A novel hybrid multi-criteria decision-making approach for offshore wind turbine selection

Abstract

Offshore wind power has been an important force to promote energy transformation. To build an advanced offshore wind farm, wind turbine selection requires the decision maker to explore new relevant criteria and evaluate alternatives with respect to decision criteria with assigning importance weightings to the criteria. In this paper, we devise a novel hybrid multi-criteria decision-making (MCDM) approach for offshore wind turbine selection by reconstructing analytic network process (ANP) and entropy-weight method (EWM). Based on the assigned weightings for ANP and EWM, the best alternative can be selected. For the decision-making model, five main criteria are specifically subdivided into 22 sub-criteria. The method is then applied to deal with the quantitative and qualitative inputs and the interrelation of criteria as arising from decision-making process. The results show that the proposed method can effectively select the optimal one from four different types of alternative offshore wind turbines.

Keywords

Offshore wind turbine MCDM analytic network process entropy-weight method wind turbine selection offshore wind farm

Introduction

With the less and less wind resources can be developed on land; the global wind farm construction has developed from land to offshore. Offshore wind farms have become one of the important directions of wind power generation in the future due to the advantages of being close to the coastal cities with concentrated electricity consumption, no land occupation and high wind speed (Bilgili et al., 2011; Wei et al., 2019). However, compared with onshore wind power, offshore wind power is more complicated, and the harsh natural environment such as corrosion of high salt fog, lightning strikes, and typhoons on the sea have a great impact on the operation of wind turbines, especially the deep and far sea areas under extreme weather conditions will occur more complex wind, wave, tide and surge environments, which puts forward higher requirements for the selection of offshore wind turbines (Higgins and Foley, 2014; Xie et al., 2019). Choosing appropriate wind turbine can not only save the investment of offshore wind farm, but also increase the profit from power generation, and reduce the cost of operation and maintenance (Feng and Chen, 2018; Junginger et al., 2009).

In the early stage of wind turbine selection studies, most researchers only consider the capacity factor to determine the optimal wind turbine. For example, in the literature (Bencherif et al., 2014; Jowder, 2009; Muyiwa et al., 2014), researchers evaluated the wind resources of wind farms based on Weibull distribution, then calculated the capacity factors of different wind turbines and selected the wind turbine with the highest capacity factor. In fact, this classical method focuses on achieving the best match between the wind turbines and wind resources, without taking into account the maximum benefit of the whole life cycle of the wind farm. On this basis, the economic criteria, power generation, capacity factor and generating cost are further considered in literature (Abdulrahman and Wood, 2017; Adaramola et al., 2014; Dong et al., 2013; Helgason, 2012; Quan and Leephakpreeda, 2015; Sajid et al., 2017; Sedaghat et al., 2019; Souma et al., 2016). The selection system is constructed with the goal of minimizing the generating cost and maximizing the capacity factor and power generation. However, with the increase of evaluation criteria, sometimes the criteria conflict with each other, the optimal wind turbines often fail to get the best evaluation for all criteria at the same time. Therefore, faced with this MCDM problem, the researchers further applied some decision method to the selection process in order to make a comprehensive decision for the alternative wind turbines. For example, Rehman and Khan (2016) proposed a two-level decision turbine selection strategy based on fuzzy logic and MCDM approach. The approach comprehensively considered six decision criteria of 20 wind turbines include turbine’s power rating, height of tower, energy output, rotor diameter, cut-in wind speed, and rated wind speed, analysed the effectiveness of the approach with the wind farm in Saudi Arabia. Bagočius et al. (2014) established a decision-making model with five main criteria consisting rated power, maximum power, annual power generation, investments and CO2 emissions, applying the AHP method determine the criteria weights and selected the best type of wind turbines suitable for wind farm is REpower M5 5.0 MW. Furthermore, in literature (Sagbansua and Balo, 2017), the selection of best wind turbine is determined by using analytic hierarchy process (AHP) technique. Four main criteria consisting technical, economic, environmental, and customer attributes have been taken into consideration. Six alternative wind turbines are compared using AHP technique, and the larger evaluated weight, the more advantage the wind turbine. Although the above studies provide a variety of methods for wind turbine selection, these methods only consider a few main criteria, ignoring the impact of wind turbine historical performance, and the after-sales service of manufacturer on wind turbine selection, but such selection standard is not a complete set for wind turbine selection. In practical terms, for the special operation environment of offshore wind turbine, some criteria such as anti-corrosion, lightning protection, typhoon prevention technology and occupied sea area cannot be ignored (Bi et al., 2017; China Huaneng Group, 2016; Q/HN-1-0000.09.002-2016, 2016). In addition, the criteria for wind turbine selection are not actually independent, but often interrelated and dependent on each other. For instance, the more advanced wind turbine technology, usually the lower cost of maintenance, but the higher price of wind turbine. Similarly, technology, economy, matching with the wind resources and after-sales service of manufacturer inevitably affect the historical performance of the wind turbine. However, the current selection methods often default that these criteria are independent of each other. Therefore, in view of the above problems, beside of the technology, economy, matching with the wind resources, this paper further considers the historical performance of wind turbine and the after-sales service of manufacturer. Moreover, there are many criteria that affect the selection of offshore wind turbine. Considering the relationship between these criteria, this paper put forward a new approach for wind turbine selection.

