AFS Structures and Concept Lattices
Formal concept analysis has been discussed for decades, some new concept structures are formulated and studied. In order to cope with the data and fuzzy objects, AFS theory was proposed by Xiaodong Liu (Journal of Mathematical Analysis and Applications, vol. 217, 1998, Fuzzy Sets and Systems, vol.95, 1998). In this paper, first we define the product, semi-product and direct sum of AFS algebra. Then we prove that the product, semi-product and direct sum in concept lattice are only the special cases of the ones in AFS algebra. Thus we pave the theoretical ways to discuss the concept lattices with AFS theory