Regional technological innovation and green economic efficiency based on DEA model and fuzzy evaluation

Abstract

With the advent of green economy, it is of great significance to objectively calculate the green innovation efficiency of provincial industrial enterprises in China for achieving sustainable economic development. In this paper, the author analyzes the regional technological innovation and green economic efficiency based on DEA model and fuzzy evaluation. Based on the latest development of traditional efficiency and productivity analysis theory, this study calculates the green innovation efficiency of 30 provincial industrial enterprises by using SBM model, while considering the relaxation of economic input-output problem. The results show that the SBM model improves the accuracy and authenticity of the economic efficiency evaluation of green innovation. The efficiency of green economy in most provinces is on the rise. At the same time, the intensity of R&D and industrial structure play a positive role in improving the efficiency of green economy. Through cluster analysis, the differences and causes of green economic efficiency of regional industrial enterprises are analyzed. In addition, the provinces should also consider the factors affecting the green economic efficiency of industrial enterprises, implement the innovation-driven development strategy in an all-round way, and promote the development of green economy.

Keywords

DEA model Fuzzy evaluation Technological innovation Particle swarm optimization

1 Introduction

With the development of reform, China has acquired a significant growth in economy and society. However, the development approach of high input, low output and high pollution is a serious constraint on the China’s social sustainability [1]. In addition, the world has been paying more attention on global warming and carbon emission problem. China is facing the shortage of domestic resource and serious environmental pollution [2]. Therefore, China must take into account the impact of environmental pollutions in the rapid development [3, 4].

The construction of an innovative country has become the inevitable choice for China to the road of healthy and sustainable development [5]. At present, as more attention to ecological environment problems given by the world, scholars started to study the green innovation efficiency of various industries. The industry is gradually becoming the significant force in promoting the development of China’s economy and society [6, 7]. With the tide of green economy comes, objectively calculating the green innovation efficiency of China’s provincial industrial enterprises has a vast importance to realizing the sustainable economic development.

The green innovation efficiency, as the important part of green innovation, is mainly studied by Data Envelopment Analysis (DEA). The DEA method was initially raised by Charnes et al. (1978), who used mathematical programming model to evaluate the object and to assess the relative efficiency of a decision-making unit (DMU) containing multiple-input and multiple-output. The DEA method promotes the development of production function theory and efficiency theory [8].

2 Related work

Scholars have used the DEA efficiency evaluation model to achieve a lot of related research results. Han (2012) used DEA method and Tobit regression method to estimate the green innovation efficiency and its influencing factors [9]. Feng (2013) analyzed the industries enterprises of 30 provincial regions and 8 economic zones by using the DEA-SBM method. Zhang (2015) used SE-DEA Model and Malmquist index model to analyze and compared 30 provinces’ green innovation efficiency in China. In addition, other methods are used by some scholars to evaluate the green innovation efficiency. Hua (2011) used the factor method to study the green innovation efficiency of Northeast in China. On the one hand, the relaxation of input-output and the undesirable output were rarely considered in previous researches. On the other hand, the traditional DEA model assumes that all outputs are desirable outputs, and ignores that some outputs have characteristics of reducing output to improve efficiency, which are called undesirable outputs [10 –13].

The above researches on innovation activities rarely consider environmental factors in exploring innovation efficiency [14]. The researches on regional differences of green innovation efficiency of industrial enterprises are obviously insufficient. Moreover, this ignores the inter-regional correlation and spatial effects. Therefore, this study will expand the previous studies through different ways [15 –17]. First, it selects data from 2009 to 2013. 30 provinces, municipalities and autonomous regions of China are studies in this study. Based on the latest development of traditional efficiency and productivity analysis theory, this study calculates the green innovation efficiencies of industrial enterprises of China’s 30 provinces [18], municipalities and autonomous regions by using the SBM model considering relaxation of input-output problem to reflect the concept of sustainable development from the perspective of green innovation, and compare with the traditional innovation efficiencies calculated by the DEA model without considering the undesirable output [19]. Second, it is of great theoretical and practical significance to analyze the differences and causes of the green innovation efficiency of industrial enterprises in the regions [20, 21], so this study uses the cluster analysis to classify the green innovation efficiencies of 30 provinces, municipalities and autonomous regions in China. Third, as China’s innovation-driven development policy deeps, the spatial mobility of regional innovation elements are enhanced [22]. The importance of spatial effect is gradually significant. Therefore, the spatial effect of green innovation efficiency of Chinese provincial industrial enterprises is measured from the perspective of green GDP [23]. This research uses the spatial econometric models to evaluate the spatial effect of the green innovation efficiency of Chinese provincial industrial enterprises. It will be beneficial to improve the green innovation efficiencies of China’s regional industrial enterprises and promote regional ecological civilization construction.

3 Theoretical analysis

3.1 Similarity-based link prediction method

The problem of link prediction in social networks was firstly modeled by the Markov chain, which is a guide for the study of link prediction. The methods based on node similarity indicators include indicators based path, indicators based on common neighbor information, and indicators based on random walks [24].

