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c
I
and M, we judge that evaluating index x locates at
left side or right side of point M, and according these to select (1) or (2) for calculating
difference function
I
Based on matrixes
,
[,]
ab
[, ]
of indexes to standards. Here h is grade number and
h
= 1,
2, 3, 4;
i
is indexes number and i = 1, 2;
j
is the sample number and
μ
()
hij
u
j
=
1, 2
L
3 2
.
i
=
1
, its attracting matrix [a, b], interval matrix [c, d] and point values matrix
M respectively are
When
[a, b] = ([0, 46.7] [46.7, 136.7] [136.7, 283.3] [283.3, 1000] )
[c, d] = ([0, 136.7] [0, 283.3] [46.7, 1000] [136.7, 1000] )
M = (0 76.7 234.4333 1000 )
i
=
1
j
=
7
x
(1, 7 )
For sample 7, when
,
, the first index value
=97.60, it locates in
c
=
0,
a
=
46.7,
b
=
136.7,
d
=
283.3
the interval of degree 2 [46.7,136.7],
.
12
12
12
12
ch h
−
−
1
M
=
76.7
M
=
a
+
b
It is obtained that
by
(5) (chen 2009), then
12
ih
ih
ih
c
−
1
c
−
1
1
M
and belongs to
we can see that index value (97.60) locates at right side of point
xb
−
M b
β
[
M
11
b
,
]
μ
() 0.5[1 (
x
=
+
)]
interval
, so we select equation
in Eq. (4).
11
−
Substituting β=1 and other relevant parameters into this equation then we obtain
μ
(
X
)
=
μ
(
X
)
0.8258. Analogously, we get relative membership function
of
12
ih
each single index under i = 1, 2 to degrees h = 1, 2, 3, 4 as:
0.2172
0.8258
0.2828
0
⎡
⎤
0
(5)
μ
()
0.2163
X
=
⎢
⎥
ih
0.8244
0.2837
0
⎣
⎦
And according to ([6]) we obtain weights of two evaluation indexes as:
w
′
=(0.7388,
w
′
0.6739) =
()
. Then normalized weights vector of indexes is:
w
= (0.5230 0.4770) =
w
.
To get synthetic RMD of each index, we use variable fuzzy recognition model pre-
sented by Chen ([1]) as follows,
()
−
1
⎧
α
⎫
⎡
m
⎤
p
⎪
∑
⎪
p
[ 1 ()]
w
−
μ
x
⎢
⎥
i
ij h
⎪
⎪
(6)
′
ux
() 1
=+
⎢
i
=
1
⎥
⎨
⎬
h
j
m
⎢
⎥
⎪
∑
⎪
p
[
wx
μ
(
) ]
⎢
⎥
i
ij h
⎪
⎪
⎣
⎦
i
=
1
⎩
⎭
ux
(7)
()
hj
H=(1,2,3,4)*
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