Clonal sets of a binary relation
Lemnaouar Zedam, Raúl Pérez‐Fernández, Hassane Bouremel, Bernard De Baets · International Journal of General Systems · 2018
In a recent paper, we have introduced the notion of clone relation of a given binary relation. Intuitively, two elements are said to be “clones” if they are related in the same way w.r.t. every other element. In this paper, we generalize this notion from pairs of elements to sets of elements of any cardinality, resulting in the introduction of clonal sets. We investigate the most important properties of clonal sets, paying particular attention to the introduction of the clonal closure operator, to the analysis of the (lattice) structure of the set of clonal sets and to a distance metric expressing how close two elements are to being clones.