(1) Indicator based path

The probability of a link between nodes in a network can be calculated using the length of the path between nodes.

The smaller the path length between two nodes, the greater the similarity of nodes. The formula for calculating the similarity of nodes is as follows: $score (x, y) = Length (Shorts (x, y))$ (1)

Compared with the shortest path algorithm, the Katz algorithm takes more comprehensive consideration of the path information of the node in the network and more network topology information. Moreover, the algorithm weights all paths between two nodes in the network. The Katz algorithm exponentially decays path calculations of different lengths, and the node similarity score is calculated as follows: $score (x, y) = \sum_{1}^{\infty} (β^{1} \times | paths (x, y, 1) |)$ (2)

Among them, |paths (x, y, 1) | represents a set of all paths of length 1 between nodes x and y. β (0 ≤ β ≤ 1) is a parameter that controls the influence of the path length on the node similarity.

The HN2 algorithm is the Leicht-Holme-Newman Index algorithm, which is a variation of the Katz algorithm [25]. The idea of the algorithm is whether the two nodes are similar and whether they are closely related to their neighbor nodes. The algorithm uses the idea of recursion, and the similarity calculation formula of nodes is shown in Equation (3):

$\begin{matrix} score (x, y) = Φ AS + Ψ I = Ψ {(I - Φ A)}^{- 1} \\ = Ψ (I + Φ A + Φ^{2} A^{2}) \end{matrix}$ (3)

The local path similarity algorithm is abbreviated as LPA, and the algorithm idea is very simple, that is, the node of the target node path length 1 and the node of the target node path length 2 are counted. The similarity calculation formula of the node is shown in the formula (4):

$score (x, y) = A^{2} + ɛ A^{3}$ (4)

In the formula, A is a path matrix describing the network, and ɛ is a parameter ranging from – 1 to 1. The different exponential forms of A represent the number of different paths whose length is an exponent. The local path algorithm is a local algorithm and its time complexity is low.

(2) Indicators based on common neighbor information

The co-neighbor is the pair of nodes x, y. The remaining nodes in the network are sorted in descending order according to the number of their co-neighbors. The more the number of common neighbors, the greater the probability of having edges between the two nodes. τ (x) , τ (y) are used to indicate the degrees of nodes x and y, respectively. The similarity is calculated according to the following formula [24]:

$score (x, y) = | τ (x) \cap τ (y) |$ (5)

The main idea of the Jaccard algorithm is to use the ratio of the intersection and union of neighbor nodes between nodes x and y. This ratio is a score for the similarity between two nodes. The calculation formula of the similarity score of the algorithm node is as follows:

$score (x, y) = \frac{| τ (x) \cap τ (y) |}{| τ (x) \cup τ (y) |}$ (6)

The Adamic-Adar algorithm is mainly to calculate the similarity between two web pages. When calculating the similarity of web pages, the algorithm first finds all the public keywords in the two web pages, then sums the importance of all the keywords, and calculates the weight value of the public keywords. The word frequency of the keyword is F, and the importance of the keyword is W, then W is inversely proportional to 1/ - F. The common neighbor of the node is C, and the degree of the node is D. According to the algorithm, the formula for calculating the similarity score is obtained: $score (x, y) = \sum_{z \in τ (x) \cap τ (y)} \frac{1}{log | τ (z) |}$ (7)

The formula for calculating the similarity score in the RA algorithm is as follows: $score (x, y) = \sum_{z \in τ (x) \cap τ (y)} \frac{1}{k (z)}$ (8)

Formula (8) is extended, and after considering more information, the improved formula is: $score (x, y) = \frac{1}{k (x)} \sum_{z \in τ (x) \cap τ (y)} \frac{1}{k (z)}$ (9)

(3) Indicator based random walk

The Random Walk algorithm is based on random walks to define similarity. Its basic assumptions are: The similarity between the starting node and the target node is determined by the average number of steps from the starting node to the target node.

The link prediction algorithm based on random walk has methods such as Average Commute Time, Random Walk with Restart, Local Random Walk and SimRank algorithm [25].

Assuming that m (x, y) is the average number of steps a walker needs to go from node x to node y, the ACTs of nodes x and y are defined as: $act (x, y) = m (x, y) + m (y, x)$ (10)

Fig.1

Particle Swarm Optimization.

