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In the design of mathematical methods for a medical problem, one of the kernel issues is the identification of symptoms and measures that could help in the diagnosis. Discovering connections among them constitute a big challenge because it allows to reduce the number of parameters to be considered in the mathematical model. In this work, we focus on formal concept analysis as a very promising technique to address this problem. In previous works, we have studied the use of formal concept analysis to manage attribute implications. In this work, we propose to extend the knowledge that we can extract from every context using positive and negative information, which constitutes an open problem. Based on the main classical algorithms, we propose new methods to generate the lattice concept with positive and negative information to be used as a kind of map of attribute connections. We also compare them in an experiment built with datasets from the UCI repository for machine learning. We finally apply the mining techniques to extract the knowledge contained in a real data set containing information about patients suffering breast cancer. The result obtained have been contrasted with medical scientists to illustrate the benefits of our proposal.

The field of application of closure systems goes from theoretical areas as algebra or geometry to practical areas as databases and artificial intelligence. In these practical areas, a kind of constraint named functional dependencies have an important role. Given a set of attributes X and a set of functional dependencies Γ, the computation of the closure of X for Γ, denoted as X + is abundantly used in artificial intelligence and database literature and is one of the key points in many problems: knowledge compilation, redundant constraint elimination, query optimization, the finding key problem, etc. We outline the main classical closure algorithms and we compare them with a novel algorithm named SL F D -Closure. We show an empirical study with the execution of the closure algorithms, and we establish that SL F D -Closure is the fastest.