A first fuzzy relation to be composed. It must be a numeric matrix with values within the
[0,1] interval. The number of columns must match with the number of rows of the
y matrix.
y
A second fuzzy relation to be composed. It must be a numeric matrix with values within the
[0,1] interval. The number of columns must match with the number of rows of the
x matrix.
e
An excluding fuzzy relation. (EXPERIMENTAL FEATURE!)
If not NULL, it must be a numeric matrix with dimensions equal to the y matrix.
alg
An algebra to be used for composition. It must be one of 'goedel' (default),
'goguen', or 'lukasiewicz'.
type
A type of a composition to be performed. It must be one of 'basic' (default),
'sub', 'super', or 'square'.
quantifier
If not NULL, it must be a function taking a single argument, a vector of relative
cardinalities, that would be translated into membership degrees.
Details
Function composes a fuzzy relation x (i.e. a numeric matrix of size (u,v))
with a fuzzy relation y (i.e. a numeric matrix of size (v,w)) and possibly with the
use of an exclusion fuzzy relation e (i.e. a numeric matrix of size (v,w)).
The style of composition is determined by the algebra alg, the composition type
type, and possibly also by a quantifier.
Value
A matrix with v rows and w columns, where v is the number of rows of x
and w is the number of columns of y.