基于格结构的概念代数研究

近年来，概念格作为一种有效的概念分析、表示与应用模型，被越来越多的领域所应用。概念代数是在概念 格理论基础上提出的一种新的代数系统。目前，概念代数系统还只是雏形，很多方面的内容还需要扩展与进一步的研 究。基于格结构的概念代数研究分别对Nilsson概念代数、Wille概念代数和认知信息学中的概念代数的基本概念与 内容进行了介绍，对各方法进行了分析与比较，并证明Nilsson概念代数是一种广义概念代数，为进一步的应用与研 究提供支持。

Concept Algebra Based on Lattice

Concept lattice, as an effective model for concept analysis, representation and application,has been widely uti- lined in many fields. Based upon concept lattice, concept algebra is a newly developing algebra system which needs fur- ther enhancement and extension. We introduced and analyzed the Nilsson concept algebra, Wille concept algebra as well as concept algebra in cognitive informatics. Furthermore, this paper elaborated comparative analysis among above three theories of concept algebra. In addition, we proved that Nilsson concept algebra belongs to Wille concept algebra. The findings and conclusions of this paper lay a solid foundation for further improvements and applications of concept alge- bra.