From the perspective of geographical spatial aggregation, the Yellow River Basin is connected by railway and highway trunk lines, and the distribution of culture, sports and tourism industry is based on transportation. The basin takes Xining, Lanzhou, Yinchuan, Hohhot, Taiyuan, Xi’an, Zhengzhou, and Jinan as the regional core points, with railroads and highways as connecting lines. The basin extends to the east and northwest, from the trail adventure tourism area with snowy mountains on the Tibetan plateau in the west to the Confucian and Mencian cultural tourism area in the east, via the exotic Silk Road tourism area, Chinese Antiquities and Treasure Tourist Area and Red Cultural Revolution Tourist Area [21]. In the basin, the west-middle-east traffic trunk line is the development axis, including the west axis Baolan line, the middle axis along the Yellow River highway, and the east axis Longhai line (Figure 3).

Taking the urban area as the unit, the tourism belt of the basin covers a total of 32 prefecture-level and above urban areas, with the Baotou-Lanzhou line, the Yellow River highway, and the Longhai line as the driving forces, influencing the surrounding areas and the hinterland of the basin [22]. The Baotou-Lanzhou

line connects the main axis of Lanzhou, Yinchuan, and Baotou in the upper reaches of the basin, and brings along the central and eastern parts of Gansu Province, northern Ningxia, and southern Inner Mongolia. The traffic line passes through deserts, canyons, and ethnic minority areas, which provides rich sports tourism resources. The highway along the Yellow River connects the middle reaches of the basin, starting from Fugu in Yulin, Shaanxi Province in the north to Weinan at the foot of Mount Hua in the south. The middle reach of the Yellow River basin takes Taiyuan and central Xi’an as two core axes, radiating western Shanxi, eastern Shaanxi, and northern Henan region. The river flows southward along the Loess Plateau, passing through ancient temples, famous mountains, and pavilions, forming rich cultural tourism resources. The Longhai Line connects Lanzhou, Xi’an, and Zhengzhou axis, radiating eastern Shandong, north-central Henan, and eastern Shaanxi. The river in this region flows slowly. With large rivers and streams all around the basin and beautiful scenery, it is rich in water and tourism resources (Table 1).

CRITIC (CRiteria Importance Through Intercriteria Correlation) method proposed by D. Diakoulaki is one of the weighting methods which determines objective weights for criteria [25]. This method includes the intensity of the contrast and the conflict in the structure of the decision-making problem.

First, is dimensionless quantitative processing.

Positive indicators: x ′ i j = x j − x min x max − x min Reverse indicator: x ′ i j = x max − x j x max − x min

(The larger the value of the positive index is, the better the result is. The smaller the value of the negative index is, the better the result is.)

Second, using standard deviation as the variability measure standard, the larger the weight, the larger the standard deviation.

{ x ¯ j = 1 n ∑ i = 1 n x i j S j = ∑ 1 = 1 n ( x i j − x ¯ j ) 2 n − 1 (Among them, S j represents the standard deviation of item j, and the standard deviation is used to represent the variation of the value in the CRITIC method. The size of the standard deviation represents the size of the variation of the index. The greater the standard deviation, the greater the difference, and the more information can be reflected. The evaluation intensity becomes stronger and the weight is heavier with the increase of the standard deviation.)

Third, the conflict is represented by the correlation coefficient between indicators. Conflict, weight, and the correlation between indicators are negatively correlated.

R j = ∑ i = 1 p ( 1 − r i j ) ( r i j is the correlation coefficient between index i and index j, using the correlation coefficient to represent the correlation of the index. The stronger the correlation is, the smaller the conflict of the index is, and the greater the amount of information is, the higher the repeatability is, which reduces the evaluation intensity of the index to a certain extent, so the weight of this index should be appropriately reduced.)

Fourth, the amount of information is calculated by the product of index variability and conflict.

C j = S j ∑ i = 1 p ( 1 − r i j ) = S j × R j (The importance of the i index in the evaluation system is rising with the increase of the value of C j , and more weight will be allocated to the i index).

Fifth, the final normalization process to determine the weight.

W j = C j ∑ i = 1 p C j (The weight of indicator j is W j ).

A fuzzy comprehensive evaluation is a method proposed by L. A. Zade for the evaluation of uncertain or complex things, which is derived from the set of fuzzy mathematics theories [26].