The ANP is a practical decision-making method proposed by Professor Saaty (1996) based on analytic hierarchy process (AHP) (Saaty and Erdener, 1980). AHP is a method that simulate the decision-making mode of human brain. It hierarchizes the complex decision-making system and analyses the importance of each criteria layer by layer. Due to its concise and clear characteristics, it is often used as a MCDM approach. However, AHP defaults that the criteria at the same layer are independent of each other and criteria of the two non-adjacent layers are irrelevant, which obviously does not meet the requirements of selection model in this paper. But ANP cancels the strict hierarchical relationship of AHP in the network layer and considers the interaction of criteria in the decision system and gives feedback. The proposal of ANP not only continues the advantages of AHP, but also made up for the deficiencies of AHP (Saaty, 2004). Therefore, it can better solve the decision-making problems of multi-criteria interaction. However, ANP model is a relatively subjective method. On the contrary, the EWM as a relatively objective method can give weight to the evaluated object according to the dispersion degree of criteria (Lin et al., 2010). The more dispersion of criteria is, the more information it provides, the more entropy it has, and the higher weight it takes. On the contrary, the smaller information entropy is, the smaller weight is. Therefore, subjective ANP combined with objective EWM will be more conducive to scientific wind turbine selection (Tang, 2019). In the paper, ANP and EWM are combined (ANP-EWM) to select the wind turbine by giving full play to their own advantages. Furthermore, comparing the selection results of ANP- EWM with traditional decision-making methods include AHP, ANP, EWM and AHP-EWM, the model with the largest final weight is taken as the optimal choice, so as to establish a more complete and scientific comprehensive selection system.

Background of methods

Method for ANP

Structure of ANP

A typical ANP structure can be divided into control layer and network layer. The control layer includes the target layer and the criteria layer. The target layer controls the decision-making factors in the criteria layer, and each decision-making factor is independent of each other. It can be seen that the control layer is similar to the hierarchical structure of AHP, so the AHP can be used to calculate the weights of criteria in the control layer. In addition, there may be no criteria layer in the control layer, but at least there should be a target layer. The network layer is composed of all the criteria controlled by the control layer, which affect each other to form a complex network structure. Therefore, the ANP structure not only retains the strict hierarchical relationship in AHP, but also takes into account the interaction and feedback among criteria (Saaty, 1996, 2004).

The decision-making problems need to be systematically described and classified. The most important thing is to sort out whether the different levels are independent of each other, and whether the criteria at same level are interdependent and feedback. Then, according to the hierarchical structure in the control layer and the influence relationship among the criteria in the network layer, the Structure of ANP is constructed, as shown in Figure 1.

Figure 1.

Typical ANP structure.

