Application of Multiattribute Decision-Making for Evaluating Regional Innovation Capacity

The growing imbalance in regional innovation development has become an urgent issue in China’s strategy to build an innovative country. To enrich the regional innovation capacity evaluation system, scientiﬁcally assess regional innovation capacity, and explore available pathways to improve regional innovation capacity, this paper introduces a multiattribute decision-making method for evaluating regional innovation capacity. First, a random forest model and the DEMATEL-based analytic network process (DANP) method are applied to calculate the weights of the evaluation attributes. Second, the multiobjective optimization by the ratio analysis method based on the maximum and minimum (MOORA-min-max method) is used to calculate the evaluation attribute gap ratios and regional innovation capacity of each region. Finally, the limitations of regional innovation development are identiﬁed based on the evaluation attribute gap ratios and the critical inﬂuence strength roadmap (CISR) to explore the regional innovation capacity improvement pathways. The results show that “output capacity of R&D personnel in universities and research institutes” is the most fundamental evaluation attribute in the regional innovation capacity evaluation, while “output eﬃciency of R&D funds in universities and research institutes” is the most inﬂuential evaluation attribute. Research in Sichuan and Inner Mongolia reveals that regions need to identify critical constraints in four aspects: knowledge creation, knowledge acquisition, enterprise innovation, and innovation environment, to improve regional innovation capacity.


Introduction
Persistent imbalance in the development of regional innovation capacity constitutes a substantial bottleneck constraining the effort to upgrade countries' integrated innovation capacity. China's regional innovation development is influenced by its history, economy, and geography and thus varies significantly [1][2][3]. To better promote the role of regional innovation in high-quality economic development, Chinese policymakers have placed innovation at the centre of overall national development. e 19th National Congress of the Communist Party of China proposed that "innovation is the first impetus for leading development" and issued a strategic plan to accelerate the construction of an innovation-oriented country.
Regional innovation capacity is an essential indicator of an innovation-oriented country, and many scholars have focused on regional innovation capacity in recent years [4,5]. Scholars have thoroughly studied the conceptual definition of regional innovation capacity, including its differences, indicators, influencing factors, and formation mechanisms [6][7][8][9][10]. For example, Shan constructed a system for evaluating regional innovation capacity based on four aspects: input capacity, innovation environment, management capacity, and innovation output [11]. Hamidi et al. examined the relationship between regional compactness and regional innovation capacity in the United States [12]. Tang et al. studied the spatial effect of absorptive capacity on regional innovation capacity from the perspective of knowledge spillover theory [13]. Many organizations have also published reports on the evaluation of innovation. e World Intellectual Property Organization and others cofounded the Global Innovation Index (GII), which ranks countries according to their innovation capacity and economic performance. Similarly, the National Research Group on S&T Development Strategy released the China Regional Innovation Capability report, which provides an objective, dynamic, and comprehensive assessment of China's innovation capacity in each region.
With the advent of the Fourth Industrial Revolution, the ability to innovate has once again become a vital capacity for countries to compete for the right to global value distribution. For China, which displays significant differences in regional innovation development, improving regional innovation is an urgent issue. An accurate evaluation of regional innovation capacity is the basis for monitoring the current state of regional innovation development, identifying constraints on regional innovation development, and exploring pathways for improving regional innovation capacity. Accordingly, this paper selects evaluation indicators from four aspects, namely, knowledge creation, knowledge acquisition, enterprise innovation, and innovation environment and then applies the multiattribute decisionmaking method to evaluate the innovation capacity of all 31 provinces in China and to explore pathways for improving regional innovation capacity. e main contributions of this paper are as follows: (1) e random forest model and the decision-making trial and evaluation laboratory-(DEMA-TEL-) based analytic network process (DANP) method are introduced to innovation capacity evaluation research, thereby enriching the method for calculating objective weights; moreover, a multiattribute decision-making evaluation model of regional innovation capacity provides a new method to evaluate regional innovation objectively. (2) e multiobjective optimization by ratio analysis (MOORA) method and the critical influence strength roadmap (CISR) are introduced into the field of innovation research to provide a new approach to scientifically identify the factors limiting regional innovation capacity.

