A method for obtaining transitive approximations of a binary relation

Abstract

A binary relation R does not always possess the desirable property of transitivity. Consequently, this needs to be imposed artificially by deviating as little as possible from R. In this paper, three approaches to transitive approximation are analyzed within a common distance-based framework: exterior (transitive closure), interior (openings or maximal transitive sub-relations contained in R) and mixed (transitive fittings) approximation. Additionally, we propose a method for obtaining all these transitive approximations. The method is based on a distance function optimization framework that leads to straightforward goal programming models.

On transitive subrelations of binary relations

“…Existing work on transitive subrelations has focused on constructing maximal transitive subrelations of relations on finite sets [FR95,GPR08,Heu69]. Our work here, of course, is concerned solely with relations on infinite sets.…”