Research on the influence of fuzzy mathematics simulation model in the development of Wushu market

The core competitiveness of the martial arts industry is a continuous and relative concept, and the evaluation of the core competitiveness of the martial arts industry is also a continuous process. When selecting the evaluation index for evaluating the core competitiveness of the sports industry, the selected index should be motivated not only by the need to reflect the current core competitive advantage but also by the need to consider the evaluation after the development of the sports core competitiveness in the future. The indicators involved are required to reflect all the information pertaining to core competitiveness to the greatest extent. Therefore, when selecting evaluation indicators, the selected indicators must be comprehensive and extensive, and capable of fully reflecting the constituent elements of core competitiveness; further, the selection of indicators must be comprehensive [2].

The evaluation system for the core competitiveness of the martial arts industry uses corresponding indicators to reflect its competitive advantages. The selected indicators should reflect most of the information about the core competitiveness. Therefore, the indicators must be representative, accurate and reliable. They should not only be suitable for the horizontal comparison of the core competitiveness of the martial arts industry between different regions but also lend themselves to longitudinal comparison of the core competitiveness of the martial arts industry in the same region to ensure the validity of the evaluation results.

For the construction of the core competitiveness evaluation system of the martial arts industry, it must conform to the scientific principle. First of all, the selection process and operation process of various indicators must be scientific and conform to a certain scientific basis. Second, the information contained in various indicators must be able to scientifically reflect the information of core competitiveness. Third, the choice of evaluation methods for constructing core competitiveness must be scientific and feasible [3].

The so-called objectivity mainly refers to the evaluation content that needs objective contemplation after the evaluation system stands established. First of all, the evaluation indicators must be objectively measured and subjective indicators should be avoided to the extent possible; second, the statistical data and data sources collected when constructing the evaluation system must be true and reliable; third, the seriousness and standardisation of evaluation methods must be emphasised.

In the evaluation index system of core competence martial arts industry, the core competitiveness of martial arts industry is currently evaluating the establishment of martial arts as a means to the ultimate goal, mainly in the evaluation system, to detect and determine the core competitiveness of martial arts industry, to further develop and improve the core competitiveness of the industry and to promote the development of martial arts industry. Therefore, the evaluation system, the establishment of evaluation results, the evaluation processes and the core competitiveness of the martial arts industry as the main direction should be strengthened to promote the development of martial arts industry. Preparation of the evaluation system must have a practical effect, in order to assess the usefulness of the evaluation model meaningfully.

In order to be able to establish a persuasive and intuitive response to the level of the core competence of the martial arts industry, quantitative evaluation is necessary. However, just stacking and listing some quantitative data cannot fully reflect the core competitiveness of the martial arts industry. Moreover, many indicators that reflect the core competitiveness of the martial arts industry are objectively difficult to quantify. Therefore, when establishing an evaluation system, it is necessary to fully consider the combination of qualitative and quantitative evaluation methods to fully ensure the integrity of the evaluation results.

There are four core competitiveness components of industries’ martial arts techniques: martial arts supply industrial core competitiveness, martial arts talent core competitiveness of industries, martial arts culture industry core competitiveness index layer of the main criteria and the martial arts industry's core competitiveness of the target layer. We set U = {U1, U2, U3, U4}, U1 = core competitiveness of martial arts technology industry, U2 = martial arts supplies core competitiveness of industries, U3 = martial arts core competitiveness of industry talent and U4 = martial arts and cultural industry's core competitiveness; the layer index set of primary criteria assessment of core competitiveness of martial arts industry (U) is: U = {U1, U2, U3, U4} = {U1 = martial art core competitiveness of industries, U2 = martial arts supplies core competitiveness of industries, U3 = martial arts core competitiveness of industry talent, U4 = martial arts culture industry core competitiveness}.

Every four main criteria level indicator (U1, U2, U3, U4) follows the sub-index layer criteria: U1 = {U11, U12, U13, U14} = {martial fitness market, martial arts competitions performance market, martial arts training market, martial labour market}; U2 = {U21, U22, U23, U24, U25} = {martial apparel market, martial arts equipment market, martial souvenirs, martial beverage market, martial science market}; U3 = {U31, U32, U33} = {high-level athletes, folk martial artist, martial arts broker}; U4 = {U41, U42, U43, U44, U45} = {audio books martial arts, martial arts tourism market, finance and insurance martial arts, martial arts events, martial arts information}.

