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Representing lattices using many-valued relations
- Source :
-
Information Sciences . Jul2009, Vol. 179 Issue 16, p2729-2739. 11p. - Publication Year :
- 2009
-
Abstract
- Abstract: This paper provides a representation theorem of lattices using many-valued relations. We show that any many-valued relation can be associated to a unique lattice which is a meet-sublattice of a product of chains. Conversely, to any lattice we can associate a many-valued relation such that its associated lattice is isomorphic to the initial one. Thereby, we obtain a representation theorem of lattices using many-valued relations. Moreover, since several many-valued relations might have the same associated lattice, we give a characterization of the minimal many-valued relation that can be associated to a lattice. We then sketch a polynomial time algorithm which computes such a minimal relation from either a lattice or an arbitrary relation. This representation presents several advantages: it is smaller than the usual binary representation; all known reconstruction algorithms working on binary relation can be used without loss of efficiency; it can be used by existing data mining processes. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00200255
- Volume :
- 179
- Issue :
- 16
- Database :
- Academic Search Index
- Journal :
- Information Sciences
- Publication Type :
- Periodical
- Accession number :
- 40635966
- Full Text :
- https://doi.org/10.1016/j.ins.2009.03.018