基于概念复合的对偶三支概念格及其概念约简  

Dual Three-way Concept Lattice Based on Composition of Concepts and Its Concept Reduction

作　　者：刘津 米据生[1,2] 李仲玲[1,2,3] 李美争[4] LIU Jin;MI Jusheng;LI Zhongling;LI Meizheng(College of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang 050024,China;HuiHua College of Hebei Normal University,Shijiazhuang 050024,China;College of Computer and Cyberspace Security,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,石家庄050024 [2]河北省计算数学与应用重点实验室(河北师范大学),石家庄050024 [3]河北师范大学汇华学院,石家庄050024 [4]河北师范大学计算机与网络空间安全学院,石家庄050024

出　　处：《计算机科学》2023年第6期122-130,共9页Computer Science

基　　金：国家自然科学基金(62076088,12101182,61502144);河北省高等学校科学技术研究项目(BJ2019014);河北省研究生创新资助项目(CXZZBS2022068)。

摘　　要：三支概念格通过正负算子相结合,既表示出了共同拥有的信息,又表示出了共同不拥有的信息,是对经典概念格的扩展。但在处理一些实际问题时,人们也会从反向出发,考虑集合的补集可能不拥有的信息和可能拥有的信息,对偶三支概念格应运而生。文中提出了一种基于形式背景的对偶概念及其补背景中对偶概念的复合来构造对偶三支概念格的方法,经验证,通过概念复合方法得到的对偶三支概念与通过对偶三支算子得到的概念相同。进一步讨论了基于可辨识矩阵求解对偶三支概念格的属性约简方法,并借助此思想,给出了基于概念可辨识矩阵的对偶三支概念约简方法。Three-way concept lattice not only represents the information jointly owned,but also represents the information that is not owned by each other by combining positive operators and negative operators.It is an extension of the classical concept lattice.However,when dealing with some practical problems,we sometimes start from the reverse,considering the information that the complementary sets may not have and the information that they may have,so the dual three-way concept lattice came into being.In this paper,a novel method to construct dual three-way concept lattices based on the composition of dual concepts in formal context and its complementary context is proposed.It is proved that the dual three-way concepts obtained by concepts composition are the same as those obtained by dual three-way operators.Then,we discuss the attribute reduction method of dual three-way concept lattices based on discernibility matrices.With the help of this idea,this paper proposes an approach to reducing the dual three-way concepts based on concept discernibility matrices.

关 键 词：概念格 对偶三支概念 属性约简 概念约简 辨识矩阵 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]