First, we determine the influence weight of each sub-criteria level index on the main criterion level index. Let us suppose that K is the unified code of 16 sub-criteria level indicators to 4 main criterion level indicators; then, 42 sets of weights can be obtained, namely Ki (I = l, 2, 3, 4), where K1 = [K11, K12, K13, K14], respectively, represent the weight value of the martial arts fitness market, martial arts competition performance market, martial arts training market and martial arts labour market. The value is positive, and the sum of each value is 1. K2 = [K21, K22, K23, K24, K25] represent the weight values of the martial arts clothing market, martial arts equipment market, martial arts souvenir market, martial arts beverage market, and martial arts science and education market. The value is positive and the sum of the values is 1. K3 = [K31, K32, K33], respectively, represent the weight values of high-level athletes, folk martial artists and martial arts agents. The value is positive, and the sum of the values is 1. K4 = [K41, K42, K43, K44, K45], respectively, represent the weight value of Wushu books, audio and video, Wushu tourism market, Wushu financial market, Wushu large-scale activities and Wushu information consultation. The value is positive and the sum of each value is 1. Figure 3 shows the process of calculating the weight of each indicator layer of core competitiveness.

Fig. 3

Then, the priority is to determine the influence of each main criterion layer indicator right on target layer weight. Provided Z is a four main criteria level indicator of target layer (martial arts industry core competitiveness) having a weight that is set, Z = [Z1, Z2, Z3, Z4], wherein Z1, Z2, Z3, Z4 represent martial art industry core competencies, core competitiveness of industries martial arts supplies, martial arts talent core competitiveness of industries and martial arts culture core competitiveness of industries affecting the right of the core competitiveness of martial arts industry's heavy components; the values are positive, and each value is 1. For each of the above main criteria level indicators (level indicators), sub-criteria layer index (secondary indexes) influence weight data obtained in this study by two experts investigating the score, and thereafter dealing with the specific relevant statistical data (Table 2).

For the evaluation of the core competitiveness of the martial arts industry at all levels, five comment levels can be selected: good, good, fair, poor and poor. Let V be the comment set; then, V = {V1, V2, V3, V4, V5} (good, better, fair, poor, poor).

Suppose Uij (that is, the specific indicators of the 16 sub-criteria levels) belongs to the t-th review Vt (Vt represents 5 reviews that are good, good, fair, poor and poor) as yijt, then the main criterion level Ui can be obtained. The initial fuzzy judgement matrix Yi is as follows: (1) Y1=[y111y112y113y114y115y121y122y123y124y125y131y132y133y134y135y141y142y143y144y145] Y1 = \left[ {\matrix{{y111} & {y112} & {y113} & {y114} & {y115} \cr {y121} & {y122} & {y123} & {y124} & {y125} \cr {y131} & {y132} & {y133} & {y134} & {y135} \cr {y141} & {y142} & {y143} & {y144} & {y145} \cr}} \right] (2) Y2=[y211y112y113y114y115y221y122y123y124y125y231y132y133y134y135y241y142y143y144y145] Y2 = \left[ {\matrix{{y211} & {y112} & {y113} & {y114} & {y115} \cr {y221} & {y122} & {y123} & {y124} & {y125} \cr {y231} & {y132} & {y133} & {y134} & {y135} \cr {y241} & {y142} & {y143} & {y144} & {y145} \cr}} \right] (3) Y3=[y311y112y113y114y115y321y122y123y124y125y331y132y133y134y135] Y3 = \left[ {\matrix{{y311} & {y112} & {y113} & {y114} & {y115} \cr {y321} & {y122} & {y123} & {y124} & {y125} \cr {y331} & {y132} & {y133} & {y134} & {y135} \cr}} \right] (4) Y4=[y411y112y113y114y115y421y122y123y124y125y431y132y133y134y135y441y142y143y144y145] Y4 = \left[ {\matrix{{y411} & {y112} & {y113} & {y114} & {y115} \cr {y421} & {y122} & {y123} & {y124} & {y125} \cr {y431} & {y132} & {y133} & {y134} & {y135} \cr {y441} & {y142} & {y143} & {y144} & {y145} \cr}} \right]

On this basis, we may suppose the fuzzy judgement set of the main criterion level index Ui to be Ai; then: (5) Ai=KiOY1={ai1,ai2,ai3,ai4,ai5} Ai = KiOY1 = \left\{{{a_{i1}},{a_{i2}},{a_{i3}},{a_{i4}},{a_{i5}}} \right\} where Ki is the influence weight of each sub-criteria level index (such as martial arts fitness industry) on the main criterion level index (such as the core competitiveness of martial arts technology industry); ‘O’ is the operator M(, ⊕), ait=∑j=1nKijYijt {a_{it}} = \sum\limits_{j = 1}^n {K_{ij}}{Y_{ijt}} which can calculate the core competitiveness of the martial arts technology industry. The fuzzy evaluation set consists of four main criterion-level indicators: the competitiveness of the martial arts supplies industry, the competitiveness of the martial arts talent industry and the competitiveness of the martial arts culture industry. From this, the fuzzy evaluation set of the target level (the core competitiveness of the martial arts industry) can be obtained as A, and the secondary evaluation matrix would be as follows: (6) A={A1,A2,A3,A4}T=[aa11a12a13a14a15a21a22a23a24a25a31a32a33a34a35a41a42a43a44a45] A = \left\{{A1,A2,A3,A4} \right\}T = \left[ {\matrix{{{a_{a11}}} & {{a_{12}}} & {{a_{13}}} & {{a_{14}}} & {{a_{15}}} \cr {{a_{21}}} & {{a_{22}}} & {{a_{23}}} & {{a_{24}}} & {{a_{25}}} \cr {{a_{31}}} & {{a_{32}}} & {{a_{33}}} & {{a_{34}}} & {{a_{35}}} \cr {{a_{41}}} & {{a_{42}}} & {{a_{43}}} & {{a_{44}}} & {{a_{45}}} \cr}} \right]