Literature Review
To date, scholars have not reached a consensus on how to evaluate regional innovation [14]. In the existing literature, innovation capacity evaluation research is divided into two aspects: evaluation indexes and evaluation methods. In terms of research on evaluation indexes, common indicators for evaluating regional innovation capacity include innovation resource inputs, innovation outputs, and innovation environments [15][16][17]. Other scholars have proposed patents as an essential indicator of regional innovation capacity [18][19][20][21]. For example, Hamidi et al. used the number of patents as one indicator of regional innovation capacity [12]. In addition, scholars have assessed the selection of indicators for evaluating regional innovation capacity in terms of system structure and green innovation. For example, Han et al. used the innovation participant framework [17] to classify innovation participants into eight categories, including government departments, research institutes, colleges and universities, enterprises, and technology intermediaries. ey selected 63 innovation participant indexes to analyse the innovation capacity of 16 cities in Korea [22]. Chen et al. established regional innovation capabilities based on knowledge management from 6 aspects: knowledge base, knowledge creation, knowledge dissemination, knowledge sharing, knowledge application, and innovation environment [23]. Wang et al. constructed a system of regional innovation evaluation indicators from green innovation inputs, green innovation outputs, and green innovation environments [24]. e research on evaluation methods for innovation capacity is divided into the calculation of evaluation index weights and the comprehensive evaluation of innovation capacity. e subjective weighting method and objective weighting method are the most common approaches for calculating the weights of evaluation indexes [25]. e former refers to weights determined subjectively through people's experience; for example, Shan developed a hierarchical analysis model of regional innovation capacity and used the analytic hierarchy process to calculate the weight of each evaluation indicator [11]. e latter refers to the analysis of the relationships between indicators based on objective data; for example, Yan et al. determined the indicator weights of regional technological innovation capacity by using the entropy method and empirically analysed the technological innovation capacity of 80 regions in Hubei Province, China [26]. Scholars have also proposed to comprehensively determine the weights of index combinations. For example, Xu et al. used the cloud model method and the entropy method to determine the initial weight of an index.
en, the cloud model was combined with the DEMATEL method to determine the final comprehensive weight of the indicator [27]. In terms of the comprehensive evaluation of innovation capacity, Sheng et al. used grey system theory and the Delphi method to establish a system of indicators for evaluating regional S&T innovation capacity. ey then applied a new grey cluster model based on a mixed centre-point triangular whitenization weight function to evaluate the regional S&T innovation capacity of five cities in Jiangsu Province, China [28]. Yang et al. proposed a method based on uncertain linguistic variables for evaluating enterprise innovation capacity and analysed the innovation capacity of five firms [29]. Similarly, Zhen introduced the induced 2-tuple linguistic Choquet ordered harmonic average (I-2TCOHA) operator to aggregate the 2-tuple linguistic information corresponding to each alternative and rank the alternatives to evaluate the technological innovation capacity of a firm [30]. Li et al. proposed a multidimensional grey fuzzy decision-making method with feedback based on the weight vector and weight matrix and applied the method to evaluate regional financial innovation capacity [31]. Wang et al. used the fuzzy analytic hierarchy process to evaluate regional green innovation capacity [24].
In summary, the subjective evaluation method (represented by the analytic hierarchy process) determines evaluation indicator weights based on subjective ideas, while ignoring the information provided by data, resulting in the lack of an objective scientific basis for the resulting weights. In contrast, the objective evaluation method can effectively avoid subjective problems but suffers from certain deficiencies; for example, the entropy method ignores the lack of a horizontal comparison between indicators. e random forest model can calculate the influence strength among indicators, thereby avoiding the problem of subjectivity, and thus can make comparisons between evaluation indicators. Existing scholars have performed a considerable amount of work on methods to evaluate innovation capacity and have proposed a series of policy recommendations; however, these suggestions are generally universal. Due to the differences among individual entities, the pathways to improving innovation capacity also vary. e MOORA method and critical influence strength roadmap (CISR) are introduced to evaluate innovation capacity; the former identifies the maximum gap ratio among the evaluation indicators, while the latter is a diagram showing the influence pathways among the evaluation indicators. e combination of these two can effectively identify the factors that restrict the development of individual innovation capacity and enables improvements in innovation capacity with individual differences.

