Relations in Mathematical Morphology with Applications to Graphs and Rough Sets

摘要

Rough sets have been applied in spatial information theory to construct theories of granularity - presenting information at different levels of detail. Mathematical morphology can also be seen as a framework for granularity, and the question of how rough sets relate to mathematical morphology has been raised by Bloch. This paper shows how by developing mathematical morphology in terms of relations we obtain a framework which includes the basic constructions of rough set theory as a special case. The extension of the relational framework to mathematical morphology on graphs rather than sets is explored and new operations of dilations and erosions on graphs are obtained.