A comprehensive study of value reducts and bireducts

Résumé

In Rough Set Theory some mechanisms have been considered to reduce the size of datasets without lossof information. For instance, the notion of value reduct arises to remove unnecessary information for aspecific object, allowing a data analysis at an object level. On the other hand, bireducts propose to reducethe sets of objects and aributes of a decision table simultaneously, obtaining different subtables withoutredundancies or contradictions. Hence, the use of both notions in data analysis provides a higher reduction ofunnecessary data. This contribution is focused on the study of the relationship between bireducts and valuereducts, facilitating the computation of ones from the others and viceversa [1]. For instance, in informationtables, if a value reduct B for an object x is known, we can ensure the existence of a bireduct (X, B)with x ∈ X. On the other hand, given all the bireducts with a fixed subset of aributes B, for the objectsbelonging to all these bireducts it is possible to obtain value reducts B′ with the property that B′ ⊆ B.