Abstract: 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.

Key words: Lattice, Concept lattice, Concept algebra, Concept representation, Cognitive informatics