| closure {sets} | R Documentation |
Closure and reduction
Description
Closure and reduction of (g)sets.
Usage
## S3 method for class 'set'
closure(x, operation = c("union", "intersection"), ...)
binary_closure(x, operation = c("union", "intersection"))
## S3 method for class 'set'
reduction(x, operation = c("union", "intersection"), ...)
binary_reduction(x, operation = c("union", "intersection"))
Arguments
x |
For |
operation |
The set operation under which the closure or reduction shall be computed. |
... |
Currently not used. |
Details
The closure of a set S under some operation OP
contains all elements
of S, and the results of OP applied to all element pairs
of S.
The reduction of a set S under some operation OP
is the minimal subset
of S having the same closure than S under OP.
Note that the closure and reduction methods for sets are currently only implemented for sets of (g)sets (families) and will give an error for other cases.
binary_closure and binary_reduction
interface efficient C code for computing
closures and reductions of binary patterns.
They are used by the
high-level methods if x contains only objects of class sets.
Value
An object of same type than x.
Author(s)
The C code for binary closures is provided by Christian Buchta.
See Also
Examples
## ordinary set
s <- set(set(1),set(2),set(3))
(cl <- closure(s))
(re <- reduction(cl))
stopifnot(s == re)
(cl <- closure(s, "intersection"))
(re <- reduction(cl, "intersection"))
stopifnot(s == re)
## multi set
s <- set(gset(1,1),gset(2,2),gset(3,3))
(cl <- closure(s))
(re <- reduction(cl))
stopifnot(s == re)
## fuzzy set
s <- set(gset(1,1/3),gset(2,2/3),gset(3,3/3))
(cl <- closure(s))
(re <- reduction(cl))
stopifnot(s == re)
## fuzzy multiset
s <- set(gset(1,list(set(1,0.8))), gset(2, list(gset(1,3))), gset(3,0.3))
(cl <- closure(s))
(re <- reduction(cl))
stopifnot(s == re)