r.fuzzy.logic - GRASS GIS manual

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.

NAME

r.fuzzy.logic - Performs logical operations on membership images created with r.fuzzy.set or different method. Use families for fuzzy logic.

KEYWORDS

raster, fuzzy logic

SYNOPSIS

r.fuzzy.logic

r.fuzzy.logic --help

r.fuzzy.logic xmap=name [ymap=name] output=name [operator=string] [family=string] [--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:

xmap=name [required]: x operand (membership map)
ymap=name: y operand (membership map)
output=name [required]: Resulting map
operator=string: Fuzzy logic operation; Options: AND, OR, NOT, IMP; Default: AND
family=string: Fuzzy logic family; Options: Zadeh, product, drastic, Lukasiewicz, Fodor, Hamacher; Default: Zadeh

OPTIONS
OUTPUTS
SEE ALSO
REFERENCES
AUTHOR

OPTIONS

xmap

Name of input x membership operand. This map must be of type FCELL with range 0 :1 and may require null values. Otherwise program will print error message and stops.

ymap

Name of input y membership operand. This map must be of type FCELL with range 0 :1 and may require null values. Otherwise program will print error message and stops. This map is optional bit is required for all operation except NOT

operator

A fuzzy set operators are generalization of crisp operators. There is more than one possible generalization of every operator. There are three operations: fuzzy complements, fuzzy intersections, and fuzzy unions. Additional implication operator is also provided.

fuzzy intersection (AND) use T-norm of given family for calculation;
fuzzy union (OR) use T-conorm of given family for calculation;
fuzzy complement (NOT) fuzzy negation usually 1-x;
fuzzy implication (IMP) use residuum of given family if available;

family

T-norms, T-conorms and residuals are a generalization of the two-valued logical conjunction, disjunction and implication used by boolean logic, for fuzzy logics. Because there is more than one possible generalisation of logical operations, r.fuzzy.logic provides 6 most popular families for fuzzy operations:

Zadeh with minimum (Godel) t-norm and maximum T-conorm;
product with product T-norm and probabilistic sum as T-conorm;
drastic with drastic T-norm and drastic T-conorm;
Łukasiewicz with Łukasiewicz T-norm and bounded sum as a T-conorm;
Fodor with nilpotent minimum as T-norm and nilpotent maximum as T-conorm;
Hamacher (simplified) with Hamacher product as T-norm and Einstein sum as T-conorm;

There is no residuum for drastic and Hamacher families. For more details see Meyer D, Hornik K (2009); T-norms;

OUTPUTS

output: Map containing result of two-values operations. Map is always of type FCELL and contains values from 0 (no membership) to 1 (full membership). Values between 0 and 1 indicate partial membership

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. . ISSN 0019-9958.
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.

AUTHOR

Jarek Jasiewicz

SOURCE CODE

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

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