Establishing the Indicator System and
Building the Model is section briefly introduces the construction of the indicators and models for evaluating regional innovation capacity. First, the main participants of the regional innovation system are universities, research institutes, companies, government agencies, and intermediaries [7,17,32], which are responsible for different roles: universities and research institutions with excellent researchers and sufficient innovation resources assume the role of knowledge creation; enterprises, as core participants in regional innovation systems, take on a greater role in transferring innovation knowledge; and government and intermediaries are responsible for providing a suitable environment for regional innovation. Second, the evaluation model uses the "dropcolumn importance" concept proposed by Terence et al. to measure the influence strength between evaluation indicators [33,34]. e calculated influence strength is used as the raw data for the DANP approach, replacing the expert scoring approach. e DANP method is used to obtain a diagram of the influence strength network and the weight of each evaluation indicator. e MOORA method is then combined with maximum or minimum values to develop the MOORA-max-min method, which can calculate the gap ratio between the current level of an evaluation indicator and its maximum or minimum value. e regional innovation capacity is then calculated according to the weights of the evaluation indicators and the gap ratios. e model construction process is shown in Figure 1.

Establishing the Indicator System.
e concept of the regional innovation system was first proposed by the British scholar Cooke in 1992. A regional innovation system is a regional organizational system formed by the division of labour, interconnected enterprises, universities, research institutions, intermediary services, and local governments within a specific geographical area [35]. Evaluation indicators should consider the generation and application of knowledge and the underlying environment of regional innovation [36][37][38][39]. After analysing the characteristics and linkages of China's regional innovation system, this paper constructs an evaluation indicator system from four aspects: knowledge creation, knowledge acquisition, enterprise innovation, and innovation environment. (1) Knowledge creation: knowledge creation is a source of regional innovation and refers to the process involving universities and research institutes, research funding, and inputs from researchers, including the inputs and outputs of innovation, measured mainly as research inputs, patents, and thesis outputs. (2) Knowledge acquisition: knowledge acquisition refers to the flow and utilization of knowledge within a region, measured mainly by thesis cooperation, corporate financial support, and the use of foreign investment. (3) Enterprise innovation: the translation of innovation results into products by firms is an important part of regional innovation. Corporate innovation is measured by corporate research inputs, patent outputs, and new product development. (4) Innovation environment: a good innovation environment can promote regional innovation. e innovation environment is measured mainly in terms of regional development, quality of intermediary services, and sustainability capacity. e resulting system of indicators for the evaluation of regional innovation capacity is shown in Table 1.
To guarantee the reproducibility of this study, the data in this paper come from publicly published statistical yearbooks and government reports, mainly including the China Statistical Yearbook, China Statistical Yearbook of Science and Technology, China Statistical Yearbook of High-Tech Industry, China Industry Economy Statistical Yearbook, China Torch Statistical Yearbook, statistical and analytical reports on Chinese science and technology papers, and related data released by the Ministry of Science and Technology, State Intellectual Property Office, State Administration for Industry and Commerce, and the Technology Innovation Fund for Science and Technology-based Smalland Mid-Size Enterprises (SMEs).

