On links between mathematical morphology and rough sets

摘要

Based on the observation that rough sets and mathematical morphology are both using dual operators sharing similar properties, we investigate more closely the links existing between both the domains. We establish the equivalence between some morphological operators and rough sets defined from either a relation, or a pair of dual operators or a neighborhood system. Then we suggest some extensions using morphological thinning and thickening, and using algebraic operators. We propose to define rough functions and fuzzy rough sets using mathematical morphology on functions and fuzzy mathematical morphology.