A Two-Step Fuzzy MCDM Method for Implementation of Sustainable Precision Manufacturing: Evidence from China

Abstract

Despite that products of precision manufacturing are widely used in many fields involving the national economy, precision manufacturing processes are more unfriendly to the environment, resources and social development than general manufacturing. Hence, the implementation of sustainable precision manufacturing (SPM) is of great strategic significance. There is no literature identifying and ranking the drivers of implementation of SPM and the impact on sustainability owing to the application of advanced manufacturing technologies in SPM has not been explored. To resolve these problems, drivers of SPM are identified based on combined support of prior studies and six groups of experts consisting of 71 individuals from six precision manufacturing enterprises. The drivers are calculated and ranked by a two-step fuzzy MCDM method which integrated the fuzzy AHP (fuzzy analytic hierarchy process) and fuzzy TOPSIS (fuzzy technique for order of preference by similarity to ideal solution) algorithms. The evaluation of drivers is based on the basic principles of sustainable development (environmental criterion, social criterion and economic criterion). The paper concludes that technological innovation, government support and current legislation are the most critical drivers during SPM implementation. Additionally, the result of sensitivity verification of the proposed method conducted proves the robustness and correctness of the algorithm and results.

1. Introduction

The manufacturing industry provides the necessities of life and the manufacturing output was USD 13,739B, accounting for 15.8% of global GDP in 2019 [1]. Meanwhile, CO₂ emissions account for up to 56.1% of total emissions [2]. Precision manufacturing is a huge and important branch of the manufacturing industry, as the products of precision manufacturing are supplied to the fields of aerospace, high-end equipment and optical instruments which involve the national economy and people’s livelihoods [3,4]; however, many of the processes of precision manufacturing are extremely unfriendly to the environment due to high energy consumption and low efficiency, such as grinding, polishing and electrochemical machining, which produce a large amount of toxic and harmful liquids and gases; meanwhile, the processing cost of a single precision part is as high as thousands of dollars, and the efficiency is extremely low [5,6,7,8], which brings about negative effects on society and the environment [9]. Therefore, the implementation of SPM (sustainable precision manufacturing) is of extremely important strategic significance to China and even the world.

The OECD (Organization for Economic Co-operation and Development) took the leading role in proposing a framework of sustainable manufacturing, insisting that sustainable manufacturing needs to be carried out in an environmentally and socially responsible way [10]. Jeurissen and Elkington (2000) [11] proposed the triple bottom line of sustainable manufacturing, namely, environmental stewardship, economic growth and social well-being. Joung et al. [9] further elaborated on sustainable manufacturing based on the definition of the ITA (International Trade Administration). Statistics show that the manufacturing industry has high carbon emissions and is also one of the main sources of waste water and exhaust gas [1,2]. The realization of sustainable manufacturing will bring huge potential benefits to business and manufacturing [12,13,14,15], which will bring huge opportunities. Sustainable manufacturing has become a global consensus, as “sustainable manufacturing” has been listed by the U.S. Department of Energy as a strategic framework, with the European Union and China following suit [16,17,18]. It is known that the precision manufacturing industry faces policy pressure from countries around the world for sustainable manufacturing, as well as stress from nongovernmental organizations and social organizations to eliminate the negative effects of manufacturing [19]. At present, the implementation of SPM faces both huge opportunities and great pressure under the framework of sustainable manufacturing, and is the only way forward for precision manufacturing.

In recent years, many scholars have studied the drivers, frameworks and indicators of sustainable manufacturing and sustainable paths for the development of precision manufacturing. Abubakr et al. [20] integrated intelligent manufacturing into the evaluation system of sustainable manufacturing by comprehensively considering environmental, social and economic factors, analyzed the sustainable development of intelligent manufacturing and conducted research on the influence of computer technology development and the Internet of Things on smart manufacturing sustainability. Bilge et al. [19] presented a new manufacturing architecture to create sustainable value and analyzed new attributes for engineering practice based on sustainable principles. Qiu et al. [21] analyzed and empirically studied the relationship between the green manufacturing innovation ability of Chinese manufacturing enterprises and competitive advantage, and the results showed that there is a positive correlation between the two factors. Shankar et al. [22] established a framework of advanced sustainable manufacturing which was analyzed by AHP (analytical hierarchy process) technology to study the multi-objective decision-making approach of advanced sustainable manufacturing in an Indian enterprise. In terms of sustainable manufacturing indicators, the relevant database shows that about 96 indicators were proposed to solve the problem of environmental deterioration by the United Nations Commission on Sustainable Development; these metrics can be used to measure the relationship between sustainable manufacturing and the environment [23]. The National Institute of Standards and Technology categorizes sustainability indicators into subcategories that can be chosen based on the actual situation of production and manufacturing processes by companies to evaluate their own sustainability. Joung et al. [9] summarized the indicators of sustainable manufacturing and classified these indicators into five dimensions, including an indicator set which was applied to assess sustainable performance in a company’s manufacturing process. Yip et al. [3] proposed that with precision manufacturing and sustainable manufacturing, it is difficult to achieve sustainable ultra-precision manufacturing due to the gap in technology and knowledge. It can be seen from the above research that although scholars have explored sustainable manufacturing and achieved rich research results, there is still no literature that integrates sustainable manufacturing and precision manufacturing, and the drivers of SPM have not been evaluated and ranked.

Moreover, various advanced manufacturing technologies and intelligent manufacturing technologies have emerged one after another from the perspective of manufacturing technology, which have a deep effect in the precision manufacturing industry. In terms of improving the precision of parts or products, these manufacturing methods can be summarized as [3,24,25,26,27]: composite energy field-assisted manufacturing, extreme manufacturing technologies with near-atomic-level precision for material removal, ultra-precision additive manufacturing, and atomic-level in situ processing and detection technology. From the perspective of improving the intelligence and flexibility of precision manufacturing systems, there are [3,28,29]: the Internet of Things, cloud computing, digital twins, CAD/CAD/CAM technology, etc. The emergence of these advanced manufacturing technologies and intelligent manufacturing technologies will have a profound impact on sustainable precision manufacturing. However, there has been no literature focusing on the effect of these advanced manufacturing technologies and intelligent manufacturing technologies on the implementation of SPM. This forces policy makers, managers and practitioners related to precision manufacturing to analyze the drivers promoting SPM implementation based on industry and technical characteristics of precision manufacturing. Therefore, identifying drivers and properly calculating the effect on SPM implementation are the core goals of this paper. In order to determine the drivers and their effect, 15 drivers that most affect the implementation of SPM divided into four categories were identified by reviewing the existing literature and obtaining experts’ opinions. Unlike traditional precision manufacturing which only focuses on product performance and economic aspects, the research takes the three sustainable criteria, namely, environmental, social and economic criteria as the basic evaluation criteria for the drivers of implementation of SPM to identify the drivers and properly calculate the effect. A two-step fuzzy MCDM method based on the integrated fuzzy AHP and fuzzy TOPSIS is proposed, and the fuzzy environment is adopted to resolve the issue that experts cannot give accurate scores of drivers and criteria. Each criterion’s actual weight is calculated based on all experts and the influence of drivers that affect the implementation of SPM is computed by the fuzzy MCDM method. The value of aggregate CCi and each perspective (criterion) CCi are calculated and the drivers are ranked according to their influence on the implementation of SPM. Then, the sensitivity analysis of the algorithm is applied to confirm the robustness and correctness of the algorithm.

In light of above information, identifying the drivers of SPM and their influence are the primary issue to achieve sustainable precision manufacturing. The analysis and ranking of the drivers of sustainable precision manufacturing from multiple perspectives of the environment, society and economy are helpful for relevant policy makers and company managers who need to analyze the drivers of SPM and also expands related research fields and research methods. This paper mainly attempts to solve the following problems:

RQ1: What are the critical drivers in SPM implementation?

RQ2: How to rank these key drivers based on the three sustainable principles?

RQ3: Which driver has the greatest effect on SPM implementation?

The article conducts algorithmic and empirical research on the unsustainable development of traditional precision manufacturing. The origin and contribution of the study are as follows: First, the paper fills the gap of sustainable precision manufacturing theory and literature research, connects sustainable development with precision manufacturing and proposes the concept of SPM. Second, the paper proposes a two-step fuzzy MCDM method for implementation of sustainable precision manufacturing, which fuzzifiers the weight of the sustainability evaluation criteria and the scores of drivers under the criteria to solve the problem that the subjective judgment of experts cannot be accurately quantified. Third, based on interviews with a large number of experts and enterprises and mining of the relevant literature, 15 drivers for the implementation of sustainable precision manufacturing under the three sustainable principles are identified, and these influencing factors are prioritized through fuzzy MCDM calculations. The results of theoretical and empirical analyses are conducive to the relevant government departments, enterprise managers, and engineering and technical personnel to deeply understand sustainable precision manufacturing and promote the implementation of sustainable precision manufacturing.

2. Literature Review

This content reviews the existing literature by searching the Scopus database and Web of Science database for the following keywords: “Sustainable manufacturing drivers”, “Green manufacturing drivers”, “Sustainable precision manufacturing drivers” and “MCDM techniques”. This part is divided into three sections: Section 2.1 describes the drivers of SPM, the second section (Section 2.2) focuses on MCDM techniques and Section 2.3 discusses the gap areas of SPM.

