A categorical representation of algebraic domains based on variations of rough approximable concepts

In this paper, we propose two variations of rough approximable concepts and investigate the order-theoretic properties of the associated concept hierarchies. We first show that every rough pseudo-concept hierarchy is a completely distributive lattice and its completely compact elements are exactly the rough pseudo-concepts generated from individual attributes. Next, we propose the notions of hyper-contexts and hyper-concepts, and prove that they provide an approach to restructuring algebraic domains. Finally, we set hyper-contexts into a category in which hyper-mappings serve as the morphisms. It turns out that this category is precisely equivalent to that of algebraic domains.