Finite lattices and its properties

Abstract

Sub–modular functions play an important role in optimization, Matroid Theory and Geometry. These functions are considered a Boolian Algebras. Application of Latteles in information Science in based Belief functions introduced M. Garbesi. We focus on sub modular and super modular functions and establish their quantitative interpretation specially closure and kernel operators. The quantitative analysis and statical structure of observation is based on measure–theoretic aspects of set where the collection of sets is s–Algebra. The formal concept analysis developed so far by the quantitative data analyses depend on closure operators introduced by fuzzy measure and its lattice structure.