2.1. Drivers of Sustainable Precision Manufacturing

The literature [11] proposed four basic principles of sustainability, namely, environmental protection, stewardship, economic growth and social well-being. The U.S. Department of Commerce (2011) proposed that sustainable manufacturing is “the creation of manufactured products which uses processes that minimizes negative environmental impacts, conserve energy and natural resources”, and are “safe for employees, communities, consumers and are economically sound”. By combining current definitions of sustainable and sustainable manufacturing with previous definitions of precision manufacturing, the definition of sustainable precision manufacturing (SPM) in this paper and the scope of related industries can be clarified. As reported by Xia et al. [25], although we have clearly defined the concept of sustainable precision manufacturing, there are still many difficulties in transforming traditional precision manufacturing into sustainable precision manufacturing. First, it is still unclear what the drivers are and their influence on the implementation of SPM. Second, although the drivers of SPM for the transformation from precision manufacturing to SPM have not been identified yet, the current literature has studied the opportunities and challenges faced by precision or ultra-precision manufacturing, as well as the drivers of sustainable manufacturing or green manufacturing. Third, precision manufacturing and general manufacturing are quite different in terms of technical difficulty, environmental influence, requirements, products of corporate social responsibility, manufacturing characteristics and so on, thus drivers of sustainable manufacturing in the general sense are not fully suitable for sustainable precision manufacturing. To achieve the identification of drivers and their impact on the implementation of SPM, relevant experts and scholars in the field of precision manufacturing are required to participate in depth. Therefore, we chose six groups of experts consisting of 71 individuals who have a deep and broad understanding of sustainable precision manufacturing. The expert groups in this article are from China, and mainly include three types of leaders of experts: (1) CEOs/CTOs of companies of precision manufacturing industry; (2) professors in the field of precision manufacturing with entrepreneurial or industrialization experience; and (3) experts who have experience in industry associations (e.g., the Chinese Mechanical Engineering Society).

In recent years, many research results on drivers of sustainable manufacturing have played a positive role in promoting relevant corporate decision making, policy designation and academic research, and have great theoretical value and practical guiding significance. It is difficult to reach a consistent conclusion [26] because the objectives and research angles of sustainable manufacturing research are different. The research of the existing literature on sustainable manufacturing mainly focuses on two aspects. Firstly, according to the classification of sustainable manufacturing objectives, the main perspectives of research on sustainable manufacturing drivers are: industry or enterprise scale, specific empirical research on a certain enterprise, countries or regions with different industrial policies and technology characteristics. Secondly, based on evaluations of criteria, the drivers of sustainable manufacturing are classified as: an environmental perspective, social perspective, economic perspective, technical perspective, the combination of the above research dimensions or a more subdivided part of the above research dimensions. The following part focuses on the analysis and discussion about the aspects of object classification, research angles, basic research methods and the corresponding drivers. Gandhi et al. [27] integrated the dimension of lean manufacturing and green manufacturing to study Indian manufacturing SMEs evaluated by three criteria of economy, society and environment. Two MCDM methods were used to calculate the effect of drivers and obtain the ranking and the results, which indicated that the top management plays the most significant role among all drivers. Lin et al. [28] proposed that the method of fuzzy Delphi questionnaire analysis was applied to study drivers of sustainability, with the drivers including “product safety, user satisfaction, product quality, product serviceability, and product usability demand priority”. The main perspective of the research was the economy’s sustainable development. As reported by Zhang et al. [29], the sustainable development capability of a remanufacturing enterprise was analyzed and evaluated based on specific data. Because the specific experimental data were obtained, the TOPSIS analysis based on the entropy weight method and using the dimensions of energy, economy and environment was adopted to eliminate the interference of scoring; the results are helpful for enterprises to comprehensively consider and make decisions. Singh et al. [30] adopted AHP and TOPSIS methods to compare and analyze the drivers that promote green manufacturing implementation in small and medium-sized manufacturing enterprises in India, and concluded that green supply chain management, customers’ attributes, organizational practices and adoption of new/supportive technology in the organizations are dominant parameters to ensure the successful implementation of green manufacturing practices. Ali et al. [31] collected relevant data of 288 SMEs in China and applied structural equation modeling with partial least squares to analyze the obtained receipts. The results showed that sustainable manufacturing practices make SMEs more competitive. The research of Ali et al. also proved to some extent that the implementation of SPM in China should be good for the development of enterprises themselves and for the improvement of their global competitiveness. This paper has theoretical and practical value for research on drivers of sustainable development and transformation of Chinese precision manufacturing enterprises. Ullah et al. (2021) proposed that green innovation friendly to the environment and a hybrid methodology method including fuzzy Delphi and interpretive structural modeling be adopted to analyze green innovation drivers. According to Ullah et al., attention should be paid to cost reduction and government support. Some studies on drivers focus on a single dimension or some factors in a certain dimension for analysis and discussion. References [32,33,34] took social responsibility and material utilization efficiency of manufacturing enterprises as the respective criteria, and evaluated corresponding enterprises in Bangladesh and Malaysia using MCDM methods. A dynamic perspective was used by Orij et al. [35], as they applied a dynamic model to calculate the priority of innovation-led lean approaches and revealed the dynamic behavior of “Government regulations” and “Conducive working conditions” exponentially influences sustainable performance for a long time in the manufacturing supply chain. Misopoulos et al. [36] studied the manufacturing sustainability drivers with project management methodological approaches. According to the analysis of the lean life cycle in manufacturing project management, they posited that stakeholders and communications management are two of the knowledge areas that need to integrate the above pressures to achieve cohesive sustainable industrial results. Sustainable consumption behaviors in China were studied by Qu et al. [37], and their paper adopted the Q methodology to analyze data of sustainable consumption characteristics by classifying consumers with similar traits. They explained that the results indicate what influence sustainable consumption brought about and provided suggestions on how governments can inspire sustainable consumption. Mreover, drivers behind sustainable or green manufacturing in one or two dimensions in different countries or different industries were studied by other researchers, such as in China [38,39], the U.S. [40], India [41], Egypt [42], Spain [43], Nigeria [44] and Iran [45]. The main methods which were used by these researchers include: structural model and analysis, energy flow measure model for manufacturing systems, TOPSIS, fuzzy AHP, etc. The specific methods are discussed in Section 2.2. There is very little research on SPM and no relevant literature on the mathematical analysis and calculation of drivers of SPM. We discuss the literature on sustainable ultra-precision manufacturing. Yip et al. [3] analyzed the characteristics of sustainable precision manufacturing technology and precision manufacturing. The author proposed that due to the gaps in sustainable precision manufacturing technology and knowledge, it is very difficult to achieved sustainable ultra-precision manufacturing. From the perspective of advanced manufacturing technology, the author analyzed that the combination of the Internet of Things technology and ultra-precision manufacturing is conducive to the sustainable development of ultra-precision manufacturing, discussed the challenges in the process of technology integration and revealed its impact on sustainable ultra-precision manufacturing. Sealy et al. [46] researched energy consumption and modeling in precision manufacturing. A new set of parameters were defined to characterize power and energy consumption in manufacturing at the process level and the relationship between total and spindle energy with MRR was described. Some studies focused on how to save materials and energy consumption or improve the effectiveness of manufacturing, or the technology of improving the surface quality of parts in precision manufacturing [47,48,49,50,51,52,53,54]. Schneider et al. [55] reviewed the sustainability in ultra-precision and micro-machining processes, as the paper analyzed findings and issues of process design with regard to three dimensions of sustainability, discussed how to increase sustainability in the field of precision and micro-machining, and finally, provided recommendations.

By combing the literature related to driver research, we can see that although the research on drivers for sustainable precision manufacturing has great theoretical value and practical significance, there is no relevant literature research at present. In order to clarify and find suitable research methods for drivers of SPM, we analyze and discuss the MCDM methods in the existing literature in Section 2.2.

2.2. MCDM Methods

If the output of a system is affected by multiple factors, the identification of key influencing factors is important, and the order that these factors affect the system should be studied [56,57]. MCDM (multiple-criteria decision making) methods provide the most effective means for the study of multi-objective or multi-criteria problems related to engineering, natural sciences and social sciences [26,58,59]. The MCDM method is also considered to be the most effective method in analyzing factors which affect sustainable manufacturing [60]. There are some available methods, including the Delphi method, AHP (analytic hierarchy process), WSM (weighted sum method), WASPS (aggregated sum product assessment), SAW (simple additive weighting), fuzzy AHP (fuzzy analytic hierarchy process), WPM (weighted product method), TOPSIS, EWM (entropy weight method), Borda method, ISM (interpretive structural modeling) method, SEM (structural equation modeling), etc.

