Measurement and characteristics of high-quality development level of innovation and entrepreneurship based on EM-AHP-TOPSIS

Abstract

By constructing an evaluation system for the high-quality development of innovation and entrepreneurship, an evaluation index system was established in this study from five aspects: the background, process, input, output, and transformation of innovation and entrepreneurship, and analytic hierarchy process (AHP) and entropy method (EM) were adopted to perform combination weighting. Then, the core of each subsystem and the comprehensive score were calculated based on the TOPSIS method, the high-quality development level of urban innovation and entrepreneurship in 19 vice-ministerial cities like Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, Shenzhen, and Chengdu in China was measured, and the innovation and entrepreneurship development level and structural characteristics were analyzed from five aspects. The results show that Shenzhen, Shanghai, Beijing, Nanjing, and Guangzhou take the lead in the high-quality development of innovation and entrepreneurship, while Xi’an, Chengdu, Hangzhou, Wuhan, Qingdao, Jinan, and Ningbo are in the medium level. Chongqing, Shenyang, Dalian, Harbin, Xiamen, and Changchun perform poorly in the development of innovation and entrepreneurship with problems of interregional large gradient difference in capacity and unbalanced development, which provides an important reference for understanding the current situation, advantages, and disadvantages of innovation and entrepreneurship education development in various economic zones.

Keywords

Innovation and entrepreneurship entropy method analytic hierarchy process TOPSIS method level measurement

1. Introduction

As China’s economy changes from a high-speed growth stage to a high-quality development stage, innovation and entrepreneurship have become the core and pillar of promoting high-quality economic development. Promoting the high-quality development of innovation and entrepreneurship is conducive to further enhancing the ability of entrepreneurship to drive employment, enhancing the ability of scientific and technological innovation and the vitality of industrial development, promoting the integration and innovation of large, medium, and small enterprises in the industrial chain, increasing high-quality supply, and expanding effective demands. This is of great significance for strengthening the endogenous power of economic development [1]. Therefore, measuring the high-quality development level of innovation and entrepreneurship and understanding its development characteristics have become the first problem to be solved in the current research. The research on innovation and entrepreneurship measurement started abroad and is more authoritative. In 2001, the European Innovation Scoreboard issued by the European Commission established an evaluation index system for innovation and entrepreneurship from the macro-level [2]. In 2006, IMD of Switzerland published the Global Competitiveness Report and established the evaluation index system for innovation and entrepreneurship from four levels: technical infrastructure, scientific infrastructure, education, and employment [3]. In 2007, the World Intellectual Property Organization (WIPO) organized some countries to release the Global Innovation Index Report jointly. This innovation index system measures the innovation ability of an economy by evaluating the maturity of institutions and policies, infrastructure, commerce and markets, and human skills. In addition, it can also analyze the innovation trends and status quo and analyze the development advantages and disadvantages of various countries based on index values.

In the rapid development of higher education in China, many colleges and universities have integrated innovation entrepreneurship education and professional education into the compulsory curriculum system and promoted the high-quality development of innovation and entrepreneurship education through measures such as entrepreneurship competition and the construction of entrepreneurship parks. Success has been achieved in quantity, form, and effect. Facing the realistic requirements for deepening the reform of innovation and entrepreneurship education and realizing the breakthrough from quantitative change to qualitative change, it is urgent to conduct scientific and systematic research on the quality evaluation of innovation and entrepreneurship [4]. The quality evaluation of innovation and entrepreneurship education can objectively present the current situation of innovation and entrepreneurship education in China and effectively promote the deepening of innovation and entrepreneurship education reform in the new era [5]. In this study, the high-quality development level of innovation and entrepreneurship in 19 vice-ministerial cities, such as Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, Shenzhen, and Chengdu in Beijing, was taken as the research object. The quality evaluation of innovation and entrepreneurship in China was empirically studied from two aspects: process and result. According to the survey results, the suggestions for deepening the reform of innovation and entrepreneurship in the new period were put forward.

