Research on a Union Algorithm of Multiple Concept Lattices

Abstract

Concept lattice has played an important role in data mining and data processing. The paper gives definitions of same-field contexts, consistent contexts, same-field concept lattices, and consistent concept lattices, provides definitions of the addition operation of two same-field and consistent contexts as well as the union operation of two same-field and consistent concept lattices, and proves that the two operations above are isomorphic and satisfy other interesting mathematical properties, such as commutative and associative laws as well as having left and right identity elements. According to the definitions and properties of the union operation, a union algorithm of multiple concept lattices is deduced, in which some heuristic knowledge from order relation of the concepts is used, so the time efficiency of the algorithm can be improved. Experiments show that using the algorithm to merge two concept lattices distributed on different sites into one is evidently superior to the method of using Gordin’s algorithm to insert the objects of the formal context corresponding to second concept lattice one by one into the first lattice. Evidently, the algorithm provided in the paper is an effective parallel algorithm to construct concept lattice.