Determining each criterion’s weight and each driver’s weight under each criterion seems to be an important premise and step of MCDM analysis. It is difficult for experts and respondents to give accurate factor weights when analyzing with traditional methods. When using traditional methods for evaluation and calculation of drivers of SPM, it is difficult for experts and respondents to give accurate factor weights because the experts are inevitably affected by various subjective factors in the understanding and processing of natural language [60,61]. Currently, the ambiguity normally arises from available information. According to the research, the fuzzy set theory would be helpful to overcome the inevitable fuzziness in human judgment and preference and obtain a just result so that the theory can be applied to resolve worse-defined MCDM problems. Jamwal et al. [62] suggested that the fuzzy AHP method for calculating factors’ weight should be applied more, especially in the case of large drivers and vague descriptions in natural language. The method of TOPSIS was proposed by Hwang and Yoon in 1981 [63], where the basic principle is to determine and sort the influence of all alternatives by calculating the minimum distance between each alternative and the positive ideal solution and the maximum distance from the negative ideal solution. As Wang and Lee argued [64], TOPSIS is a very effective MCDM method, especially in solving the driver ranking problem, which is appreciated and accepted by much of the literature and many engineering cases. Behzadian et al. [65] reported that the TOPSIS method was used in about 130 papers in peer-reviewed journals between the years 2000 and 2012 and accounted for as much as 48.9 percent of the total papers which used MCDM methods. That proves the importance of TOPSIS and fully demonstrates the importance and effectiveness of TOPSIS in solving MCDM problems. In the process of using TOPSIS to solve practical MCDM problems in the real world, there is uncertainty and imprecision in natural language descriptions and expert opinions that make it difficult for experts to achieve unambiguous or completely accurate judgments [66]. Moreover, some criteria in the traditional TOPSIS method are also described in natural language, which make it difficult to quantify into precise numbers [62,67]. The fuzzy set theory was adopted to resolve the above-mentioned TOPSIS disadvantages, and fuzzy TOPSIS was more suitable in analyzing driver priority [61].

Some scholars conducted in-depth research on the AHP-TOPSIS method, applied it to the fields of environmental and financial analysis, and achieved good results. Riaz [68,69] et al. proposed the spherical fuzzy soft AHP-TOPSIS method and applied it to the environment mitigation system. The case analysis results showed that the method is very effective for multiple-criteria group decision making. Riaz also proposed the rough set method, which uses the mean value of the uncertain boundary area to replace the membership value, and uses the rough set as the basis for multi-attribute group decision making to deal with uncertainty. In recent years, there also emerged many applications of TOPSIS methods based on fuzzy models, such as Crisp-TOPSIS, FSS-TOPSIS, IFSS-TOPSIS, HFS-TOPSIS, etc., which solve many real-life problems.

To resolve the mentioned issues and ensure the robustness and effectiveness of the identification and ranking of drivers for sustainable manufacturing implementation, this paper adopts the MCDM method which has been tested in a large number of studies and cases and in many fields. The method is composed of AHP and TOPSIS method fuzzification.

To ensure the validity and reliability of driver analysis results in SPM implementation, this research uses a two-step fuzzy MCDM method which integrates fuzzy AHP, used to determine the weight, and fuzzy TOPSIS, used to calculate and rank fifteen drivers which can be divided into four categories. The main contribution of this paper is that drivers which promote the implementation of sustainable precision manufacturing are ranked and deeply analyzed, which enriches the research on sustainable manufacturing and is beneficial for the decision making of sustainable precision manufacturing at different levels of government and the implementation of sustainable precision manufacturing in enterprises.

2.3. Gap Areas and Highlights

Through the above review and discussion on the literature, the following gap areas are proposed:

Precision manufacturing plays a very important role in the national economy and people’s lives. However, its own characteristics and development opportunities and challenges are different from ordinary manufacturing. There is still no relevant literature to analyze and systematically study the drivers on the implementation of SPM.

Through the review of the existing literature and expert opinions, the drivers of SPM can be divided into four groups: internal drivers, social drivers, technology drivers and government and regulation drivers, which were taken into account to consider the actual situation of China’s precision manufacturing industry.

The two-step fuzzy MCDM method integrates the fuzzy AHP method used to calculate weights and fuzzy TOPSIS method used to calculate and rank drivers that promote SPM implementation. The bottom line of the three sustainability principles, namely, environmental criterion, social criterion and economic criterion, are applied to evaluate the drivers. The two-step method model is closer to the real world and deals with the uncertainty of natural language for the evaluation of experts due to the adoption of the fuzzy mathematical model. Finally, the sensitivity analysis verifies the robustness of the method and the correctness of the results.

3. Methodology

3.1. Calculation of Drivers’ Weights Using Proposed Fuzzy AHP Method

The fuzzy AHP method was adopted to calculate the criteria’s and drivers’ weights, which requires the application of triangular fuzzy numbers and related operations. The fuzzy AHP method was adopted to resolve the issue that accurately measuring factor weights is difficult when experts assess the weights of criteria. All experts’ opinions under fuzzy semantics were used as the original data to calculate each factor’s weight. Compared with the traditional method, it is more scientific and reasonable to use the intuitive method or the arithmetic mean method in the criterion weight calculation. The method achieves the goal that the criterion with greater influence on the target has a higher weight, and the criterion with less impact on the target has a lower weight. According to Rouhani et al. [67] and Sun [70], triangular fuzzy numbers can be defined as a triplet (l, m, u), assuming that the fuzzy set on the universe R is M, and x is an element on the universe R; if the membership function of M is μ_M: R → [0, 1], it can be expressed as Formula (1):

$${\mu }_{\tilde{M}}\left(x\right)=\{\begin{array}{cc}\frac{x-l}{m-l},& x\in \left[l,m\right]\\ \frac{x-u}{m-u},& x\in \left[m,u\right]\\ 0,& others\end{array}$$

(1)

where l and u represent the lower and upper bound values of M, m is the value when the membership degree is 1 and the triangular fuzzy numbers are expressed by Figure 1. If the two triangular fuzzy number are expressed as $\widetilde{M_1}$ = (l₁, m₁, u₁) and $\widetilde{M_2}$ = (l₂, m₂, u₂), then the operation rules of triangular fuzzy numbers can be defined as Equations (2)–(5):

The addition of triangular fuzzy numbers is defined as ⊕

$$\widetilde{M_1}\oplus \widetilde{M_2}=(l_1+l_2,m_1+m_2,u_1+u_2)$$

(2)

The multiplication of triangular fuzzy numbers is ⊗

$$\widetilde{M_1}\otimes \widetilde{M_2}=(l_1{l}_2,m_1{m}_2,u_1{u}_2)$$

(3)

$$\mathsf{\lambda }\otimes \widetilde{M_1}=(\mathsf{\lambda }{l}_1,\mathsf{\lambda }{m}_1,\mathsf{\lambda }{u}_1)$$

(4)

where λ is a positive real number, for l₁; l₂ > 0; m₁; m₂ > 0; u₁; u₂ > 0

The reciprocal of a triangular fuzzy number is defined as:

$${\left(\widetilde{M_1}\right)}^{-1}=(1/u_1,1/m_1,1/l_1)$$

(5)

for l₁; l₂ > 0; m₁; m₂ > 0; u₁; u₂ > 0

The fuzzy AHP that is adopted to calculate fuzzy preference weights can be given as the following:

Step 1: determining linguistic variables of criteria and alternatives.

Suppose there are m alternatives that form the set of driving factors D = {D1, D2, …, Dm}, these drivers are evaluated by n criteria, and the set of evaluation criteria is denoted as C = {C1, C2, …, Cn}, and the fuzzy weights are the criteria of ω_j, where j = 1, 2, …, n. By taking the performance rating of alternative Di with respect to criterion Cj evaluated by the kth decision maker, then the corresponding fuzzy performance rating can be denoted ${\tilde{x}}_{ij}^k=\left(l_{ij}^k,m_{ij}^k,n_{ij}^k\right)$. According to [27,71], the description of variables in natural language using word or sentence units is converted into a 5-level membership degree function, as shown in

Table 1. Membership function of natural language represented by triangular fuzzy numbers.

Fuzzy Number	Linguistic Terms for Criteria	Linguistic Terms for Alternatives	Scale of Fuzzy Number
1	Very low	Equally important (Eq)	(1,1,3)
3	Low	Weakly important (Wk)	(1,3,5)
5	Medium	Essentially important (Es)	(3,5,7)
7	High	Very strongly important (Vs)	(5,7,9)
9	Very high	Absolutely important (Ab)	(7,9,9)

, where the membership function is described by triangular fuzzy numbers.

Step 2: construct pairwise comparison matrices M of criteria.

According to Sun [70], by assuming that the expert committee of the decision makers is composed of K experts, through the pairwise comparison and rating of linguistic terms by experts the required critical pairwise comparison matrix is obtained, as shown in Formula (6):

$$\begin{gathered} M=\left[\begin{array}{cccc}1& {\tilde{m}}_{12}& \cdots & {\tilde{m}}_{1n}\\ {\tilde{m}}_{21} \\ ⋮& 1 \\ ⋮& \\ \cdots & {\tilde{m}}_{2n} \\ ⋮\\ {\tilde{m}}_{n1}& {\tilde{m}}_{n2}& \cdots & 1\end{array}\right]=\left[\begin{array}{cccc}1& {\tilde{m}}_{12}& \cdots & {\tilde{m}}_{1n}\\ 1/{\tilde{m}}_{21} \\ ⋮& 1 \\ ⋮& \\ \cdots & {\tilde{m}}_{2n}\\ 1/{\tilde{m}}_{1n}& 1/{\tilde{m}}_{2n}& \cdots & 1\end{array}\right] \end{gathered}$$

(6)

where

$${\tilde{m}}_{ij}=\{\begin{array}{cc}1\hfill & \hfill ,i=j\\ {\tilde{9}}^{-1},{\tilde{7}}^{-1},{\tilde{5}}^{-1},{\tilde{3}}^{-1},{\tilde{1}}^{-1},\tilde{1},\tilde{3},\tilde{5},\hfill & \hfill \tilde{7},\tilde{9},i\ne j\end{array}$$

(7)

Step 3: compute the synthetic pairwise comparison matrix.

