1.1 Uncertain Data Model
In the general case, the occurrence of items may be de-
pendent. For example, the decision to purchase a new music
The uncertain data model applied in this paper is based
video DVD may mean they are unlikely to purchase a mu-
on the possible worlds semantic with existential uncertain
sic CD by the same artist. Alternatively, some items must
items.
be bought together. If these conditional probabilities are
Definition 2. An uncertain item is an item x ∈ I whose
known, they can be used in our methods. For example,
presence in a transaction t ∈ T is defined by an existential
the probability that both a video and music are purchased
probability P (x ∈ t) ∈ (0, 1). A certain item is an item
by customer B is P ({V ideo, M usic} ∈ t B ) = P (V ideo ∈
where P(x ∈ t) ∈ {0, 1}. I is the set of all possible items.
t B ) ∗ P (M usic ∈ t B |V ideo ∈ t B ).
Definition 3. An uncertain transaction t is a transac-
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