Much of my current research involves the development of fuzzy-rough set theory with a view to deployment in real-world applications. The properties of fuzzy-rough sets are particularly well-suited to handling data due to its effective modelling of uncertainty.
Vaguely quantified rough sets (VQRS)
(VQRS lower and upper approximations)
Although fuzzy-rough sets can handle uncertainty present in data quite well, it is still possible that rogue objects can adversely affect the resulting models. VQRS attempts to address this by using fuzzy quantifiers to determine inclusion and overlap. The two movies below show how these methods compare in modelling the classification surfacefor the first two features in the Iris dataset.
The way that fuzzy-rough set are defined naturally lead to developing nearest neighbour style approaches to classification. This has been applied to mammographic image analysis.