Title :
Betweenness, Metrics and Entropies in Lattices
Author :
Simovici, Dan A.
Author_Institution :
Dept. of Comp. Sci., Univ. of Massachusetts, Boston, MA
Abstract :
We investigate a class of metrics on lattices that are compatible with the partial order defined by the lattice using the ternary relation of betweenness that can be naturally defined on a metric space. The relationships between entropy-like functions and metrics defined on lattices are studied and we show the links that exists between various properties of entropies and properties of metrics. Applications to metrics defined on the lattice of partitions of finite sets are examined.
Keywords :
Boolean algebra; entropy; lattice theory; set theory; Boolean algebra; betweenness ternary relation; entropy; entropy-like function; lattice metrics; partial ordered set; Absorption; Algebra; Biodiversity; Circuit synthesis; Data mining; Entropy; Extraterrestrial measurements; Information theory; Lattices; Multivalued logic; compatible metric; modular lattices; sub-modularity;
Conference_Titel :
Multiple Valued Logic, 2008. ISMVL 2008. 38th International Symposium on
Conference_Location :
Dallas, TX
Print_ISBN :
978-0-7695-3155-7
DOI :
10.1109/ISMVL.2008.21