The basic idea of the random walk algorithm with restart algorithm is to assume that when the random rambler takes a step, he returns to the initial position with a certain probability. The formula for calculating the similarity score between nodes is as follows: $score (x, y) = q_{xy} + q_{yx}$ (11)

Local random walk algorithm LRW only considers random walks with finite steps. In the algorithm, a walker starts to walk from node x at time t. Assuming that the probability that the walker just reaches node y at time t + 1 is π_xy (t), then the probability formula for the model to stabilize is: π_x (t + 1) = p^Tπ_x (t) , t ≥ 0. The formula for calculating the similarity score is as follows: $score (x, y) = q_{x} π_{xy} (t) + q_{y} π_{yx} (t)$ (12)

3.2 Path sorting algorithm

3.2.1 Algorithm introduction

Path Sorting Algorithm PRA is an algorithm for random walks on graphs proposed by Lao and Cohen. The algorithm is mainly applied to knowledge reasoning and link prediction in the knowledge base, and it is also applicable to the problem of link prediction in the small knowledge base of the student online learning system. The PRA algorithm is similar to the remote monitoring method. The set of entities connected by path relationship p, and the PRA performs a random walk on the graph, starting from all source nodes. The path to the target node is successful, and the quality of these paths can be determined by measuring their support and precision as in the association rule mining. The path predicted by the PRA algorithm link can be treated as a rule. Because multiple rules or paths may be applicable to any given pair of entities, experiments can fuse these multiple rules through a binary classifier (logically implemented). In the PRA algorithm, the eigenvalues are the probability values of these different paths from the source node to the target node.

The PRA algorithm sorts the Node y associated with the query node x. PRA The algorithm begins with a list of path types that enumerate a large number of length limit markers, which are considered “expert” rankings. Each of the random walks on the graph is performed according to the type constraint of the edge type, and the result nodes y are sorted according to the weight values in the result distribution. Finally, the PRA algorithm combines these “experts” with logistic regression.

3.2.2 Algorithm solving

The path sorting algorithm PRA is specifically described as: the relationship path p is defined as a sequence of relationships (R₁, R₂, ⋯ , R_i).

Moreover, in order to highlight the type of each step, p can also be described as: $T_{0} \overset{R_{1}}{\to} \dots \overset{R_{i}}{\to} T_{i}$

Among them, T_i is defined as $\begin{matrix} T_{i} = Range (R_{i}) = Domain (R_{i + 1}), \\ domain (p) = T_{0}, range (p) = T_{i} \end{matrix}$

Nodes can be connected to each other through different types of relationships, which can be represented by paths: $p_{1} = conpent \overset{AtheleteplayesForTeam}{\to} concept$ $\begin{matrix} p_{2} = conpent \overset{AtheleteplayesForTeam}{\to} concept \\ \overset{TeamPlayesForLeagure}{\to} concept \end{matrix}$

For any one of the relationship paths p = (R₁,R₂, ⋯ , R_i), one seed node s ∈ domain (p) is selected. A random walk of a path constraint is recursively defined as a distribution h_s, p. If p is an empty path, then $h_{s}, p (e) = {\begin{array}{l} 1 i f e = s \\ 0 o t h e r w i s e \end{array}$ (13)

If p = R₁, R₂, ⋯ , R_i is non-null, then

p′ = R₁, R₂, ⋯ , R_i-1, h_s, p is defined as follows: $h_{s}, p (e) = \sum_{e^{'} \in range (p^{'})} h_{s}, p^{'} (e^{'}) \cdot p (e / - e^{'}; R_{1})$ (14)

Among them, $p (e / - e^{'}; R_{1}) = \frac{R_{1} (e^{'}, e)}{| R_{1} (e^{'}, \cdot) |}$ is the probability of reaching the node e from the node e′ with a one-step random walk of the type R₁ of the edge. R₁ (e′, e) indicates whether there is a probability that the type of the edge between e′ and e is R. A path set {P₁, P₂, ⋯ P_n } is given, h_s, p_i (e) is set to the path feature value of the node e, and the nodes are sorted according to the following linear model: $θ_{1} h_{s}, p_{1} (e) + θ_{2} h_{s}, p_{2} (e) + \dots + θ_{n} h_{s}, p_{n} (e)$ (15)θ_i in the above formula is the path weight value. Moreover, the node e related to the query node s is sorted according to the following scoring function. $score (e; s =) \sum_{p \in p_{1}} h_{s}, p (e) \times θ_{p}$ (16)p₁ in the above formula is a relation path set whose length is less than or equal to 1.

The algorithm uses the gradient descent method to calculate the path weight parameter θ, and it gives a set R and a set of node pairs { (s_i, t_i)}. At the same time, the experiment can construct a training data set D ={ (x_i, r_i) }. Among them, x_i is a path eigenvalues vector of all node pairs (s_i, t_i), the j-th component of x_i is R (s_i, t_i), r_i indicates whether it is a true parameter, and θ is estimated using the maximized value of the regularized objective function below: $O (θ) = \sum_{i} o_{i} (θ) - λ_{1} {| θ |}_{1} - λ_{2} {| θ |}_{2}$ (17)

The λ₁ control L₁ regularization in Equation (17) and help structure selection and λ₂ controls L₂ regularization, which prevents overfitting. w_i is the importance weight value for each instance, and O_i (θ) is the objective function of each instance, which is defined as follows: $o_{i} (θ) = w_{i} [r_{i} In p_{i} + (1 - r_{i}) In (1 - p_{i})]$ (18)

Among them, p_i is the predicted correlation value and is defined as follows: $p (r_{i} = 1 | x_{i}; θ) = \frac{exp (θ x_{i})}{1 + exp (θ x_{i})}$ (19)

Fig.2

Algorithm calculation process diagram.

