Representation of approximate functional dependencies using partitions, discernibility matrix and association rules

Abstract

Approximate Functional Dependencies (AFD) and Association Rules are really meaningful knowledge in data mining. In this article, we first recall some basic concepts of rough set theory, error measures \(g_1\), \(g_2\) and \(g_3\) for functional dependencies. Then, based on the method of partitions and expectation in probability theory, we propose an error measure \(g_4\) to construct the discernibility matrix in a different way, defined error measures \(g_1\), \(g_2\), dependency degree \(\gamma\) and significance of Attributes \(\sigma\) from the discernibility matrix. Finally, a relationship between AFD and Association Rules via error measure \(g_4\) and confidence is presented.