On the basis of Eq. (6), the final FCE mathematical model E of the core competitiveness of the martial arts industry is obtained, as follows: (7) E=ZOA=(Z1,Z2,Z3,Z4)0[aa11a12a13a14a15a21a22a23a24a25a31a32a33a34a35a41a42a43a44a45] E = ZOA = (Z1,Z2,Z3,Z4)0\left[ {\matrix{{{a_{a11}}} & {{a_{12}}} & {{a_{13}}} & {{a_{14}}} & {{a_{15}}} \cr {{a_{21}}} & {{a_{22}}} & {{a_{23}}} & {{a_{24}}} & {{a_{25}}} \cr {{a_{31}}} & {{a_{32}}} & {{a_{33}}} & {{a_{34}}} & {{a_{35}}} \cr {{a_{41}}} & {{a_{42}}} & {{a_{43}}} & {{a_{44}}} & {{a_{45}}} \cr}} \right]

After Eq. (7), a set of data et (t = 1, 2, 3, 4, 5) can be obtained. At this time, the sum of all et values is not equal to 1. After normalised data processing, a FCE of the core competitiveness of the martial arts industry can be carried out. The basis of the evaluation is based on the principle of maximum membership degree of fuzzy mathematics, that is, the comment level that the maximum e value falls in indicates the core competitiveness of the martial arts industry that is most likely to be at that level. The final calculation result of the model yields the following set of data: 0.715, 0.022, 0.089, 0.171, 0.13. According to the comment set originally set by the model, it can be considered that the core competitiveness of the martial arts industry is at the ‘good’ level. According to the analysis of the weight data, the martial arts training industry occupies the best competitive position in the martial arts technology industry. We continue to make a more comprehensive evaluation of the core competitiveness of the martial arts industry, and we can also use the relevant data in the initial judgement matrix and the secondary judgment matrix in Eqs (5) and (6) to get some more specific and practical significance for the conclusion.

According to the above evaluation, the Wushu industry development condition score is only 22 points, and the existing industry development foundation is weak and small. Therefore, the thrust towards development of the martial arts industry must first concentrate on promoting related industries in the martial arts industry, such as various martial arts equipment supplies, clubs, packaging advertising, martial arts books, pictorials, CDs, martial arts tourism spots etc., extending from upstream industries to downstream industries, through the integration of information, technology, capital and human resources between industries, which will form an industry cluster around the martial arts industry, and enhance the influence and competitiveness of the martial arts industry [8]. This can be achieved by improving the industrial chain of the martial arts industry, implementing the development strategy of ‘going out and introducing’, promoting representative martial arts products to other regions, especially in martial arts competitions and martial arts-related activities, and improving the quality and popularity of martial arts products. On the basis of promoting the development of martial arts-related industries, it is necessary to fully consider whether related products in the industrial framework can meet the needs of different consumer groups, and develop different martial arts consumer products or services in accordance with the differences in demand, age, income, class and occupation. The project will give priority to martial arts products that are easy to translate into market demand; it is also necessary to respect consumer feedback, improve service awareness and quality, and create distinctive martial arts products, so as to better promote and create influence [9].

In view of the insufficient development conditions of the existing martial arts cultural industry, insufficient government support is also a reason. For example, it is difficult to approve policies and funds related to the construction of martial arts schools, martial arts fitness clubs and the government's construction of martial arts platforms and martial arts competitions. Possibly due to the lack of awareness of the importance of the government, the government is not clear about the martial arts development policy in terms of related laws and policies. It can be seen from this that the government plays an extremely important role in improving the competitiveness of the martial arts industry [10]. The role of the government is embodied in the rationality and timeliness of policy formulation, the soundness of laws and regulations, the support to the industry and the establishment of efficient financing channels. For example, the establishment of a cultural industry financing platform, on the one hand, can establish a network platform to promote the martial arts industry; on the other hand, it can increase the construction of cultural industry infrastructure, establish martial arts-related supporting equipment in parks and other leisure places, and can also establish martial arts halls. Further, through the supervision of relevant departments, it is necessary to standardise market order, strengthen industry self-discipline mechanism and industry management system etc., to standardise the martial arts market order and correctly guide the development direction of the martial arts industry [11]. Policy support for the martial arts industry is an important guarantee for the long-term development of the martial arts industry. It can not only increase the commercial radiation of the martial arts industry to other domestic provinces from a market perspective but also enhance the spread and development of regional culture in the country.