Open AccessThe Models of Granular System and Algebraic Quotient Space in Granular Computing
Author(s) -
Chen Linshu,
Wang Jiayang,
Li Li
Publication year - 2016
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2016.08.001
Subject(s) - granular computing , quotient space (topology) , quotient , congruence relation , mathematics , equivalence relation , algebra over a field , algebraic number , theoretical computer science , computer science , pure mathematics , rough set , mathematical analysis , artificial intelligence
Granular computing (GrC) 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 GrC.