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of “Quantitative Prediction and Assessment of Induced
Area and its Neighboring Area”; in section 3, apply AHP
method on weights calculation. The case study is given
in Section 4.
II. HIERARCHY EVALUATION MODEL
According to the investigation result in previous
researches, this paper constructs the fuzzy evaluation
system of reservoir-induced earthquake in two main
factors such as water permeation-accumulations factor
( U
1
) and strain energy accumulation-elimination factor
( U
2
), and they are corresponding to six sub-factors such
as rock (R), karsts (K), fracture (F), crack (C), water load
(W) and fracture angles of superimposed (A). Let U be
the set of all induced earthquake indexes:
U = { U , U }
(1)
1 2
U1 = { R, K, F, C}
(2)
U2 = { W, A}
(3)
V = V V V , and V
t
Remark set is ( 1 2
...
n )
( t 1,2,... n)
= shows remark from low to high. This paper
adopts four levers of earthquake scale, and takes n=4,
define remark set:
V = { V1, V2, V3, V4}
(4)
Where V
1
stands for micro-earthquake, V 2
stands for
sensible earthquake, V
3
stands for devastating
earthquake, V
4
stands for strong earthquake.
The state classifications of reservoir-induced
earthquake factors show in TABLE I. The hierarchy
evaluation model shows in Figure 1.
III. FUZZY MATRICES AND WEIGHTS
The fuzzy matrixes and weights show below:
TABLE Ⅰ.
THE FUNDAMENTAL SCALE OF ABSOLUTE NUMBERS
Attributes Alternatives explanations
1 Igneous rocks
2 Metamorphic rocks
R
3 Non-carbonates Sedimentary rocks
4 Carbonates sedimentary rocks
1 Undeveloped
2 Poor developed
K
3 Developed
4 Well developed
1 Undeveloped, far from fault
2 Undeveloped, near by fault
F
3 Developed
4 Well developed
1 Undeveloped
2 Poor developed
C
3 Developed
4 Well developed
1 Not submerge, far from reservoir
2 Not submerge, near by reservoir
W
3 Submerge, peripheral regions of reservoir
4 Submerge, in the middle of reservoir
1 A=0~10; 71~90
2 A=11~24; 51~71
A
3 A=25~50
4 A=25~50
Seismicity Risk in Yangtze Three-Gorge Reservoir Head
A. Fuzzy Matrix
Fuzzy matrix is constructed to calculate the weights,
each factor in an upper level is used to compare the
factor in the lever immediately below with respect to it.
To make comparisons, we need a scale of numbers that
indicates how many times more important or dominant
one factor is over another factor with respect to the
criterion or property with respect to which they are
compare, TABLE II exhibits the scale.[16]
The fuzzy matrix of U 1
is show in TABLE III, the
fuzzy matrix of U
2
is show in TABLE IV.
B. Weights
After established reciprocal matrix, ascertain the
weights of each lever of evaluation index by solving
characteristic vectors of the matrix.
W = W W W L is weight of the
Suppose ( )
index, Where 0< w i
≤ 1,
1 2 3
n
∑ w
i
= 1
1
• = n× n
λ max
(5)
A W W
We get weight sets of sub-factors:
W =
1 ( 0.5650 0.0553 0.2622 0.1175)
( )
W
2
= 0.90 0.10
And weight set of main-factors is:
W = 0.6667 0.3333
( )
The consistency ratio (CI) is used to directly estimate
the consistency of pairwise comparisons. The closer
inconsistency index to zero, the greater the consistency.
If the CR less than 0.10, the comparisons are acceptable,
otherwise, the decision makers should go back and redo
the assessments and comparisons.
Intensity of
importance
1
3
5
7
9
TABLE Ⅱ.
STATE CLASSIFICATION OF RIS FACTORS
Definition
Equally importance
Moderate importance
Strong importance
Very strong importance
Extreme importance
2,4,6,8 Interval values between two adjacent choices
reciprocal
Less important level
TABLE Ⅲ.
FUZZY MATRIX OF U
1
R K F C
R 1 7 3 5
K 1/7 1 1/5 1/3
F 1/3 5 1 3
C 1/5 3 1/3 1
TABLE Ⅳ.
THE FUZZY MATRIX OF U
2
W
A
W 1 9
A 1/9 1
102