According to Buckley [72], the elements of the matrix are calculated by the geometric mean method, such as:

$${\tilde{a}}_{ij}={\left({\tilde{a}}_{ij}^1\otimes \dots \otimes {\tilde{a}}_{ij}^k\otimes \dots \otimes {\tilde{a}}_{ij}^K\right)}^1$$

(8)

for 1 ≤ k ≤ K, K is the number of experts or decision makers, and ${\tilde{a}}_{ij}$ is the element of the synthetic pairwise comparison matrix.

Step 4: calculate the fuzzy weights for each criterion and each alternative.

This study used the geometric mean method to calculate fuzzy weights, which can be obtained from Equations (8) and (9) that aggregate fuzzy weights for the criteria with respect to the goal.

$${\tilde{r}}_i={({\tilde{a}}_{i1}\otimes {\tilde{a}}_{i2}\otimes \dots \otimes {\tilde{a}}_{ij}\otimes \dots \otimes {\tilde{a}}_{in})}^{1/n}$$

(9)

$${\tilde{w}}_i={\tilde{r}}_i\otimes {({\tilde{r}}_1\oplus {\tilde{r}}_2\dots \oplus {\tilde{r}}_i\oplus \dots \oplus {\tilde{r}}_n)}^{-1}$$

(10)

where $a_{ij}$ is the ith alternative fuzzy comparison value for criterion j; then, ${\tilde{r}}_i$ is a geometric mean of fuzzy comparison value and ${\tilde{w}}_i$ is the fuzzy weight of the ith criterion. It can be obtained by the triangular fuzzy number ${\tilde{w}}_i=\left(l{w}_i,m{w}_i,u{w}_i\right)$.

Step 5: compute the BNP (best nonfuzzy performance) value of the fuzzy weights of each criterion by using the COA (center of area) method.

The BNP value can be found by Equation (11):

$$BN{P}_i=\left[\right(u{w}_i-l{w}_i)+(m{w}_i-l{w}_i\left)\right]/3+l{w}_i$$

(11)

3.2. Fuzzy TOPSIS Method

As discussed about the fuzzy TOPSIS in the Literature Review section, this method is very beneficial for solving the issue that the contribution of alternative criteria is assigned with a precise performance rating by a decision maker (Wang and Chang, 2007). This method is very suitable for solving the MCDM problem in this fuzzy environment. According to the discussion in the literature (Sun, 2010; Hsieh et al., 2004; Wang and Chang, 2007; Hwang and Yoon, 1981; Buckley 1985) [70,71,72,73,74], the steps of the TOPSIS method adopted are as follows:

Step 1: construct the fuzzy decision matrix with respect to the alternative criteria evaluated by each expert.

The experts can use Table 1 or other membership functions of triangular fuzzy numbers (for example, Jamwal et al., 2021; Wang and Lee, 2009; Sun, 2010; Hsieh et al., 2004; Wang and Chang, 2007) to reveal a degree of variation based on their judgments. Assuming that $x_{ij}^k$ is the element of the fuzzy decision matrix obtained by the kth expert evaluation, then the fuzzy decision matrix can be expressed as:

$${\tilde{D}}^k=\left[\begin{array}{ccccc}{\tilde{x}}_{11}^k& \cdots & {\tilde{x}}_{1j}^k& \cdots & {\tilde{x}}_{1n}^k\\ ⋮& & ⋮& & ⋮\\ {\tilde{x}}_{i1}^k& \text{⋯}& {\tilde{x}}_{ij}^k& \ddots & {\tilde{x}}_{in}^k\\ ⋮& & ⋮& & ⋮\\ {\tilde{x}}_{m1}^k& \cdots & {\tilde{x}}_{mj}^k& \cdots & {\tilde{x}}_{mn}^k\end{array}\right]$$

(12)

for i = 1, 2, …, m; j = 1, 2, …, n; k = 1, 2, … K.

Step 2: compute the aggregate fuzzy decision matrix.

If ${\tilde{b}}_{ij}$ is the element of the aggregate fuzzy decision matrix, then ${\tilde{b}}_{ij}$ can be calculated by the following equation:

$${\tilde{b}}_{ij}=\frac{1}{K}\left({\tilde{x}}_{ij}^1\oplus \dots {\tilde{x}}_{ij}^k\oplus \dots {\tilde{x}}_{ij}^K\right)$$

(13)

According to Equation (13), if the number of criteria is n and the total number of alternatives with respect to the criteria is m in the process of MCDM, then the aggregate fuzzy decision matrix can be expressed by the following fuzzy matrix:

$$\tilde{D}=\left[\begin{array}{ccccc}{\tilde{b}}_k& \cdots & {\tilde{b}}_{1j}& \cdots & {\tilde{b}}_{1n}\\ ⋮& & ⋮& & ⋮\\ {\tilde{b}}_{i1}& \text{⋯}& {\tilde{b}}_{ij}& \ddots & {\tilde{b}}_{in}\\ ⋮& & ⋮& & ⋮\\ {\tilde{b}}_{m1}& \cdots & {\tilde{b}}_{mj}& \cdots & {\tilde{b}}_{mn}\end{array}\right]$$

(14)

Step 3: normalize the fuzzy decision matrix.

The normalized matrix is represented by $\tilde{R}$, shown as the following equation:

$$\tilde{R}={\left[{\tilde{r}}_{ij}\right]}_{m\times n},i=1,2,\dots ,m;j=1,2,\dots ,n$$

(15)

where ${\tilde{r}}_{ij}=u_j^{*}\otimes {\tilde{b}}_{ij}=\left(\frac{l_{ij}}{u_j^{*}},\frac{m_{ij}}{u_j^{*}},\frac{u_{ij}}{u_j^{*}}\right)$, and $u_j^{*}=ma{x}_i\left\{u_{ij}|i=1,2,\dots ,n\right\}$.

${\tilde{r}}_{ij}$ is the element of $\tilde{R}$ and is still a fuzzy number, thus the weighted normalized fuzzy matrix can be given as:

$$\tilde{V}={\left[{\tilde{v}}_{ij}\right]}_{m\times n},i=1,2,\dots ,m;j=1,2,\dots ,n\mathrm{where},{\tilde{v}}_{ij}={\tilde{r}}_{ij}\otimes {\tilde{w}}_i$$

(16)

Step 4: determine the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS).

Based on the weighted normalized fuzzy matrix, we know that the element ${\tilde{v}}_{ij}$ is still a trapezoidal fuzzy number and the range is [0, 1]. Then, the FPIS A+ and FNIS A- can be obtained by the following formula [71]:

$$A^{+}=\left({\tilde{v}}_1^{*},\dots ,{\tilde{v}}_j^{*},\dots ,{\tilde{v}}_n^{*}\right)$$

(17)

$$A^{-}=\left({\tilde{v}}_1^{-},\dots ,{\tilde{v}}_j^{-},\dots ,{\tilde{v}}_n^{-}\right)$$

(18)

where ${\tilde{v}}_j^{*}=ma{x}_i\left\{v_{ij3}\right\}$ and ${\tilde{v}}_j^{-}$ = $mi{n}_i\left\{v_{ij3}\right\}$, j = 1, 2, …, n; i = 1, 2… m.

Step 5: compute the distance of each weighted alternative from the FPIS and FNIS.

Suppose ${\tilde{e}}_1=\left(l_1,m_1,u_1\right)$ and ${\tilde{e}}_2=\left(l_2,m_2,u_2\right)$ are two triangular fuzzy numbers, we can define the distance between ${\tilde{e}}_1$ and ${\tilde{e}}_2$ by using the vertex method, given by following equation:

$$d\left({\tilde{e}}_1,{\tilde{e}}_2\right)=\sqrt{\frac{1}{3}\left[{\left(l_1-l_2\right)}^2+{\left(m_1-m_2\right)}^2+{\left(u_1-u_2\right)}^2\right]}$$

(19)

According to Equation (19), the weighted alternative from $A^{+}$ and $A^{-}$ can be obtained using the following formulas:

$$d_{\mathrm{i}}^{+}={{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{n}}\mathrm{d}\left({\tilde{v}}_{ij},{\tilde{v}}_j^{*}\right),i=1,2,\dots ,m;j=1,2,\dots ,n$$

(20)

$$d_{\mathrm{i}}^{-}={{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{n}}\mathrm{d}\left({\tilde{v}}_{ij},{\tilde{v}}_j^{-}\right),i=1,2,\dots ,m;j=1,2,\dots ,n$$

(21)

Step 6: compute the closeness coefficient CCi of each alternative for ranking.

If the fuzzy satisfaction degree is in the ith weighted alternative, the closeness coefficient denoted by CCi can be obtained as:

$${\mathrm{CC}}_i=\frac{d_{\mathrm{i}}^{-}}{d_{\mathrm{i}}^{-}+d_{\mathrm{i}}^{+}}$$

(22)

According to the discussion and analysis of drivers for the implementation of sustainable precision manufacturing in the Literature Review section, fully combined with the discussions and feedback from groups of experts, 15 significant drivers of implement of SPM were selected. Based on the industrial and technical characteristics of SPM, the drivers (D1–D15) were classified into four groups: internal drivers, social drivers, technology drivers and government and regulation drivers. Considering it is inevitable that SPM relies on technology heavily and considering the current situation of sustainable manufacturing in China, technology was divided into a separate category and the drivers were extracted, as shown in Figure 1. The SPM drivers with a brief description are listed in

Table 2. Drivers for sustainable precision manufacturing.

