Applying AHP-IFNs-DEMATEL in Establishing a Supplier Selection Model: A Case Study of Offshore Wind Power Companies in Taiwan

Abstract

Offshore wind power has emerged as a relatively new industry in Taiwan in recent years. Energy companies strive to achieve maximum production capacity and product lifespan at the lowest cost. Therefore, selecting the most suitable supplier is a primary objective. This research has identified 23 evaluation criteria for supplier selection based on a literature review. By employing the Analytic Hierarchy Process (AHP), individual weights were assigned to each criterion. Subsequently, the Intuitionistic Fuzzy Numbers Decision Making Trial and Evaluation Laboratory (IFNs-DEMATEL) method was used to analyze the 11 criteria with weights higher than the average, thereby exploring the overall causal relationships. Additionally, by utilizing the four quadrants of the Influential Relation Map (IRM), offshore wind power suppliers can adjust resource allocation to maximize benefits. The findings of this research can provide recommendations for offshore wind power shipping companies in their supplier selection and resource allocation. Furthermore, offshore wind power suppliers can adjust their development criteria and enhance their competitiveness based on the criterion weights and the analysis derived from the Influential Relation Map.

1. Introduction

From the viewpoint of the offshore wind (OSW) energy companies, the suppliers’ product manufacturing process, quality of components, after-sales service, and the ability to steadily provide service at a reasonable price are all crucial factors. The quality of the supplier’s service will affect the long-term operation of Offshore Wind Power (OWP) and Taiwan’s green energy policy on OSW. The purchasing department within OWP energy companies must regularly evaluate the performance of corresponding suppliers in their execution, thus ensuring that the supplier could meet their needs. However, due to the different characteristics of each OWP energy company, the evaluation criteria they prioritize may not be entirely the same. Therefore, in order to deal with this problem, a motivation of this research was to find out how OWP energy companies develop evaluation criteria and guidelines based on its own characteristics, needs, and project schedule to select the most suitable suppliers. We can see that the operation and maintenance (O&M) market of OWP is still an emerging industry, which lacks rich O&M experienced material suppliers and the integration of material supply chains (SCs). As wel, OWP energy companies and traditional energy companies have different operational characteristics, and there are significant differences between the two in terms of aspects, such as logistics material planning, business model, supplier selection criteria, wharf requirements, and the required support in the storage area. To effectively address the evaluation criteria for selecting OWP material suppliers, this research analysis is divided into two parts.

The first part of this study involves the application of the Analytic Hierarchy Process (AHP) for weight comparison. This method enables OWP suppliers to understand the weight of each criterion and to identify their own areas for improvement. By doing so, the suppliers can gain insight and make improvements, which is one of the main objectives of this research. The second part involves using the IFNs-DEMATEL method to explore the interdependencies and complex causal relationships between criteria. Through the DEMATEL questionnaire survey, we can identify which factors are more likely to influence other factors in the evaluation criteria for selecting OWP, as well as which factors are more susceptible to being influenced by other factors. Furthermore, we can establish an influence relationship diagram to interpret the causal relationships between each criterion, and thereby improve and adjust the operational performance. This is the second objective of this research.

Through a comprehensive review of the literature, this study explores the content and context of the evaluation criteria and analyzes them through a hybrid model that integrates AHP and IFNs-DEMATEL with the methodology of multi-criteria decision-making (MCDM). The application of AHP can effectively accommodate the opinions of most experts and decision-makers. This method has the characteristic of the Consistency Index, so it can use the properties of hierarchical structure to evaluate uncertain factors and conditions or to apply to decision-making problems of multiple evaluation criteria [1,2]. The AHP method can effectively meet the mathematical transitivity condition and pairwise comparison of standards, and the resulting AHP weight calculation has a relatively small error [3]. The IFNs combine the concepts of degree of membership and degree of non-membership to more accurately describe fuzziness [4]. DEMATEL can effectively collect and organize expert knowledge to clarify the causal relationships and the degree of mutual influence among criteria. It can also transform causal relationships into a clear structural model and handle the interdependence relationship among criteria [5]. This study utilizes a hybrid model of IFNs-DEMATEL, which cannot only quantify multiple criteria, but also transforms complex problem sets into a structured model, thereby allowing the identification of priority rankings among criteria, causal relationships, and the correlation strength of their mutual influences. It will improve the selection of material suppliers in the OWP. This was the reason for using AHP and IFNs-DEMATEL as a mixed model in this study.

The structure of this thesis is as follows: (1) Introduction: provides an overall introduction to the background, motivation, purpose, and framework of this research. (2) Literature review: reviews important literature and provides a summary. (3) Research methodology: explains the method of constructing the research model and the design of the questionnaire. (4) Empirical results: presents the research analysis and results. (5) Conclusion and recommendations: summarizes the study and provides suggestions for future research directions.

2. Reference

Against the background of promoting green energy and energy conservation and carbon reduction in various countries, OWP is a sustainable renewable energy, and has enormous potential value for its power and related industries [6].

OWP can be considered by material suppliers as an initial and enormous market [7]. Although the OWP has huge market potential, the development of this technology, the integration of the SCs, and the formulation of related policies have gradually developed in the Asia-Pacific region in recent years [8]. For China, which is in desperate need of energy to maintain its supply for heavy industry, how the OWP industry is expanded to meet its inland needs is an urgent problem [9]. It can be seen that the suppliers’ selection in the OWP industry and their performance evaluation have become the focal point among the countries.

Arabsheybani et al. [10] defined supplier selection as the buyer’s specification of various material requirements for suppliers; the buyer evaluates the supplier’s eligibility, the process of signing a contract after both parties reach a consensus. In particular, choosing a suitable OWP industry material supplier, and cooperating with the results can have a significant impact on a company’s costs and revenue [11]. Therefore, the functional operation and composition of any SCs are very critical, and it will also make great contributions and benefits to the operation and cost maintenance of the overall OWP’s SCs [12].

According to Christiansen and Maltz [13], engineering purchasing and material supply contracts are regarded as an important point. In the business review and audit, the transparency of the project and the sense of trust in the transaction are the key factors for the long-term cooperation between the two parties and the success of the organization. Products are delivered to the customer through SCs consisting of suppliers, manufacturers, and distributors. Each company is part of the SCs. The efficiency and quality of the SCs depend on the emphasis that material suppliers place on cost, time management, and work efficiency. Ultimately, this will affect customer satisfaction with service providers [14]. However, whether energy companies can achieve sustainability in the OWP industry together with material suppliers and further achieve their core values, business philosophy, vision, goals, and material suppliers play an important role [15].

Meena and Sarmah [16] used the buyer’s perspective to explore supplier performance evaluation and supplier selection. The main issues are as follows: product delivery, after-sales service, technical capabilities, warranty and maintenance, location, and order management. Moreover, Hudnurkar and Ambekar [17] applied multi-criteria decision-making (MCDM) to measure the evaluation criteria for selecting suppliers and found that the criteria of trust between buyers and sellers, good quality, after-sales service, business review and audit, product delivery, work efficiency and whether suppliers are willing to cooperate and adjust in a timely manner affect buyers’ satisfaction with the supplier.

Shanka and Buvik [18] showed that whether the supplier can meet the buyer’s satisfaction has been regarded as a necessary requirement in the current competitive environment.

Pulles et al. [19] defines supplier after-sales service and warranty and repair as the ability to meet or exceed buyer expectations of the perceived value.

The research of Bharadwaj and Dong [20] also reflects the expectations and satisfaction of buyers and sellers. Based on this, in the study of Schiele et al. [21], purchasing personnel should regard suppliers as the competitive advantage and strive to gain customer trust and status. Ramsay and Wagner [22] showed that the source of supplier value is mainly the company’s historical performance, asset status, after-sales service, business philosophy, vision and goals, technical capabilities, goodwill and industry status and trust. For suppliers’ parts prices, technical capabilities, order management, quality, production capacity, product delivery, goodwill and industry status, and historical performance also have important reference values for organizations to select material suppliers [23,24,25,26]. More notably, suppliers’ cost management capabilities, quality, product delivery, service attitude, and staff training are usually the conditions for the purchasing team to select material suppliers [27].

