Minimal Generators from Positive and Negative Attributes: Analysing the Knowledge Space of a Mathematics Course

Formal concept analysis is a data analysis framework based on lattice theory. In this paper, we analyse the use, inside this framework, of positive and negative (mixed) attributes of a dataset, which has proved to represent more information on the use of just positive attributes. From a theoretical point of view, in this paper we show the structure and the relationships between minimal generators of the simple and mixed concept lattices. From a practical point of view, the obtained theoretical results allow us to ensure a greater granularity in the retrieved information. Furthermore, due to the relationship between FCA and Knowledge Space theory, on a practical level, we analyse the marks of a Mathematics course to establish the knowledge structure of the course and determine the key items providing new relevant information that is not evident without the use of the proposed tools.