Rough Semiconcept Analysis for Gray Interval Data in Incomplete Formal Contexts

In recent years, semiconcept analysis and rough set theory have become important theoretical tools for knowledge representation and uncertain information processing. However, existing semiconcept models have limited ability to characterize conceptual structures involving both roughness and gray interval information. To address this issue, this paper combines the basic ideas of semiconcept analysis and rough set theory to propose rough semiconcept analysis. Based on this, this paper introduces gray numbers and grayness degrees to address concept lattice construction for gray interval data in rough semiconcept analysis. A gray rough semiconcept analysis model is then developed within a gray formal context. We propose the corresponding gray rough semiconcept lattices, and then systematically investigate their properties. The effectiveness and feasibility of the proposed model are verified via an illustrative example. This study broadens the scope of rough semiconcept analysis by incorporating gray interval information and offers a new perspective for understanding uncertain conceptual structures.