Efficiency of decision rule sets in classification problems

Resumen

Decision algorithms are considered in Rough Set Theory in order toextract non-redundant and exhaustive information from relational datasets in termsof decision rules. These algorithms are analyzed by using the notion of efficiency, which provides their classification quality through a value in the unit interval.Recently, we have introduced the notion of decision algorithm and efficiency in FuzzyRough Set Theory. The first one to model and obtain the most relevantinformation from the dataset, and the second one to determine the suitability of theconsidered algorithm. However, it can be difficult to interpret the fuzzy notion ofefficiency because it takes values greater than one, unlike the classical efficiency. Inorder to overcome this drawback, this work introduces a normalized efficiency, whosevalues belong to the unit interval. Moreover, the normalized efficiency is defined froma new relevance indicator of strength of decision rules, which highlights the mostsupported rules in the algorithm. Finally, some properties satisfied by the normalizedefficiency are presented, which facilitate its interpretation.