3.3 SBM model

This study uses CCR model to measure the traditional innovation efficiencies of China’s industrial enterprises. The CCR model uses linear programming to estimate the production frontier of the decision making units and evaluate the relative efficiency of each decision making unit. It’s assumed that there are n decision making units (DMU). Each DMU has m input variables, n output variables. For a particular decision making unit, the efficiency evaluation formula can be expressed as: ${\begin{matrix} max \frac{u^{T} Y^{0}}{v^{T} X^{0}} \\ \frac{u^{T} Y_{j}}{v^{T} X_{j}} \leq 1, j = 1, 2, . . ., 31 . \\ u \geq 0, r = 1, 2, . . . s . \\ v \geq 0, i = 1, 2, . . . m . \end{matrix}$ (20)y using the Charnes-Cooper transform, the fractional programming form of the CCR model can be transformed into an equal order linear programming. Therefore, Equation 1 can be transformed into: ${\begin{matrix} max μ^{T} Y_{0} \\ v^{T} X_{j} - μ^{T} Y_{j} \geq 0, j = 1, 2, . . ., n . \\ ω^{T} X_{0} = 1 \\ ω \geq 0, μ \geq 0 \end{matrix}$ (21)

It’s assumed that there are n decision making units (DMU). Each DMU has three vectors, including X (input), Y^g (expected output) and Y^b (non-expected output), which can be expressed as: $\begin{matrix} X = [x_{1}, . . ., x_{n}] \in R^{m @ chn} \\ Y^{g} = [y_{1 X > 0}^{g}, . . ., y_{n}^{g}] \in R^{s 1 @ chn} \\ Y^{b} = [y_{1}^{b}, . . ., y_{n}^{b}] \in R^{s 2 @ chn} \end{matrix}$ (22)

The traditional SBM model considering the undesirable outputs is as follows: $\begin{matrix} ρ^{*} = min \frac{1 - \frac{1}{m} \sum_{i = 1}^{m} \frac{s_{i}^{-}}{x_{i 0}}}{1 + \frac{1}{s_{1} + s_{2}} [\sum_{r = 1}^{s_{1}} \frac{s_{r}^{g}}{y_{r 0}} + \sum_{r = 1}^{s_{2}} \frac{s_{r}^{b}}{y_{r 0}^{b}}]} \\ s . t . x_{0} = X λ + s^{-} \\ y_{0}^{g} = Y^{g} λ - s^{g} \\ y_{0} = Y^{b} λ + s^{b} \\ s^{-} \geq 0, s^{g} \geq 0, s^{b} \geq 0, λ \geq 0 \end{matrix}$ (23)

Fig.3

Carbon emission in china.

4 Empirical results

4.1 Index selection and data description

China’s 30 provinces, municipalities and autonomous regions are collected as the object excluding Tibet. In addition, because of the time lag between innovation input and innovation output, the time lag between input and output is set as 1. Based on the connotation of green innovation, this study selected two input factors including labor and financial resources. Therefore, the amount of research specialist staff and research funds are used to measure the labor and financial resources of innovation activities. On the other hand, there are expected output and non-expected output in the production process. In terms of desirable output index, the number of patent applications of industrial enterprises can reflect the true level of innovation to a great extent. So this study selects the number of patent applications of industrial enterprises to measure the desirable output. In terms of undesirable output index, the amount of carbon dioxide emissions, waste water emissions, and solid waste emissions can represent the environmental benefits brought by innovation activities of industrial enterprises in China.

4.2 The overall average green innovation efficiency analysis in the two cases

According to Tables 1, 2, in the two cases (with and without non-expected output), the overall average efficiency of innovation activities of Chinese provincial industrial enterprises present a steady upward trend. The traditional innovation’ average efficiency of Chinese provincial industrial enterprises, calculated by the DEA method, increases from 0.564 in 2009-0.694 in 2013. The average efficiency of green innovation activities of Chinese provincial industrial enterprises considering non-expected output increases from 0.504 in 2009-0.622 in 2013, which are calculated by the SBM method. In addition, from the overall point of view, the traditional innovation efficiency without considering the undesirable output is higher than the green innovation efficiency containing the undesirable output, but the innovation efficiencies in both cases need to be improved. This means that environment pollution has an impact on the innovation efficiency. Therefore, the SBM model considering undesirable output contributes to increase the accuracy and authenticity in evaluating efficiency.