Building the Multiattribute Decision-Making Evaluation
Model of Regional Innovation Capacity

Using a Random Forest Model to Construct an Initial Influence Strength Matrix
Step 1: discretize the data for all evaluation attributes through a three-level interval discretization method comprising the top third (marked "H"), the middle third (marked "M"), and the bottom third (marked "L") of the value range for each evaluation attribute [40].
Step 2: divide the n evaluation attributes (x 1 , x 2 , . . . , x n ) into n groups according to the individual evaluation attributes (called decision evaluation Mathematical Problems in Engineering attributes x 1 ) and n − 1 evaluation attributes (called conditional evaluation attributes x 2 , , x 3 , . . . , x n ).
Step 3: use the random forest model to calculate the influence strength relationship among conditional evaluation attributes (x 2 , x 3 , . . . , x n ) and decision evaluation attributes (x 1 ); the calculated influence vector of conditional evaluation attributes x 2 , . . . , x n on x 1 is (a 11 , a 21 , . . . , a n1 ), where a 11 � 0. Steps 2 and 3 are repeated n times for each decision variable x i (i � 1, 2, . . . , n) to obtain n combinations of vectors. Furthermore, these n combinations of vectors are combined into an n-dimensional matrix D � [d ij ] nxn , where matrix D is called the direct influence strength matrix and d ij represents the degree of influence of the i th evaluation attribute on the j th evaluation attribute when i � j, d ij � 0. Steps 2 to 4 are repeated k times (k, one of the parameters of the random forest model, is the number of n estimators obtained through the learning curve) to obtain k direct influence strength matrices D.

Applying the DANP Method to Draw the Influence Strength Network Diagram and Calculate the Evaluation Attribute Weights
Step 1: calculate the initial influence strength matrix. e k direct influence strength matrices D are measured by averaging them using the following equation to obtain the initial influence strength matrix A: (1) Step 2: normalize the initial influence strength matrix. e initial influence strength matrix A is converted by

MOORA-min-max method
Inputs: Raw data for 31 provinces in China Weight of each evaluation indicator Calculation steps: Step 1: create the decision matrix U and normalize it using equation (10) Step 2: calculate the gap ratio and the regional innovation capacity of each province based on the normalized decision matrix using equation (12) and (13) DANP method Output: k direct influence strength matrices Research objective 1. Calculation of regional innovation capacity per province 2. Identifying constraints to regional innovation development 3.Exploring pathways to improve regional innovation capacity Outputs: Regional innovation capacity for each province Gap ratios for each evaluation indicator

Random forest model
Input: Raw data of 31 provinces in china Calculation steps: Step 1: obtain an initial influence strength matrix A by averaging the k direct influence strength matrices using equation (1) Step 2: obtain the normalized matrix Y by using equation (2) and (3), based on the initial influence strength matrix A Step 3: obtain the total influence strength matrix T by using equation (4), based on the normalized matrix Y Step 4: calculate gi and ri using equation (5) and (6) based on the total influence strength matrix T, and plot the influence strength network diagram (INSD) Step 5: construct a net influence strength matrix based on the total influence strength matrix T, and draw a critical influence strength roadmap (CISR) Step 6: establish the unweighted supermatrix W and the weighted supermatrix W w by using equation (7) Step 7: multiply the weighted supermatrix W w by equation (8) to obtain the limit supermatrix W * and the weights of each evaluation indicator Calculation steps: Step 1: discretize the data for all evaluation attributes through a three-level interval discretization method with the top third (marked "H"), the middle thrid (marked "M"), and the bottom third (marked "L") of the value range for each evaluation attribute Step 2: divide n evaluation attributes (x 1 , x 2 , … x n ) into n groups according to the principle of individual evaluation attributes (called decision evaluation attributes x 1 ) Step 3: use the random forest model to calculate the influence strength relationship between conditional evaluation attributes (x 2 , x 3 , … x n ) and decision evaluation attributes (x 1 )