2. State of art

The literature on innovation and entrepreneurship education in colleges and universities at home and abroad mainly focuses on the influencing factors, practice paths, and institutional context of innovation and entrepreneurship education. For influencing factors, Cao and Li [6] believe that entrepreneurial cognitive ability is an internal factor affecting innovation and entrepreneurship education, including communication ability, creative thinking, problem-solving ability, and logical thinking ability. According to Kuratko’s research, entrepreneurial skills are an important factor affecting students’ entrepreneurial attitude, and universities should pay attention to cultivating students’ ability to take entrepreneurial risks and other key skills [7]. Based on the theory of educational psychology and the theory of planned behavior (TPB), Zhang [8] conducted a questionnaire survey and modelling analysis on the influencing factors of college students’ entrepreneurial intention and found that college students’ entrepreneurial intention is positively correlated with their entrepreneurial attitude and perceived behavior. Entrepreneurial intention is not only influenced by school education but also directly influenced by social factors. Therefore, innovation and entrepreneurship education should focus on improving college students’ entrepreneurial practical experience. Grkan and Dolapiolu [9] believe that the objectives, content, teaching methods, and cooperation among social entrepreneurs of entrepreneurship courses are important factors that affect innovation and entrepreneurship education in colleges and universities for the practice paths. Harkema and Schout [10] put forward a teaching plan to encourage students to establish innovative and entrepreneurial ideas through the integration process, which is conducive to students’ in-depth understanding of the entrepreneurial environment and accumulation of entrepreneurial practical experience. Zhu et al. [11] believed that for innovation and entrepreneurship education in colleges and universities, efforts should be made to innovate teaching methods and promote the organic combination of innovation and entrepreneurship education and professional education through case teaching. Pittaway and Cope [12] held that colleges and universities should organize students to acquire entrepreneurial knowledge through interaction and experience and cultivate students’ leadership, creativity, critical thinking, and ability to deal with social relations. For the institutional content, Alias and Zainuddin [13] thought that the innovation and entrepreneurship education curriculum system in research universities should set up more extracurricular practical courses and organize students to participate in extracurricular practical courses extensively. McGill and Klobas [14] established a sustainable development-oriented innovation and entrepreneurship education system and believed that creativity is an important index to evaluate the effectiveness of innovation and entrepreneurship education. Colleges and universities should scientifically design innovative entrepreneurship education curriculum systems according to different educational levels and train students with entrepreneurial intentions to become practical entrepreneurs with innovative abilities.

Chinese and foreign scholars have paid attention to the practice paths, existing problems, and ecosystem construction of innovation and entrepreneurship education in colleges and universities. For the research on practice paths, Yueh and Hsu [15] discussed the practice path of innovation and entrepreneurship education in colleges and universities from practical teaching and entrepreneurial desire. Wang et al. [16] believed that colleges and universities should take reform as a breakthrough, take innovation and entrepreneurship education reform as a systematic project with promoting the construction of innovation and entrepreneurship demonstration bases as a starting point, and implement it in classroom teaching, curriculum system construction, and other links. Colleges and universities should be guided by the concepts of “combining the first class with the second class” and “combining individuals with groups”, and fully integrate innovation and entrepreneurship education courses into the curriculum system from three aspects: basic quality education, professional skill education, and general interest education [17]. For the existing problems. Rhode et al. [18] discussed the problems in innovation and entrepreneurship education from four aspects: universities, students, educational elements, and society, and put forward solutions from five aspects: educational methods, national policies, and project feasibility. Popovic et al. [19] believed that there are difficulties in theory, policy, and practice in the innovation and entrepreneurship education of colleges and universities, and put forward two development paths for implementation: adaptation and extension. Horvat et al. [20] stated that there are deep-rooted problems in the cognition, popularization, and ontology defects of innovation and entrepreneurship education in colleges and universities, and proposed that innovation and entrepreneurship education should go deep into the daily life of higher education. It is believed that there are some problems in innovation and entrepreneurship education in local engineering colleges, such as system disharmony, resource bottleneck, and system obstacles, and the “135” innovation and entrepreneurship education model reform has been explored and implemented [21, 22] thought that the popularization effect of innovation and entrepreneurship education in colleges and universities in China is not ideal, put forward three development directions of “integral” system construction, “discipline-supported” education model, and “practical rationality”-dominated knowledge production, and pointed out the popularization path of innovation and entrepreneurship education. In terms of ecosystem construction. Long built an innovation and entrepreneurship education ecosystem with projects as the carrier and competitions as the starting point [23] Yu [24] analyzed the innovation and entrepreneurship ecosystem in land-grant universities from seven aspects, including offering innovation and entrepreneurship courses, and thought that universities in China should build an all-round and multi-level innovation and entrepreneurship ecosystem. Brcz [25] obtained the participants, constituent parts, and key components of the innovation and entrepreneurship education ecosystem through a number of case studies of universities in the United States, Britain, and Japan, and constructed an innovation and entrepreneurship education ecosystem model suitable for universities in China. To sum up, foreign countries have conducted in-depth research on the influencing factors, practice paths, and system content of innovation and entrepreneurship education in colleges and universities [26]. China has made great achievements in the practice paths, existing problems, and ecosystem construction of innovation and entrepreneurship education in colleges and universities, but few scholars have explored the construction of innovation and entrepreneurship education systems in colleges and universities under the background of “double first-class” construction [27, 28]. In the “double first-class” construction period, establishing and perfecting the innovation and entrepreneurship education system is an important way for colleges and universities to comprehensively deepen the reform of innovation and entrepreneurship education and realize the goal of cultivating top-notch innovative talents [29]. Based on the existing research, therefore, it is very important and urgent in this study to explore the theoretical basis and content framework of the development level of innovation and entrepreneurship education in 19 sub-ministerial and above cities, such as Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, Shenzhen, and Chengdu in China.

