On 17/06/2019 7:34 p.m., Bert Gunter wrote:
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.
Right, that's a good point.
Duncan Murdoch
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 <mailto: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
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