Table 1
Innovation efficiency without considering the undesirable output based on the DEA model

DMU 2009 2010 2011 2012 2013 Annual average

Beijing 0.922 0.917 0.958 0.989 0.992 0.956

Tianjin 0.887 0.910 0.908 0.939 0.951 0.919

Hebei 0.722 0.773 0.784 0.789 0.803 0.774

Shanxi 0.559 0.572 0.589 0.615 0.657 0.598

Inner Mongolia 0.296 0.324 0.453 0.470 0.516 0.412

Liaoning 0.676 0.725 0.748 0.772 0.802 0.745

Jilin 0.925 0.911 0.920 0.917 0.926 0.920

Heilongjiang 0.770 0.789 0.812 0.847 0.875 0.819

Shanghai 0.926 0.948 0.953 0.959 0.963 0.950

Jiangsu 0.916 0.927 0.948 0.939 0.925 0.931

Zhejiang 0.865 0.943 0.953 0.962 0.949 0.934

Anhui 0.560 0.638 0.672 0.669 0.756 0.659

Fujian 0.633 0.662 0.712 0.733 0.775 0.703

Jiangxi 0.399 0.427 0.536 0.569 0.673 0.521

Shandong 0.652 0.712 0.754 0.825 0.871 0.763

Henan 0.463 0.553 0.559 0.580 0.588 0.549

Hubei 0.582 0.626 0.657 0.684 0.695 0.649

Hunan 0.426 0.439 0.525 0.626 0.659 0.535

Guangdong 0.668 0.747 0.801 0.823 0.876 0.783

Guangxi 0.367 0.412 0.436 0.453 0.476 0.429

Hainan 0.676 0.690 0.724 0.721 0.737 0.715

Chongqing 0.544 0.578 0.602 0.615 0.648 0.597

Sichuan 0.527 0.552 0.617 0.602 0.655 0.591

Guizhou 0.194 0.262 0.384 0.398 0.484 0.344

Yunnan 0.387 0.435 0.421 0.463 0.478 0.437

Shanxi 0.274 0.307 0.353 0.427 0.479 0.368

Gansu 0.325 0.412 0.417 0.445 0.468 0.413

Qinghai 0.326 0.376 0.391 0.411 0.436 0.388

Ningxia 0.256 0.271 0.304 0.338 0.359 0.306

Xinjiang 0.194 0.211 0.297 0.290 0.358 0.270

National average 0.564 0.599 0.640 0.662 0.694 0.632

DMU	2009	2010	2011	2012	2013	Annual average
Beijing	0.922	0.917	0.958	0.989	0.992	0.956
Tianjin	0.887	0.910	0.908	0.939	0.951	0.919
Hebei	0.722	0.773	0.784	0.789	0.803	0.774
Shanxi	0.559	0.572	0.589	0.615	0.657	0.598
Inner Mongolia	0.296	0.324	0.453	0.470	0.516	0.412
Liaoning	0.676	0.725	0.748	0.772	0.802	0.745
Jilin	0.925	0.911	0.920	0.917	0.926	0.920
Heilongjiang	0.770	0.789	0.812	0.847	0.875	0.819
Shanghai	0.926	0.948	0.953	0.959	0.963	0.950
Jiangsu	0.916	0.927	0.948	0.939	0.925	0.931
Zhejiang	0.865	0.943	0.953	0.962	0.949	0.934
Anhui	0.560	0.638	0.672	0.669	0.756	0.659
Fujian	0.633	0.662	0.712	0.733	0.775	0.703
Jiangxi	0.399	0.427	0.536	0.569	0.673	0.521
Shandong	0.652	0.712	0.754	0.825	0.871	0.763
Henan	0.463	0.553	0.559	0.580	0.588	0.549
Hubei	0.582	0.626	0.657	0.684	0.695	0.649
Hunan	0.426	0.439	0.525	0.626	0.659	0.535
Guangdong	0.668	0.747	0.801	0.823	0.876	0.783
Guangxi	0.367	0.412	0.436	0.453	0.476	0.429
Hainan	0.676	0.690	0.724	0.721	0.737	0.715
Chongqing	0.544	0.578	0.602	0.615	0.648	0.597
Sichuan	0.527	0.552	0.617	0.602	0.655	0.591
Guizhou	0.194	0.262	0.384	0.398	0.484	0.344
Yunnan	0.387	0.435	0.421	0.463	0.478	0.437
Shanxi	0.274	0.307	0.353	0.427	0.479	0.368
Gansu	0.325	0.412	0.417	0.445	0.468	0.413
Qinghai	0.326	0.376	0.391	0.411	0.436	0.388
Ningxia	0.256	0.271	0.304	0.338	0.359	0.306
Xinjiang	0.194	0.211	0.297	0.290	0.358	0.270
National average	0.564	0.599	0.640	0.662	0.694	0.632

Table 2

The green innovation efficiency considering the undesirable output based on the SBM model