S. No.	Drivers	Significance	References
1	Cost reduction (D1)	The reduction of cost in resource and energy consumption to gain more profits	Ullah et al. (2021) [32] Gandhi et al. (2018) [27] Orji et al. (2020) [35]
2	Top management commitment (D2)	The commitment of owner or manager or major investors towards SPM	Ullah et al. (2021) [32] Luo et al. (2018) [26] Gandhi et al. (2018) [27] Mittal et al. (2015) [75] Neri et al. (2021) [76]
3	Social responsibility awareness (D3)	Nonprofit activities and implementation of environmentally friendly and green initiatives	Moktadir et al. (2018) [33] Ullah et al. (2021) [32] Neri et al. (2021) [76] Zhang et al. (2021) [77]
4	Employee training (D4)	Improve SPM-related skills and awareness	Gandhi et al. (2018) [27] Shankar (2016) [22] Ullah et al. (2021) [32] Seth et al. (2018) [40] Neri et al. (2021) [76]
5	Investor pressure (D5)	The continuous pressure from stakeholders/investors pushes firms to become more sustainable	Orji et al. (2020) [35] Shankar (2016) [22] Ullah et al. (2021) [32]
6	Competitive (D6)	For new market opportunities and partnerships	Luo et al. (2016) [26] Moktadir et al. (2018) [33] Neri et al. (2021) [76]
7	Public pressure (D7)	Sustainability demand from local communities, politicians, NGOs, media	Luo et al. (2016) [26] Gandhi et al. (2018) [27] Mittal et al. (2015) [75] Seth et al. (2018) [40]
8	Supplier chain demand (D8)	SPM enhances green and lean supply chain for sustainability demand	Mittal et al. (2015) [75] Orji et al. (2020) [35] Shankar (2016) [22] Ullah et al. (2021) [32]
9	Customer’s request (D9)	Customers’ purchasing criteria and choices have changed due to sustainable awareness, which has translated into growing demand for products	Ullah et al. (2021) [32] Luo et al. (2018) [26] Shankar (2016) [22] Moktadir et al. (2018) [33] Seth et al. (2018) [40]
10	Corporate green image (D10)	Increase corporate image and reputation	Ososanmi et al. (2022) [44] Gandhi et al. (2018) [27] Ullah et al. (2021) [32] Seth et al. (2018) [40]
11	Technological innovation (D11)	New high-performance and low-cost products to replace similar functional products by realizing product revolution	Schneider et al. (2019) [55] Luo et al. (2018) [26] Yip et al. (2021) [3] Shankar (2016) [22] Neri et al. (2021) [76] Zhang et al. (2021) [77]
12	Technology andequipment import (D12)	Improve the total sustainable factor productivity for manufacturing enterprises, involving energy savings, emission reduction, resource reuse, cost savings, and so on	Schneider et al. (2019) [55] Luo et al. (2018) [26] Yip et al. (2021) [3] Ullah et al. (2021) [32] Neri et al. (2021) [76]
13	Government support (D13)	Government’s attention and policy guidance, financial support, R&D investment support, tax rebates, etc.	Ososanmi et al. (2022) [44] Orji et al. (2020) [35] Shankar (2016) [22] Ho et al. (2021) [34] Seth et al. (2018) [40] Neri et al. (2021) [76]
14	Current legislation (D14)	Pollution control, carbon emission requirements, eco-labels, stricter laws, and so on	Ullah et al. (2021) [32] Luo et al. (2018) [26] Schneider et al. (2019) [55] Gandhi et al. (2018) [27] Ososanmi et al. (2022) [44] Malek et al. (2022) [78]
15	Future legislation (D15)	Expected initiation of new laws, increased level of enforcement	Ososanmi et al. (2022) [44] Ullah et al. (2021) [32] Luo et al. (2018) [26] Gandhi et al. (2018) [27]

.

In the present case, the three criteria included were environmental perspective (criteria), social perspective (criteria) and economic perspective (criteria), which were used to evaluate and rank the selected drivers. The hierarchical structure of the analysis of the 15 drivers by MCDM is shown in Figure 2 and the analysis of the three criteria is shown in Figure 3 and Figure 4. We selected six groups of experts from the precision manufacturing industry and academia, consisting of 71 individuals. We entrusted the leader of each group to integrate the expert opinions of the group by interview. Each expert group was composed of managers, engineers, financial personnel, sales personnel and experienced technical workers. Each leader of the groups of experts were either CEOs/CTOs of precision manufacturing-related companies, professors in the field of precision manufacturing with entrepreneurial or industrial experience or members of professional committees of government and industry associations. Telephone surveys and interviews were used to obtain drivers, suitable criteria and weights. Each expert quantified the weight of each criterion with respect to the goal (ranking the drivers) and each driver’s weight relative to each criterion according to their own judgment; then, the natural language description was transferred to the fuzzy environment and triangular fuzzy number based on Table 1, which evaluated criteria by five basic linguistic terms with respect to a fuzzy five-level scale. Detailed profiles of the leaders of each expert group are shown in

Table 3. General description of the leaders of groups of experts.

S. No	Position	Years of Experience	Education Level
1	CEO of precision manufacturing enterprise (PME)	23	Master’s
2	CTO of PME	21	PhD
3	General manager of PME	12	PhD
4	Former director of Key Laboratory of PM	25	PhD, professor
5	Chief engineer of PME	28	Bachelor’s
6	Chairman of PME	13	Master’s

.

4. Application of the Two-Step Fuzzy MCMD Method

The fuzzy AHP method was used to evaluate the weights of different criteria for ranking the drivers of SPM. According to the committee of six representatives regarding the relative importance of the criteria, we obtained the pairwise comparison matrices of criteria. The five-scaled fuzzy number defined in Table 1 was applied to transfer the linguistic terms to the fuzzy numbers, as shown in

Table 4. Linguistic scale of each expert’s evaluation of criteria.

C. No.	Group 1 of Experts			Group 2 of Experts			Group 3 of Experts			Group 4 of Experts			Group 5 of Experts			Group 6 of Experts
	C1	C2	C3	C1	C2	C3	C1	C2	C3	C1	C2	C3	C1	C2	C3	C1	C2	C3
C1	1	$\tilde{3}$	${\tilde{3}}^{-1}$	1	$\tilde{1}$	${\tilde{3}}^{-1}$	1	$\tilde{5}$	${\tilde{5}}^{-1}$	1	$\tilde{7}$	$\tilde{1}$	1	$\tilde{1}$	$\tilde{1}$	1	$\tilde{5},$	${\tilde{3}}^{-1}$
C2	${\tilde{3}}^{-1}$	1	${\tilde{5}}^{-1}$	${\tilde{1}}^{-1}$	1	${\tilde{3}}^{-1}$	${\tilde{5}}^{-1}$	1	${\tilde{7}}^{-1}$	${\tilde{7}}^{-1}$	1	${\tilde{9}}^{-1}$	${\tilde{1}}^{-1}$	1	${\tilde{3}}^{-1}$	${\tilde{5}}^{-1}$	1	${\tilde{7}}^{-1}$
C3	$\tilde{3}$	$\tilde{5}$	1	$\tilde{3}$	$\tilde{3}$	1	$\tilde{5}$	$\tilde{7}$	1	${\tilde{1}}^{-1}$	$\tilde{9}$	1	${\tilde{1}}^{-1}$	$\tilde{3}$	1	$\tilde{3}$	$\tilde{7}$	1

. Equation (8) was applied to obtain the elements of the synthetic pairwise comparison matrix shown in

Table 5. Synthetic pairwise comparison matrix of weights of criteria.

C. No.	C1	C2	C3
C1	1	(1.89, 2.84, 5.20)	(0.32, 0.44, 1.20)
C2	(0.19, 0.35, 0.53)	1	(0.14, 0.19, 0.35)
C3	(0.83, 2.26, 3.09)	(2.84, 5.20, 7.09)	1

. Based on Equation (9), we computed the fuzzy weights of each criterion and the calculated procedures, which are shown as following:

$${\tilde{r}}_1={({\tilde{a}}_{11}\otimes {\tilde{a}}_{12}\otimes {\tilde{a}}_{i3})}^{1/3}=({(1\times 1.88\times 0.32)}^{1/3},{(1\times 2.81\times 0.44)}^{1/3},{(1\times 5.20\times 1.20)}^{1/3})=(0.84,1.08,1.84)$$

Similarly, we obtained ${\tilde{r}}_2$ and ${\tilde{r}}_3$: ${\tilde{r}}_2$ = (0.30, 0.41, 0.57) and ${\tilde{r}}_3$ = (1.33, 2.27, 2.80).

The fuzzy weights of the criteria were calculated based on Equation (10) and the BNP of fuzzy weights of criteria were calculated using Equation (11). The weights, the value of BNP and the rank of weight of criteria are shown in

Table 6. Weights of criteria.

Criteria	Weights	BNP	Rank
Environmental	(0.162, 0.287, 0.744)	0.398	2
Social	(0.057, 0.109, 0.231)	0.132	3
Economic	(0.260, 0.605, 1.131)	0.664	1

.