Schiele et al. [28] pointed out that the supplier’s reputation and industry status are the basis for evaluating when it comes to cooperation. At the same time, the perception of purchasing organization performance when selecting suppliers is also an important criterion [15,29]. Suppliers’ focus on quality, purchasing cost, product delivery and order management is the focus of purchasers’ selection [30,31,32].

In addition, Supplier Development (S.D.) is an important management practice and business philosophy in management and organization, and allows companies to remain competitive [33].

Furthermore, each company maintains its own corporate culture. This culture enables members to learn independently through the sharing of social resources and can reduce the misunderstanding of suppliers or purchasing members in the execution of business or purchasing process due to language differences, resulting in the subsequent record of bad relations between labor and management in each company [34].

Therefore, how material suppliers can maintain their own corporate culture and avoid resulting in negative labor-management relationship records due to differences in terminology and cultural conflicts between suppliers and procurement members will be a key factor [35].

Organizational Culture (O.C.) is a reaction performance that affects the attitude of internal members of the organization to the external service of handling incidents [34,36,37]. In addition, the supplier’s O.C. will also directly affect the interaction between the supplier team and the partner companies, which will affect whether the cooperation can be sustained develop. Based on this, the supplier’s O.C. can also appropriately instruct and train employees to deal with the problems caused by external incidents, whether it can be properly handled with a customer-oriented attitude and be properly disposed of. Therefore, the supplier’s appropriate employee training and O.C. can maintain the ability of internal members of the organization to deal with external events. According to Blome et al. [38], each dimension of supplier selection criteria in different O.C. has an impact on its operational performance.

After reviewing the literature mentioned above, this study will list 23 criteria for evaluating suppliers below, and provide tabulated sources of literature (

Table 1. List of Criteria for Selecting OWP Industry Material Suppliers and Literature. Sources.

Code	Criteria for Evaluation	Literature Sources	Code	Criteria for Evaluation	Literature Sources
Ct1	Quality	[17,23,24,25,26,27]	Ct13	Management and organization	[33]
Ct2	Product delivery time	[16,23,24,25,26,27]	Ct14	Work efficiency	[14,17]
Ct3	Historical performance	[22,23,24,25,26]	Ct15	Warranty and maintenance	[16,19]
Ct4	After-sales service	[16,17,22]	Ct16	Service attitude	[27,34,36,37]
Ct5	Production capacity	[23,24,25,26]	Ct17	Trust	[17,21,22]
Ct6	Part prices	[23,24,25,26]	Ct18	Business review and audit	[13,17]
Ct7	Technical capability	[16,22,23,24,25,26]	Ct19	Labor relations records	[34,35]
Ct8	Asset condition	[22]	Ct20	Location	[16]
Ct9	Core values of the company	[15]	Ct21	Cost management ability	[27,36]
Ct10	Management philosophy	[15,22,33]	Ct22	Employee training	[27,36]
Ct11	Reputation and industry status	[15,22,23,24,25,29]	Ct23	Order management	[16,23,24,25,26,30,31,32]
Ct12	Vision and objectives	[15,22]

) and explanations of the criteria (

Table 2. List of Explanations of Evaluation Criteria for Selection Criteria for OWP Industry Material Suppliers.

Code	Criteria for Evaluation	Explanations
Ct1	Quality	Whether the quality of the wind turbine components sold by the supplier meets international standards and can be guaranteed.
Ct2	Product delivery time	Whether the supplier delivers goods in accordance with the contract and can meet the needs and expectations of the energy companies.
Ct3	Historical performance	Whether the supplier has a history of poor records or poor performance in past cooperation transactions.
Ct4	After-sales service	Whether the supplier provides professional consultation services to assist in the correct installation of wind turbine components.
Ct5	Production capacity	Whether the supplier can ensure regular production of wind turbine components to ensure stable supply.
Ct6	Part prices	Whether the supplier sells wind turbine components at a reasonable price.
Ct7	Technical capability	Whether the technical level of the precision components inside the wind turbines sold by the supplier are higher than the level of onshore wind turbines.
Ct8	Asset condition	Whether the supplier’s asset structure, debt repayment ability, and net assets are higher than normal operating capabilities.
Ct9	Core values of the company	Whether the supplier’s core values are oriented towards sustainable management.
Ct10	Management philosophy	Whether the supplier’s business philosophy is close to environmental protection and promotes green industries.
Ct11	Reputation and industry status	Whether the supplier’s status and reputation in the industry are in a positive state.
Ct12	Vision and objectives	Whether the supplier’s future vision and goals are diversified or conservative.
Ct13	Management and organization	Whether the supplier develops management practices and wind turbine business philosophies to keep the company competitive.
Ct14	Work efficiency	Whether the supplier is willing to cooperate and adjust in a timely manner to meet the implementation of maritime engineering by the energy companies.
Ct15	Warranty and maintenance	Whether the supplier provides warranties and maintenance to meet the expectations and perceived value of the energy companies.
Ct16	Service attitude	Whether the supplier’s internal members can handle external events with a service-oriented approach.
Ct17	Trust	Whether the supplier can meet the expectations and satisfaction of both the buyer and the seller and establish a sense of trust between them.
Ct18	Business review and audit	Whether the supplier has effective quality control and audit for transparent engineering.
Ct19	Labor relations records	Whether there are improper records or cultural differences among members of the supplier.
Ct20	Location	Whether the wind turbine component sources sold by the supplier are located near maritime engineering.
Ct21	Cost management ability	Whether the supplier’s cost management ability is appropriate and does not arbitrarily raise prices.
Ct22	Employee training	Whether the supplier has the ability to handle external events with internal members.
Ct23	Order management	Whether the supplier has the ability to provide appropriate sources of goods for different needs.

), as shown below: (Ct1) Quality; (Ct2) Product delivery time; (Ct3) Historical performance; (Ct4) After-sales service; (Ct5) Production capacity; (Ct6) Part prices; (Ct7) Technical capability; (Ct8) Asset condition; (Ct9) Core values of the company; (Ct10) Management philosophy; (Ct 11) Reputation and industry status; (Ct12) Vision and objectives; (Ct13) Management and organization; (Ct14) Work efficiency; (Ct15) Warranty and maintenance; (Ct16) Service attitude; (Ct17) Trust; (Ct18) Business review and audit; (Ct19) Labor relations records; (Ct20) Location; (Ct21) Cost management ability; (Ct22) Employee training; (Ct23) Order management.

Summary

In summary, previous researchers [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38] have explored numerous studies related to material supplier collaboration. However, offshore wind power is a newly emerging industry in Taiwan in recent years. There is still a need for researchers to delve into the discussion of selecting suitable material suppliers specifically in Taiwan context, to make research findings more relevant to the needs of industry practitioners. Therefore, this study extends from the literature of [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38] as a research foundation and combines AHP-IFNs-DEMATEL as a hybrid model to provide more comprehensive research results.

Then, using AHP-IFNs-DEMATEL to establish Multi-Criteria Decision-Making (MCDM) as a model, carrying out weight assessment on the 23 evaluation criteria for selecting suppliers, quantifying criteria in order to establish supplier selection model. According to this system, the purchasing department can obtain the total scores of each material supplier, rank them, eliminate poor suppliers, and provide results to suppliers as a direction for improvement.

3. Research Methods

This research adopts two methodologies. The first one is the Analytic Hierarchy Process (AHP). Firstly, after literature review, the 23 items as the evaluation criteria for selecting the material suppliers in the OWP industry is structured, build a hierarchical structure, set the evaluation scale for each question to establish a pairwise comparison matrix, and performed consistency check after calculating the relative weights. Finally, selecting the data that met the consistency check to calculate the weights of each level and the overall level. Then, the list of abbreviations for terminology (see shown Appendix A) and list of the meaning for each variable (see shown Appendix B).

