On the stability of fuzzy classifiers to noise induction

Tabular data classification is one of the most important research problems in the artificial intelligence. One of the most important desired properties of the ideal classifier is that small changes in its input should not result in dramatic changes in its output. However, this might not be the case for many classifiers used in present day. Fuzzy classifiers should be stronger than their crisp counterparts, as they should be able to handle such changes using fuzzy sets and their membership functions. However, this hypothesis has not been empirically tested. Besides, the concept of 'small change' is somewhat imprecise and has not been quantified yet. In this work we propose to use small and progressively bigger changes in test samples to study how different crisp and fuzzy classifiers behave. We also study how to optimize classifiers to be more resistant to such kind of changes. Our results show that different fuzzy sets have different responses to this problem and have a smoother performance response compared to crisp classifiers. We also studied how to improve this and found that resistance to small changes can also result in a worse overall performance.