Redundant object and dependency of domain attributes in α-coverings of the universe

α-coverings of the universe induced by a conditional probability relation offers a generalization model of standard rough sets which are mainly defined by a partition induced by an equivalence relation. The paper improves the concept of α-coverings of the universe by some properties and applications related to knowledge discovery and data mining (KDD). A concept of α-redundancy of objects based on α-coverings of the universe is proposed in order to reduce the number of decision rules in the presence of a decision table. Moreover, an important concept of dependency of domain attributes corresponding to the concept of fuzzy functional dependency in the presence of a fuzzy relational database is also introduced