Feature Discovery through Hierarchies of Rough Fuzzy Sets

Rough set theory and fuzzy logic are mathematical frameworks for granular computing forming a theoretical basis for the treatment of uncertainty in many real-world problems, including image and video analysis. The focus of rough set theory is on the ambiguity caused by limited discernibility of objects in the domain of discourse; granules are formed as objects and are drawn together by the limited discernibility among them. On the other hand, membership functions of fuzzy sets enables efficient handling of overlapping classes. The hybrid notion of rough fuzzy sets comes from the combination of these two models of uncertainty and helps to exploit, at the same time, properties like coarseness, by invoking rough sets, and vagueness, by considering fuzzy sets. We describe a model of the hybridization of rough and fuzzy sets, that allows for further refinements of rough fuzzy sets. This model offers viable and effective solutions to some problems in image analysis, e.g. image compression.