Construct judgment matrix

Usually, the judgment matrix is determined by experts according to the relative importance of the criteria. The value in the judgment matrix indicates which of the two criteria is more important. Saaty and Erdener (1980) proposed a method called 1–9 scale assignment to determine the values in the judgment matrix. The meanings of the scale are shown in Table 1.

Table 1.

One to Nine scale method.

Scale T = A/B	Meaning
1	A and B have the same importance
3	A is slightly more important than B
5	A is obviously more important than B
7	A is more important than B
9	A is extremely important than B
2, 4, 6, 8	Intermediate value of the above adjacent judgment
1/T	The ratio of importance of B and A

Construct unweighted super matrix

There are m criteria $(A_{1} \dots A_{m})$ in the control layer, N criteria sets $(B_{1} \dots B_{n})$ in the network layer, and $B_{i 1} \dots B_{in} (i = 1 \dots n)$ is the criteria in $B_{i}$ . Taking the control layer factor $A_{s} (s = 1 \dots m)$ as the decision criteria, the $B_{jk} (k = 1 \dots j)$ in the factor group $B_{j} (j = 1 \dots n)$ as the secondary criteria. The weights of other factors in group $B_{j}$ is compared with that of $B_{jk}$ , constructing the judgment matrix and normalizing it. After that, the normalized eigenvector $(w_{i 1}^{jk} \dots w_{in}^{jk})^{T}$ must pass the consistency test of $CR < 0.1$ , otherwise the elements in the judgment matrix need to be adjusted, and the above steps are recalculated until the consistency test passes. Similarly, we can get the normalized eigenvectors of other factors. By arranging these eigenvectors into matrix form, we can get the local weight vector matrix $W_{ij}$ (Luo et al., 2010; Wang, 2001):

W_{ij} = [\begin{matrix} w_{i 1}^{(j 1)} & w_{i 1}^{(j 2)} & \dots & w_{i 1}^{({jn}_{j})} \\ w_{i 2}^{(j 1)} & w_{i 2}^{(j 2)} & \dots & w_{i 2}^{({jn}_{j})} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ w_{{in}_{i}}^{(j 1)} & w_{ini}^{(j 2)} & \dots & w_{ini}^{(jnj)} \end{matrix}]

(1)

The column vector of $W_{ij}$ is the factor $B_{i 1} \dots B_{in}$ in $B_{i}$ . When the factor in $B_{j}$ is not affected by the factor in $B_{i}$ , $W_{ij} = 0$ . Repeat the above steps, we can get the super matrix $W$ under $A_{s}$ criterion. Similarly, the super matrix of other control factors can be calculated with the following formula.

W = [\begin{matrix} \begin{matrix} w_{11} & w_{12} \dots w_{1 n} \\ w_{21} & w_{22} \dots w_{2 n} \end{matrix} \\ ⋮ ⋮ ⋮ ⋮ \\ w_{n 1} w_{n 2} \dots w_{nn} \end{matrix}]

(2)

Construct weighted super matrix

First, we need to normalize the super matrix by comparing the importance of each factor $B_{j} (j = 1 \dots n)$ under the $A_{s}$ criterion, and obtain a normalized ranking vector as follows (Luo et al., 2010; Wang, 2001):

\begin{matrix} \underline{B_{j}} | \underline{B_{1} \dots B_{n}} | \underline{Normalized eigenvector} \\ B_{1} | | α_{1 j} \\ ⋮ | | ⋮ \\ B_{n} | | α_{n j} \end{matrix}

(3)

Then, the coefficient matrix can be acquired according to the following formula.

A = [\begin{matrix} a_{11} & \dots & a_{1 n} \\ ⋮ & ⋮ \\ a_{n 1} & \dots & a_{nn} \end{matrix}]

(4)

Finally, we can calculate the weighted super matrix by formula 5.

\bar{W} = a_{ij} W_{ij}, i = 1 \dots n; j = 1 \dots n

(5)

Construct limit super matrix

In order to reflect the dependency relationship between the elements, the weighted super matrix $\bar{W}$ needs to be stabilized, that is, calculate the limit relative ranking vector of each weighted super matrix according to the following formula (Luo et al., 2010; Wang, 2001).