The second one is through the method of Intuitionistic Fuzzy Numbers Decision Making Trial and Evaluation Laboratory (IFNs-DEMATEL). This study utilizes the DEMATEL questionnaire and combines the practical experience of purchasing personnel from OWP energy companies to clarify the causal relationships between various criterion variables. By transforming the causal relationships between criteria into a clear structural model, not only we can know the interdependence and degree of dependence between criteria, but also establish an influence relationship diagram for analysis.

3.1. Analytic Hierarchy Process (AHP)

AHP simplifies complex problems into an clear hierarchical system, and then make comprehensive evaluations through quantitative results and then judgments [2,39]. Saaty [1] points out that the AHP execution process is divided into three stages:

• Stage 1: Building the Hierarchy

Firstly, this study is divided into two levels: the objective level and the criterion level, as shown in Figure 1. Firstly, a total of n criteria items are selected for OWP industry material suppliers, and pairwise comparisons are made by experts ($E_k$ = $\left\{E_1,E_2,\dots ,E_p\right\}$) representing p evaluators. Ratio scales are obtained, and a total of n (n − 1)/2 reasonable comparisons are made.

• Stage 2: Calculating the weight of each level

It included setting a pairwise comparison matrix, calculating eigenvalues, and completing the consistency check.

(1)

Setting the pairwise comparison matrix

According to Zhang [2], the evaluation scale of AHP could be summarized into five evaluation scales, as shown in

Table 3. Definition and Explanation for Evaluation Scale of AHP.

Scale	Definition	Explanation
1	Equally important	The contribution degree is equally important and equally strong after comparison.
3	Slightly important	The interviewee’s own experience and judgment are slightly biased towards a certain plan.
5	Relatively important	The interviewee’s own experience and judgment strongly favor a certain plan.
7	Secondary importance	The interviewee’s own experience and judgment strongly favor a certain plan with absolute evidence.
9	Absolute importance	When a compromise value is needed.
2, 4, 6, 8	Evaluation scale at the midpoint	Explanation

. Moreover, if there were N indicators to be compared in pairs, it would be C(n,2), as shown in Equation (1):

$$B=\left[\begin{array}{ccc}{b}_{11}& \cdots & b_{1n}\\ ⋮& \ddots & ⋮\\ b_{n1}& \cdots & b_{nn}\end{array}\right]$$

(1)

(2)

Calculating eigenvalues and eigenvectors

After obtaining the pairwise comparison matrix, calculated the weight of each level element. Utilizing the eigenvalue solution method that commonly was used in numerical analysis to find the eigenvectors; the obtained priority order represented the relative importance of each factor. $w_i$ Represents the weight of criterion i. “n” is the number of evaluation criteria. $b_{ij}$ represents the importance of criterion i relative to criterion j, as evaluated by experts ($E_k$) (i.e., the ratio between the pairwise factors). The calculation method for the weight of criterion i ($w_i$) as shown in Equation (2):

$$W_i=\frac{1}{n}{\sum }_{j=1}^n\frac{b_{ij}}{{\sum }_{i=1}^n{b}_{ij}}, i, j=1,2,\dots ,n$$

(2)

(3)

Consistency Index (C.I.)

As it is difficult to achieve complete consistency when making pairwise comparisons during decision-making, it is necessary to conduct a consistency index test to serve as a consistency indicator. ${\mathsf{\lambda }}_{max}$ represents the maximum eigenvalue of matrix B, and n corresponds to the random index table for the number of criteria, as shown in

Table 4. Random Index Table.

n	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
R.I.	0.00	0.00	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49	1.51	1.48	1.56	1.57	1.58

. If ${\mathsf{\lambda }}_{max}$ = n, it indicates that pairwise comparison matrix B is consistent, as shown in Equation (3):

$$C.I.=\frac{{\mathit{\lambda }}_{\mathit{m}\mathit{a}\mathit{x}-\mathit{n}}}{\mathit{n}-\mathbf{1}}$$

(3)

when C.I. = 0, it indicates that the judgments made before and after are consistent. When C.I. > 0, it means there are errors and inconsistencies in the judgments, made before and after.

When C.I. < 0, it means the judgments made before and after are somewhat inconsistent but still within an acceptable range [1]. In this study, this value was also used to make judgments in the AHP expert questionnaire survey.

(4)

Consistency Ratio (C.R.)

When there are more questions, there will also be more criteria to compare, and the order of the pairwise comparison matrix will increase. Therefore, maintaining consistency in judgments will be more difficult. To solve this problem, the Random Index (as shown in Table 4) can be used to adjust the degree of C.I. values generated under different orders and obtain the Consistency Ratio as shown in Equation (4). When C.R. ≤ 0.1, the consistency level of matrix B is satisfactory, which means that the evaluation results have a certain degree of “reliability” [1].

$$C.R.=\frac{C.I.}{R.I.}$$

(4)

• Stage 3: Calculation of Overall Hierarchy Weights

Assuming there are q experts in this study, through consistency index testing, and letting $E_{ij}^k$, k = 1, 2, …, q;$\forall$i,j = 1, 2, …, n, represent the relative importance that expert $E_k$ assigns to each main criterion $C_i$ with respect to main criterion $C_j$, and the pairwise comparison matrix (M) assigned to all main criteria by q experts can be represented as M = ${\left[m_{ij}\right]}_{n\times n}$.

In addition, through consistency checks, the evaluation results of q experts can also obtain the pairwise comparison matrices of n sub-criteria ($C_{t1},\dots ,C_{tn}$) under each main criterion ($C_t=1,2,\dots ,n$). Assuming that $B{w}_t=\left(w_1,w_2,\dots ,w_n\right)$ is the eigenvector of the pairwise comparison matrix M = ${\left[m_{ij}\right]}_{n\times n}$ the overall level weight can be expressed by Equation (5).

$$B{w}_t=\frac{\left({\sum }_{i=1}^n(m_{ij}/{\sum }_{j=1}^n{m}_{ij})\right)}{n},i=1,\dots ,n$$

(5)

3.2. Intuitionistic Fuzzy Numbers Decision Making Trial and Evaluation Laboratory (IFNs-DEMATEL)

Atanassov [4] proposed the concept of Intuitionistic Fuzzy Numbers (IFNs), which consider not only membership degrees but also non-membership degrees, to more accurately describe uncertainty and fuzziness. Therefore, IFNs have been widely applied in the field of Multiple Criteria Decision Making (MCDM) [40,41]. Gabus and Fontela [42] proposed the concept of DEMATEL to describe the complex causal relationships among criteria. This study combines IFNs and DEMATEL into a decision-making model. Firstly, Intuitionistic Fuzzy Numbers are used to address the impact matrix among various evaluation factors assessed by experts. Then, the DEMATEL procedure is executed accordingly. Using this model, this study provides three contributions: firstly, using precise mathematical language to analyze the relationships between factors; secondly, determining the causal relationships and the degree of mutual influence among the factors; and thirdly, establishing the Influential Relation Map (IRM). The IRM, which is established in this study, provides decision-makers with an intuitive explanation of the dependence relationships among the factors by the direction of arrows. In addition, the four quadrants can be used to analyze how to improve and provide insights on the evaluated criteria under limited resources. In this study, the IFNs-DEMATEL method is divided into five steps:

• Step 1: Using a fuzzy linguistic scale to evaluate the relationships between factors

After the DEMATEL questionnaires were collected, the matrices were established (as in Equation (8)), where $B_k$ refers to the questionnaire matrix of the K respondent, and H is the total number of questionnaires. Additionally, according to the evaluation scales of the criteria in

Table 5. Comparison of Fuzzy Semantic Scales and Their Representation.