First, determine indicator set V and comment set U.

V = ( v 1 , v 2 , v 3 , ⋯ , v m ) ( v i represents the i-th factor of the evaluation index, and usually, all factors contain uncertainty and complexity).

U = ( u 1 , u 2 , u 3 , ⋯ , u n ) ( u i represents the results of the i-th evaluation, where we use the names of nine provinces of the Yellow River Basin to characterize).

Second, the membership function set and weight judgment matrixR are determined, and the membership degree and evaluation matrix R are obtained.

(If the first element in the index set V and the first element in the comment set U tocompose the membership degree r i 1 , then the single factor evaluation fuzzy set of the first element is: R = ( r i 1 , r i 2 , r i 3 , ⋯ , r i n ) . The matrix R m ∗ n is formed by m single factor evaluation sets, and finally the fuzzy comprehensive matrix is formed.)

Third, through matrix R, the weight set is calculated, and a comprehensive evaluation is concluded by the weight.

Entropy weight TOPSIS analysis is a comprehensive evaluation method combining the entropy method and TOPSIS method [27].

First, the entropy method is used to calculate the weight.

1) The original data matrix is composed of n evaluation samples and p evaluation indexes: X = ( x 11 ⋯ x 1 p ⋮ ⋱ ⋮ x n 1 ⋯ x n p ) ( X i j denotes the j-th index of sample i).

2) Ratio p i j = x i j ∑ i = 1 n x i j , information entropy e j = − 1 ln n ∑ i = 1 n p i j ln p i j , e j ∈ [ 0 , 1 ] .

3) The calculation of information entropy redundancy: d = 1 − e j , vector normalization standardization: z i j = x i j ∑ i = 1 n x i j 2 .

4) The construction of weighted degree matrix: z i j * = z i j × w j . Then we get matrix Z * = [ z 11 ⋅ w 1 z 12 ⋅ w 2 ⋯ z 1 p ⋅ w p z 21 ⋅ w 1 z 22 ⋅ w 2 ⋯ z 2 p ⋅ w p ⋮ ⋮ ⋱ ⋮ z n 1 ⋅ w 1 z n 2 ⋅ w 2 ⋯ z n p ⋅ w p ] to find the optimal and the worst solution: { z i j ∗ + = max n , p ( z 1 ∗ + , z 2 ∗ + , ⋯ , z p ∗ + ) z i j ∗ − = min n , p ( z 1 ∗ − , z 2 ∗ − , ⋯ , z p ∗ − ) . The optimal worst distance is calculated: D i + = ∑ j ( z i j * − z j ∗ + ) 2 D i − = ∑ j ( z i j * − z j ∗ − ) 2 . Relative proximity C is calculated: C i = D i − D i + + D i − .

5) The optimal solution is obtained by ranking the final proximity of C i .

The nearest point index can measure the mutual proximity of point elements in the geographic space, and determine the spatial layout attributes of point resources accurately [4]. Through Formulas (1) and (2) below, the spatial distribution of the culture, sports, and tourism resources in the Yellow River Basin are calculated. If R was less than 1, it indicates that the culture, sports, and tourism resources in the Yellow River Basin are distributed in a state of aggregation. If R is equal to 1, it indicates that the culture, sports, and tourism resources in the basin are randomly distributed. If R is greater than 1, it means the resources are evenly distributed.

(R represents the nearest neighbor index. r E represents the ideal proximity index, r i represents the actual proximity value, A represents the area, and n represents the number of statistical resources).

R = r i / r E (1)

r E = 1 2 n A = 1 2 D (2)

Kernel density analysis can reflect the spatial agglomeration or dispersion characteristics of geographical elements more vividly [4] (h represents the location of scenic spot i in the geographical space coordinate of radius. s represents the location of pre-estimated scenic spots. s i represents the range of scenic spots with s as the actual radius).

