where tmiis the middle year of tenure of Si. And thenx1'i x1i pi i 1,2, ,n .
3.3.2. The influence of time on the winning-percentage
As for the winning-percentage, sports were underdeveloped at an earlier time, and the quality disparity between teams is comparatively narrow. Therefore, the standard deviation of winning-percentage of each coach is closer to zero. Thus we should put less weight on the coaches active in a mediocre time period. We define ICT here as qi (i=1,2, ,n), we assume
that the standard deviation of all winning-percentage in t is s t .s t can be obtained by
statistical regression and simulating and curve fitting of selected data. So we define:
mo.crotha.mww w模数
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1
stmiqi
'
and x2i x2i qi i 1,2, ,n .
3.3.3. Fuzzy Analysis
As for SM indexes, we assume that they can be divided into five levels: Excellent, Very Good, Good, Not Good, Bad . And we correspond the five levels into 5,4,3,2,1 successively For continuous quantification, we assume: As for Excellent , we suppose f 5 1. As for Very Good , f 3 0.7. As for Bad , f 1 0.1.
校
苑
We employ partial large Cauchy distribution and the logarithmic function as the subordinate function[2]:
1 ax b 2 1,1 x 3
f(x)
clnx d,3 x 5
where a, b, c, d stands for undetermined constants. We use the initial conditions above to define their values. And solution of the subordinate function( Figure 2) is:
1 2.8049x 0.4417 2 1,1 x 3
f(x) (1)
0.5873lnx0.0548,3x5
Figure 2: Trend of f(x)
Media popularity is measured by the number of search results via Google. The impact of duplication of names can be neglected by means of adding search keywords in order to rule out the redundant information.
We map xj ( j=5,6)into interval [1,5], through function (1),we can obtain:
mo.crotha.mww w模数
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4 xji mj
i 1,2, ,n,j 5,6 (2) x f 1
Mj mj
'
ji
where Mj max xij ,mj min xij j 5,6 .
1 i n
1 i n
As for x3 and x4, we define that x3’= x3, x4’= x4.
we use x'j j 1,2, ,6 to proceed the following calculation.
3.3.4. Nondimensionalization process
We employ extreme difference method to nondimensionalize the different indexes so that we can compare them[2]on the same level. The method is as follows:
校
苑
x''ji
''''''''
and x''j xj1,xj2,xj3, ,xjn
T
x'ji mjMj mj
(3)
where Mj max xij ,mj min xij j 1,2, ,6 .
1 i n
1 i n
and then we obtain the final evaluation index matrix:
''''''''''
x1,x'' x* 2,x3,x4,x5,x6 (4)
3.3.5. Final result
By using AHP as the subjective evaluation method and GRAP as the objective method, the final represents a comprehensive evaluation combined the merits of these two methods.
Analytic Hierarchy Process[3] (AHP)
By comparing the effect of two indexes x'j,the weights of the two methodwx'j(j=1,2, ,m)are given. Then we construct the pairwise comparison matrixA.
We can obtain the largest eigenvalue of A:λ=6.0496 and its weight vector:
mo.crotha.mww w模数
j 1,2, ,6
T
1 1 3A
7 1 5 2
11
1
3131
3
5151361513
171516117151 2 53
53
75
1 1
3 31 5
w 0.1248,0.1469,0.4593,0.8125,0.0775,0.2928
T
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After that, we must check the consistency of matrix A. The consistency index is calculated
as follows:
n
9.92 10 3CI
n 1
From Table 2, the random consistency index RI=1.24
Table 2: The Quantitative Values of RI[2]
n RI
1 0
2 0
3 0.58
4 0.90
5 1.12
6 1.24
7 1.32
8 1.41
9 1.45
10 1.49
11 1.51
校
Then, we can obtain consistency ratio:
苑
CI
0.008 0.1RI
Therefore, we can safely draw the conclusion that the inconsistent degree of matrix A is in a tolerable range, and we can take its eigenvector as weight vector w[3].
We define B as the evaluation vector of AHP, and B can be calculated as follows:
'
B x w (5)
CR
In evaluation vector, the greaterBi is, the higher rankingSi is.
Gray Relational Analysis Grade Method[4] (GRAP)
We use integral grey relational degree to analyze the metrics data. And we take the total number of wins as the reference sequence:
and then we can obtain the gray relational coefficient[4]:
Where:
For every coachSi, we determine its weight as wi, which should satisfy the requirements:
After determining the weight, we can obtain the relational degree[4]: rj rx,x
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