2.7 Mining of tiMe-ConstraineD assoCiation rules 69
converge to normal sup(X ⇒ Y) and conf (X ⇒ Y). Furthermore, for t
1
= 0 and
t
2
= +∞ they converge to forward_sup and forward_conf and for t
1
= –∞ and t
2
= 0
they converge to backward_sup and backward_conf.
2.7.2 Properties of Time Constraints
From the definitions of time_sup and time_conf, two special measures called
support_ratio and confidence_ratio can be defined as follows:
support_ratio (t
1
, t
2
)(X ⇒ Y) =
timettXY
XY
_(,)()
()
sup
sup
12
⇒
⇒
confidence_ratio (t
1
, t
2
)(X ⇒ Y) =
timeconfttXY
conf
_(,)()
12
⇒
⇒(XY)
It should be noted that both ratios are within the range of 0 to 1 because
time_sup ...
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