A necessary and sufficient condition for two relations to induce the
  same definable set family
  In Pawlak rough sets, the structure of the definable set families is simple
and clear, but in generalizing rough sets, the structure of the definable set
families is a bit more complex. There has been much research work focusing on
this topic. However, as a fundamental issue in relation based rough sets, under
what condition two relations induce the same definable set family has not been
discussed. In this paper, based on the concept of the closure of relations, we
present a necessary and sufficient condition for two relations to induce the
same definable set family.
