Formal Concept Analysis has proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notions of attribute continuous formal context and continuous formal concept are introduced by considering a selection F of fnite subsets of attributes. Our decision of a selection F relies on a kind of generalized interior operators. It is shown that the set of continuous formal concepts forms a continuous domain, and every continuous domain can be obtained in this way. Moreover, an notion of F-morphism is also identified to produce a category equivalent to that of continuous domains with Scott-continuous functions. This paper also consider the representations of various subclasses of continuous domains such as algebraic domains, bounded complete domains and stably continuous semilattices. These results explore the fundamental idea of domain theory in Formal Concept Analysis from a categorical viewpoint.
A General Theory of Concept Lattice (II): Tractable Lattice Construction and Implication Extraction
As the second part of the treatise 'A General Theory of Concept Lattice', this paper speaks of the tractability of the general concept lattice for both its lattice structure and logic content. The general concept lattice permits a feasible construction that can be completed in a single scan of the formal context, though the conventional formal-concept lattice and rough-set lattice can be regained from the general concept lattice. The logic implication deducible from the general concept lattice takes the form of μ_1 { \rightarrow } μ_2 where μ_1,μ_2 { \in } M^{ \ast } are composite attributes o…
Non-monotonic Extensions to Formal Concept Analysis via Object Preferences
University of Cape Town（开普敦大学）；CAIR, South Africa（南非计算与推理研究所）；Technische Universität Dresden（德累斯顿工业大学）；Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig（德累斯顿/莱比锡可扩展数据分析与人工智能中心）
A General Theory of Concept Lattice (I): Emergence of General Concept Lattice
作为《概念格的一般理论》（A General Theory of Concept Lattice，I-V）论文的第一部分，本文针对对象的属性范畴化问题，建立了一般概念格。与传统的方法，如形式概念格和粗糙集格，一般概念格的设计，坚持的一般原则，即信息内容应该是不变的，无论如何变量/参数的。在这里，我们将通过与传统格结构兼容的一系列实现来明确地证明这种构造的存在。广义概念格可以根据对象类所具有的属性对它们进行全面的分类。结果表明，从一般概念格出发，可以得到形式概念格和粗糙集格。
INSA Centre Val de Loire（卢瓦尔河谷国立应用科学学院）；Univ. Orléans（奥尔良大学）；Technion（以色列理工学院）；VU School of Business and Economics（阿姆斯特丹自由大学商学院与经济学院）；University of Johannesburg（约翰内斯堡大学）；Amsterdam Business School（阿姆斯特丹商学院）；College of Business and Economics（商学院与经济学院）
