Certain, Generalized Decision, and Membership Distribution Reducts Versus Functional Dependencies in Incomplete Systems

An essential notion in the theory of Rough Sets is a reduct, which is a minimal set of conditional attributes that preserves a required classification feature, e.g. respective values of an original or modified decision attribute. Certain decision reducts, generalized decision reducts, and membership distribution reducts belong to basic types of Rough Sets reducts. In our paper, we prove that reducts of these types are sets of conditional attributes functionally determining respective modifications of a decision attribute both in complete and incomplete information systems. However, we also prove that, unlike in the case of complete systems, the reducts in incomplete systems are not guaranteed to be minimal sets of conditional attributes that functionally determine respective modifications of the decision attribute.

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