Implication of Hamacher T-norm on Two Fuzzy-Rough Rule Induction Algorithms

Abstract

From the rule induction algorithms we can obtain models in If-Then form that are very easy to be interpreted by humans. To further improve this class of algorithms, in this paper we focus on QuickRules and Vaguely Quantified Rough fuzzy-rough rule induction algorithms, by introducing the novel Hamacher T-norm. It is important to know that T-norms as well as the fuzzy tolerance relationship metrics, implicators and vague quantifiers play an important role in model accuracy because they are used to calculate the lower and upper approximations. For this purpose, in our models’ evaluation, we use five fuzzy tolerance relationship metrics to evaluate the performance of the models that are obtained with the new Hamacher T-norm. The AUC ROC metric was used to evaluate the performance, and later was used to evaluate the statistical significance. The results revealed that fuzzy tolerance relationship metrics have greater influence than the k-parameter from the Hamacher T-norm on models’ performance, and this was also compared to the vaguely quantified algorithm that uses vague quantifiers. For future work, we plan to conduct further investigation of the influence of another T-norms and fuzzy tolerance relationship metrics on this type of algorithms.