According to Equations (12)–(14), the fuzzy decision matrix of drivers under each criterion was calculated, as shown in

Table 7. Fuzzy decision matrix of the five levels of linguistic variables.

Drivers	C1 (Environmental)	C2 (Social)	C3 (Economic)
D1	(1.7, 2.7, 4.7)	(1.3, 2.3, 4.3)	(6.0, 8.0, 9.0)
D2	(6.3, 8.3, 9.0)	(4.7, 6.7, 8.0)	(5.0, 7.0, 7.7)
D3	(2.0, 4.0, 6.0)	(2.3, 4.3, 6.3)	(2.3, 4.0, 6.0)
D4	(2.0, 3.3, 5.3)	(3.0, 5.0, 7.0)	(2.0, 3.7, 5.7)
D5	(1.0, 3.0, 5.0)	(1.0, 2.3, 4.3)	(6.0, 8.0, 8.7)
D6	(3.3, 5.3, 7.3)	(4.0, 5.7, 7.7)	(6.3, 8.3, 9.0)
D7	(4.3, 6.3, 8.3)	(1.0, 3.0, 5.0)	(1.0, 2.3, 4.3)
D8	(2.0, 4.0, 6.0)	(1.0, 1.3, 3.3)	(3.3, 5.3, 7.0)
D9	(1.7, 3.7, 5.7)	(1.0, 3.0, 5.0)	(3.3, 4.7, 6.0)
D10	(5.3, 7.3, 8.7)	(2.0, 3.7, 5.7)	(2.3, 4.3, 6.3)
D11	(6.0, 8.0, 9.0)	(4.7, 6.7, 8.7)	(7.0, 9.0, 9.0)
D12	(3.3, 5.3, 7.3)	(3.0, 4.3, 6.3)	(4.3, 6.3, 8.3)
D13	(6.0, 8.0, 9.0)	(4.3, 6.3, 8.3)	(6.7, 8.7, 9.0)
D14	(7.0, 9.0, 9.0)	(5.3, 7.3, 8.7)	(5.7, 7.7, 9.0)
D15	(5.0, 7.0, 9.0)	(2.3, 4.0, 6.0)	(2.3, 4.3, 6.3)

. Based on Equation (15), the normalized fuzzy decision matrix was obtained and presented in

Table 8. Normalized fuzzy decision matrix.

Drivers	C1 (Environmental)	C2 (Social)	C3 (Economic)
D1	(0.19, 0.30, 0.52)	(0.15, 0.27, 0.50)	(0.67, 0.89, 1.00)
D2	(0.70, 0.93, 1.00)	(0.54, 0.77, 0.92)	(0.56, 0.78, 0.85)
D3	(0.22, 0.44, 0.67)	(0.27, 0.50, 0.73)	(0.26, 0.44, 0.67)
D4	(0.22, 0.37, 0.59)	(0.34, 0.57, 0.80)	(0.22, 0.41, 0.63)
D5	(0.11, 0.33, 0.56)	(0.11, 0.27, 0.50)	(0.67, 0.89, 0.96)
D6	(0.37, 0.59, 0.81)	(0.46, 0.65, 0.88)	(0.70, 0.93, 1.00)
D7	(0.48, 0.70, 0.93)	(0.11, 0.34, 0.57)	(0.11, 0.26, 0.48)
D8	(0.22, 0.44, 0.67)	(0.11, 0.15, 0.38)	(0.37, 0.59, 0.78)
D9	(0.19, 0.41, 0.63)	(0.11, 0.34, 0.57)	(0.37, 0.52, 0.67)
D10	(0.59, 0.81, 0.96)	(0.23, 0.42, 0.65)	(0.26, 0.48, 0.70)
D11	(0.67, 0.89, 1.00)	(0.54, 0.77, 1.00)	(0.78, 1.00, 1.00)
D12	(0.37, 0.59, 0.81)	(0.34, 0.50, 0.73)	(0.48, 0.70, 0.93)
D13	(0.67, 0.89, 1.00)	(0.50, 0.73, 0.96)	(0.74, 0.96, 1.00)
D14	(0.78, 1.00, 1.00)	(0.61, 0.84, 1.00)	(0.63, 0.85, 1.00)
D15	(0.56, 0.78, 1.00)	(0.27, 0.46, 0.69)	(0.26, 0.48, 0.70)
$u_j^{*}$	9.0	8.7	9.0

. Using Equations (16)–(18) and the calculated criteria weights, the weighted normalized fuzzy decision matrix (

Table 9. Weighted normalized fuzzy decision matrix.

Drivers	C1 (Environmental)	C2 (Social)	C3 (Economic)
D1	(0.031, 0.086, 0.387)	(0.009, 0.029, 0.116)	(0.174, 0.538, 1.131)
D2	(0.087, 0.221, 0.684)	(0.031, 0.084, 0.213)	(0.375, 0.472, 0.961)
D3	(0.036, 0.126, 0.498)	(0.015, 0.055, 0.169)	(0.146, 0.266, 0.758)
D4	(0.036, 0.106, 0.439)	(0.019, 0.062, 0.185)	(0.057, 0.248, 0.713)
D5	(0.018, 0.095, 0.417)	(0.006, 0.029, 0.116)	(0.147, 0.538, 1.086)
D6	(0.060, 0.169, 0.603)	(0.026, 0.071, 0.203)	(0.469, 0.563, 1.131)
D7	(0.078, 0.201, 0.692)	(0.006, 0.037, 0.132)	(0.077, 0.157, 0.543)
D8	(0.036, 0.126, 0.498)	(0.006, 0.016, 0.088)	(0.041, 0.357, 0.882)
D9	(0.031, 0.118, 0.469)	(0.006, 0.037, 0.132)	(0.137, 0.315, 0.785)
D10	(0.096, 0.232, 0.714)	(0.013, 0.046, 0.150)	(0.096, 0.290, 0.792)
D11	(0.109, 0.255, 0.744)	(0.031, 0.084, 0.231)	(0.203, 0.605, 1.131)
D12	(0.060, 0.169, 0.60)	(0.019, 0.055, 0.169)	(0.374, 0.424, 1.052)
D13	(0.109, 0.255, 0.744)	(0.029, 0.080, 0.222)	(0.355, 0.581, 1.131)
D14	(0.126, 0.287, 0.744)	(0.035, 0.092, 0.231)	(0.466, 0.514, 1.131)
D15	(0.091, 0.224, 0.744)	(0.015, 0.050, 0.159)	(0.164, 0.290, 0.792)
FPIS (A+)	(0.744, 0.744, 0.744)	(0.231, 0.231, 0.231)	(1.131, 1.131, 1.131)
FNIS (A−)	(0.018, 0.018, 0.018)	(0.006, 0.006, 0.006)	(0.029, 0.029, 0.029)
${\tilde{w}}_i$	(0.162, 0.287, 0.744)	(0.057, 0.109, 0.231)	(0.260, 0.605, 1.131)

) was obtained. The fuzzy positive ideal solution (FPIS(A⁺)) and the fuzzy negative ideal solution (FNIS(A⁻)) were identified by Equation (18), and the calculation results are also presented in Table 9.

Equations (20) and (21) were applied in the distance calculation from fuzzy positive ideal solution d(Di, D*) and the distance from the fuzzy negative ideal solution d(Di, D⁻), and the results are presented in

Table 10. Distance of drivers from FPIS and FNIS.

Distance	C1	C2	C3	Distance	C1	C2	C3
d(D1,D*)	0.5970	0.1857	0.6498	d(D1,D−)	0.2168	0.0645	0.7063
d(D2,D*)	0.4858	0.1438	0.8020	d(D2,D−)	0.4044	0.1280	0.6001
d(D3,D*)	0.5608	0.1649	0.8743	d(D3,D−)	0.2847	0.0979	0.4433
d(D4,D*)	0.5778	0.1586	0.9019	d(D4,D−)	0.2487	0.1083	0.4150
d(D5,D*)	0.5933	0.1866	0.9124	d(D5,D−)	0.2345	0.0645	0.6828
d(D6,D*)	0.5222	0.1509	0.8247	d(D6,D−)	0.3496	0.1203	0.7127
d(D7,D*)	0.4972	0.1807	0.8858	d(D7,D−)	0.4048	0.0746	0.3061
d(D8,D*)	0.5608	0.1976	0.9249	d(D8,D−)	0.2847	0.0474	0.5295
d(D9,D*)	0.5706	0.1807	0.8620	d(D9,D−)	0.2667	0.0746	0.4539
d(D10,D*)	0.4771	0.1716	0.8952	d(D10,D−)	0.4231	0.0862	0.4663
d(D11,D*)	0.4628	0.1434	0.8977	d(D11,D−)	0.4442	0.1380	0.7252
d(D12,D*)	0.5222	0.1631	0.8523	d(D12,D−)	0.3496	0.0981	0.6357
d(D13,D*)	0.4628	0.1461	0.8532	d(D13,D−)	0.4442	0.1320	0.7181
d(D14,D*)	0.4436	0.1390	0.8370	d(D14,D−)	0.4515	0.1398	0.6999
d(D15,D*)	0.4821	0.1677	0.8696	d(D15,D−)	0.4378	0.0921	0.4663

. According to Equations (19)–(21), we calculated the distances (di⁺, di⁻) and the closeness coefficient (CCi) of each weighted driver, as shown in

Table 11. Closeness coefficients to different drivers.

