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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Lower and Upper Approximations of Rules in Non-deterministic Information Systems
verfasst von : Hiroshi Sakai, Ryuji Ishibashi, Michinori Nakata
Erschienen in: Rough Sets and Current Trends in Computing
Verlag: Springer Berlin Heidelberg
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A rule in a
Deterministic
Information
System
(
DIS
) is often defined by an implication
τ
such that both
support
(
τ
) ≥
α
and
accuracy
(
τ
) ≥
β
hold for the threshold values
α
and
β
. In a
Non
-
deterministic
Information
System
(
NIS
), there are
derived
DISs
due to the information incompleteness. The definition of a rule in a
DIS
is extended to the
lower
and
upper
approximations
of a rule in a
NIS
. This definition explicitly handles non-deterministic information and incomplete information. To implement the utility programs for two approximations,
Apriori
algorithm is extended. Even though the number of derived
DISs
increases in exponential order, this extended algorithm does not depend upon the number of derived
DISs
. A prototype system is implemented, and this system is applied to some data sets.