Generally speaking, the research on the high-quality development evaluation of innovation and entrepreneurship in China has attracted attention, but a scientific and reasonable quality evaluation system has not yet been formed. The existing research on innovation and entrepreneurship evaluation mainly focuses on normative research, and empirical methods have been less used in the research. Especially in innovation and entrepreneurship, the elements and effectiveness of innovation and entrepreneurship education have been insufficiently cognized, without evidence support from any empirical research. Generally, empirical research needs to be supported by normative research, which, in turn, needs to be verified by empirical research. Enlightened by the existing research, it was thought in this study that the high-quality development of innovation and entrepreneurship should be evaluated based on the process and results of innovation and entrepreneurship. And innovation and entrepreneurship process could be evaluated from such dimensions as the background, process, input, output, and transformation of innovation and entrepreneurship. In addition, the high-quality development of innovation and entrepreneurship should be evaluated from entrepreneurial knowledge and skills, and entrepreneurial intention and spirit.

3. Modeling

3.1 TOPSIS method

TOPSIS method can eliminate the dimensional influence of different indexes by normalizing and co-trending the initial data, and can objectively reflect the real gap between schemes, so it has a wide scope of application. Firstly, $m$ objectives (limited objectives) and $n$ attributes were set. The evaluation value given by experts to the attribute $j$ of the objective $i$ is $x_{ij}$ , and then the initial judgment matrix $V$ is shown as Eq. (1):

$\displaystyle V=\left[{{\begin{array}[]{*{20}c}{x_{11}}&{x_{12}}&\ldots&{x_{1n% }}\\ {x_{21}}&{x_{22}}&\ldots&{x_{2n}}\\ \vdots&\vdots&\vdots&\vdots\\ {x_{i1}}&\ldots&{x_{ij}}&\ldots\\ \vdots&\vdots&\vdots&\vdots\\ {x_{m1}}&{x_{m2}}&\ldots&{x_{mn}}\\ \end{array}}}\right]$ (1)

Considering the different possibilities of index dimensions, the initial judgment matrix $V$ was normalized to obtain the judgment matrix ${V}^{\prime}$ , as seen in Eq. (2).

$\displaystyle V^{\prime}=\left[{{\begin{array}[]{*{20}c}{x_{11}^{\prime}}&{x_{% 12}^{\prime}}&\ldots&{x_{1n}^{\prime}}\\ {x_{21}^{\prime}}&{x_{22}^{\prime}}&\ldots&{x_{2n}^{\prime}}\\ \vdots&\vdots&\vdots&\vdots\\ {x_{i1}^{\prime}}&\ldots&{x_{ij}^{\prime}}&\ldots\\ \vdots&\vdots&\vdots&\vdots\\ {x_{m1}^{\prime}}&{x_{m2}^{\prime}}&\ldots&{x_{mn}^{\prime}}\\ \end{array}}}\right]$ (2)

In Eq. (3),

$\displaystyle x_{ij}^{\prime}=x_{ij}\left/\sqrt{\sum_{k=1}^{n}x_{ij}^{2}},i=1,% 2\ldots m;j=1,2\ldots n\right.$ (3)

According to the AHP method, the information weight matrix $B$ of expert groups for attributes was then obtained to form a weighted judgment matrix $Z$ , as seen in Eq. (4).

$\displaystyle Z=V^{\prime}B=\left[{{\begin{array}[]{*{20}c}{x_{11}^{\prime}}&{% x_{12}^{\prime}}&\ldots&{x_{1n}^{\prime}}\\ {x_{21}^{\prime}}&{x_{22}^{\prime}}&\ldots&{x_{2n}^{\prime}}\\ \vdots&\vdots&\vdots&\vdots\\ {x_{i1}^{\prime}}&\ldots&{x_{ij}^{\prime}}&\ldots\\ \vdots&\vdots&\vdots&\vdots\\ {x_{m1}^{\prime}}&{x_{m2}^{\prime}}&\ldots&{x_{mn}^{\prime}}\\ \end{array}}}\right]\left[{{\begin{array}[]{*{20}c}{w_{11}}&{w_{12}}&\ldots&{w% _{1n}}\\ {w_{21}}&{w_{22}}&\ldots&{w_{2n}}\\ \vdots&\vdots&\vdots&\vdots\\ {w_{i1}}&\ldots&{w_{ij}}&\ldots\\ \vdots&\vdots&\vdots&\vdots\\ {w_{m1}}&{w_{m2}}&\ldots&{w_{mn}}\\ \end{array}}}\right]=\left[{{\begin{array}[]{*{20}c}{f_{11}}&{f_{12}}&\ldots&{% f_{1n}}\\ {f_{21}}&{f_{22}}&\ldots&{f_{2n}}\\ \vdots&\vdots&\vdots&\vdots\\ {f_{i1}}&\ldots&{f_{ij}}&\ldots\\ \vdots&\vdots&\vdots&\vdots\\ {f_{m1}}&{f_{m2}}&\ldots&{f_{mn}}\\ \end{array}}}\right]$ (4)

