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

## 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

Jarek Jasiewicz

## SOURCE CODE

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

Latest change: Monday Jan 30 19:52:26 2023 in commit: cac8d9d848299297977d1315b7e90cc3f7698730

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

© 2003-2023 GRASS Development Team, GRASS GIS 8.2.2dev Reference Manual