Incomplete Information: Rough Set Analysis
Incomplete Information: Rough Set Analysis
Digital Image Processing
Generalizing Graphs Using Amalgamation and Selection
SSD '99 Proceedings of the 6th International Symposium on Advances in Spatial Databases
The Algebraic Structure of Sets of Regions
COSIT '97 Proceedings of the International Conference on Spatial Information Theory: A Theoretical Basis for GIS
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
International Journal of Approximate Reasoning
To be and not to be: 3-valued relations on graphs
COSIT'09 Proceedings of the 9th international conference on Spatial information theory
Relational granularity for hypergraphs
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Granular description of qualitative change
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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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.