λ h ( s ) = ∑ i = 1 n 3 π h 4 [ 1 − ( s − s i ) 2 h 2 λ ] 2

The culture, sports, and tourism resources in the Yellow River Basin directly influence its overall effect on high-quality development. In order to comprehensively measure the three resources in the basin, it is necessary to analyze their characteristics and development status. Because the high-quality development of the basin has the characteristics of diversity and comprehensiveness, to evaluate the Yellow River Basin needs to calculate the indicators of the three resources. This paper selected the CRITIC method, and followed the principles of science, independence, ease of operation, and representativeness when selecting the evaluation index. Based on the spatial evolution and systematic change of culture, sports and tourism resources and the analysis of the national policy on the high-quality development of the basin, this paper has constructed a comprehensive evaluation system through a series of indicators and directions of development. The evaluation system contained the development level of culture, sports, and tourism resources and 13 secondary indexes including the number of art groups, museums, athletes, and tourism income. The weight of each index was calculated by the CRITIC method. All primary indexes had a positive correlation with secondary indexes. Among the 13 secondary evaluation indexes, the level of cultural resources was mainly measured by the number of art performance organizations, art performance venues, museums, public libraries, and the total collection number of public libraries. The level of sports resources was mainly measured by the number of Master Sportsmen and Women, first-class athletes, second-class athletes, and senior coaches. The level of tourism resources was mainly measured by the foreign exchange income of international tourists, the number of international tourists, and foreign tourists (The difference between foreign tourists and international tourists is whether they are Chinese residents or not) (Table 2).

CRITIC is a typical objective weighting method including two indicators, namely contrast intensity, and conflict. The contrast intensity is calculated by standard deviation which determines the size of volatility [28]. The greater the volatility is, the greater the weight is. Conflict represents the correlation coefficient. The larger the correlation coefficient is, the smaller the conflict is, and the smaller the weight is. In the weight calculation, the weight is calculated by comparing the product of contrast intensity and conflict index, and then making the data normalized.

Through the comprehensive calculation of the development level of culture, sports and tourism resources in the basin, it has been concluded that the highest weight was in Shaanxi Province, accounting for 34.66%, and the lowest was in Qinghai Province, accounting for 1.65%. Shaanxi Province boasts not only high GDP, but also rich culture and tourism resources. Qinghai Province is located in the central and western regions of China with underdeveloped economy, inconvenient traffic, and therefore has a low level of development of the three resources. So, there is an urgent need to develop Qinghai. It could be seen that the development level of culture, sports and tourism resources in the nine provinces of the Yellow River Basin varied greatly and the development imbalance was obvious.

Furthermore, the development level of cultural resources in the study area was calculated. According to the result, Henan ranked first, while Qinghai was

the last. In addition, Shandong, Henan, and Shanxi were the top three, which were 43.44%, 19.86%, and 8.41% respectively. They are all located in the central region. In the western region, Sichuan is a province with outstanding performance accounting for 8.95%. Sichuan was also the first province with cultural resources weighing more than 8% in the western region (Table 3). In the calculation of sports resources, Shandong had the highest weight value of 38.33%. The lowest was in Gansu, accounting for 2.63%. Sichuan was the first province with

a sports resource weight of more than 10% in the western region. Shandong had obvious advantages in the number of athletes and senior coaches, which was the main reason for the high level of sports development. The gap between other provinces and Shandong was obvious (Table 4). In the calculation of tourism resources, Shandong, Shaanxi, and Inner Mongolia demonstrated a high level of tourism resources development, accounting for 31.60%, 25.57%, and 25.08 respectively, which were significantly ahead of other provinces. In the provinces with less developed tourism resources, Qinghai, Gansu and Ningxia accounted for 0.22%, 0.79%, and 0.68% respectively, all less than 1% on average. It can be seen that the development level of tourism resources in the Yellow River Basin was extremely unbalanced, and the gap between the western and central regions was obvious (Table 5).

Then comprehensive measurement of the development level of culture, sports, and tourism resources in the Yellow River Basin was carried out. Two evaluation models were used for secondary measurement. By comparing the current situation and development level of the three resources in nine provinces in the basin through different models, more accurate resource development evaluation and test values can be obtained.

A fuzzy comprehensive evaluation is a comprehensive method based on fuzzy mathematics, which can carry out quantitative comprehensive evaluation for some unclear boundaries and difficult quantitative factors. Therefore, we can use this method to measure the comprehensive development level of the resources in the basin. Before the fuzzy calculation, we optimized the 13 indicators by deleting and adding the same amount of evaluation indicators, so that the evaluation results can reflect the overall development level more accurately. The quantitative

calculation was carried out through the sample size of 13 secondary indicators and the data of 9 comment sets. The M (., +) operator was used for the research. The vector matrix A of index weight and the 13 × 9 weight judgment matrix R were established.