Evaluation Scale	Code	Semantic Wording	Membership Degree ${\mathit{\vartheta }}_{\tilde{\mathit{B}}}\left(\mathit{x}\right)$	Non-Membership Degree ${\mathit{\tau }}_{\tilde{\mathit{B}}}\left(\mathit{x}\right)$
0	VL	No influential	(0.05, 0.15, 0.20)	(0.00, 0.15, 0.25)
1	L	Slightly influential	(0.15, 0.30, 0.45)	(0.10, 0.30, 0.50)
2	M	Medium influential	(0.30, 0.45, 0.60)	(0.25, 0.45, 0.65)
3	H	Influential	(0.45, 0.60, 0.75)	(0.50, 0.60, 0.80)
4	VH	Significantly influential	(0.75, 0.90, 0.95)	(0.70, 0.90, 1.00)

, the membership degree ${\vartheta }_{\tilde{B}}\left(x\right)$ and non-membership degree ${\tau }_{\tilde{B}}\left(x\right)$ of the triangular fuzzy numbers were transformed, as defined by Wan et al. [43] (as in Equations (6) and (7)). Then, the average fuzzy matrix was obtained (as in Equation (9)).

$${\vartheta }_{\tilde{B}}\left(x\right)=\{\begin{array}{c}\frac{X-l}{m-l}, l<x\le m \\ \frac{u-x}{u-m}, m<x\le u\\ 0, otherwise\end{array}$$

(6)

$${\tau }_{\tilde{B}}\left(x\right)=\{\begin{array}{c}\frac{m-x}{m-l^{\prime }}, l^{\prime }<x\le m \\ \frac{x-m}{u^{\prime }-m}, m<x\le u^{\prime }\\ 1, otherwise\end{array}$$

(7)

$$B=\frac{1}{H}{\displaystyle \sum }_{k=1}^H{B}_1, \dots ,+\frac{1}{H}{\displaystyle \sum }_{k=1}^H{B}_p={\left[B_{ij}\right]}_{n\times n}=\left[\begin{array}{ccc}{b}_{11}& \cdots & b_{1n}\\ ⋮& \ddots & ⋮\\ b_{n1}& \cdots & b_{nn}\end{array}\right]$$

(8)

$$\frac{1}{H}{\sum }_{k=1}^H\widetilde{B_k}=\frac{1}{H}{\sum }_{k=1}^H\left({\vartheta }_{\tilde{B}}\left(x\right);{\tau }_{\tilde{B}}\left(x\right)\right)=\frac{1}{H}{\sum }_{k=1}^H\left[{\vartheta }_{\tilde{B}}\left(l_{ij}^k,m_{ij}^k,u_{ij}^k\right);{\tau }_{\tilde{B}}\left(l_{ij}^{\prime k},m_{ij}^k,u_{ij}^{\prime k}\right)\right]=\left[\begin{array}{c}\begin{array}{ccc}\widetilde{b_{11}}& \widetilde{b_{12}}& \begin{array}{cc}\dots & \widetilde{b_{1n}}\end{array}\end{array}\\ \begin{array}{ccc}\widetilde{b_{21}}& \widetilde{b_{22}}& \begin{array}{cc}\dots & \widetilde{b_{2n}}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{ccc}⋮& ⋮& \begin{array}{cc}\ddots & ⋮\end{array}\end{array}\\ \begin{array}{ccc}\widetilde{b_{n1}}& \widetilde{b_{n2}}& \begin{array}{cc}\dots & \widetilde{b_{nn}}\end{array}\end{array}\end{array}\end{array}\right]$$

(9)

The Equation $E_k$ = $\left\{E_1,E_2,\dots ,E_p\right\}$ represents the scores given by p experts (p indicates number), which also represent the fuzzy evaluations of the impact of criterion i on criterion j. From Figure 2, we can know that ${\vartheta }_{\tilde{B}}\left(x\right)=\left(l,m,u\right) \mathrm{and} {\tau }_{\tilde{B}}\left(x\right)=\left(l^{\prime },m,u^{\prime }\right), \mathrm{and} 0\le l^{\prime }\le l\le m\le u\le u^{\prime }\le 1$ and ${\tau }_{\tilde{B}}\left(x\right)$.

• Step 2: Defuzzification of the Average Fuzzy Matrix

According to Singh and Yadav [44], the defuzzification of the average fuzzy matrix can be obtained to yield crisp values (as shown in Equation (10)). A direct relationship matrix B is then constructed with its diagonal elements set to 0, as shown in Equation (11).

$$\tilde{B}\to B=l+u+4m+l^{\prime }+u^{\prime }/8$$

(10)

$$B=\frac{1}{H}{\sum }_{k=1}^H{B}_k, \dots ,+\frac{1}{H}{\sum }_{k=1}^H{B}_k={\left[B_{ij}\right]}_{n\times n}=\left[\begin{array}{ccc}0& b_{21}& b_{n1}\\ b_{12}& 0& b_{32}\\ b_{1n}& b_{2n}& 0\end{array}\right]$$

(11)

• Step 3: Normalize the Direct Relationship Matrix (B) to Obtain Normalized Direct Relationship Matrix (X)

After calculating the sum of each row in the B, the maximum value of each row can be obtained (as shown in Equation (12)). Then, the direct relationship matrix B can be divided by the maximum value to obtain the normalized direct relationship matrix (X), as shown in Equation (13).

$$S=max\left[\underset{1\le j\le n}{\underset{1\le i\le n}{max}({\sum }_{j=1}^n{B}_{ij}), max}({\sum }_{i=1}^n{B}_{ij})\right]$$

(12)

$$X=\frac{B}{S}=X_{3\times 3}=\left[\begin{array}{ccc}0& 1& 0\\ 3& 0& 1\\ 0& 1& 0\end{array}\right], \left[\begin{array}{c}1\\ 4\\ 1\end{array}\right]; X_{3\times 3}=\left[\begin{array}{ccc}0.00& 0.25& 0.00\\ 0.75& 0.00& 0.25\\ 0.00& 0.25& 0.00\end{array}\right]$$

(13)

• Step 4, Creating the Total Influence Matrix (T):

Through T, we can calculate the influence and affected degrees of the criteria on other criteria. Additionally, after obtaining X, it can be transformed into Equation (14) through the unit matrix I.

$$T=X{\left(\mathrm{I}-X\right)}^{-1}=\frac{X}{I-X}, I=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$$

(14)

In addition, the threshold value (the average of R + C in this study is 0.239, as shown in Table 7) can be set to eliminate less significant causal relationships, and the simplified total relationship matrix $T_R$ can be obtained as shown in Equation (15):

$$T_R=\left[\begin{array}{ccc}0.339& \sout{0.238}& 0.309\\ \sout{0.232}& 0.311& 0.412\\ 0.240& 0.312& \sout{0.119}\end{array}\right]$$

(15)

• Step 5, Establishing the Influence Relationship Map (IRM):

Let $t_{ij}\left(i,j=1,2,\dots ,n\right)$ be the elements in T. The total sum of each row and column in T are denoted as R and C, respectively. Equation (16) represents the total sum of each row, while Equation (17) represents the total sum of each column.

$$R=R_{n\times 1}={\left[{\sum }_{j=1}^n{t}_{ij}\right]}_{n\times 1}$$

(16)

$$C=C_{n\times 1}={\left[{\sum }_{i=1}^n{t}_{ij}\right]}_{1\times n}$$

(17)

R represents the factors that influence other factors, while C represents the factors that are influenced by other factors. R + C represent the strength of the relationship between factors (centrality), while R − C represents the strength of the factor’s influence or being influenced (causality). Based on the calculation results, the causal relationships between factors can be analyzed.

The IRM (as shown in Figure 3) examines the rows and columns (R + C), where rows represent the degree of influence on other criteria. Simply put, the larger the positive value, the more it can influence other factors. The columns represent the degree to which other criteria affect it. Simply put, the larger the negative value, the more easily it can be influenced by other factors. From the analysis of the four quadrants, quadrant I is the core factor, as it has high importance and correlation. Quadrant II is the driving factor, as it has low importance but high correlation. Quadrant III is the independent factor, with relatively low importance and correlation. Quadrant IV is the influencing factor, with relatively high importance but lower correlation and is more easily influenced by other factors and cannot be directly improved. From this graph, decision-makers can intuitively find the causal relationships between factors in complex situations and provide valuable insights for decision-making.

