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12.5 Mining General Fuzzy Association Rules
The main method of mining association rules about digital attributes to disperse
continuous data, which transform the mining association rules about digital
attibutes into the mining association rules about boolean attibutes. One method is
dividing the universe of discourse about attributes into nonoverlapping intervals,
and then mapping the discreted data into these intervals. Nonoverlapping interval
may ignore elements which are nearby the boundery of some intervals. This may
lead to the ignorance of meaningful interval. The other method is dividing the
universe of discourse about attibutes into overlapping intervals, and then the
elements nearby boundary may be located in two invervals meanwhile. This may
lead to over-emphasized on some invervals because the contribution of elements
nearby boundery. The main weak point of the above two methods is that the
boundary is too rigid. A solution proposed by Jianjiang Lu is to vague the
boundary with fuzzy set which is defined on the domain of attributes (Lu, 2000),
beacause fuzzy set can supply a smooth transition between elements in set and
elements not in set. With this transition, all elements nearby boundary will not be
excluded and will not be over emphasized. The degree of membership of the
elements of fuzzy set in the domain of attributes is language value. The language
value is expressed as closed positive fuzzy number and zero fuzzy number with
boundary. So the problem of mining association rules about digit attibutes is
transformed into the problem of mining association rules about fuzzy association
rules.
Definition 12.1
Suppose R is real number field, the closed interval [a,b] is called
the number of closed interval, and a,b R, a b.
Definition 12.2
0
[
c
,
d
]
Suppose a,b , c,d are two closed intervals, and
,
then:
[ , ]
a b
+
[ ,
c d
]
=
[
a
+
c b
,
+
d
];
[ , ]
a b
[ ,
c d
]
=
[
a
d b
,
c
];
[ , ] [ ,
a b
×
c d
]
=
[
ac
ad
bc
bd ac
,
ad
bc
bd
];
a
a
b
b a
a
b
b
[ , ]
a b
÷
[ ,
c d
]
=
[
,
],
0
[ , ].
a b
c
d
c
d
c
d
c
d
Definition 12.3
Suppose A is a fuzzy set on R
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