Research and Analysis of AHP on the Factors Affecting the Development of Dalian Sports Culture Industry

: This study takes the development of Dalian's sports and cultural industry as the research object


Introduction
Dalian is one of the first coastal open cities in China.It has a long history and cultural resources.It is also one of the cradles of sports culture in China.It is also a famous sports city in China [1].Dalian is a famous sports city.It is known as "Football City", "Hometown of Track and Field" and "Hometown of Swimming".Dalian's sports culture has rich connotation and deep cultural accumulation.Dalian has cultivated a large number of sports talents for China's sports cause, made an indelible contribution to the rise of China's sports cause, and also laid a stable foundation for the construction of Dalian's sports culture [2].
Many factors affecting the development of sports industry, such as industry development resources, industry development guarantee ability, industry development innovation ability, industry magnetization degree, etc., in addition to individual factors such as industrial investment, most of the factors affecting the sports culture industry on the role of sports culture industry is often difficult to quantify, so also difficult to quantitative evaluation of such factors.Based on this, the following research group used the data of questionnaire and field investigation, and the AHP method combining subjective evaluation and objective evaluation to analyze the factors promoting the sports culture industry in Dalian.

Construction of the Index System of Factors Influencing the Development of Sports Culture Industry
On the basis of the existing research, the research group summarized many factors into five factors: industrial magnetization level, industrial product market development, industrial development potential, industrial development guarantee and industrial development resources.The evaluation index system is shown in Table 1.

Selection of Research Methods
In this paper, the hierarchical analysis method is selected in the research method, which is a qualitative and quantitative, systematic and hierarchical analysis method, which is the formal expression, treatment and objective description of people's subjective judgment [3][4][5][6][7].Choose AHP method, the reason is that the method is suitable for the analysis of small samples, poor information problems, and environmental factors are more subjective, qualitative indicators, according to this characteristic, the method of questionnaire survey from the subjective demand of the construction of sports culture industry, and scientifically use the advantages of quantitative analysis of the objective data.The design of questionnaire follows the index system used in hierarchical analysis; to reflect the consistency of survey index and result analysis.

Analysis of Data
Through the questionnaire survey, the criterion level and scheme level in AHP analysis are determined.Among them, the criteria level is the level of industrial marketization [8], the market development of industrial products [9], the industrial development potential [10], the industrial development guarantee [11,13,14] and the industrial development resources [12,15].The five criteria level indicators correspond to 16 indicator level factors.
According to the above index system, the questionnaire was designed, and distributed to some scholars of Liaoning Normal University, Dalian University, Liaoning School of Foreign Business and Economics and some operators of sports culture enterprises.A total of 120 questionnaires were distributed and 114 were collected, among which 109 were valid.This paper uses hierarchical analysis method to analyze the questionnaire results and uses AHP software.The calculation results of criterion layer weight vector are as follows: The results of weight vector of each index layer are as follows: Hierarchical single ordering and consistency testing.
In this paper, taking the judgment matrix of the first-level index as an example, the specific steps of the weight calculation and the matrix consistency test are shown as follows: (1) Normalized to each column of the judgment matrix: (2) Mean the normalized judgment matrix of each column by rows:

j W i W
If the largest feature root must be greater than 0, the corresponding feature vector is the positive vector, and any other feature root of A must be smaller than the largest feature root.λ max λ The maximum feature root of the resulting judgment matrix is =5.2386.
(4) The consistency index CI and the consistency ratio CR were calculated.Where, is the maximum eigenvalue, CI is the consistency indicator, and n is the number of indicators.
When n=2, the positive reciprocal matrix of order 2 is always consistent, so no consistency test is required.When n is greater than 2, the matrix consistency is represented by CR.CR=CI/RI.RI takes values, as shown in Table 8.When CR <0.1, the judgment matrix meets the consistency test.
The consistency test result of the first-level index judgment matrix is CI=0.0596;CR=0.0533 <0.1.Meet the requirements of the consistency test.
Similarly, the weight coefficient and the consistency test of each judgment matrix of the index layer can be calculated.max λ The calculation results of the first-level index and the index layer judgment matrix are summarized in Table 9-Table 14.
Where W represents the within-group weight of each indicator, representing the maximum eigenvalue.CI represents the consistency index, and CR represents the consistency ratio.With CR <0.1 from the above results, the above can pass the consistency test.Hierarchical total ranking and consistency test, using the results of the single ranking of all indicators at the same level, can calculate the weight of the importance of all factors at the level of the previous level, which is the total ranking of the hierarchy.The comprehensive weight in the table is the total ranking corresponding to each index.

Conclusion
First, according to the analysis results of the comprehensive weight, the Dalian sports culture industry, influence the weight of ranking for professional talents, industrial capital, regulations and policies, industrial financing channels, modern enterprise system construction, industrial innovation ability, sports infrastructure, industrial market system perfect degree, market main body diversification, industrial structure optimization degree, product brand construction, product structure optimization, sports culture industry chain, product marketing level, resource development and configuration, residents' total consumption.
Second, from the perspective of the weight distribution of the first-level index, the weight of industrial development resources is the largest, accounting for 0.3032; the second is industrial development guarantee, the weight is 0.2828; the weight of industrial development potential index is 0.1581, the third is market development 0.1355; the first-level index with the smallest weight is the marketization level index, the weight is 0.1204.
Third, from the perspective of the weight distribution of the second-level indicators, professional talents and industrial capital rank the first and second in the industrial development resource indicators, and the two indicators are the necessary resource conditions to measure the development of the sports industry.Among the industrial development indicators, the weight of policy and regulation system construction is the largest, which reflects the demand of policies and regulations in Dalian sports culture industry.In the potential index of industrial development, the modern enterprise system construction occupies the largest weight.The industry is composed of micro individual enterprises.The development of individual enterprises will undoubtedly bring the development and growth of the industry.

W
Where, it represents the element in the column j in row i of the normalized judgment matrix, indicating the weight of the i th indicator.And n represents the number of indicators.iThe weight coefficient of the first-level index is obtained:

3 )a
Calculate the maximum eigenvalue of the judgment matrix.max λ Where, it represents the maximum eigenvalue, the element in the column j column of the i th row of the original judgment matrix, and the weight of the j th indicator and the weight of the i th indicator.And n represents the number of indicators.
the weight of the i th index in the first-level index and the average random consistency index of the first-level index.

Table 1 .
Evaluation index system of key factors for the development of sports culture industry in Dalian city.

Table 2 .
Judgment matrix of first-level indicators.

Table 3 .
Industrial magnetization, the judgment matrix of each index.

Table 4 .
Judgment matrix of each indicator of product market development.

Table 5 .
Judgment Matrix of each indicator of industrial development potential.

Table 6 .
Judgment Matrix of each indicator of industrial development guarantee.

Table 7 .
Judgment Matrix of each indicator of industrial development resources.
kj a Where, it represents the original judgment matrix, the element in the k-row and j-column of the original judgment matrix, and the normalized judgment matrix.ij A

Table 8 .
The mean random agreement indicators.

Table 9 .
Weight coefficient and consistency test of the first-level index-target layer.

Table 10 .
The weight coefficient and consistency test of the index layer-industrial marketization.

Table 11 .
Index layer-the weight coefficient and consistency test of product market development.

Table 12 .
Weight coefficient and consistency test of index layer-industrial development potential.

Table 13 .
Weight coefficient and consistency test of index layer-industrial development guarantee.

Table 14 .
Weight coefficient and consistency test of index layer-industrial development resources.