Classes of association rules

The classes of association rules are defined by classes of 4ft quantifiers. There are various classes of 4ft-quantifies defined already in [Ha 78], e.g. implicational quantifiers and associational quantifiers. Further classes of 4ft-quantifiers are defined e.g. in [Ra 98A] and [Ra 98C].

Classes of 4ft-quantifiers can be defined using TPC – truth preservation condition. An example of TPC is a truth preservation condition TPC_⇒ for implicational quantifiers:

TPC_⇒: a' ≥ a ∧ b' ≤ b.

The TPC_⇒ is used in the definition of implication quantifier such in the following way:

The 4ft quantifier ≈ is implicational if for all quadruples 〈a,b,c,d〉 and 〈a',b',c',d'〉 of integer non-negative numbers such that a + b + c + d > 0 and a + b + c + d > 0 the following is satisfied:

If ≈(a,b,c,d) = 1 and a' ≥ a ∧ b' ≤ b then also ≈(a,b,c,d) = 1.

The following quantifiers implemented in the 4ft-Miner procedure are implicational: founded implication ⇒_{p, Base}, lower critical implication ⇒^!_{p, αBase} and upper critical implication ⇒^?_{p, αBase}.

Double implicational quantifiers, ∑-double implicational quantifiers and furthers classes of 4ft-quantifiers are defined and studied e.g. in [Ra 98A] and [Ra 98C], see also [Bu 03].

There are interesting results related to defined classes of association rules – see e.g. deduction rules and some further properties of association rules.