On the one hand, fuzzy sets model vague information: they recognize that membership to certain concepts (e.g., being a “relevant” internet resource), or logical truth of certain propositions, is a matter of degree. Fuzzy sets have found their way into numerous fields of application, such as engineering and control theory, databases and information retrieval, data analysis, etc. On the other hand, rough sets originated in the machine learning (ML) domain, and deal with incomplete information: this occurs when the available feature set describing data samples does not suffice to discern between them. As many concepts cannot be represented exactly under these conditions, they are approximated from below and from above, using the equivalence classes of the indiscernibility relation as information blocks. Fuzzy sets and rough sets are highly complementary formalisms, and their hybridization, which focuses on the approximation of a (potentially vague) concept using a fuzzy relation, has been particularly successful in ML applications, including
data pre-processing (feature and instance selection), as well as classification tasks.