多概念格的横向合并算法

由于概念格自身的完备性,构造概念格的时间复杂度一直是影响形式概念分析应用的主要因素.本文首先从形式背景的纵向、横向合并出发,定义了内涵独立和内涵一致的形式背景和概念格;还定义了内涵一致的形式背景、概念的横向加运算和概念格的横向并运算,并证明了横向合并的子形式背景的概念格和子背景所对应的子概念格的横向并是同构的.最后结合子概念格中概念间固有的泛化－特化关系,提出一种多概念格的横向合并算法来构造概念格.试验表明,该算法和直接用形式背景来构造概念格的算法相比,其时间复杂度有显著改善.显然,该算法适用于对概念格进行分布并行构造.

Horizontal Union Algorithm of Multiple Concept Lattices

Since the completeness of concept lattice,the time complexity of building concept lattice is a factor restricting the application of formal concept analysis.Based on the horizontal and vertical combination in formal contexts,this paper defines the independent or consistent contexts and lattices in attribute field;and also defines the horizontal addition operation between contexts or concepts and the horizontal union operation between concept lattices.In addition,we prove that the concept lattice of subcontexts horizontally combined is isomorphic to the horizontal union of sublattices of these subcontexts.Using the inherent general-special relation between concepts in sublattice,the horizontal union algorithm of multiple concept lattices to construct the concept lattice is also presented.Experimental results show that the time complexity of this algorithm is much better than that of other construction algorithm of concept lattice from whole formal context.Evidently,our algorithm is very suitable for constructing concept lattice in parallel and distributed system.