W^{\infty} = lim_{k \to \infty} (1 / n) \sum_{k = 1}^{n} {\bar{W}}^{k}

(6)

If the limit has a solution, the value of the corresponding row in the original matrix is the stable weight of each evaluation criterion.

Since ANP relies on very complex matrix calculation, it is almost impossible to calculate it manually for complex systems. Therefore, in this paper, “Super Decision” software, a special software of ANP method, is used to calculate the complex matrix (Wang and Sun, 2010). The software is developed based on the principles of AHP and ANP, which is very helpful for solving MCDM problem.

Method for EWM

The specific steps for EWM to calculate the weight are as follows (Lin et al., 2010; Tang, 2019): there are n samples, m criteria, $x_{ij}$ is the value of the $jth$ indicator of the $ith$ sample $(i = 1 \dots n; j = 1 \dots m)$ .

In order to eliminate the dimensional influence among the criteria, it is necessary to normalize the criteria with different measurement units and convert the absolute value of the criteria into relative values for the purpose to facilitate calculation. The normalized formula can be divided into two types: positive and negative, which represent different meanings. And the larger value of the positive criterion is, the better evaluation of the criteria is, while the negative criterion is just opposite. The normalized data $r_{ij}$ is computed by the formula 7 and 8.

positive criterion : r_{ij} = \frac{x_{ij} - \min {x_{1 j} \dots x_{nj}}}{max {x_{1 j} \dots x_{nj}} - \min {x_{1 j} \dots x_{nj}}}

(7)

negative criterion : r_{ij} = \frac{max {x_{1 j} \dots x_{nj}} - x_{ij}}{max {x_{1 j} \dots x_{nj}} - \min {x_{1 j} \dots x_{nj}}}

(8)

$p_{ij}$ is the proportion of the $ith$ sample under the criteria of $jth$ .

p_{ij} = \frac{r_{ij}}{\sum_{i = 1}^{n} r_{ij}}, i = 1 \dots n; j = 1 \dots m

(9)

Therefore, the entropy of the $jth$ criteria is $e_{j}$ .

e_{j} = - k \sum_{i = 1}^{n} p_{ij} In (p_{ij}), j = 1 \dots m, k = \frac{1}{In (n)} > 0, e_{j} ⩾ 0

(10)

Then, we can get the weight of the evaluation criteria is $w_{j}$ .

w_{j} = \frac{1 - e_{j}}{\sum_{j = 1}^{m} (1 - e_{j})}

(11)

Finally, the weight of samples is $s_{i}$ .

s_{i} = \sum_{j = 1}^{m} w_{j} r_{ij}, i = 1 \dots n

(12)

Determination for ANP-EWM weight

In this paper, the comprehensive weight of criteria and alternatives is a combination of ANP and EWM weight. The specific steps are as follows:

It is assumed that the weight obtained by ANP method is $φ_{1}$ , and the weight obtained by EWM is $φ_{2}$ . This paper uses the distance function to determine the distribution coefficients of the $φ_{1}$ and $φ_{2}$ (Zhang and Miao, 2015). The formula of distance function as follows:

d (φ_{1}, φ_{2}) = {[\frac{1}{2} \sum_{i = 1}^{n} {(φ_{1} - φ_{2})}^{2}]}^{1 / 2}

(13)

We can calculate the comprehensive weight $φ$ by the linear combination of $φ_{1}$ and $φ_{2}$ .

φ = α φ_{1} + β φ_{2}

(14)

In formula 14, $α$ and $β$ are the distribution coefficients of the $φ_{1}$ and $φ_{2}$ .

In addition, the following relationship needs to be satisfied:

{\begin{matrix} d (φ_{1}, φ_{2})^{2} = (α - β)^{2} \\ α + β = 1 \end{matrix}

(15)

Through the formula 13 to 15, the distribution coefficients $α$ and $β$ can be calculated, and then the comprehensive weight $φ$ can be obtained.