DMU	2009	2010	2011	2012	2013	Annual average
Beijing	0.901	0.902	0.924	0.937	0.956	0.924
Tianjin	0.802	0.853	0.872	0.896	0.902	0.865
Hebei	0.511	0.541	0.567	0.559	0.613	0.558
Shanxi	0.423	0.456	0.489	0.472	0.525	0.473
Inner Mongolia	0.265	0.325	0.423	0.467	0.481	0.392
Liaoning	0.515	0.554	0.587	0.612	0.618	0.577
Jilin	0.753	0.813	0.819	0.837	0.863	0.817
Heilongjiang	0.609	0.622	0.647	0.625	0.660	0.633
Shanghai	0.884	0.925	0.927	0.935	0.947	0.924
Jiangsu	0.843	0.876	0.889	0.917	0.946	0.894
Zhejiang	0.833	0.886	0.890	0.932	0.948	0.898
Anhui	0.474	0.534	0.554	0.567	0.579	0.542
Fujian	0.587	0.603	0.612	0.670	0.669	0.628
Jiangxi	0.394	0.421	0.436	0.439	0.458	0.430
Shandong	0.513	0.559	0.590	0.622	0.698	0.596
Henan	0.448	0.507	0.526	0.534	0.539	0.511
Hubei	0.521	0.515	0.586	0.639	0.646	0.581
Hunan	0.338	0.362	0.417	0.522	0.590	0.446
Guangdong	0.722	0.727	0.817	0.922	0.904	0.818
Guangxi	0.316	0.369	0.421	0.447	0.483	0.407
Hainan	0.625	0.684	0.721	0.712	0.704	0.691
Chongqing	0.503	0.525	0.534	0.552	0.575	0.538
Sichuan	0.525	0.529	0.547	0.552	0.598	0.550
Guizhou	0.234	0.279	0.315	0.342	0.352	0.304
Yunnan	0.354	0.403	0.423	0.415	0.428	0.405
Shanxi	0.236	0.280	0.312	0.365	0.412	0.321
Gansu	0.287	0.336	0.387	0.425	0.442	0.375
Qinghai	0.264	0.336	0.398	0.425	0.437	0.372
Ningxia	0.254	0.309	0.332	0.385	0.420	0.340
Xinjiang	0.198	0.187	0.220	0.254	0.272	0.226
National average	0.504	0.536	0.573	0.599	0.622	0.568

Table 1 shows that the average traditional innovation efficiencies of China’s provincial industrial enterprises without considering the undesirable outputs in Beijing, Tianjin, Jilin, Heilongjiang, Shanghai, Jiangsu, and Zhejiang are higher than 0.800 during the sample period. Table 2 demonstrates that from 2009 to 2013 the average green innovation efficiencies of Chinese industrial enterprises consideringthe undesirable outputs in Beijing, Tianjin, Jilin, Shanghai, Jiangsu, Zhejiang, and Guangdong also exceed 0.800. Figure 5 demonstrates that the above provinces (municipalities and autonomous regions) with high green innovation efficiency in both cases are mostly in the eastern coastal areas. The average green innovation efficiency in Guizhou, Shanxi, Qinghai, Ningxia and Xinjiang are all lower than 0.400 in two cases, which are almost in the western remote areas.

Figure 4 compares the provincial green innovation efficiencies in the two cases. The majority of China’s provincial traditional innovation efficiencies containing non-expected output are lower than the green innovation efficiencies without considering the non-expected output. However, the average green innovation efficiencies of China’s industrial enterprises considering the undesirable outputs in Guangdong and Ningxia are higher than the traditional innovation efficiencies without considering the non-expected outputs.

Fig.4

The change tendency of green innovation efficiencies of China’s industrial enterprises based on the SBM model.

Fig.5

The change tendency of green innovation efficiencies.

4.3 Analysis on regional difference of green innovation efficiencies

In the average innovation efficiencies of industrial enterprises of 30 provinces, municipalities and autonomous regions in China from 2009 to 2013, the highest efficiency is 0.924, while the lowest efficiency is 0.226, and the variance is 0.093. It indicates that provincial green innovation efficiencies have a certain gap. In order to further analyze the regional differences and causes of green innovation efficiencies in different provinces, this study systematically classifies provincial green innovation efficiencies by SPSS 22, and divides them into the first, second and third groups according to the level of efficiencies. The results can be seen in Table 3.

Table 3
Cluster analysis of green innovation efficiencies of provincial industrial enterprises

Category Provinces

The first group Beijing; Tianjin; Jilin; Shanghai; Zhejiang; Jiangsu; Guangdong

The second group Hebei; Liaoning; Heilongjiang; Anhui; Fujian; Shandong; Henan; Hubei; Hainan; Chongqing; Sichuan

The third group Shanxi; Inner Mongolia; Jiangxi; Hunan; Guangxi; Guizhou; Yunnan; Shanxi; Gansu; Qinghai; Ningxia; Xinjiang

Category	Provinces
The first group	Beijing; Tianjin; Jilin; Shanghai; Zhejiang; Jiangsu; Guangdong
The second group	Hebei; Liaoning; Heilongjiang; Anhui; Fujian; Shandong; Henan; Hubei; Hainan; Chongqing; Sichuan
The third group	Shanxi; Inner Mongolia; Jiangxi; Hunan; Guangxi; Guizhou; Yunnan; Shanxi; Gansu; Qinghai; Ningxia; Xinjiang

According to Table 3, the average efficiency of green innovation in the first group is 0.904, the second group is 0.613, and the third group is 0.354. The first group is mainly the provinces in the eastern coastal regions including Beijing, Tianjin and Shanghai et al., which have higher efficiencies and better economic development. The second and third groups are mainly the provinces in the central and western regions. The low efficiency of these areas is mainly due to the less green innovation output and serious environmental pollution.