S. No.	di+	di−	CCi	Rank
D1	1.4324	0.9876	0.4081	6
D2	1.5109	1.1325	0.4284	4
D3	1.6299	0.8259	0.3363	12
D4	1.6383	0.7719	0.3203	15
D5	1.6828	0.9818	0.3685	10
D6	1.5865	1.1826	0.4271	5
D7	1.5831	0.7854	0.3316	13
D8	1.6618	0.8616	0.3414	11
D9	1.6291	0.7952	0.3280	14
D10	1.5550	0.9757	0.3855	9
D11	1.5039	1.3075	0.4651	1
D12	1.6198	1.0834	0.4008	7
D13	1.5149	1.2944	0.4607	2
D14	1.5126	1.2911	0.4605	3
D15	1.5561	0.9963	0.3903	8

.

5. Results and Discussion

5.1. Results

Almost all precision manufacturing companies pay high attention to the improvement of production efficiency and profit margin, and to the reduction of costs to achieve sustainable and healthy economic development; in addition, talents and human resources are the most critical factors for company development and related industries. Knowing how to deal with the corresponding social relations (for example: corporate social responsibility, corporate culture, public pressure, etc.) is very important for the development of precision manufacturing enterprises. Meanwhile, under the constraints of China’s national and local policies on carbon emissions and environmental protection, many precision manufacturing companies must also pay close attention to the relationship between the company’s production operations and the environment. Only when the requirement of the three sustainable principles is met can the goal of SPM be truly realized. For the purpose of promoting the implementation and application of sustainable precision manufacturing, government authorities at all levels, business managers and industry associations need to have a deep understanding of the drivers of sustainable manufacturing implementation and their respective importance.

In order to integrate sustainable manufacturing into precision manufacturing and promote sustainable development of precision manufacturing, this research proposed the concept of “sustainable precision manufacturing”, and explored drivers of sustainable precision by calculating with a two-step fuzzy MCDM method which integrated FAHP (fuzzy analytic hierarchy process) and fuzzy TOPSIS algorithms. According to Equations (19)–(21), the closeness coefficient (CCi) of each weighted driver was calculated and the scores of CCi of every weighted driver are shown in Figure 5.

The order of the 15 drivers of SPM were ranked by the value of CCi and the result is as follows: D11 > D13 > D14 > D2 > D6 > D1 > D12 > D15 > D10 > D5 > D8 > D3 > D7 > D9 > D4. Similarly, the value of CCi for each driver under the corresponding individual criterion was also calculated, as summarized in Figure 6.

Sensitivity analysis was applied to the integrated fuzzy AHP and fuzzy TOPSIS method which was proposed. For the above reasons, the mutual weights were obtained by the two following ways. In the first way, all weights were set to the same value, represented by the triangular fuzzy numbers (1, 1, 3), (1, 3, 5), (3, 5, 7), (5, 7, 9) and (7, 9, 9). The second way used the method of univariate analysis, which fixes the weight of one criterion and exchanges two other criteria’s weights. The sensitivity curves of 15 SPM drivers in nine scenarios were obtained by using the above two methods, as shown in Figure 7.

5.2. Discussion

According to the result, “Technological innovation” (D11) is considered to be the most important driving factor for sustainable precision manufacturing implementation. There are mainly two reasons behind this. On the one hand, the precision manufacturing industry in China is still in a situation of being at a large scale but is weak, with low profit margins, high costs and poor manufacturing precision. It has not yet met the requirement of high-end manufacturing. Technological innovation and revolution are extremely important ways to solve the above problems. On the other hand, precision manufacturing has the attribute of “precision”. Many parts of high-end precision and high value-added equipment require micron or sub-micron geometric accuracy, and nanometer or sub-nanometer surface roughness. No matter if the industry was to open up to new markets or improve profit margins and productivity, it still requires the support of technological innovation, and the iteration and revolution of new technologies.

The discussion on the role of technological innovation by Mittal and Sangwan (2015) [14] also indirectly confirms the analysis above. “Government support” (D13) and “Current legislation” (D14) are the second and third most important drivers of SPM implementation, respectively. China proposed “Made in China 2025” in 2015. Since then, government departments at all levels are highly aware of the importance of developing the real economy and manufacturing industry, and have adopted various active and stable measures including finance, taxation and high-end equipment R&D support. The measures above greatly promote sustainability in the precision manufacturing industry. Additionally, due to existence of many high-polluting enterprises in the precision manufacturing industry, the current laws and policies have great impact on the development of sustainable precision manufacturing. Traditional methods such as precision casting, electrochemical polishing, MEMS chemical etching, parts surface treatment and other common process methods for precision manufacturing, as well as all relative companies will be affected by environmental policies, with companies being forced to implement sustainable precision manufacturing. Furthermore, in China and other countries, many parts and products of precision manufacturing are closely related to the national economy and people’s livelihoods. The development of many industries, such as the national defense and military industry and the medical equipment industry, reflect national interests to some extent. Therefore, it is not difficult to understand the role of “Government support” (D13) and “Current legislation” (D14) ranking as the second and third most important on SPM implementation, respectively. The “Top management commitment” is the fourth most significant driver of SMP implementation. The reason behind this may be as follows: a company is the basic unit of precision manufacturing, and the management of the company needs to take the future development of the precision manufacturing enterprise into consideration. Under the macroeconomic and policy conditions, the demands for the sustainable development of precision manufacturing force the management to give a clear commitment to SPM implementation and the macroroute of the enterprise’s sustainable development, which are indispensable to the sustainable development of the entire precision manufacturing industry. Mittal and Sangwan (2015) [75] argued that the will and commitment of the top management of the enterprise is conducive to mobilizing new technologies and resources, and can drive the enterprise to develop in the relevant direction. “Competitiveness” (D6) is the fifth most important driver in the implementation of SPM. This is because those enterprises need to pay attention to environmental protection, talent accumulation and social responsibility, and must realize the sustainable economic development of their enterprises while they explore new markets and find new partners. “Cost reduction” is the sixth most important driver of SPM implementation. The reason may be that it is closely related to sustainable development factors such as reducing costs and emissions, indirectly promoting technological innovation through the implementation of remanufacturing production models by precision manufacturing enterprises, caring for employees, etc.

“Technology and equipment import” (D12), “Future legislation” (D15), “Corporate green image” (D10), “Investor pressure (D5)” and “Supplier chain demand” (D8) are important factors for SPM implementation, and their importance is ranked 7–11, respectively. “Technology and equipment import” was ranked seventh. Compared with technological innovation, the difference lies in the use of external factors, that is, the introduction of overseas technology and equipment to solve the sustainable development of precision manufacturing. Due to the particularity of the precision manufacturing industry, it is possible to introduce some technical equipment from overseas to solve some sustainable development problems, but the cost of imported products and technologies is very high; for example, precision machine tools’ price and maintenance costs are often several times that of similar domestic products. More importantly, the technology and equipment of many overseas precision manufacturing industries are kept secret and prohibited from being exported to China. Therefore, “Technology and equipment import” has far less influence on SPM implementation than “Technological innovation”. “Future legislation” (rank 8) is an important driver of SPM identified, and the reason is that many large group companies in the precision manufacturing industry are very sensitive to future legislation and often need to plan ahead. Moreover, [79] argued that “Future legislation” affected pollution control and emissions, which in turn affected environmental principles in corporate SPM implementation. Further, the next driver is “Corporate green image” (rank 9), because the corporate green image can enhance corporate image. The role of “Investor pressure” for enterprises to implement SPM is more reflected in the fact that precision manufacturing enterprises must meet the requirements of environmental protection and meet the requirements of precision and enterprises’ sustainable development. “Supplier chain demand” (rank 10) also plays a critical driving role in SPM implementation, as improvement of the supply chain can promote enterprises’ efficiency and reduce costs, and then promote the sustainable development of precision manufacturing enterprises. Zhang, J. et al. (2018) [79] also confirmed the effect of supply chain pressure on sustainable development of manufacturing enterprises from the perspective of the environmental principle of sustainable development.

“Social Responsibility Awareness” (D3), “Public pressure” (D7), “Customer’s request” (D9) and “Employee training” (D4) are the four drivers that have the least impact on SMP implementation. The results show that, recently, as government, society and the precision manufacturing industry paid more attention to SPM, social awareness of sustainable manufacturing in precision manufacturing enterprises increased, but a deeper understanding of the importance of SPM is still lacking. “Public pressure” (rank- 3) means that pressure from local governments, environmental organizations, media, etc., also has a certain role in promoting the sustainable development of precision manufacturing enterprises. The reason behind this may be a lack of understanding of the role and value of SPM implementation across the precision manufacturing industry. “Customer’s request” (rank 14) is the 14th important SMP driver. The reason can be attributed to the characteristics of the precision manufacturing industry. Customers in this industry are normally more concerned about the accuracy and quality of products, and less concerned about the manufacturing process of upstream enterprises. Besides, there are not too many optional suppliers which meet accuracy and quality requirements. The fact reveals the truth that the implementation of SPM requires the understanding and consensus of the whole society, not only the precision manufacturing industry itself. The driver of “Employee training” is the last driver of the SMP implementation. The analysis above shows that implementation of SPM requires not only the understanding and attention within the precision manufacturing enterprise, but also the understanding and attention of the entire industry and even the entire society. Only in this way can the implementation of SPM in China be improved at a high level.