3.3. Questionnaire Design

Based on the research topic, this study designed a questionnaire on the selection criteria of OWP materials suppliers, mainly referring to domestic and foreign literature. The questionnaire was used as a quantitative research tool for this study. Additionally, a semi-structured expert interview method was employed to achieve opinion exchange between the interviewer and interviewee through oral communication. The motivation and views of the interviewees were analyzed based on the interview content, and the obtained interview data will have certain representativeness in the industry, which can solve the problem of small samples and support the reliability of the article.

To enhance the reliability and validity of the questionnaire, before formulating the questionnaire, Zhang’s [2] relevant books and literature were referred to. Moreover, expert interviews with the procurement personnel of energy companies were conducted to establish the validity of the expert questionnaire.

3.4. Sample Selection

In order to ensure the quality of the samples, the samples in this study were all selected from the members of the OWP industry purchasing department of the OWP energy companies as the research objects, and the members of the purchasing department completed the questionnaires, so as to ensure the acquisition of sample data and having reference value.

The OWP project undertaken by the OWP energy companies was briefly sketched as follows: it was mainly responsible for the tubed-frame underwater construction and underwater foundation piles of the OSW farm that included laying and maintenance the arrayed submarine cable of the series connected wind turbines. Besides, the main required material SCs were coils, fan props, foundation piles, fan towers, and tower sections.

4. Empirical Results

The pre-test of the study was conducted on 15 March 2023, a total of 25 questionnaires were both distributed and recovered (100% questionnaire recovery), 3 invalid questionnaires (missing answers), and 22 valid questionnaires. After analyzing the pre-test questionnaire, it still needed to be adjusted in terms of semantics (upon inquiries, the omission of 3 pre-test questionnaires due to the unclear meaning of it). Once the questionnaire was compiled, it was reviewed and revised by experts to obtain a formal questionnaire. Formal questionnaires of this study were filled out by purchasing department staff of the OWP energy companies on 27 March 2023. A total of 25 samples were sampled in this study (see

Table 6. Sample’s Basic Narrative Statistics Table.

Sample ID	Job Position	Age	Years of Service	Education	APQ	AFQ	DQ
1	Manager	56	29	Doctorate	○	○	○
2	Junior Manager.	52	28	Master’s	○	○	○
3	Team leader	46	24	Master’s	○	○	○
4	Team leader	47	23	Master’s	○	○	○
5	Staff	42	21	Bachelor’s	○	○	○
6	Staff	47	24	Bachelor’s	○	○	○
7	Staff	48	25	Bachelor’s	○	○	○
8	Staff	50	27	Bachelor’s	○	○	○
9	Staff	42	16	Bachelor’s	○	○	○
10	Staff	43	18	Bachelor’s	○	○	○
11	Staff	47	24	Bachelor’s	○	○	○
12	Staff	41	17	Bachelor’s	○	○	○
13	Staff	28	4	Bachelor’s	╳	○	○
14	Staff	24	2	Bachelor’s	╳	╳
15	Staff	47	22	Bachelor’s	○	○	○
16	Staff	44	21	Bachelor’s	○	○	○
17	Staff	53	30	Bachelor’s	○	○	○
18	Staff	41	18	Bachelor’s	○	○	○
19	Staff	35	9	Bachelor’s	○	○	○
20	Staff	45	25	Bachelor’s	○	○	○
21	Staff	43	19	Bachelor’s	○	○	○
22	Staff	49	26	Bachelor’s	○	○	○
23	Staff	50	31	Bachelor’s	○	○	○
24	Staff	48	27	Bachelor’s	○	○	○
25	Staff	26	3	Bachelor’s	╳	○	○

Symbol notation; ○: Valid questionnaire (○); ╳: Invalid questionnaire (╳); AFQ: AHP pre-test questionnaire (APQ); AFQ: AHP formal questionnaire (AFQ); DQ: DEMATEL questionnaire (DQ).

), 25 questionnaires were received (100% of questionnaires were received), where 1 questionnaire is invalid (missing answers), and 24 questionnaires are valid. The average values of the valid questionaries are shown in Appendix C). And we then proceed to AHP weight analysis.

$$B_{Wt}=\left[\begin{array}{c}\mathrm{Average}\mathrm{Weight}\mathrm{of}\mathrm{Each}\mathrm{Criterion}\\ \mathrm{Quality}\left(0.154\right)\left(\mathbf{1}\right)\\ \mathrm{Reputation}\mathrm{and}\mathrm{industry}\mathrm{status}\left(0.108\right)\left(\mathbf{2}\right)\\ \mathrm{Part}\mathrm{prices}\left(0.095\right)\left(\mathbf{3}\right)\\ \mathrm{Product}\mathrm{delivery}\mathrm{time}\left(0.090\right)\left(\mathbf{4}\right)\\ \mathrm{Technical}\mathrm{capability}\left(0.086\right)\left(\mathbf{5}\right)\\ \mathrm{Work}\mathrm{efficiency}\left(0.065\right)\left(\mathbf{6}\right)\\ \mathrm{Business}\mathrm{review}\mathrm{and}\mathrm{audit}\left(0.061\right)\left(\mathbf{7}\right)\\ \mathrm{Production}\mathrm{capacity}\left(0.060\right)\left(\mathbf{8}\right)\\ \mathrm{Location}\left(0.054\right)\left(\mathbf{9}\right)\\ \mathrm{Management}\mathrm{philosophy}\left(0.053\right)\left(\mathbf{10}\right)\\ \mathrm{Asset}\mathrm{condition}\left(0.053\right)\left(\mathbf{11}\right)\\ \mathrm{After}-\mathrm{sales}\mathrm{service}\left(0.019\right)\left(\mathbf{12}\right)\\ \mathrm{Warranty}\mathrm{and}\mathrm{maintenance}\left(0.015\right)\left(\mathbf{13}\right)\\ \mathrm{Service}\mathrm{attitude}\left(0.013\right)\left(\mathbf{14}\right)\\ \mathrm{Core}\mathrm{values}\mathrm{of}\mathrm{the}\mathrm{company}\left(0.010\right)\left(\mathbf{15}\right)\\ \mathrm{Order}\mathrm{management}\left(0.009\right)\left(\mathbf{16}\right)\\ \mathrm{Labor}\mathrm{relations}\mathrm{records}\left(0.009\right)\left(\mathbf{17}\right)\\ \mathrm{Vision}\mathrm{and}\mathrm{objectives}\left(0.008\right)\left(\mathbf{18}\right)\\ \mathrm{Historical}\mathrm{performance}\left(0.008\right)\left(\mathbf{19}\right)\\ \mathrm{Management}\mathrm{and}\mathrm{organization}\left(0.008\right)\left(\mathbf{20}\right)\\ \mathrm{Trust}\left(0.008\right)\left(\mathbf{21}\right)\\ \mathrm{Cos}\mathrm{t}\mathrm{management}\mathrm{ability}\left(0.008\right)\left(\mathbf{22}\right)\\ \mathrm{Employee}\mathrm{training}\left(0.007\right)\left(\mathbf{23}\right)\end{array}\right]$$

(18)

$$C.I.=\frac{\left({\lambda }_{max-n}\right)}{n-1}=\frac{0.069}{22}=0.003$$

(19)

$$C.R.=\frac{C.I.}{R.I.}=\frac{0.003}{1.59}=0.002$$

(20)

After the AHP calculation, the consistency index and consistency ratio values of the pairwise comparison matrices are both less than 0.1 (see Equations (19) and (20)), indicating that the judgments of the experts on the evaluation criteria before and after the evaluation are consistent and satisfactory. In addition, according to Equation (18), the average weights and ranking of the criteria are as follows: quality (Ct1:0.154) > reputation and industry status (Ct11:0.108) > part price (Ct6:0.095) > product delivery time (Ct2:0.090) > technical ability (Ct7:0.086) > work efficiency (Ct14:0.065) > business review and audit (Ct18:0.061) > production capacity (Ct5:0.060) > location (Ct20:0.054) > management philosophy (Ct10:0.053) > asset status (Ct8:0.053) > after-sales service (Ct4:0.019) > warranty and maintenance (Ct15:0.015) > service attitude (Ct16:0.013) > core values (Ct9:0.010) > order management (Ct23:0.009) > labor-management relationship records (Ct19:0.009) > vision and goals (Ct12:0.008) > historical performance (Ct3:0.008) > management and organization (Ct13:0.008) > trust (Ct17:0.008) > cost management ability (Ct21:0.008) > employee training (Ct22:0.007).

