Depends on what you mean by "simple" of course, but suppose that:
M[i,j] & M[j,k] & M[k,n] are TRUE and M[i,k] and M[i,n] are FALSE. Then the procedure would see that M[i,k] needs to change to TRUE, but not that M[i,n] needs to also become TRUE *after* M[i,k] changes. This seems to imply that an iterative solution is necessary. One such procedure, via repeated matrix multiplication to check for and impose transitivity, appears to be suggested by this discussion: https://math.stackexchange.com/questions/228898/how-to-check-whether-a-relation-is-transitive-from-the-matrix-representation Cheers, Bert On Mon, Jun 17, 2019 at 10:29 AM Duncan Murdoch <murdoch.dun...@gmail.com> wrote: > On 17/06/2019 1:19 p.m., Duncan Murdoch wrote: > > Suppose I have a square logical matrix M which I'm thinking of as a > > relation between the row/column numbers. > > > > I can make it into a symmetric relation (i.e. M[i,j] being TRUE implies > > M[j,i] is TRUE) by the calculation > > > > M <- M | t(M) > > > > Is there a simple way to ensure transitivity, i.e. M[i,j] & M[j,k] both > > being TRUE implies M[i,k] is TRUE? > > > > The operation should only change FALSE or NA values to TRUE values; TRUE > > values should never be changed. > > I also want the changes to be minimal; changing everything to TRUE would > satisfy transitivity, but isn't useful to me. > > Duncan Murdoch > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