Random forest model
Step 1: perform parameter adjustment through learning curve on n sets of data to obtain k (k ≤ n) "n_estimators" (one of the parameters of the random forest model) when out-ofbag error is optimal Step 2: according to the discretized data, build several unpruned trees through bootstrap.
Step 3: calculate the degree of influence of conditional evaluation attributes on decision evaluation variables through the difference of out-of-bag error Step 4: Repeat Steps 2 and 3 of the random forest model n times and combine these n vectors into a direct influence strength matrix D Figure 1: Procedure of constructing the multiattribute decision-making evaluation model. Average full-time personnel equivalent of research and experimental development per 10,000 population (personyears per 10,000 population) Regional government R&D investment ( Number of technology business incubators graduating in a year (number of enterprises) GDP level per capita (yuan/ person) Regional sustainability (C24) Integrated value of regional energy consumption and sewage emissions 1 means of the following equations to obtain the normalized initial influence strength matrix Y: where Δ is the reciprocal of the maximum value of the sum of the rows or the columns of the initial influence strength matrix and is used to normalize the initial influence strength matrix.
Step 3: solve the total influence strength matrix. Based on the initial influence strength matrix D and the Markov chain matrix, the total influence strength matrix T is calculated using the following equation: where E is the n-dimensional identity matrix.
Step 4: draw the influence strength network diagram. e following equations are used to obtain g i and r i , and then the influence strength network diagram is plotted: where ′ represents the matrix transposition and g i represents the total influence strength of the i th evaluation attribute on the other evaluation attributes, called the degree of influence of the i th evaluation attribute. r i represents the total influence strength of the other evaluation attributes on the i th evaluation attribute and is called the degree of influence of the i th evaluation attribute. e centrality degree c i � g i + r i reflects the importance of the i th evaluation attribute in the system. e causality degree h i � g i − r i , when h i > 0, indicates that the i th evaluation attribute is the causality attribute and influences the other evaluation attributes; if h i < 0, then the i th evaluation attribute is the result attribute and is influenced by the other evaluation attributes.
Step 5: build the unweighted supermatrix W and the weighted supermatrix W w . e unweighted supermatrix W is calculated using the total influence strength matrix T and equation (7). In addition, the unweighted supermatrix W is the weighted supermatrix W w because all the evaluation attributes in this paper are of the same level: Step 6: calculate the weights for each evaluation attribute. Equation (8) is iterated until the results converge to a stable limit supermatrix W * to obtain the weights:

Calculating Regional Innovation Capacity Using the MOORA-Min-Max Method
Step 1: establish a decision matrix. e decision matrix U � [u xy ] m×n , x ∈ 1, 2, . . . , m { }, y ∈ 1, 2, . . . , n { }, where m represents the number of regions, n represents the number of evaluation attributes, and u xy represents the value of the y th evaluation attribute in province x consisting of actual data from the 31 provinces in China.
Step 2: normalize the decision matrix. Given the quantitative variation among the indicators for the evaluation of regional innovation capacity, the decision matrix must be normalized. Equation (9) is rewritten as equation (10) based on the concept of range normalization: Step 3: determine the gap ratio for each province. e gap ratio equation (11) is rewritten as equation (12) based on the normative decision matrix, and equation (13) is used to calculate the regional innovation capacity for each province: where w y represents the weight of the y th evaluation attribute, Z * x represents the gap ratio of regional innovation capacity in province x, and RIC x represents the regional innovation capacity in province x.

Empirical Study
is paper applies the constructed multiattribute decisionmaking evaluation model of regional innovation capacity to assess the regional innovation capacity of the 31 provinces in China and to explore ways to improve regional innovation capacity.

Calculating the Direct Influence Strength between Evaluation Attributes Based on a Random Forest Model.
After the three-level interval discretization of the original data, the evaluation attributes are divided into 24 groups according to the individual evaluation attributes (called decision attributes x 1 ) and 23 attributes (called conditional attributes x 2 , x 3 , . . . , x 24 ). en, learning curves are used to train random forest models. For example, "regional technology manpower investment (C1)" is set as a decision attribute, C2 to C24 are set as the conditional attributes, and a learning curve is used for parameter tuning. ese steps are repeated to determine that the value of k is 20. After k is determined, the direct influence strength between the evaluation attributes is calculated using a random forest model to obtain 20 direct influence strength matrices; then, the initial influence strength matrix A is obtained via equation (1), as shown in Table 2.