Furthermore, as shown in Figure 4, the weights of the 12 evaluation criteria are all lower than the mean (1/23 = 0.043). Therefore, this study excludes the criteria with weights lower than the mean. Additionally, in order to explore the causal relationships among the evaluation criteria for selecting material suppliers, 11 evaluation criteria with weights higher than the mean are retained (as shown in Table 7), and a DEMATEL questionnaire is developed and coded.

On 27 April 2023, the researchers returned to the energy companies and had 24 samples filled out the questionnaire by the procurement staff (as shown in Table 6). 24 questionnaires were collected, resulting in a 100% response rate and 24 valid questionnaires. After the questionnaire collection, the evaluation scale of the evaluated criteria was converted into a triangular fuzzy number according to Table 5, and the overall values of the questionnaire were summed and divided by the number of questionnaires to obtain the average fuzzy matrix (as shown Appendix D).

Then, the average fuzzy matrix was defused and the direct relation matrix (B) was established (as shown in Equation (21)).

$$B=\left[\begin{array}{ccccccccccc}0.000& 0.259& 0.452& 0.574& 0.300& 0.138& 0.300& 0.414& 0.485& 0.300& 0.450\\ 0.554& 0.000& 0.138& 0.450& 0.613& 0.300& 0.138& 0.495& 0.300& 0.300& 0.450\\ 0.554& 0.300& 0.000& 0.300& 0.300& 0.246& 0.553& 0.495& 0.320& 0.138& 0.253\\ 0.524& 0.678& 0.434& 0.000& 0.372& 0.138& 0.315& 0.485& 0.372& 0.313& 0.138\\ 0.554& 0.450& 0.344& 0.138& 0.000& 0.300& 0.300& 0.434& 0.291& 0.339& 0.613\\ 0.554& 0.138& 0.362& 0.613& 0.300& 0.000& 0.553& 0.434& 0.138& 0.372& 0.300\\ 0.554& 0.613& 0.481& 0.300& 0.300& 0.346& 0.000& 0.333& 0.138& 0.280& 0.174\\ 0.425& 0.372& 0.138& 0.539& 0.300& 0.613& 0.450& 0.000& 0.613& 0.300& 0.300\\ 0.554& 0.469& 0.398& 0.300& 0.322& 0.300& 0.300& 0.394& 0.000& 0.300& 0.138\\ 0.469& 0.613& 0.286& 0.450& 0.613& 0.300& 0.450& 0.436& 0.450& 0.000& 0.2\\ 0.459& 0.236& 0.545& 0.667& 0.503& 0.236& 0.144& 0.445& 0.485& 0.164& 0.000\end{array}\right]$$

(21)

From Equation (23), we know S = max$\left[\underset{1\le j\le 11}{\underset{1\le i\le 11}{max}({\sum }_{j=1}^{11}{B}_{ij}), max}({\sum }_{i=1}^{11}{B}_{ij})\right]$ = max$\left[5.198,4.312\right]$ = 5.198.

In addition, the normalized direct relationship matrix X can be directly obtained by dividing matrix B by matrix S, as shown in Equation (22).

$$X=\left[\begin{array}{ccccccccccc}0.000\hfill & 0.050\hfill & 0.087\hfill & 0.011\hfill & 0.058\hfill & 0.027\hfill & 0.058\hfill & 0.080\hfill & 0.093\hfill & 0.058\hfill & 0.087\hfill \\ 0.107\hfill & 0.000\hfill & 0.027\hfill & 0.087\hfill & 0.118\hfill & 0.058\hfill & 0.027\hfill & 0.095\hfill & 0.058\hfill & 0.058\hfill & 0.087\hfill \\ 0.107\hfill & 0.058\hfill & 0.000\hfill & 0.058\hfill & 0.058\hfill & 0.047\hfill & 0.106\hfill & 0.095\hfill & 0.062\hfill & 0.027\hfill & 0.049\hfill \\ 0.101\hfill & 0.130\hfill & 0.083\hfill & 0.000\hfill & 0.072\hfill & 0.027\hfill & 0.061\hfill & 0.093\hfill & 0.072\hfill & 0.060\hfill & 0.027\hfill \\ 0.107\hfill & 0.087\hfill & 0.066\hfill & 0.027\hfill & 0.000\hfill & 0.058\hfill & 0.058\hfill & 0.083\hfill & 0.056\hfill & 0.065\hfill & 0.118\hfill \\ 0.107\hfill & 0.027\hfill & 0.070\hfill & 0.118\hfill & 0.058\hfill & 0.000\hfill & 0.106\hfill & 0.083\hfill & 0.027\hfill & 0.072\hfill & 0.058\hfill \\ 0.107\hfill & 0.118\hfill & 0.093\hfill & 0.058\hfill & 0.058\hfill & 0.067\hfill & 0.000\hfill & 0.064\hfill & 0.027\hfill & 0.054\hfill & 0.033\hfill \\ 0.082\hfill & 0.072\hfill & 0.027\hfill & 0.104\hfill & 0.058\hfill & 0.118\hfill & 0.087\hfill & 0.000\hfill & 0.118\hfill & 0.058\hfill & 0.058\hfill \\ 0.107\hfill & 0.090\hfill & 0.077\hfill & 0.058\hfill & 0.062\hfill & 0.058\hfill & 0.058\hfill & 0.076\hfill & 0.000\hfill & 0.058\hfill & 0.027\hfill \\ 0.090\hfill & 0.118\hfill & 0.055\hfill & 0.087\hfill & 0.118\hfill & 0.058\hfill & 0.087\hfill & 0.084\hfill & 0.087\hfill & 0.000\hfill & 0.047\hfill \\ 0.088\hfill & 0.045\hfill & 0.105\hfill & 0.128\hfill & 0.097\hfill & 0.045\hfill & 0.028\hfill & 0.086\hfill & 0.093\hfill & 0.032\hfill & 0.000\hfill \end{array}\right]$$

(22)

Using T$=X{\left(I-X\right)}^{-1}$ to establish the total impact relation matrix (T), as shown in Equation (23):

$$T=\left[\begin{array}{ccccccccccc}0.234\hfill & 0.239\hfill & 0.246\hfill & 0.297\hfill & 0.233\hfill & 0.163\hfill & 0.214\hfill & 0.273\hfill & 0.258\hfill & 0.186\hfill & 0.224\hfill \\ 0.337\hfill & 0.193\hfill & 0.197\hfill & 0.285\hfill & 0.291\hfill & 0.195\hfill & 0.190\hfill & 0.292\hfill & 0.233\hfill & 0.192\hfill & 0.235\hfill \\ 0.317\hfill & 0.233\hfill & 0.156\hfill & 0.241\hfill & 0.220\hfill & 0.174\hfill & 0.248\hfill & 0.274\hfill & 0.218\hfill & 0.152\hfill & 0.184\hfill \\ 0.332\hfill & 0.313\hfill & 0.242\hfill & 0.201\hfill & 0.251\hfill & 0.168\hfill & 0.220\hfill & 0.290\hfill & 0.243\hfill & 0.193\hfill & 0.179\hfill \\ 0.337\hfill & 0.271\hfill & 0.232\hfill & 0.235\hfill & 0.185\hfill & 0.195\hfill & 0.217\hfill & 0.281\hfill & 0.230\hfill & 0.196\hfill & 0.261\hfill \\ 0.337\hfill & 0.225\hfill & 0.237\hfill & 0.311\hfill & 0.236\hfill & 0.139\hfill & 0.264\hfill & 0.281\hfill & 0.202\hfill & 0.204\hfill & 0.203\hfill \\ 0.322\hfill & 0.288\hfill & 0.242\hfill & 0.246\hfill & 0.227\hfill & 0.193\hfill & 0.154\hfill & 0.252\hfill & 0.190\hfill & 0.179\hfill & 0.176\hfill \\ 0.333\hfill & 0.276\hfill & 0.209\hfill & 0.313\hfill & 0.250\hfill & 0.257\hfill & 0.256\hfill & 0.218\hfill & 0.291\hfill & 0.203\hfill & 0.212\hfill \\ 0.320\hfill & 0.262\hfill & 0.226\hfill & 0.243\hfill & 0.228\hfill & 0.184\hfill & 0.208\hfill & 0.260\hfill & 0.162\hfill & 0.182\hfill & 0.168\hfill \\ 0.356\hfill & 0.330\hfill & 0.242\hfill & 0.308\hfill & 0.316\hfill & 0.214\hfill & 0.265\hfill & 0.309\hfill & 0.277\hfill & 0.156\hfill & 0.218\hfill \\ 0.326\hfill & 0.242\hfill & 0.269\hfill & 0.321\hfill & 0.273\hfill & 0.184\hfill & 0.197\hfill & 0.289\hfill & 0.266\hfill & 0.170\hfill & 0.153\hfill \end{array}\right]$$

