0

How to define a metric on a partially ordered set especially on the power set ?

The problem I see is that some elements which are related can be managed but what about the elements which are not related.

Tutankhamun
  • 366
  • 1
    What do you want the metric to do? – Thomas Andrews Jun 13 '17 at 16:06
  • I want the metric to preserve the notion of distances between sets, in a heuristic way I find that sets which are related to each other are some sense "near" to each other but when it comes to sets which are not comparable under the order relation. – Tutankhamun Jun 14 '17 at 03:57
  • 1
    Without any further information about what you would like this metric to behave like, it is quite difficult to answer, as there are many possibilities. Extending relations to distances (not necessarily metrics, but also pseudometrics or hemimetrics) is an area of active research in computer science, see e.g. this book, this paper. – mrp Jun 15 '17 at 11:09

0 Answers0