violations {relations}

Violations of Relation Properties

Description

Computes a measure of remoteness of a relation from a specified property.

Usage

relation_violations(x,
                    property =
                    c("complete", "match",
                      "reflexive", "irreflexive", "coreflexive",
                      "symmetric", "antisymmetric", "asymmetric",
                      "transitive", "negatively_transitive",
                      "Ferrers", "semitransitive",
                      "trichotomous",
                      "Euclidean"),
                    tuples = FALSE,
                    na.rm = FALSE)

Arguments

x

an endorelation.

property

a character string specifying one of the properties for which the number of violations can be computed.

tuples

a logical indicating whether to return the amount of violations (default), or the tuples for which the property is violated.

na.rm

a logical indicating whether to remove tuples for which the property information is not available (due to missing memberships).

Value

If tuples is false (default), the amount of violations for the specified property: for crisp relations, the minimum number of object tuples involved in the definition of the property (e.g., singletons for reflexivity, pairs for antisymmetry, and triples for transitivity) that must be modified/added/removed to make the relation satisfy the property.

If tuples is true, a set of tuples of objects for which the respective property is violated.

See Also

predicates for the definitions of the properties.

Examples

## partial order:
R <- as.relation(1:3)
relation_incidence(R)
## R clearly is transitive, but not symmetric:
relation_violations(R, "transitive")
relation_violations(R, "symmetric")
## Pairs for which symmetry is violated:
relation_violations(R, "symmetric", TRUE)

## create a simple relation:
require("sets")				# set(), pair() etc.
R <- relation(domain = letters[1:2],
              graph = set(pair("a","b"), pair("b","a")))
relation_incidence(R)
## R is clearly symmetric, but not antisymmetric:
relation_violations(R, "symmetric")
relation_violations(R, "antisymmetric")