multiplex (version 3.7)

partial.order: The Partial Order of String Relations or of Galois Derivations

Description

Construct the partial order table of unique relations of the semigroup, or else of the concepts produced by Galois derivations.

Usage

partial.order(x, type = c("strings", "galois", "pi.rels"), lbs, sel, 
              po.incl, dichot)

Value

An object of ‘Partial.Order’ class with the partial order table in a matrix form.

Arguments

x

an object of a ‘Strings’ or a ‘Galois’ class

type

whether the object corresponds to

• strings for string relations

• galois for Galois derivations

• pi.rels for \(\pi\)-relations

lbs

(optional) the labels of the unique relations

sel

(optional) selected elements in x for the partial order

po.incl

(optional, works only with type pi.rels) should the partial order in the \(\pi\)-relations be included

dichot

(optional) should the string relations in x be dichotomized?

Author

Antonio Rivero Ostoic

Details

To get the partial order of an entire semigroup, both generators and compound relations must be considered. This information and the labels of the unique relations are given by the strings function. cf. semigroup to see how the x should be specified properly.

Galois derivations are now possible to be partially ordered as well, and this option is based on the output given by the galois function.

References

Pattison, P.E. Algebraic Models for Social Networks. Cambridge University Press. 1993.

Ganter, B. and R. Wille Formal Concept Analysis -- Mathematical Foundations. Springer. 1996.

See Also

as.strings, strings, galois, perm, diagram, fltr.

Examples

# load the data to obtain its partial order
data("incubA")

# strings in the structure and partial order
strings(incubA$IM) |> 
  partial.order()