Simplification of Triadic Contexts and Concept Trilattices

DOI：10.11896/j.issn.1002-137X.2017.09.010

 作者 单位 E-mail 祁建军 西安电子科技大学计算机学院 西安710071 qijj@mail.xidian.edu.cn 魏玲 西北大学数学学院 西安710127

三元概念分析是对形式概念分析理论的扩展,三元背景作为其数据基础在实际生活中普遍存在。三元背景所反映的三元关系是形成概念三元格的基础,它比形式概念分析中的二元关系更复杂,因而在此基础上形成的三元概念以及概念三元格就更为复杂。对此,提出一种三元背景和概念三元格的信息简化方法,该方法将三元关系拆解为最本质的二元关系,并在保证所有二元关系不变的基础上,同时考虑三元背景的3个论域,删减其中不必要的元素,以减少数据量,简化三元背景和概念三元格的表达方式。进而,得到简化后概念三元格的一些性质以及简化前后三元概念的关系等理论结果,为进一步的算法研究与应用以及更深入的理论分析工作奠定基础。

Triadic concept analysis (TCA) is an extension of formal concept analysis (FCA).As the data foundation,the triadic contexts is commonly used in the real world.The ternary relationship shown in a triadic context is the base to forming concept trilattice,it is more complicated than binary relationship shown in a formal context.It results in intrication of triadic concepts and concept trilattices.Aiming to the information simplification of a concept trilattice,an approach to simplifying a triadic context and its concept trilattice on the basis of binary relationship was proposed,since the binary relationship is essential to some extent.The main idea is to delete the redundant elements in each universe while keeping all the binary relationship of the original triadic context.Actually,three universes of a triadic context can be considered at the same time using this method.After the simplification,we obtained some properties about the simplified concept trilattice,and we also discussed the relationship between former triadic concept and later triadic concept.These conclusions are research basis for the future algorithm research and application,also the base for the deeper theoretic study.