Based on the weighted judgment matrix, the positive ideal solution $f_{j}^{\ast}$ and negative ideal solution ${f}_{j}^{\prime}$ of the evaluation objective were acquired as seen in Eq. (5).

$\displaystyle f_{j}^{\ast}=\left\{{{\begin{array}[]{l}{\max(f_{ij}),j\in J^{% \ast}}\\ {\min(f_{ij}),j\in J^{\prime}}\\ \end{array}}}\right.,j=1,2,\ldots,n$ (5) $\displaystyle f_{j}^{\prime}=\left\{{{\begin{array}[]{l}{\min(f_{ij}),j\in J^{% \ast}}\\ {\max(f_{ij}),j\in J^{\prime}}\\ \end{array}}}\right.,j=1,2,\ldots,n$

In Eq. (5), $J^{\prime}$ is a cost index and $J^{\ast}$ is a benefit index. The Euclidean distance between each objective value and ideal value was solved as per Eq. (3.1).

$\displaystyle S_{i}^{\ast}=\sqrt{\sum\limits_{j=1}^{m}{(f_{ij}-f_{j}^{\ast})^{% 2}}},j=1,2,\ldots,n$ $\displaystyle S_{i}^{\prime}=\sqrt{\sum\limits_{j=1}^{m}{(f_{ij}-f_{j}^{\prime% })^{2}}},j=1,2,\ldots,n$ (6)

Finally, the relative closeness $C_{i}^{\ast}$ of each objective was calculated according to Eq. (7).

$\displaystyle C_{i}^{\ast}=\frac{S_{i}^{\prime}}{S_{i}^{\ast}+S_{i}^{\prime}}i% =1,2,\ldots,m$ (7)

The objectives were ranked according to the relative closeness $C_{i}^{\ast}$ to form a decision basis.

3.2 Determination of index weights

At present, control variables have been ranked by scholars mostly using the Delphi method or questionnaire survey method, but the ranking results are usually highly subjective, failing to change according to the relative change extent of each control variable. Consequently, the evaluation results lack objectivity and rationality. In this study, the importance of evaluation indexes was ranked using the AHP-EM combination weighting method, which ensured the objectivity and rationality of the evaluation index system for the high-quality development of innovation and entrepreneurship.

(1) Analytic hierarchy process (AHP)

In a hierarchical structural model, the bottom layer is generally the factor layer, and all kinds of basic risk factors identified are regarded as the second-level risk evaluation indexes; the middle layer is the criterion layer, which classifies risk factors as the first-level risk evaluation indexes; the top layer is the objective layer, that is, the decision goal that risk quantification needs to achieve. After the evaluation objectives, plans, standards, and indexes are determined, the hierarchical model of the system can be constructed to comprehensively identify and analyze the risk factors. Then, the judgment matrix is established. According to the established risk hierarchy, every two factors are compared and the quantitative scale between them is made through the nine-point scale method based on their importance, thereby obtaining a judgment matrix.

The product of elements $a_{ij}$ in the judgment matrix is calculated by rows to obtain a new vector $M_{i}$ , as seen in Eq. (8).

$\displaystyle M_{i}=\prod\limits_{j=1}^{n}{a_{ij}}(i,j=1,2,3\ldots,n)$ (8)

The $n$ -th root is taken from each element of the new vector $M_{i}$ , so as to obtain the vector $r_{i}$ , as seen in Eq. (9).

$\displaystyle r_{i}=\sqrt[n]{M_{i}}$ (9)

Subsequently, $r_{i}$ is normalized to obtain the weight vector $W_{i}$ , maximum characteristic root $\lambda_{\max}$ , consistency index $T$ , and consistency ratio $Q$ , and whether the matrix passes the consistency check is judged through the consistency ratio.