Drawing an Influence Strength Network Diagram and Calculating the Evaluation Attribute Weights Based on the DANP Method.
e DANP method uses DEMATEL to calculate the total influence strength matrix of the evaluation attributes and then solves the evaluation attribute weights, and the method is used to draw an influence strength network diagram. is paper calculates the accuracy of the random forest model and verifies the consistency of the 20 direct influence strength matrices before calculating the total influence strength matrix to ensure the reliability of the evaluation results. e former step tests the accuracy of the influence strength calculated by the random forest models, and the latter step tests the consensus among the 20 direct influence strength matrices. e random forest model typically uses the out-of-bag error (OOB error) rate to measure the model quality. As shown in Table 3, the average OOB error is between 0.01 and 0.26, with the evaluation attribute "cooperation between enterprises and universities and research institutes (C8)" having the worst quality and an average OOB error of 0.26 with an average accuracy of 74.20%. e evaluation attribute "regional technology manpower investment (C1)" has the highest quality with an average accuracy of 99%. A consistency test among the 20 direct influence strength matrices yields an average consistency gap ratio of 3.129% (less than 5%), as shown in Table 4, indicating that the 20 direct influence strength matrices have a high degree of consensus and that the results are reliable. e initial influence strength matrix A is transformed by using equations (2) and (3) to obtain the normalized initial influence strength matrix Y. en, matrix Y is calculated according to (4)fd4 to obtain the total influence strength matrix T (Table 5). Finally, the degree of influence (g i ), degree of being influenced (r i ), centrality degree (c i ), and causality degree (h i ) for each evaluation attribute are calculated using equations (5) and (6) ( Table 6). Table 6 shows that evaluation attributes C1, C2, C3, C6, C10, C11, C17, C19, C20, C21, C22, and C23 are the cause attributes and C4, C5, C7, C8, C9, C12, C13, C14, C15, C16, C18, and C24 are the result attributes. e influence strength network diagram is then drawn according to the calculated centrality and causality of each evaluation attribute (Figure 2). e influence strength network diagram visualizes the importance and grouping of each evaluation attribute (cause or result attribute), but it remains challenging to demonstrate the complex associations among each attribute. is paper introduces the concept of the net influence strength ζ to reflect the relation between each pair of attributes. e net influence strength ζ is the relative magnitude of t ij and t ji in the total influence strength matrix T, ζ ij � t ij − t ji . When ζ ij > 0, the i th evaluation attribute greatly influences the j th evaluation attribute, and C i influences C j ; when ζ ij < 0, C j influences C i . For example, t 13 � 0.013 and t 31 � 0.042 in the total influence strength matrix T, ζ 13 < 0, C3 influences C1, and thus, ζ 13 � 0, ζ 13 � 1 in the net influence strength matrix ζ. Additionally, given that influence strength exists between two or more evaluation attributes, ζ ij is null when i � j. Similar calculations are repeated to obtain the net influence strength matrix ζ (Table 7). For the i th evaluation attribute, ζ ij � 1 is grouped to obtain a net influence grouping for each evaluation attribute (Table 8). e number of net influence groupings indicates the net influence strength level of the        Table 8, C2 influences C1, and C10 and C10 influence C1. e relations between the evaluation attributes are clarified through net influence groupings, and the CISR is finally drawn (Figure 3).   e CISR illustrates that the "output capacity of R&D personnel in universities and research institutes (C3)" is the most prominent evaluation attribute of net influence strength and can be considered the most fundamental evaluation attribute, while the "cooperation between enterprises and universities and research institutes (C8)" is at the end of the CISR with the smallest net influence strength.

Mathematical Problems in Engineering
e unweighted supermatrix W and the weighted supermatrix W w are obtained from equations (7) and (8), and multiplicative operations are performed on the weighted supermatrix W w until the resultant convergent stable limit supermatrix W * is obtained. en, the weights for each evaluation attribute can be determined (Table 9).

