**--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): 338–353. .
- 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 http://CRAN.R-project.org/package=sets.

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

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