(23)

By Equation (23), the summation of each row of T gives the R values of each criterion, the summation of each column gives the C values of each criterion, and the summation of $\left(R_1+C_1\right),\dots ,\left(R_{11}+C_{11}\right)$ gives the R + C values of each criterion. The summation of $\left(R_1-C_1\right),\dots ,\left(R_{11}-C_{11}\right)$ gives the R − C values of each criterion, as shown in Table 7.

Table 7. The corresponding values between centrality and reasonableness of the evaluation criteria for selecting offshore wind power industry material suppliers.

Criteria	R	C	R + C	Rank of Importance	AHP Rank of Weight	R − C
Quality (C1)	2.567	3.551	6.118	NO.1	NO.1	−0.984
Product delivery time (C2)	2.640	2.872	5.512	NO.4	NO.4	−0.232
Production capacity (C3)	2.417	2.498	4.915	NO.8	NO.8	−0.081
Part prices(C4)	2.632	3.001	5.633	NO.3	NO.3	−0.369
Technical capability (C5)	2.640	2.710	5.350	NO.5	NO.5	−0.070
Asset condition (C6)	2.639	2.066	4.705	NO.11	NO.11	+0.573
Management philosophy (C7)	2.469	2.433	4.902	NO.10	NO.10	+0.036
Reputation and industry status (C8)	2.818	3.019	5.837	NO.2	NO.2	−0.201
Work efficiency (C9)	2.443	2.570	5.013	NO.6	NO.6	−0.127
Business review and audit (C10)	2.991	2.013	5.004	NO.7	NO.7	+0.978
Location (C11)	2.690	2.213	4.903	NO.9	NO.9	+0.477

Table 7. The corresponding values between centrality and reasonableness of the evaluation criteria for selecting offshore wind power industry material suppliers.

Criteria	R	C	R + C	Rank of Importance	AHP Rank of Weight	R − C
Quality (C1)	2.567	3.551	6.118	NO.1	NO.1	−0.984
Product delivery time (C2)	2.640	2.872	5.512	NO.4	NO.4	−0.232
Production capacity (C3)	2.417	2.498	4.915	NO.8	NO.8	−0.081
Part prices(C4)	2.632	3.001	5.633	NO.3	NO.3	−0.369
Technical capability (C5)	2.640	2.710	5.350	NO.5	NO.5	−0.070
Asset condition (C6)	2.639	2.066	4.705	NO.11	NO.11	+0.573
Management philosophy (C7)	2.469	2.433	4.902	NO.10	NO.10	+0.036
Reputation and industry status (C8)	2.818	3.019	5.837	NO.2	NO.2	−0.201
Work efficiency (C9)	2.443	2.570	5.013	NO.6	NO.6	−0.127
Business review and audit (C10)	2.991	2.013	5.004	NO.7	NO.7	+0.978
Location (C11)	2.690	2.213	4.903	NO.9	NO.9	+0.477

According to Table 7, observing that R − C > 0 (correlation) represents the “cause” category of causal relationships, i.e., asset condition (C6), management philosophy (C7), business review and audit (C10), and geographic location (C11) represent the causal factors, while R − C < 0 (causality) represents the “effect” category of causal relationships, i.e., quality (C1), product delivery (C2), production capacity (C3), parts price (C4), technical ability (C5), reputation and industry status (C8), and work efficiency (C9) represent the influencing factors. Therefore, using the DEMATEL questionnaire can help understand the causality of the selection and evaluation criteria for OWP industry material suppliers. In addition, to present significant causal relationships, the values within the total impact relation matrix (T) are deleted by setting a threshold value to show more significant causal relationships. The threshold value is the arithmetic mean (0.239) of the total impact relation matrix (T), i.e., ((2.567 + 2.640 + 2.417 + 2.632 + 2.640 + 2.639 + 2.469 + 2.818 + 2.443 + 2.991 + 2.690)/121 = 0.239).

Finally, the values greater than or equal to the threshold value are compared according to the evaluation criteria and plotted on a coordinate map. This makes it easier to see the causal relationships between criteria. If only the numbers greater than the threshold value in the total impact relation matrix (T) are retained, the simplified total relationship matrix $T_R$ can be obtained, as shown in Equation (24).

$$T_R=\left[\begin{array}{ccccccccccc}\sout{0.234}\hfill & 0.239\hfill & 0.246\hfill & 0.297\hfill & \sout{0.233}\hfill & \sout{0.163}\hfill & \sout{0.214}\hfill & 0.273\hfill & 0.258\hfill & \sout{0.186}\hfill & \sout{0.224}\hfill \\ 0.337\hfill & \sout{0.193}\hfill & \sout{0.197}\hfill & 0.285\hfill & 0.291\hfill & \sout{0.195}\hfill & \sout{0.190}\hfill & 0.292\hfill & \sout{0.233}\hfill & \sout{0.192}\hfill & \sout{0.235}\hfill \\ 0.317\hfill & \sout{0.233}\hfill & \sout{0.156}\hfill & 0.241\hfill & \sout{0.220}\hfill & \sout{0.174}\hfill & 0.248\hfill & 0.274\hfill & \sout{0.218}\hfill & \sout{0.152}\hfill & \sout{0.184}\hfill \\ 0.332\hfill & 0.313\hfill & 0.242\hfill & \sout{0.201}\hfill & 0.251\hfill & \sout{0.168}\hfill & \sout{0.220}\hfill & 0.290\hfill & 0.243\hfill & \sout{0.193}\hfill & \sout{0.179}\hfill \\ 0.337\hfill & 0.271\hfill & \sout{0.232}\hfill & \sout{0.235}\hfill & \sout{0.185}\hfill & \sout{0.195}\hfill & \sout{0.217}\hfill & 0.281\hfill & \sout{0.230}\hfill & \sout{0.196}\hfill & 0.261\hfill \\ 0.337\hfill & \sout{0.225}\hfill & \sout{0.237}\hfill & 0.311\hfill & \sout{0.236}\hfill & \sout{0.139}\hfill & 0.264\hfill & 0.281\hfill & \sout{0.202}\hfill & \sout{0.204}\hfill & \sout{0.203}\hfill \\ 0.322\hfill & 0.288\hfill & 0.242\hfill & 0.246\hfill & \sout{0.227}\hfill & \overline{\sout{0.193}}\hfill & \sout{0.154}\hfill & 0.252\hfill & \sout{0.190}\hfill & \overline{\sout{0.179}}\hfill & \overline{\sout{0.176}}\hfill \\ 0.333\hfill & 0.276\hfill & \sout{0.209}\hfill & 0.313\hfill & 0.250\hfill & \overline{0.257}\hfill & 0.256\hfill & \sout{0.218}\hfill & 0.291\hfill & \overline{\sout{0.203}}\hfill & \overline{\sout{0.212}}\hfill \\ 0.320\hfill & 0.262\hfill & \sout{0.226}\hfill & 0.243\hfill & \sout{0.228}\hfill & \overline{\sout{0.184}}\hfill & \sout{0.208}\hfill & 0.260\hfill & \sout{0.162}\hfill & \overline{\sout{0.182}}\hfill & \overline{\sout{0.168}}\hfill \\ 0.356\hfill & 0.330\hfill & 0.242\hfill & 0.308\hfill & 0.316\hfill & \overline{\sout{0.214}}\hfill & 0.265\hfill & 0.309\hfill & 0.277\hfill & \overline{\sout{0.156}}\hfill & \overline{\sout{0.218}}\hfill \\ 0.326\hfill & 0.242\hfill & 0.269\hfill & 0.321\hfill & 0.273\hfill & \overline{\sout{0.184}}\hfill & \sout{0.197}\hfill & 0.289\hfill & 0.266\hfill & \overline{\sout{0.170}}\hfill & \overline{\sout{0.153}}\hfill \end{array}\right]$$