Calculating Regional Innovation Capacity Based on the MOORA-Min-Max Method.
is paper normalizes the data from the 31 provinces in China for 2017 using equations (10) and (12) and calculates the gap ratio, and the results are shown in Table 10. Finally, the regional innovation capacity and ranking of each province are calculated using equation (13), as shown in Table 11.

Exploring Regional Innovation Capacity Improvement
Pathways Based on CISR. Table 11 illustrates the differences in regional innovation capacity among the 31 provinces in China.
is paper explores regional innovation capacity improvement pathways to improve the imbalance in regional innovation capacity. Due to page limitations, the following presents an analysis of both the possible pathways for improving regional innovation capacity based on the CISR and the regional innovation capacity gap ratio using Sichuan and Inner Mongolia as examples.

Management Implications of the Multiattribute Decision-
Making Evaluation Model. Regional innovation capacity provides a comprehensive description of regional innovation development. Improving regional innovation capacity does not involve only a single area of improvement but instead requires four main areas. (1) Knowledge creation: innovation resources are fundamental to knowledge creation. Regions need to increase investment in both human and material innovation resources to increase innovation knowledge output. In addition, each region should improve the output efficiency of R&D personnel and R&D funding through measures such as optimizing the allocation of innovative resources.
(2) Knowledge acquisition: cooperation is a meaningful way to fill resource gaps and achieve complementary strengths. Regional enterprises should strengthen financial support for universities and research institutes and actively introduce advanced technologies Output capacity of R&D personnel in universities and research institutes (C3) Quality of local workers (C19) Regional ability to use foreign capital (C11) Enterprise acquisition of technical capabilities (C10) Regional government R&D investment (C2) Regional technology manpower investment (C1) Regional economic development level (C23)      both domestically and abroad. Regional R&D personnel should develop cooperation between science, technology, and innovation research to improve the output of scientific and technological papers and other results. Local governments should develop regionally appropriate policies to encourage foreign funding for regional innovation development.
(3) Enterprise innovation: as essential participants in innovation transformation, enterprises must increase the output of their innovation results by increasing resource investment and conducting research on core technology. Additionally, enterprises should improve their new product development capabilities to achieve economic benefits. (4) Innovation environment: a good innovation environment is an important prerequisite for regional innovation development. Regions need to improve their talent training systems by increasing spending on education. Innovation intermediaries should fully play their role in supporting regional innovation by providing financial and facility resources for regional innovation. Finally, regional innovation should consider energy consumption, environmental pollution, and other issues to achieve sustainable innovation.

Conclusion
is paper builds a multiattribute decision-making evaluation model of regional innovation capacity. e model uses a random forest model to determine the influence strength between evaluation attributes and obtains the objective weights of the evaluation attributes using the DANP method. Finally, the MOORA-min-max method is employed to calculate the   regional innovation capacity in each of China's 31 provinces and to explore regional innovation capacity improvement pathways. e empirical results suggest the following: (1) "Output capacity of R&D personnel in universities and research institutes (C3)" is the most fundamental evaluation attribute; this may be due to China's growing emphasis on industry-university-research as innovation-driven development strategies are proposed. Colleges and research institutes are essential subjects of industry-university-research. erefore, C3 is the most fundamental evaluation attribute. (2) "Output efficiency of R&D funds in universities and research institutes (C5)" is the evaluation attribute with the largest weight. Given the emphasis on resource efficiency in regional innovation, C5 carries the greatest weight in regional innovation capacity evaluations. (3) Regional innovation capacity is an integrated reflection of innovation development, and enhancing regional innovation capacity involves identifying and addressing critical constraints.
Despite our efforts, two limitations provide ideas for future research. First, the evaluation indicator system constructed by different methods and innovation evaluation indicators (e.g., innovation policy) that are more difficult to monitor can affect the evaluation results, and future research needs to explore a more efficient evaluation indicator system. Second, the multiattribute decision-making evaluation model for regional innovation capacity proposed in this paper is a data-driven approach, and the parameters of the evaluation model ignore the subjective preferences of decision-makers, which should be considered in the future.