$\displaystyle W_{i}={r_{i}}\left/{\sum\limits_{i=1}^{n}{r_{i}}}\right.$ (10) $\displaystyle\lambda_{\max}\approx\frac{1}{n}\sum\limits_{i=1}^{n}{\frac{\sum% \limits_{j=1}^{n}{({a_{ij}W_{j}})}}{W_{i}}}$ (11) $\displaystyle T=\frac{\lambda_{\max}-n}{n-1}$ (12) $\displaystyle Q=\frac{T}{K}$ (13)

(2) Entropy method (EM)

The entropy method (EM) is an objective weighting method to judge the statistical dispersion of indexes. In case of less information, the greater the uncertainty, the greater the entropy; with more information, the uncertainty decreases and the entropy decreases. The weight of each evaluation index is determined according to its entropy, and the greater the relative change of the index, the greater its weight. Among the evaluation methods of mutation sequences, the importance of evaluation indexes is ranked through EM to overcome the deviation triggered by subjective scoring. The general procedure of EM can be divided into the following steps:

The proportion $\gamma_{ij}$ of $x_{ij}$ is calculated. In which,

$\displaystyle\gamma_{ij}=\frac{x_{ij}}{\sum\limits_{i=1}^{m}{x_{ij}}},(i=1,2,3% ,\ldots,m,j=1,2,3,\ldots,n)$ (14)

The entropy $\rho_{j}$ of the j-th index is solved. In which,

$\displaystyle\rho_{j}=-k\sum\limits_{i=1}^{m}\gamma_{ij}\ln\gamma_{ij},(i=1,2,% 3,\ldots,m,j=1,2,3,\ldots,n),$ (15) $\displaystyle k=\frac{1}{\ln m}(m\text{ is sample size})$

The diversity coefficient $\mu_{j}$ of the j-th index is solved. In which,

$\displaystyle\mu_{j}=1-\rho_{j}$ (16)

The weight $w_{j}$ of the j-th index is calculated. In which,

$\displaystyle w_{j}=\frac{\mu_{j}}{\sum\limits_{j=1}^{n}{\mu_{j}}}$ (17)

The outermost index weights $W=(w_{1},w_{2},\ldots,w_{n})$ of the index system are determined according to the above steps, the lower-layer index weights are added to obtain the weight values of upper-layer indexes, and all weight values from the total evaluation index to the bottom-layer index for the development level of innovation and entrepreneurship education is obtained through this method.

The importance of the evaluation indexes for innovation and entrepreneurship education is ranked according to the weight vector $W=(w_{1},w_{2},\ldots,w_{n})$ , thus obtaining the total ranking of indexes.

(3) Determination of comprehensive weight

The subjective weight vector $\alpha$ and objective weight vector $\beta$ are respectively obtained by AHP-EM, the comprehensive weight consists of the two kinds of weights, and the weight of each index in the evaluation process can be fully reflected through their complementarity. To ensure that the comprehensive weight $\omega_{i}$ of indexes is as close as to $\alpha_{i}$ and $\beta_{i}$ , the comprehensive weight $\omega_{i}$ can be acquired based on the principle of the minimum distinguishing information. The objective function is shown in Eq. (18):

$\displaystyle\left\{{{\begin{array}[]{l}{\min J(\omega)=\sum\limits_{i=1}^{n}% \left(\omega_{i}\ln\frac{\omega_{i}}{\alpha_{i}}+\omega_{i}\ln\frac{\omega_{i}% }{\beta_{i}}\right)}\\ {\text{s.t.}\sum\limits_{i=1}^{n}{\omega_{i}}=1,\omega_{i}\geqslant 0\quad i=1% ,2,\ldots,n}\\ \end{array}}}\right.$ (18)

The optimization model is solved to obtain the comprehensive weight vector, shown in Eq. (19).

$\displaystyle\omega_{i}=\frac{\sqrt{\alpha_{i}\beta_{i}}}{\sum\limits_{j=1}^{n% }{\sqrt{\alpha_{i}\beta_{i}}}}$ (19)

The comprehensive weight vector is shown in Eq. (20):

$\displaystyle\omega=[{{\begin{array}[]{*{20}c}{\omega_{1},\omega_{2},\ldots,% \omega_{n}}\\ \end{array}}}]^{T}$ (20)

3.3 Index system

The evaluation of the high-quality development of innovation and entrepreneurship is a “three-in-one” (full aperture, whole process, and whole perspective) evaluation of innovation and entrepreneurship reform. Therefore, the evaluation system for the high-quality development of innovation and entrepreneurship is a complex system, and evaluation indexes should be selected following the principles of comprehensiveness, scientificity, operability, and dynamics. The evaluation principles for the high-quality development of innovation and entrepreneurship mainly start from different angles, such as the background, process, input, output, and transformation of innovation and entrepreneurship, the emphasis is laid on the final evaluation, and the most valuable is the organic combination of process evaluation, formative evaluation, and diagnostic evaluation, highlighting the sustainable improvement of the high-quality development of innovation and entrepreneurship. According to the evaluation principles for the high-quality development of innovation and entrepreneurship, 21 subindexes belonging to 5 major classes were selected (Table 1).

