A comprehensive study of fuzzy covering-based rough set models: Definitions, properties and interrelationships

Fuzzy covering-based rough set models are hybrid models using both rough set and fuzzy set theory. The former is often used to deal with uncertain and incomplete information, while the latter is used to describe vague concepts. The study of fuzzy rough set models has provided very good tools for machine learning algorithms such as feature and instance selection. In this article, we discuss different types of dual fuzzy rough set models which all consider fuzzy coverings. In particular, we study two models using non-nested level-based representation of fuzziness. In addition to the study of the theoretical properties for each model, interrelationships between the different models are discussed, resulting in a Hasse diagram of fuzzy covering-based rough set models for a finite fuzzy covering, an IMTL-t-norm and its residual implicator.