Tolerance approximation spaces
Fundamenta Informaticae - Special issue: rough sets
Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A Geometry of Approximation: Rough Set Theory Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic)
Relations in mathematical morphology with applications to graphs and rough sets
COSIT'07 Proceedings of the 8th international conference on Spatial information theory
Mathematical morphology on hypergraphs: preliminary definitions and results
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Mathematical morphology on hypergraphs, application to similarity and positive kernel
Computer Vision and Image Understanding
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A set of subsets of a set may be seen as granules that allow arbitrary subsets to be approximated in terms of these granules. In the simplest case of rough set theory, the set of granules is required to partition the underlying set, but granulations based on relations more general than equivalence relations are well-known within rough set theory. The operations of dilation and erosion from mathematical morphology, together with their converse forms, can be used to organize different techniques of granular approximation for subsets of a set with respect to an arbitrary relation. The extension of this approach to granulations of sets with structure is examined here for the case of hypergraphs. A novel notion of relation on a hypergraph is presented, and the application of these relations to a theory of granularity for hypergraphs is discussed.