Table 1
Evaluation index system for the high-quality development of innovation and entrepreneurship

First-level index	Symbol	Second-level index	Symbol
Innovation and	X1	Total number of real market subjects (ten thousand households)	X11
entrepreneurship		Year-on-year growth rate of the total number of real markets	X12
background		Newly added market subjects (ten thousand households)	X13
		Quantity of urban colleges and universities	X14
Innovation and	X2	Innovation and entrepreneurship curriculum planning	X21
entrepreneurship		Innovation and entrepreneurship theory teaching	X22
process		Implementation of innovation and entrepreneurship practice	X23
		Innovation and entrepreneurship competition	X24
Innovation and	X3	Total market value of listed companies	X31
entrepreneurship		Financing amount	X32
input		Social R&D fund input	X33
		Intensity of social R&D fund input	X34
Innovation and	X4	Number of patents granted (ten thousand pieces)	X41
entrepreneurship		Number of granted patents for invention (ten thousand pieces)	X42
output		Patent awards	X43
		Turnover of technology contracts	X44
		Growth rate of turnover of technology contracts in comparison with that in the previous year	X45
Innovation and entrepreneurship	X5	Warehousing comparison of small and medium-sized scientific and technological enterprises	X51
transformation		Effective high-tech enterprises (ea)	X52
		Total number of listed companies on science and technology innovation board (ea)	X53
		Warehousing comparison of small and medium-sized scientific and technological enterprises	X54

3.4 Data sources

In this study, the high-quality development level of innovation and entrepreneurship in 19 sub-ministerial and above cities, such as Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, Shenzhen, and Chengdu, China, was measured (Table 2). The original data of the 19 cities in 2022 come from China Statistical Yearbook, China Statistical Yearbook on Science and Technology, China Torch Statistical Yearbook, China Statistics Yearbook on High Technology Industry, China City Statistical Yearbook, and Educational Statistics Yearbook of China.

Table 2
Basic information of the samples

Item	Number	Average	Standard deviation
X11	19	197.679	95.	740
X12	19	0.099	0.	039
X13	19	34.548	16.	562
X14	19	49.421	23.	843
X21	19	74.263	37.	659
X22	19	75.579	38.	932
X23	19	71.474	30.	707
X24	19	69.105	30.	957
X31	19	1968.332	2951.	956
X32	19	208.079	307.	077
X33	19	616.379	582.	130
X34	19	0.034	0.	012
X41	19	115.146	461.	826
X42	19	1.786	1.	850
X43	19	29.000	37.	220
X44	19	1258.437	1610.	291
X45	19	0.243	0.	352
X51	19	0.182	0.	217
X52	19	7224.000	5760.	936
X53	19	8628.316	7034.	047
X54	19	16.632	22.	169

4. Determination of index weights at each level

On the basis of relevant research results and combining the evaluation method for the high-quality development of innovation and entrepreneurship, an evaluation index system containing 5 first-level indexes and 21 second-level indexes was first established for the high-quality development of innovation and entrepreneurship from the following aspects: the background, process, input, output, and transformation of high-quality development of innovation and entrepreneurship, and a three-layer index evaluation system was constructed based on the principles of scientificity, operability, and practicability. Then, the AHP, EM, and TOPSIS model were combined to construct the combination weighting-TOPSIS model for evaluating the high-quality development of innovation and entrepreneurship. First, the index weight was determined using the AHP-EM combined method, and the weight value of each third-level index was calculated (Table 3).

Table 3
Results of AHP-entropy combination method

First-level index	Symbol	Second-level index	Symbol	AHP weight	Entropy weight	Combined weight	Ranking
Innovation and entrepreneurship	X1	Total number of real market subjects (ten thousand households)	X11	0.0216	0.0501	0.0362	17
background		Year-on-year growth rate of the total number of real markets	X12	0.0581	0.0708	0.0706	2
		Newly added market subjects (ten thousand households)	X13	0.0371	0.0376	0.0411	13
		Quantity of urban colleges and universities	X14	0.0168	0.0330	0.0259	21
Innovation and entrepreneurship	X2	Innovation and entrepreneurship curriculum planning	X21	0.0530	0.0684	0.0662	5
process		Innovation and entrepreneurship theory teaching	X22	0.0699	0.0459	0.0623	6
		Implementation of innovation and entrepreneurship practice	X23	0.0426	0.0633	0.0571	9
		Innovation and entrepreneurship competition	X24	0.0906	0.0080	0.0296	18
Innovation and	X3	Total market value of listed companies	X31	0.0305	0.0553	0.0452	12
entrepreneurship		Financing amount	X32	0.0388	0.0341	0.0400	14
input		Social R&D fund input	X33	0.0687	0.0320	0.0516	10
		Intensity of social R&D fund input	X34	0.0498	0.0553	0.0577	7
Innovation and entrepreneurship	X4	Number of patents granted (ten thousand pieces)	X41	0.0324	0.0251	0.0314	17
output		Number of granted patents for invention (ten thousand pieces)	X42	0.0633	0.0580	0.0666	4
		Patent awards	X43	0.0742	0.0539	0.0695	3
		Turnover of technology contracts	X44	0.0517	0.0400	0.0500	11
		Growth rate of turnover of technology contracts in comparison with that in the previous year	X45	0.0158	0.0702	0.0366	15
Innovation and entrepreneurship transformation	X5	Warehousing comparison of small and medium-sized scientific and technological enterprises	X51	0.0150	0.0466	0.0291	19
		Effective high-tech enterprises	X52	0.0400	0.0677	0.0573	8
		Total number of listed companies on science and technology innovation board	X53	0.0475	0.0132	0.0275	20
		Warehousing comparison of small and medium-sized scientific and technological enterprises	X54	0.0826	0.0716	0.0846	1