4.4 The spatial effect of green innovation efficiency

This study used spatial econometric models to measure the spatial effect of the green innovation efficiency of China’s industrial enterprises. According to the regression analysis results in Table 3, the spatial autoregressive coefficient passes the significance test of 1%, which shows that the green innovation efficiencies of Chinese provincial industrial enterprises have spatial effect. The spatial regression coefficient is 0.245, while the spatial error coefficient is -0.133. It reflects that the degree of spatial spillover of green innovation efficiency by the adjacent area is strong than the error impact of green innovation efficiency by the adjacent area. According to the comparison of the two spatial econometric models, the spatial lag model and spatial error model result in great similarity.

According to Table 4, R&D intensity, industrial structure, government support, and laborer’s quality have a significant effect on the green innovation efficiency. Meanwhile, the R² of original and lagged variables are more than 0.85 and the likelihood ratio is more than 200, which indicates that the regression analysis of spatial econometric models are better.

Table 4
The regression analysis of spatial econometric models

Explanatory variable Original variable Lagged variable

Regression coefficient t-value Regression coefficient t-value

R&D intensity (X1) 0.492^∗∗∗ 5.384 0.522^∗∗∗ 5.123

Industry structure (X2) 0.035^∗∗ 2.246 0.078^∗∗ 2.045

Government support (x3) –0.273^∗∗ –3.372 –0.446^∗∗ –4.264

Laborer’s quality (X4) 0.137^∗∗∗ 4.911 0.298^∗∗∗ 4.683

ρ 0.245^∗∗∗ 4.121 –0.133^∗∗∗ –4.143

R ² 0.865 0.887

Likelihood Ratio 212.231 235.642

Explanatory variable	Original variable	Lagged variable
R&D intensity (X1)	0.492^∗∗∗	5.384	0.522^∗∗∗	5.123
Industry structure (X2)	0.035^∗∗	2.246	0.078^∗∗	2.045
Government support (x3)	–0.273^∗∗	–3.372	–0.446^∗∗	–4.264
Laborer’s quality (X4)	0.137^∗∗∗	4.911	0.298^∗∗∗	4.683
ρ	0.245^∗∗∗	4.121	–0.133^∗∗∗	–4.143
R ²	0.865		0.887
Likelihood Ratio	212.231		235.642

Based on the SBM model containing the relaxation of input-output, this study calculates the green innovation efficiencies of industrial enterprises of 30 Chinese provinces (municipalities, autonomous regions) from 2009 to 2013, and compares with the traditional innovation efficiencies measured by the DEA model without considering the non-expected outputs. The results indicate that the overall green innovation efficiency containing the non-expected outputs declines significantly compared with the traditional innovation efficiency without considering the undesirable outputs. This suggests that the environmental factors should be considered in the efficiency evaluation and the SBM model promotes the accuracy and authenticity of the green innovation efficiency evaluation. The research results show the green innovation efficiencies of the majority of provinces in China maintain an upward trend from 2009 to 2013.

This study analyzes the differences and causes of the green innovation efficiency of industrial enterprises in the regions by the cluster analysis, and divides 30 provinces, municipalities and autonomous regions into three groups according to the efficiency level. The first group is mainly the provinces in the eastern coastal region, the second and third group are mainly the provinces in the central and western regions.

5 Conclusion

The regression analysis of spatial econometric models shows there is spatial spillover effect in the provincial green innovation efficiencies of China’s industrial enterprises. R&D intensity, industrial structure, and laborer’s quality have a positive role in promoting the green innovation efficiency, while government support has negative effects. According to the above conclusions, this study presents some suggestions to promote the green innovation efficiency of Chinese industrial enterprises:

Innovation-driven development strategy should be fully carried out. The momentum of the long-term development of the world economy comes from innovation, so Chinese industrial enterprises must adhere to the innovation-driven development strategy, which should also focus on domestic and foreign advanced technologies and independent innovation. In the green innovation activities, we should consider resource, economy and environment at the same time, and it’s necessary to reduce non-renewable energy investment and focus on the quality of innovation output and environmental pollution.

The spatial effect of green innovation should be fully used. While exerting their own advantages in technology and location and improving green innovation efficiencies, eastern regions should actively promote the central and western regions to the direction of low input, high output, and low pollution. The central and western regions need to rely on their advantages in production, industrial structure adjustment, and policy support, and actively make use of the spatial spillover effect of green innovation efficiency, furthermore, they should actively cooperate with the eastern regions in terms of technologies, management, and personnel training et al., and strive to develop local industries. In addition, all provinces should consider the analysis on the influencing factors of green innovation efficiency of industrial enterprises so as to create a favorable environment for enhancing the green innovation efficiency in industrial enterprises according to their actual situations.

