GRASS GIS manual: r.fuzzy.logic

NAME

r.fuzzy.logic - xxxx

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] [--verbose] [--quiet]

Flags:

--overwrite: Allow output files to overwrite existing files
--verbose: Verbose module output
--quiet: Quiet module output

Parameters:

xmap=name: x operand (membership map)
ymap=name: y operand (membership map)
output=name: 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

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.

xmap

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 opeartor. There are three operations: fuzzy complements, fuzzy intersections, and fuzzy unions. Addational 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 ussualy 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 logial 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. Multivalued operations will be availabel in the future. 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

REFERENCES

Zadeh, L.A. (1965). "Fuzzy sets". Information and Control 8 (3): 338–353. doi:10.1016/S0019-9958(65)90241-X. ISSN 0019-9958.

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. URL http://www.jstatsoft.org/v31/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

Last changed: $Date$

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