As can be seen from Figure 5, the top three drivers for the implementation of SPM in China’s precision manufacturing industry are “Technological innovation” (D11), Government support” (D13) and “Current legislation” (D14). The values of their CCi are close, and their importance is much higher than that of other drivers. “Social Responsibility Awareness” (D3), “Public pressure” (D7), “Customer’s request” (D9) and “Employee training” (D4) are the last four factors in terms of overall influence. Although it ranks last, the CCi value of “Employee training” is still half of the CCi value of the most important drivers, indicating that the four drivers cannot be ignored. Figure 6 indicates the comprehensive evaluation ranking and the single-principle evaluation ranking driving the prioritization. “Current legislation”, “Future legislation”, “Government support” and “Technological innovation” are the most important drivers under the environmental criterion. From a social perspective of the precision manufacturing industry, “Current legislation”, “Government support”, “Technological innovation” and “Top management commitment” are the most significant drivers. The most significant drivers from an economic perspective of SPM implementation are “Cost reduction”, “Competitiveness”, “Government support” and “Technological innovation”. It can be seen that technological innovation is important in SPM implementation in the precision manufacturing industry from each perspective of SPM. The impact of corporate green image and cost reduction differs a lot in the three perspectives: the drivers are more important and obtain larger CCi under the economic perspective and the influence is much smaller under the social and environmental perspectives. Correspondingly, public pressure shows a strong driving force from an environmental perspective, but it is obviously insufficient from an economic and social perspective.

Further, a sensitivity analysis was applied in this study to confirm the robustness and validity of the findings. The mutual weights of the sensitivity analysis were described above. The driving force of “Technological innovation” shows the strongest influence in all experiments because its comprehensive CCi value remained the largest in all nine experiments. In addition, it can be inferred from Figure 7 that the driving rankings of the nine groups of experiments show almost no difference and maintain a basically consistent ranking trend. It can be concluded that the algorithm and paper results have good robustness and less dependence on the criterion weight.

6. Implications of the Study

This paper proposed the concept of SPM, which makes theoretical and practical contributions to the implementation and realization of sustainable precision manufacturing in China. In terms of theory, this paper analyzed the importance of the implementation of sustainable precision manufacturing and the current gaps in sustainable precision manufacturing-driven research by combing the existing literature and the characteristics of the precision manufacturing industry, and filling the gaps in the relevant research literature. The research played a theoretical guiding role in the implementation of SPM. The two-step fuzzy MCDM method based on the integration of fuzzy AHP and fuzzy TOPSIS was used to solve the problem that experts cannot accurately evaluate drivers by the two-step fuzzy method under the fuzzy environment. Thus, the weight of each criterion was scientifically and reasonably evaluated on the basis of all experts’ opinions. The research realizes that if the influence of a criterion is large, the corresponding weight is large, and if the influence of the criterion is small, the corresponding weight is small. A sensitivity analysis was performed to confirm the results obtained by the proposed two-step method are robust and right. In terms of practice, based on the analysis of drivers of SPM implementation, the paper obtained the comprehensive ranking of each driver under the three perspectives and the ranking of each driver under each single perspective. The research can help policy makers and business managers to understand drivers of SPM implementation so that they can make corresponding policy formulation plans; therefore, it has great social value and management significance. Moreover, some important practical and managerial implications are formulated by this research and summarized as follows:

• Strengthening technological innovations of SPM.

According to the drivers of SPM, it can be seen that technological innovation is the most significant driver for the sustainability of China’s precision manufacturing industry. Therefore, precision manufacturing enterprises should increase investment in innovation research in sustainable technologies and equipment. Intelligent manufacturing technology should be applied in precision manufacturing enterprises to promote the implementation of SPM. For example, the Internet of Things technique, as one way for technological innovation, can be applied to promote the sustainability of the precision manufacturing industry. It is difficult to improve sustainability due to a high experimental cost, long manufacturing cycle, lack of precise and real-time monitoring, complex energy saving models, etc. Moreover, advanced manufacturing technology is also a way to implement technological innovations of SPM. Through the improvement of traditional precision turning, precision casting, precision grinding, ultra-precision polishing, MEMS etching and other precision manufacturing (such as using precision 3D printing technology, precision laser processing technology, etc.) methods and processes, the emissions, materials and energy utilization can be reduced; therefore, the goal of sustainable precision manufacturing can be achieved.

2.

Strengthen government support and policy supervision.

“Made in China 2025” is a significant development goal of China’s manufacturing industry. The sustainable development of precision manufacturing requires more attention to the sustainable, high-quality connotative development of society and the environment and not just to economic development. Although it may affect the efficiency of precision manufacturing enterprises in the short term, it will inevitably improve the competitiveness of enterprises through reducing material and energy costs, and improving profit margins and productivity in the long run. With the purpose of sustainable development of precision manufacturing, the government’s fiscal stimulus, taxation, subsidies for manufacturing talents and policies to guide social funds to the manufacturing industry will inevitably enhance the sustainable behavior of precision manufacturing enterprises in a certain period. In addition, environmental protection policies and human resource protection policies will also strengthen precision manufacturing companies to protect the environment, reduce emissions and achieve sustainable technological innovation and human resource management innovation. Therefore, the government’s support and current legislation for the sustainable development of precision manufacturing, and the formulation of reasonable environmental and human resource policies are the core elements of SPM implementation, which need to attract more attention and investment of management departments and industry associations at all levels.

3.

Accurately use the driver ranking from different perspectives.

Government support and technological innovation are two of the main drivers from all single perspectives (environmental, social, economic). In addition, it should be noted that current legislation and future legislation are prominent and important impact factors from an environmental perspective, whereas current legislation and top management commitment are the most powerful drivers of SPM implementation from a social perspective. Correspondingly, cost reduction and competitiveness, the most important drivers from an economic perspective, promote the sustainable development of SPM in terms of economy. Relevant departments and enterprise managers should pay full attention to the performance of different drivers from different perspectives, and make full use of these important drivers to achieve the sustainable development of precision manufacturing.

7. Conclusions

The precision manufacturing industry in China has the characteristics of large volume and wide coverage, and is recognized as one of the most important industries involving the national economy and people’s livelihoods. It is a long-term and complex task of implementing SPM in China, where opportunities and challenges coexist. Since SPM involves many factors, identifying the core drivers of SPM implementation can help governments, industry organizations and enterprise management achieve the goal faster and better. By comparing and analyzing the industrial characteristics of the precision manufacturing industry and the background and connotation of sustainable development, as well as a large number of research and expert interviews, this paper extracted 15 drivers for identification. These drivers include: Cost reduction (D1), Top management commitment (D2), Social responsibility awareness (D3), Employee training (D4), Investor pressure (D5), Competitiveness (D6), Public pressure (D7), Supplier chain demand (D8), Customer’s request (D9), Corporate green image (D10), Technological innovation (D11), Technology and equipment import (D12), Government support (D13), Current legislation (D14) and Future legislation (D15). These 15 drivers were then divided into four categories: internal drivers, social drivers, technology drivers and government and regulation drivers. Based on the three criteria of sustainable development (three perspectives), namely, the environmental perspective, social perspective and economic perspective, the 15 drivers were analyzed and calculated. The two-step fuzzy MCDM method integrating fuzzy AHP and fuzzy TOPSIS was adopted and, on the basis of the fuzzy scores of all experts, the three criteria’s weights were calculated: 0.398, 0.132 and 0.664. Further, the calculations identified the most important driver and the prioritization and ranking of all drivers. The proposed method solved the problem that experts cannot give accurate quantitative judgments in real life, and introduced the fuzzy method and triangular fuzzy numbers into real-life methods. The research showed that Technological innovation, Government support, Current legislation, Top management commitment, Competitiveness and Cost reduction were the most important six factors affected SPM implementation, and Employee training had the lowest impact factor. The situation and possible causes were discussed. Sensitivity analysis was carried out on the basis of method and results of the two-step fuzzy MCDM method integrating fuzzy AHP and fuzzy TOPSIS. The analysis indicated that the adopted method had good stability and robustness. Under different mutual weights, the sorting trend was basically the same.

This research sheds light on the key elements of SPM implementation, filling the gap between the existing literature and sustainable precision manufacturing research. The analysis provides government departments at all levels, enterprise managers, engineers, technicians and related researchers with a deep understanding of sustainable precision manufacturing and its implementation. Although the research has contributed to scientific research, engineering practice and management reference, due to the limited manpower and material resources for research, the research mainly focused on the situation of precision manufacturing on the southeast coast of China for the reason that the southeast coast is the core area of China’s precision manufacturing. Differences in research results may exist when this research method is applied to other regions of China. Although our research is a pioneering study on the implementation of sustainable precision manufacturing, the algorithms and empirical analysis methods studied in this paper can still be used for research on the implementation of sustainable precision manufacturing in other countries. Political environments and industries are different among countries, and different levels of sustainable manufacturing capabilities will lead to differences in research results. In view of the possible differences between the situation in other regions of China or different countries, we hope to obtain more general results through a large number of statistical investigations and sustainability analyses of specific processes in some precision manufacturing enterprises with more adequate funding for future studies and further research.