trace: Traces of Endorelations

In relations: Data Structures and Algorithms for Relations

Traces of Endorelations

Description

Compute the left or right trace of an endorelation.

Usage

relation_trace(x, which)

Arguments

x	an endorelation.
which	one of "left" or "right", or a unique abbreviation thereof.

Details

Let R be a crisp endorelation. The left and right trace of R contain all pairs x, y for which z R x implies z R y for all z (left trace) or y R z implies x R z for all z (right trace), respectively. These are the largest (in the natural ordering of relations with the same domain) relations such that R * S \le R or S * R \le R, respectively (where * denotes composition). In the fuzzy case, the memberships of the traces can be defined as the infima over the corresponding fuzzy membership implications. See Chapter 2.3 in \bibcitetFodor+Roubens:1994 for more information.

References

\bibshow

Fodor+Roubens:1994

relations documentation built on March 26, 2026, 5:10 p.m.