Industrial enterprises should play a central role in the green innovation system. Industrial enterprises should introduce advanced equipments and excellent personnel, and learn advanced management methods from home and abroad. It promotes the utilization efficiency and configuration capability of innovation resources. In addition, enterprises should strengthen further cooperation with universities, research institutes, and governments to create a green innovation system including governments, enterprises, universities, and research institutes.

References

Lee

, Sun

and Lebanon

, et al., PREA: Personalized recommendation algorithms toolkit, Journal of Machine Learning Research 13(3) (2014), 2699–2703.

Cheng

, Jin

and Xiao

, Online social trust reinforced personalized recommendation, Personal & Ubiquitous Computing 20(3) (2016), 457–467.

Qian

, Feng

and Zhao

, et al., Personalized Recommendation Combining User Interest and Social Circle, IEEE Transactions on Knowledge and Data Engineering 26(7) (2014), 1763–1777.

Zuo

, Gong

and Zeng

, et al., Personalized Recommendation Based on Evolutionary Multi-Objective Optimization [Research Frontier], IEEE Computational Intelligence Magazine 10(1) (2015), 52–62.

Salehi

, Kamalabadi

I.N.

and Ghoushchi

M.B.G.

, Personalized recommendation of learning material using sequential pattern mining and attribute based collaborative filtering, Education and Information Technologies 19(4) (2014), 713–735.

Niu

, Peng

S.Y.

, Niu

C.H.

, et al., Study of shanxi’s green innovation efficiency of industrial enterprises based on SBM model and four-stage DEA approach, Science and Technology Management Research (10) (2015), 244–249.

Qian

, Xiao

R.Q.

, Chen

Z.W.

, et al., Research on spatial spillover effect of regional science and technology resource allocation efficiency under the environmental constraints, Chinese Soft Science(4) (2016), 71–80.

Tone

, A slacks– based measure of super – efficiency in data envelopment analysis, European Journal of Operational Research(1) (2002), 32–41.

Yin

, Cui

, Chen

, et al., Modeling Location-Based User Rating Profiles for Personalized Recommendation, ACM Transactions on Knowledge Discovery from Data 9(3) (2015), 1–41.

10.

and Tan

, Study on SINA micro-blog personalized recommendation based on semantic network, Expert Systems with Applications 42(10) (2015), 4797–4804.

11.

Fu-Guo

, Survey of Online Social Network Based Personalized Recommendation, Journal of Chinese Computer Systems 35(7) (2014), 1470–1476.

12.

Alhamid

M.F.

, Rawashdeh

, Dong

, et al., Exploring Latent Preferences for Context-Aware Personalized Recommendation Systems, IEEE Transactions on Human-Machine Systems 46(4) (2017), 615–623.

13.

Dorça

Fabiano A.

, Araújo

Rafael D.

, Carvalho

, et al., An Automatic and Dynamic Approach for Personalized Recommendation of Learning Objects Considering Students Learning Styles: An Experimental Analysis, Informatics in Education 15(1) (2016), 45–62.

14.

Liu

and Huang

, An A.Personalized recommendation with adaptive mixture of markov models, Journal of the American Society for Information Science and Technology 58(12) (2007), 1851–1870.

15.

Wang

X.M.

, Liu

and Xiong

, Improved personalized recommendation based on a similarity network, Physica A: Statistical Mechanics and its Applications 456 (2016), 271–280.

16.

Song

, Wang

, Lei

and Xing

, Credibility decay model in temporal evidence combination, Information Processing Letters 115(2) (2015), 248–252.

17.

Wang

, Zhu

and Song

, Combination of unreliable evidence sources in intuitionistic fuzzy MCDM framework, Knowledge-Based Systems 97 (2016), 24–39.

18.

Yang

, Han

and Han

, Discounted combination of unreliable evidence using degree of disagreement, International Journal of Approximate Reasoning 54 (2013), 1197–1216.

19.

Bach

N.X.

, Hai

N.D.

and Phuong

T.M.

, Personalized recommendation of stories for commenting in forum-based social media, Information Sciences 352–353 (2016), 48–60.

20.

Costa

and Ortale

, Model-Based Collaborative Personalized Recommendation on Signed Social Rating Networks, ACM Transactions on Internet Technology 16(3) (2016), 1–21.

21.

Mao

, Lu

, Li

, et al., Profiling users with tag networks in diffusion-based personalized recommendation, Journal of Information Science 42(5) (2016), 711–722.

22.

Zheng

, Ding

, Xu

, et al., Personalized recommendation based on review topics, Service Oriented Computing & Applications 8(1) (2014), 15–31.

23.

Kim

, Roh

and Ha

, Expert system based on the arrangement evaluation model for the arrangement design of a submarine, Expert Systems with Applications 42(22) (2015), 8731–8744.

24.

Shidpour

, Cunha

and Bernard

, Group multi-criteria design concept evaluation using combined rough set theory and fuzzy set theory, Expert Systems with Applications 64 (2016), 633–644.

25.

Vinodh

, Kamala

and Jayakrishna

, Application of fuzzy axiomatic design methodology for selection of design alternatives, Journal of Engineering, Design and Technology 13(1) (2015), 2–22.