Title :
Lattices from Arbitrary Relations
Author_Institution :
Sch. of Inf. Sci., Beijing Language & Culture Univ., Beijing, China
Abstract :
This paper studies relationship between lattices and relations. We show that a topology or a completely distributive lattice structure can be derived by a special mapping of sets. Applying the result to rough approximation operators, we obtain that an arbitrary binary relation can induce two completely distributive lattices. Also we consider the topological properties of binary relations.
Keywords :
set theory; topology; approximation operator; binary relation; distributive lattice; lattice structure; set mapping; topology; Approximation methods; Boolean algebra; Indexes; Lattices; Rough sets; Topology; Lattices; Relations; Rough sets; Topologies;
Conference_Titel :
Granular Computing (GrC), 2010 IEEE International Conference on
Conference_Location :
San Jose, CA
Print_ISBN :
978-1-4244-7964-1
DOI :
10.1109/GrC.2010.18
