Fuzzy-Rough Hybridization

Fuzzy sets and rough sets are known as uncertainty models. They are proposed to treat different aspects of uncertainty. Therefore, it is natural to combine them to build more powerful mathematical tools for treating problems under uncertainty. In this chapter, we describe the state of the art in the combinations of fuzzy and rough sets dividing into three parts. In the first part, we first describe two kinds of models of fuzzy rough sets: one is classification-oriented model and the other is approximation-oriented model. We describe the fundamental properties and show the relations of those models. Moreover, because those models use logical connectives such as conjunction and implication functions, the selection of logical connectives can sometimes be a question. Then we propose a logical connective-free model of fuzzy rough sets. In the second part, we develop a generalized fuzzy rough set model. We first introduce general types of belief structures and their induced dual pairs of belief and plausibility functions in the fuzzy environment. We then build relationships between belief and plausibility functions in the Dempster-Shafer theory of evidence and the lower and upper approximations in rough set theory in various situations. We also provide the potential applications of the main results to intelligent information systems. In the third part, we give an overview of the practical applications of fuzzy rough sets. The main focus will be on the machine learning domain. In particular, we review fuzzy-rough approaches for attribute selection, instance selection, classification and prediction.