Case analysis and results

Basic situation of offshore wind farm

The offshore wind farm is located in the Pinghai bay in Putian, southeast China’s Fujian Province, with coordinates of 119.29°–119.36°E and 25.09°–25.15°N. The site is adjacent to Daitou Peninsula in the West and Nanri island in the north. The water depth of the site is 10 to 20 m, and the nearest distance to the coastline is about 6 km. The installed capacity of the project is about 130 MW in plan. The wind power developer requires that the rated power of wind turbines is not less than 5 MW, and they should comply with IEC I standard or GL I standard. In the wind farm, the annual average wind speed of 100 m height measured by wind tower is 9.74 $m / s$ , and the annual average wind power density is 952 $W / m^{2}$ , which has a very good prospect of wind power generation. The wind speed of the farm is the largest in autumn and winter. It can be seen from Figure 2 that the prevailing wind direction is stable, the NNE, NE are the main wind direction in the whole year, the frequencies are 35.5% and 25%, respectively. The specific wind resource information at hub height is summarized in Table 2.

Table 2.

Wind resource information at hub height.

Parameters	Unit	Value
Hub height	m	100
Annual average wind speed	m/s	9.74
Annual wind power density	W/m²	952
Prevailing wind direction		NNE, NE
Weibull scale parameter A	m/s	10.77
Weibull shape parameter K		2.16
Wind shear index		0.08

Finger 2.

Rose chart of wind direction (left) and wind power (right) at 100 m.

Preliminary selection of wind turbines

Due to the implementation of ANP method, many multidimensional matrix operations will be involved. Moreover, wind power development enterprises also have special requirements for wind turbines. In order to meet the requirements of enterprises and reduce the complexity of calculation, this section determines some suitable offshore wind turbines through preliminary screening. The main screening factors are as follows:

(1)The rated power of wind turbine is at least 5MW.

(2)The wind turbine must meet the requirements of IEC I or GL I.

(3)Wind turbines with mature technologies and good operating performance.

(4)Consult the wind turbine manufacturers on the possibility of participating in the project.

(5)The comprehensive strength of manufacturers. Such as the enterprise scale, after-sales service, market share, supply capacity and plant location (short transport distance if close to wind farm) (Bi et al., 2017; Zhou, 2013).

After preliminary screening, four wind turbines were decided to participate in further selection, which were respectively marked as “OWT1,”“OWT2,”“OWT3,” and “OWT4.” The main information of the alternatives is shown in the Table 3. Figure 3 shows the power curves of four wind turbines in the present study. These power curves are obtained at an air density of 1.225 kg/m³.

Table 3.

Main technical parameters of the alternatives.

Alternatives manufacturermodel		OWT1	OWT2	OWT3	OWT4
		Ming yang	Sinovel	Shanghai electric	XEMC
		MySE5.5-155	SL5000/128	SWT-6.0-154	XE 128-5000
Operating parameters	Rated power (MW)	5.5	5	6	5
	Cut-in windspeed (m/s)	3	3.5	4	3
	Cut-out windspeed (m/s)	25	25	25	25
	Rated windspeed (m/s)	10.1	12.5	13	11.5
	Extreme windspeed (m/s)	70	70	70	70
	IEC class	IB	IA	IA	IB
	Hub height (m)	100	100	100	100
Blade	Number of blades	3	3	3	3
	Blade diameter (m)	155	128	154	128
	Swept area (m²)	18869	12861	18600	12773
Generator	Type	Permanentmagnet-semi-direct drive-synchronousmotor	Double-feedasynchronousmotor	Permanent magnet-direct drive- synchronousmotor	Permanentmagnet-directdrive-synchronous motor
Service life	Year	25	20	25	20

Finger 3.

The power curves of four wind turbines.

