Topology via logic
Logic of domains
Handbook of logic in computer science (vol. 3): semantic structures
Handbook of logic in computer science (vol. 3): semantic structures
Rough concept analysis: a synthesis of rough sets and formal concept analysis
Fundamenta Informaticae - Special issue: rough sets
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Modal-style operators in qualitative data analysis
ICDM '02 Proceedings of the 2002 IEEE International Conference on Data Mining
On definable concepts of rough set models
Information Sciences: an International Journal
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Formal concept analysis and rough set theory provide two different methods for data analysis and knowledge processing. Given a context K, one can get the concept lattice L(K) in Wille's sense and the object-oriented rough concept lattice RO-L(K) (resp., attribute-oriented RA-L(K)). We study relations of the three kinds of lattices and their properties from the domain theory point of view. The concept of definable sets is introduced. It is proved that the family Def (K) of the definable sets in set-inclusion order is a complete sublattice of RO-L(K) and is a complete field of sets under some reasonable conditions. A necessary and sufficient condition for Def (K) to be equal to RO-L(K) is given. A necessary and sufficient condition is also given for the complete distributivity of RO-L(K). We also study algebraicity of RO-L(K) and several sufficient conditions are given for RO-L(K) to be algebraic.