rel_irreflexive: Irreflexive Binary Relations

In Rexamine/agop: Aggregation Operators and Preordered Sets

Irreflexive Binary Relations

Description

A binary relation R is irreflexive (or antireflexive), iff for all x we have \neg xRx.

Usage

rel_is_irreflexive(R)

Arguments

R	an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set.

Details

rel_is_irreflexive finds out if a given binary relation is irreflexive. The function just checks whether all elements on the diagonal of R are zeros, i.e., it has O(n) time complexity, where n is the number of rows in R. Missing values on the diagonal may result in NA.

When dealing with a graph's loops, i.e., elements related to themselves, you may be interested in finding a reflexive closure, see rel_closure_reflexive, or a reflexive reduction, see rel_reduction_reflexive.

Value

rel_is_irreflexive returns a single logical value.

See Also

Other binary_relations: check_comonotonicity(), pord_nd(), pord_spread(), pord_weakdom(), rel_graph(), rel_is_antisymmetric(), rel_is_asymmetric(), rel_is_cyclic(), rel_is_reflexive(), rel_is_symmetric(), rel_is_total(), rel_is_transitive(), rel_reduction_hasse()

Rexamine/agop documentation built on Dec. 11, 2023, 10:02 p.m.