Detailed selection of wind turbines based on ANP-EWM

Establishment of selection criteria system

This paper brings together three experts with rich experience in the field of wind power generation to participate in the whole decision-making process (Hanson and Ramani, 1988; Remeikiene and Gaspareniene, 2016). Expert X and Z are university professors, engaged in the teaching and research of wind power system theory and technology. Expert Y is a senior engineer who works on wind farms. In this paper, AHP is used to distribute the weights of different experts according to the industry experience and education level. The structure of AHP is shown in Figure 4, and the judgment matrix is shown in Tables 4 to 6. CR < 0.1 shows that all judgment matrices pass the consistency test. Finally, the weights of experts are calculated, as shown in Table 7. The greater weight of expert, the higher impact on the results of selection.

Table 4.

The judgment matrix under “weight of experts.”

Weight of experts	Experience	Education	Weight
Experience	1	2	0.6667
Education	1/2	1	0.3333
CR = 0

Table 5.

The judgment matrix under “experience.”

Experience	Expert X	Expert Y	Expert Z	Weight
Expert X	1	1/2	1	0.25
Expert Y	2	1	2	0.5
Expert Z	1	1/2	1	0.25
CR = 0

Table 6.

The judgment matrix under “education.”

Education	Expert X	Expert Y	Expert Z	weight
Expert X	1	4	1	0.4577
Expert Y	1/4	1	1/3	0.1263
Expert Z	1	3	1	0.4160
CR = 0.0089

Table 7.

Weight of different experts.

Expert	X	Y	Z
Weight	0.32	0.38	0.3

Finger 4.

The structure of AHP.

Then, based on the references and experts’ opinions on wind turbine selection, the important criteria of offshore wind turbine selection are analyzed and summarized. The main criteria covering 5 aspects, including technology, matching with the wind resources, economy, historical performance of wind turbine and the after-sales service of manufacturer. And the criteria are specifically subdivided into 22 sub-criteria, as shown in Table 8.

Table 8.

Criteria system of offshore wind turbine selection.

Target	5 criteria	22 sub-criteria	References
Offshore windturbine selection	Technology $B_{1}$	Blade $C_{1}$	Sagbansua and Balo (2017)
		Gearbox $C_{2}$	Zhou (2013)
		Generator $C_{3}$	Zhou (2013)
		Converter $C_{4}$	CHGroup (2016)
		Intelligent monitoring andcontrol Technology $C_{5}$	Xu and Zhong (2017)
		Yaw system $C_{6}$	Xu and Zhong (2017)
		Corrosion, thunder andtyphoon Technologyprotection $C_{7}$	CHG (2016)
	Matching with the wind resources $B_{2}$	Capacity factor $C_{8}$	Abdulrahman et al. (2017)
		Wind class (IEC) $C_{9}$	Sajid et al. (2017)
		Grid connection requirements $C_{10}$	CHG (2016)
		Operating temperature $C_{11}$	CHG (2016)
		Occupied sea area $C_{12}$	Bi et al. (2017)
	Economy $B_{3}$	Ccost of per kWh $C_{13}$	Sedaghat et al. (2019)
		Annual power generation $C_{14}$	Rehman and Khan (2016)
		Cost of per kW $C_{15}$	Feng and Chen (2018)
		Service life $C_{16}$	Feng and Chen (2018)
		Cost of maintenance $C_{17}$	Feng and Chen (2018)
	Historical Performanceof wind turbine $B_{4}$	Sales performance $C_{18}$	Sagbansua and Balo (2017)
		Operating performance $C_{19}$	Feng and Chen (2018)
	After-sales service ofmanufacturer $B_{5}$	Supply of products $C_{20}$	Sagbansua and Balo (2017)
		Warranty $C_{21}$	Zhou (2013)
		Technical service $C_{22}$	Sagbansua and Balo (2017)

For ANP model, after the selection criteria are determined, it is necessary to study the interaction between the criteria, that is, the correlation of criteria. The correlation of criteria is obtained through a two-dimensional expert questionnaire. After discussion of the group, the correlation between the criteria can be obtained, as shown in Table 9. Then, according to the Tables 8 and 9, the ANP structure of wind turbine selection is drawn, as shown in Figure 5.

Table 9.

Questionnaire for criteria correlation.

