You should upgrade your GRASS GIS installation, and read the current addon manual page.

Main index | Raster index | Topics index | Keywords index | Graphical index | Full index

© 2003-2023 GRASS Development Team, GRASS GIS 7.8.8dev Reference Manual