The Models of Granular System and Algebraic Quotient Space in Granular Computing  

作　　者：CHEN Linshu WANG Jiayang LI Li 

机构地区：[1]School of Information Science and Engineering,Central South University,Changsha 410083,China [2]School of Computer Science and Engineering,Hunan University of Science and Technology,Xiangtan 411201,China [3]Harbin Institute of Technology Shenzhen Graduate School,Shenzhen 518055,China

出　　处：《Chinese Journal of Electronics》2016年第6期1109-1113,共5页电子学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.61173052);the Natural Science Foundation of Hunan Province,China(No.14JJ4007)

摘　　要：Granular computing(Gr C) is an emerging computing paradigm, and it is an umbrella term exploring multilevel granularity. we present a generic abstract mathematical model of the granular system. Supposing the inter-granule structure as an algebra, we propose the algebraic quotient space model. In this model, the granulation is based on a congruence relation and all the congruence relations on a granular system form a complete semi-order lattice, which is the theoretical basis for transformation,composition and decomposition among different granularities. The different granulation rules between the topological quotient space model and the algebraic quotient space model lead to the dissimilarity while composing granularities. A real-world case study is presented that demonstrates how the algebraic quotient space model works in the network transmission by error-correcting code. These work shows that the granular system model and the algebraic quotient space model are powerful conceptual modeling and functional specification methodologies for Gr C.Granular computing（Gr C） is an emerging computing paradigm, and it is an umbrella term exploring multilevel granularity. we present a generic abstract mathematical model of the granular system. Supposing the inter-granule structure as an algebra, we propose the algebraic quotient space model. In this model, the granulation is based on a congruence relation and all the congruence relations on a granular system form a complete semi-order lattice, which is the theoretical basis for transformation,composition and decomposition among different granularities. The different granulation rules between the topological quotient space model and the algebraic quotient space model lead to the dissimilarity while composing granularities. A real-world case study is presented that demonstrates how the algebraic quotient space model works in the network transmission by error-correcting code. These work shows that the granular system model and the algebraic quotient space model are powerful conceptual modeling and functional specification methodologies for Gr C.

关 键 词：Granular computing（GrC） Granular system Algebraic quotient space Congruence relation 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]