Concept Granular System and Granular Concept Lattice

Abstract

This paper, based on the authorpsilas new model of granular computing--the theory of granular set, puts forward the concept of granular family, granular system, concept granular system, granular concept, through upgrading the mapping to the power set and mapping from one-way to two-way. And, they are described respectively, the concept of which is the description of concept granular system in the form of five-tuple array, that is, (U, D, L, H, J), where U is the universe of the problem discussed, D describes all the elements in U, L is the operator from 2U to 2D, H is the operator from 2D to 2U, and J restricts the L and H, its restrict form goes as follows: .From this model, some basic mathematical laws of the concept granular system are given, it proves that all of the granular concepts constitute a complete lattice - concept granular lattice, thus extending the granular set theory and improving the granular set theory.