5. TOPSIS results

TOPSIS method evaluates the relative advantages and disadvantages of positive and negative ideal solutions based on their distance ranking from the evaluation object. First, evaluation indexes were determined, the forward trend (the greater, the better) of evaluation indexes was guaranteed, and the calculation results are listed (Table 4).

Table 4
Positive and negative ideal solutions

Item	Positive ideal solution A $+$	Negative ideal solution A $-$
X11	19	197.679
X12	19	0.099
X13	19	34.548
X14	19	49.421
X21	19	74.263
X22	19	75.579
X23	19	71.474
X24	19	69.105
X31	19	1968.332
X32	19	208.079
X33	19	616.379
X34	19	0.034
X41	19	115.146
X42	19	1.786
X43	19	29.000
X44	19	1258.437
X45	19	0.243
X51	19	0.182
X52	19	7224.000
X53	19	8628.316
X54	19	16.632

The positive and negative ideal solutions in Table 5 are the intermediate process values when calculating the positive and negative distances (D $+$ and D $-$ ), and their significance is relatively small. The positive ideal solution A $+$ represents the maximum value of the evaluation index; the minimum value of the evaluation index is the negative ideal solution A $-$ .

Table 5

TOPSIS evaluation calculation results

Item	Positive ideal solution distance D $+$	Negative ideal solution distance D $-$	Relative proximity C	Ranking
Shenzhen	2408.940	5954.186	0.712	1
Beijing	3562.877	4923.388	0.580	3
Shanghai	2217.837	5199.477	0.701	2
Tianjin	4853.803	2360.470	0.327	6
Chongqiong	6448.582	753.068	0.105	14
Chengdu	5405.619	1783.812	0.248	8
Guangzhou	4263.614	3184.628	0.428	5
Xi’an	5105.623	2144.716	0.296	7
Qingdao	5861.582	1404.195	0.193	11
Nanjing	4323.097	3863.288	0.472	4
Wuhan	5678.682	1575.850	0.217	10
Hangzhou	5694.325	1617.562	0.221	9
Jinan	5995.485	1240.902	0.171	12
Changchun	7082.536	64.275	0.009	19
Ningbo	6410.748	752.401	0.105	13
Shenyang	6593.311	549.306	0.077	15
Harbin	6885.558	479.673	0.065	17
Dalian	6690.333	469.756	0.066	16
Xiamen	6991.294	196.971	0.027	18

D $+$ and D $-$ respectively represent the distances of the evaluation object from the positive ideal solution and the negative ideal solution, respectively (Table 5). C indicates the closeness between the evaluation object and the optimal scheme. The larger this value is, the closer it is to the optimal scheme. The relative proximity C value of Shenzhen was 0.712, that of Shanghai was 0.701, and that of Beijing was 0.580, ranking the top three. The reason may be that these three cities have obvious advantages in the total number of listed companies on the science and technology innovation board, the year-on-year growth rate of the total number of real markets, patent awards, the number of granted patents for invention, innovation and entrepreneurship curriculum planning, and innovation and entrepreneurship theory teaching. Shenzhen, Shanghai, and Beijing have higher-high-quality development levels of innovation and entrepreneurship. Harbin’s relative closeness C value of Harbin was 0.065, that of Xiamen was 0.027, and Changchun’s was 0.009, ranking the last three. The high-quality development levels of innovation and entrepreneurship were relatively low in Harbin, Xiamen, and Changchun, which was attributed to their obvious disadvantages in the total number of listed companies on the science and technology innovation board, the year-on-year growth rate of the total number of real markets, patent awards, the number of granted patents for invention, innovation and entrepreneurship curriculum planning, and innovation and entrepreneurship theory teaching. Thus, the high-quality development level of innovation and entrepreneurship in 19 sub-provincial and above cities in China was comprehensively evaluated, with the advantages of simple principles, easy understanding, and intuitive conclusions. The proposed method, which is an upgrade and improvement of the TOPSIS method, is an effective, comprehensive evaluation method that provides new ideas and methods for evaluation in other fields.

