基于粒集的概念粒系统

The concept granular system based on granular set

在作者提出的粒计算新模型──粒集理论的基础上,提出了粒系统、概念粒系统和粒概念等概念,并对它们分别进行了描述,其中粒系统的描述是五元组形式,即(U,D,L,H,J).当约束J的形式为一种特殊形式,即为概念中内涵与外延间反变关系的数学描述时,(U,D,L,H,J)就是概念粒系统.由此给出了概念粒系统的一些基本数学性质,证明了全体粒概念构成一个完备格──粒概念格,同时初步探讨了形式背景与概念粒系统之间的关系,从而进一步扩充了粒集理论的内容,完善了粒集理论.

The paper, based on the author＇s new model of granular computing--the theory of granular set, put forward the conception of granular system, granular system and granular. It described those concepts respectively, of which the description of concept granular system was in the form of five-tuple array, that is, （U, D, L, H, J）. When the constraint J was a special form, that is, the mathematical description of the anti-change relationship between the connotation and extension of the concept, （ U, D, L, H, J） was the concept granular system. The model gave some basic mathematical laws of the concept granular system, and proved that all of the granular concepts constitute a complete lattice--concept granular lattice; meanwhile it discussed formal context related with the concept granular system, thus expanded and improved the granular set theory.