Approximate Reducts and Association Rules

We consider approximate versions of fundamental notions of theories of rough sets and association rules. We analyze the complexity of searching for α-reducts, understood as subsets discerning “α-almost” objects from different decision classes, in decision tables. We present how optimal approximate association rules can be derived from data by using heuristics for searching for minimal α-reducts. NP-hardness of the problem of finding optimal approximate association rules is shown as well. It makes the results enabling the usage of rough sets algorithms to the search of association rules extremely important in view of applications.