rel_hasse: Hasse Diagrams

In agop: Aggregation Operators and Preordered Sets

Hasse Diagrams

Description

This function computes the reflexive reduction and a kind of transitive reduction which is useful for drawing Hasse diagrams.

Usage

rel_reduction_hasse(R)

Arguments

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

Details

The input matrix R might not necessarily be acyclic/asymmetric, i.e., it may represent any totally preordered set (which induces an equivalence relation on the underlying preordered set). The implemented algorithm runs in O(n^3) time and first determines the transitive closure of R. If an irreflexive R is given, then the transitive closures of R and of the resulting matrix are identical. Moreover, if R is additionally acyclic, then this function is equivalent to rel_reduction_transitive.

Value

The rel_reduction_hasse function returns a logical square matrix. dimnames of R are preserved.

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_irreflexive(), rel_is_reflexive(), rel_is_symmetric(), rel_is_total(), rel_is_transitive()

Examples

## Not run: 
# Let ord be a total preorder (a total and transitive binary relation)
# === Plot the Hasse diagram of ord ===
# ===  requires the igraph package  ===
library("igraph")
hasse <- graph.adjacency(rel_reduction_transitive(ord))
plot(hasse, layout=layout.fruchterman.reingold(hasse, dim=2))

## End(Not run)

agop documentation built on May 29, 2024, 9:54 a.m.