FCA中的互补概念及其性质与生成

Complementary concepts and their properties and generation in FCA

在形式概念分析中,概念格上的偏序关系刻画了概念间的泛化和特化关系,而概念格中不可比概念之间也存在着值得研究的特定语义信息。受此启发,提出互补概念这一定义并给出其形式化描述。首先,通过给定两个对象子集关于某个特定属性子集互补程度的描述,根据不同实际需求分别定义强、弱互补关系。在此基础上,研究互补概念及相关性质,并在不同语义背景下探究最优强互补概念和最优弱互补概念,给出相应生成算法。最后,通过实例说明所研究内容的合理性与可适用性。

In formal concept analysis,partial order relation of concept lattice describes generalization and specialization between concepts.There also exists some specific semantic information that is worth studying between incomparable concepts.Inspired by this,complementary concepts are studied in this paper.Firstly,the complementary degree of two object subsets is described by considering a specific attribute subset in formal context,based on which the strong and weak complementary relations are defined according to different actual needs.Further,the complementary concepts and their related properties are studied,and the optimal strong complementary concept and optimal weak complementary concept are explored under different semantics,and the corresponding algorithms are also given.Finally,examples are presented given to illustrate the rationality and applicability of the content of this paper.