(24)

According to the adjusted $T_R$ the distribution map of the relationship between the influence and the affect degree of the “criteria for selecting and evaluating OWP material suppliers” can be obtained (as shown in Figure 5). Doubleline arrows indicate mutual influence between two criteria, and single-directional arrows indicate that the criteria at the arrowhead influence the criteria in front of the arrow. In addition, it can also be analyzed from the one-way and two-way arrows: R − C > 0 evaluation criteria are the leading criteria; R − C < 0 evaluation criteria are the affected criteria, and the difference in the degree of mutual influence and being influenced between each criterion can also be judged.

Furthermore, this study used the relationship distribution map of the impact and influence degree of each evaluation criterion and divided it into four quadrants based on the total average of R + C for each evaluated criterion (5.263), which is (6.118 + 5.512 + 4.915 + 5.633 + 5.350 + 4.705 + 4.902 + 5.837 + 5.013 + 5.004 + 4.903)/11 = 5.263).

The distribution relationship of the evaluated criteria is explained in each quadrant (as shown in Figure 6), which helps each OWP material supplier to adjust the development index weight moderately based on limited resources and thereby enhance their competitiveness.

According to Figure 6, criteria located in the first quadrant (R + C > 5.263, R + C > 0) are considered core criteria, which means that these criteria have a direct impact on criteria located in the fourth quadrant. In situations where OWP material suppliers have limited resources, they should prioritize improving these criteria. In this case, there is only one criterion: business review and audit (C10).

Criteria located in the second quadrant (R + C < 5.263, R − C > 0) are considered causing criteria, meaning that they are less likely to have a direct impact on other criteria. However, if criteria located in this quadrant are improved, they can indirectly affect criteria in the fourth quadrant. If suppliers have extra resources, they should consider these criteria as secondary improvement items. In this case, there are three criteria: asset condition (C6), business philosophy (C7), and location (C11).

Criteria located in the third quadrant (R + C < 5.263, R − C < 0) are considered independent criteria, meaning that they are less likely to have a direct impact on other criteria but are more easily influenced by other criteria. In this case, there are two criteria: production capacity (C3) and work efficiency (C9). Since the efficiency of criteria located in this quadrant is not high, it is not recommended to invest resources in improving these criteria.

Criteria located in the fourth quadrant (R + C > 5.263, R − C < 0) are considered influenced criteria, meaning that they are more likely to have a direct impact on other criteria and are also easily influenced by other criteria. In this case, there are five criteria: quality (C1), product delivery time (C2), component price (C4), technical ability (C5), and reputation and industry status (C8). Compared to the first and second quadrants, improving criteria located in the fourth quadrant has less impact. Therefore, suppliers should focus on improving criteria located in the first and second quadrants instead.

5. Conclusions and Suggestions

The results obtained from this study provide the following conclusions and suggestions:

5.1. Conclusions

• Based on the literature review, OWP energy companies use 23 criteria to evaluate and select material suppliers. These criteria include quality, product delivery time, historical performance, after-sales service, production capacity, part prices, technical capability, asset condition, core values of the company, management philosophy, reputation and industry status, vision and objectives, management and organization, work efficiency, warranty and maintenance, service attitude, trust, business review and audit, labor relations records, location, cost management ability, employee training, and order management. After weighting these criteria through a questionnaire filled out by purchasing personnel from OWP energy companies, 11 criteria were identified as important for selecting material suppliers. These criteria are (1) quality; (2) production capacity; (3) reputation and industry status; (4) product delivery time; (5) part prices; (6) technical capability; (7) management and organization; (8) management philosophy; (9) location; (10) business review and audit, and (11) work efficiency. These criteria can serve as valuable references for future supplier selection by the purchasing team of OWP energy companies.
• The DEMATEL questionnaire analysis conducted in this study reveals causal relationships and establishes an Importance-Relation Map (IRM) with four quadrants. It indicates that business review and audit are the criteria that OWP suppliers should prioritize for improvement, even under limited resource conditions. When surplus resources are available, the criteria for improvement include asset condition, business philosophy, and location. Quality, product delivery time, production capacity, part prices, technical ability, reputation and industry status, and work efficiency are criteria that are affected but may not be prioritized for improvement by suppliers when they have limited resources. This study suggests that material suppliers for OWP energy companies can make moderate adjustments and improvements based on these findings, which can significantly benefit future development. Empirical results demonstrate that the weight sequence derived from the Analytic Hierarchy Process (AHP) is consistent with the importance sequence obtained from IFNs-DEMATEL. This consensus among experts confirms the suitability of the model established in this study for selecting OWP material suppliers in OWP energy companies at the current stage.
• Then, this research found that the AHP method can effectively meet the mathematical transitivity condition and pairwise comparison of standards, and the resulting AHP weight calculation has a relatively small error.
• This research through actual visits to the purchasing team of OWP energy companies, this study gained insights into their thoughts on purchasing. The data obtained from AHP and IFNs-DEMATEL highlight the need for improvements in the material supply chain and supplier integration within Taiwan’s wind power industry. Localization of products, cost control, and enhancement of quality are recommended to maintain technological capabilities and promote continuous growth of the OWP industry in Asia. However, The methodology employed in this study is applicable to various industries and companies, with the potential to enhance overall performance evaluation systems or supplier selection processes.

5.2. Suggestions

• In the establishment of the OWP material supplier selection system, there were many factors that affected the logistics supply and the overall SCs in the industry, even though the study integrated the previous literature, assembled Delphi expert group, and conducted multi-criteria research method (MCDM) methods to test the evaluation indicators listed in the study. However, the offshore wind field is distributed on the sea surface around Taiwan, so there would cause variables due to different geographical factors, including the location of the offshore wind field (e.g., Taichung Port has a large tidal range), seasonal climate (the windward side is opposite in summer and winter), and other non-human factors which have not been considered as selection criteria in the study. Therefore, it is hoped that factors such as different geographical locations and weather conditions would be further included in the future to conduct more detailed research on the aspects and indicators of the evaluation item.
• Marine engineering ships used in different construction types still need to be repaired and maintained, hence, the study only studied the indicators of the material supplier selection system in the OWP industry, and there is still a lack of additional logistical supplies in the overall evaluation. In the future, the needs of various types of maintenance materials for OWP fleets could be included in the selection indicator to establish an improved evaluation system.
• OWP is a very large industry. However, the survey participants in this study were all purchasing team members of OWP energy companies. It is suggested that future researchers target the purchasing teams and senior executives of OWP energy companies in Taiwan to conduct a larger-scale study, making the research results more comprehensive.
• In the actual environment, the criteria are inextricably linked. So, in the future, Grey System Theory could be incorporated into the multi-criteria research method (MCDM), and the result could also be used as a mutual comparison and verification.
• It is suggested that future researchers use document analysis methods, with a focus on non-market mechanism government procurement laws, to expand and improve this research.