By analyzing the weight results of nine comment sets, the top three with the highest weight were: Shandong (0.249), Henan (0.183), and Sichuan (0.166). Gansu, Qinghai, and Ningxia were 0.055, 0.018, and 0.018 respectively. Again, the results proved that the development level of culture, sports, and tourism resources was positively correlated with the level of economic development, resource conditions, and development degree (Table 6).

In the entropy weight TOPSIS analysis, we used the SPSSAU statistics tool. The entropy method is used to calculate the weight of all indicators. It is an objective

assignment method, which can greatly reduce the influence of the deviation coefficient caused by subjective assignment. TOPSIS analysis is a common multi-objective and decision-making model, which is suitable for analyzing statistics with multi-objective and multi-index. Therefore, we can find sample indicators that reflect the measurement indicators or the most powerful indicators. According to the entropy method, the most influential indicator in the development of culture, sports, and tourism in the study area was the foreign exchange income of international tourists. The number of public library institutions, which belong to cultural resources, is the least influential indicator. Among the single weight values of culture, sports, and tourism resources, the development of tourism resources had the greatest influence on the overall development of the basin, and culture resources had the smallest influence. Among the comprehensive weights, the weight of cultural resources accounted for the highest proportion, reaching 34.39% (Table 7).

TOPSIS ranking analysis was carried out by using the obtained entropy weight, and the optimum and the worst solution of the three resources in the nine provinces of the Yellow River Basin were further analyzed. The development status of the nine provinces in the study area was respectively examined. Through calculation, Shandong, Henan, and Sichuan had the highest single ranking value while the lowest was in Qinghai, which is consistent with the results of the comprehensive fuzzy evaluation. According to the results obtained by different models, the overall characteristics showed that the development level of culture, sports, and tourism resources in the central and eastern regions of the study area was significantly better than that in the western region. It was mainly attributed to the convenient transportation and early development in the eastern region, and the driving effect of the core cities. The development level in Sichuan in the western region was better, which was closely related to its unique natural conditions and economic foundation (Table 8).

Comparing the development level of culture, sports, and tourism resources in the past five years horizontally, we found that the development level in the east was significantly better than that in the west, and this gap had gradually increased over time (Figure 4).

Based on the calculation of the current development of culture, sports and tourism

resources in the Yellow River Basin, we can further explore the spatial distribution pattern of these resources and provide accurate information to guide the high-quality development of the basin. After classifying, filtering, modifying, and optimizing the resource data points, the spatial distribution data of culture, sports,

and tourism resources in the basin were collected, including 24,516 sports resources (26.4%), 53,532 culture resources (57.6%), 9385 tourism resources (10.1%) and 5387 mixed resources (6%), a total of 92,820 (Figure 5 & Figure 6). Culture resource points accounted for the largest proportion, which was a reflection of the long history and rich cultural connotation in the Yellow River Basin. Sports resources, tourism resources, and mixed resources ranked second, third and fourth respectively. The area has a good foundation for sports, tourism and sports heritage and relic resources because of the large differences in terrain and complex topography.

The overall spatial distribution of sports, culture, tourism and mixed resources are densely clustered (Table 9). The overall regional characteristic of the distribution was that the three resources aggregated along with the core cities and resource-concentrated areas. We used the average nearest neighbor analysis (ANNA), which can reflect the concentration of resources, to explore the spatial aggregation of resource points in the basin. The results showed that all nearest neighbor ratios of resource points were less than 1, indicating that the four types of resources in the basin were obviously clustered. The ANNA ratio of sports resource points was 0.091, showing the highest concentration. It was followed by mixed resources (0.180) and tourism resources (0.188). The ratio of culture resources was the lowest, which was 0.118.

In order to reflect the spatial distribution pattern of different resources in the Yellow River Basin more clearly, the study used the Spatial Analyst Tools of ArcGIS10.2 to conduct kernel density analysis. The analysis results showed that the kernel density varied from resource to resource.