6. Discussion

In the evaluation system for the high-quality development of innovation and entrepreneurship, the high-quality development background, process, input, output, and transformation of innovation and entrepreneurship were the first-level indexes, and 21 indexes like the total number of listed companies on the science and technology innovation board, the year-on-year growth rate of the total number of real markets, patent awards, the number of granted patents for invention, innovation and entrepreneurship curriculum planning, and innovation and entrepreneurship theory teaching were used as the second-level indexes to evaluate the high-quality development of innovation and entrepreneurship in 19 sub-ministerial and above cities like Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, and Shenzhen, China. According to the evaluation results, it could be known that the influencing factors in the evaluation system for the high-quality development of innovation and entrepreneurship in 19 sub-ministerial and above cities in China were ranked as: the total number of listed companies on the science and technology innovation board $>$ the year-on-year growth rate of the total number of real markets $>$ patent awards $>$ the number of granted patents for invention $>$ innovation and entrepreneurship curriculum planning $>$ innovation and entrepreneurship theory teaching. According to the indexes at all levels, the analysis was as follows: The total number of listed companies on the science and technology innovation board is the key factor. Whether for the cultivation of innovation ability in the early stage or the entrepreneurial practice in the later stage, the main body is the transformation of innovation and entrepreneurship achievements, and the success or failure also lies in the transformation of achievements. The year-on-year growth rate of the total number of real markets is goal-oriented. In addition to cultivating talents, which is the first priority, the most important thing is to serve local economic construction, especially the transformation and incubation of achievements. Patent awards constitute the leading and most easily overlooked important factors. The economic development of China’s 19 sub-ministerial and above cities is unbalanced. To stimulate entrepreneurial enthusiasm through the high-quality development of innovation and entrepreneurship requires policy support higher education and the leading role of the value. This study calculated the weights of second-level evaluation indexes by combining AHP and EM. Then, an evaluation system for the high-quality development of innovation and entrepreneurship was established using the TOPSIS method. Next, 19 sub-ministerial and above cities in China, which were taken as the study objects, were empirically analyzed. Thus, all kinds of factors were comprehensively considered from multiple levels, man-made interference was relieved, and the results were more objective and reasonable, which could provide a basis for controlling the high-quality development of innovation and entrepreneurship and also lay a foundation for developing and implementing the evaluation system for the high-quality development of innovation and entrepreneurship.

7. Conclusions

In this study, influencing indexes were hierarchically classified by combining AHP and EM, followed by combination weighting of the indexes. Then, a comprehensive evaluation decision model for the high-quality development of innovation and entrepreneurship was established through the TOPSIS method. A total of 19 sub-ministerial and above cities like Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, and Shenzhen in China were empirically studied as the study objects, and the following conclusions were drawn:

(1)

An online teaching satisfaction evaluation index system was established, and an online teaching effect evaluation index system containing 5 first-level indexes and 21 second-level indexes was constructed from the following aspects: the high-quality development background, process, input, output, and transformation of innovation and entrepreneurship. Subsequently, a combination weighting-TOPSIS online teaching effect evaluation model was built by combining AHP and EM. Furthermore, indexes were ranked using the AHP-EM weighting method. It was then found that the most important factors influencing the high-quality development level of innovation and entrepreneurship were the total number of listed companies on the science and technology innovation board, the year-on-year growth rate of the total number of real markets, patent awards, the number of granted patents for invention, innovation and entrepreneurship curriculum planning, and innovation and entrepreneurship theory teaching.

(2)

The AHP-EM-TOPSIS evaluation method was adopted to evaluate the high-quality development level of innovation and entrepreneurship in 19 sub-ministerial and above cities in China, such as Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, and Shenzhen, among which Shenzhen, Shanghai, and Beijing ranked the top three, while Harbin, Dalian, and Xiamen ranked the last three. Based on the above analysis, Harbin, Dalian, and Xiamen need to strengthen the efforts into the management of the following aspects: the total number of listed companies on the science and technology innovation board, the year-on-year growth rate of the total number of real markets, patent awards, the number of granted patents for invention, innovation and entrepreneurship curriculum planning, and innovation and entrepreneurship theory teaching. Meanwhile, the proposed method can reflect the fuzziness of the evaluation object—the high-quality development level of innovation and entrepreneurship- effectively reducing information loss and thus contributing to more accurate evaluation results.

Footnotes

Acknowledgments

This study was supported by the National Social Science Foundation (No. BIA210171).

Declarations of interest

None.

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