Refining Discretizations of Continuous-Valued Attributes

The Rand index is a measure commonly used to compare crisp partitions. Campello (2007) and Hüllermeier and Rifqi (2009) respectively, proposed two extensions of this index capable to compare fuzzy partitions. These approaches are useful when continuous values of attributes are discretized using fuzzy sets. In previous works we experimented with these extensions and compared their accuracy with the one of the crisp Rand index. In this paper we propose the ε-procedure, an alternative way to deal with attributes taking continuous values. Accuracy results on some known datasets of the Machine Learning repository using the ε-procedure as crisp discretization method jointly with the crisp Rand index are comparable to the ones given using the crisp Rand index and its fuzzifications with standard crisp and fuzzy discretization methods respectively.