The kernel density of sports resources was the most aggregately distributed, with two large core aggregation areas. The results of the kernel density analysis of sports resources are the most concentrated. There are three large core aggregation areas. The radiation range includes eastern Qinghai, central Gansu, northern Ningxia, central and eastern Inner Mongolia, southern Shanxi, central and northern Henan, and eastern Shaanxi, Chengdu is the core density area. Sports resources are also the resources with the strongest aggregation and the widest coverage of the four types of resource centers. The resources are distributed along the Baolan line and the Longhai line, and the density of sports resources in Inner Mongolia and northern Shaanxi is the lowest (Figure 6).

The kernel density of tourism resources is the most scattered among the four types of core density, mainly concentrated in the three core areas of Chengdu, Zhengzhou, and Jinan, and the radiation range includes northern Ningxia, central Shanxi, and southeastern Shaanxi. Core area is rich in natural resources, with distinctive landform features and numerous famous mountains and rivers, laying a good foundation for cultural tourism and sports tourism. In Ningxia and Inner Mongolia, the distribution of tourism core density is relatively scattered and the degree of aggregation is small. The core density of tourism resources is also an intuitive reflection of the trend of natural resources in the basin (Figure 7).

The distribution of cultural resource kernel density is relatively scattered, slightly higher than the tourism core density. The distribution is mainly concentrated in Taiyuan, Zhengzhou, Jining, and Jinan, and concentrated in central Henan,

central and eastern Shaanxi, and southern and western Shanxi. The reputation of the Dragon City in Taiyuan and the hometown of Confucius and Mencius in Shandong coincide with each other. Many historical sites and ancient architectural sites are important reasons for the cultural gathering of these cities. Among them, Inner Mongolia, Ningxia, Gansu, and other places have the lowest concentration of cultural resources (Figure 8).

The highest kernel density of mixed resources is concentrated in Zhengzhou, Taiyuan, and Xi’an, and concentrated in the central and southern parts of Shanxi, northern Henan, and central and eastern Shandong. In addition, the radiation range of the mixed kernel density has the greatest potential among the four types of resource kernel densities. Over time, the mixed kernel density will gradually increase with the development of resources and economic development (Figure 9).

Considering the shortcomings and the characteristics of spatial geographic aggregation in the area, we proposed four driving theoretical model for the development of the Yellow River Basin (Table 10). The demand-driven economic development model is a kind of model in which tourism demand dominates the economic development of the basin and promotes the development of tourism and the market [30]. The supply-driven economic development model is the model in which supply dominates economic development. Its development relies on the active provision of resources [31] [32] [33]. The intermediary-supported development model emphasizes the role of the intermediary system in regional economic development. It includes media, tour guides, travel agencies, tourism

associations, we-media, and other intermediary organizations. Mixed-driven economic development model means that in the process of the economic development in the basin, the systems of supply, demand, and intermediary should drive the development as a whole. Each system has a similar proportion in this model, and we cannot tell which plays a more important role [16]. Only when these driving forces work together can we achieve the desired effect and promote high-quality development in the Yellow River Basin.

Information integration and high-quality development in the Yellow River Basin is a major regional plan of the nation, and therefore high standards should be set [34]. The development of regional industries should achieve the goal of integration, too [35]. On this basis, regional communication and cooperation should be realized with the help of the dividend of development. The regional limitation of administration should be broken to build an integrated culture, sports, and tourism brand promotion model [36]. The convenience of traffic is necessary. The transportation location problem is the bottleneck restricting the development of the region, so the establishment of a basin-wide integrated transportation facility is imperative. Transportation is the endogenous driving force of development and an important way to promote the integration of culture, sports and tourism resources and regional development [37]. Achieving regional diversity is also vital. The homogenization of cultural, sports, and tourism resources within the Yellow River Basin is obvious, which hinders regional economic development. Therefore, it is necessary to boost the differentiated development of the area [38] [39]. To achieve brand internationalization, we should properly handle the relationship between international and domestic circular markets, and build the culture and tourism integration belt, forming a new regional development pattern. Therefore, the high-quality development of the Yellow River Basin, together with the Silk Road and the development of the western region in China, can be built with international influence. To achieve this goal, it is necessary to continuously enhance communication and cooperation with the international market, shape the regional international brand of culture, sports, and tourism, and promote the high-quality development of the Yellow River Basin.