Influencedcriteria		Alternatives				B1							B2					B3					B4		B5
		OWT1	OWT2	OWT3	OWT4	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16	C17	C18	C19	C20	C21	C22
Alternatives	OWT1
	OWT2
	OWT3
	OWT4
B1	C1
	C2
	C3
	C4
	C5
	C6
	C7
B2	C8
	C9
	C10
	C11
	C12
B3	C13
	C14
	C15
	C16
	C17
B4	C18
	C19
B5	C20
	C21
	C22

The criteria in the left column influence the top criteria, please add colour in the corresponding spaces.

Figure 5.

ANP structure of wind turbine selection.

Calculation process of ANP-EWM

When ANP method considers many criteria, it is very complicated and difficult to calculate manually. It is difficult to apply ANP to solve practical decision problems without the help of software. “Super decision” software is developed by RozannW.Satty and William Adams, which provides great convenience for the practical application of ANP method. Therefore, the software is used for calculation in this case. The flow chart of the software is shown in Figure 6. Green block is the prepared work for the use of software. Then, the complete ANP model is established in the software, as shown in Figure 7.

Figure 6.

The flow chart of software for ANP.

Figure 7.

ANP model of wind turbine selection in software.

After that, according to the calculation process of ANP, each expert needs to use the 1-9 scale method in Table 1 to construct the judgment matrix. Each judgment matrix should be tested for consistency. If CR < 0.1, the judgment matrix is considered acceptable. After the judgment matrixes are inputted, the software can automatically calculate unweighted super matrix, weighted super matrix and limit super matrix. Finally, the weights of alternatives and criteria based on ANP can also be derived directly in software.

For the calculation of EWM, 22 criteria are divided into two categories: positive criteria and negative criteria, as shown in the Table 10. The larger data of the positive criteria and the smaller data of the negative criterion, the higher dominance of the criteria. The criteria that can be quantified should input the original data as much as possible to improve the objectivity of the method. However, in practical application, many criteria in the decision model cannot be compared quantitatively, such as C2 and C3 criteria. For these qualitative criteria, the paper uses scores given by experts to reflect superiority, the lowest score is 1 and the highest score is 9. When comparing the same criteria of different alternatives, the higher score is, the more advantages it has. The classified results of criteria are shown in Table 10. Then, different types of criteria need to be normalized according to formula 7 or 8, respectively. After that, the weight of each criteria can be calculated according to formula 9, 10 and 11. Finally, according to formula 12, the weight of alternatives can be obtained for EWM.

Table 10.

Classification of criteria for EWM.

Negative criteria	C12, C13, C15, C17
Positive criteria	Others
Quantitative criteria (input original data)	C1, C8, C12, 13, C14, C15, C16, C17, C18, C21
Qualitative criteria (input the scores)	C2, C3, C4, C5, C6, C7, C9, C10, C11, C19, C20, C22

Finally, the weight of ANP-EWM only needs to combine the weight of ANP and EWM according to the distance function in Section 2.3.

Decision results of Expert X

For the calculation of ANP method, firstly, according to the opinion of Expert X, the judgment matrix of criteria and alternatives are constructed according to Table 1, as shown in Tables 11 to 15. The CR of each judgment matrix is less than 0.1, which conforms to the consistency test. The same is true for the construction of the other sub-judgment matrices. After inputting all the judgment matrices into the software, the unweighted super matrix in Table 16 can be further obtained. The weighted super matrix is obtained on the basis of the unweighted super matrix, presented in Table 17. Finally, the weighted super matrix can converge into a stable super matrix, called the limit super matrix (Liao et al., 2019). The limit super matrix is obtained in Table 18. Finally, the weights of criteria are shown in Table 19, and the weights of alternatives are shown in Table 20.

Table 11.

The judgment matrix of criteria under alternatives.

Alternatives	B1	B2	B3	B4	B5	Weight
B1	1	3	1	4	4	0.35024
B2	1/3	1	1/3	2	2	0.13815
B3	1	3	1	4	4	0.35024
B4	1/4	1/2	1/4	1	1	0.08069
B5	1/4	1/2	1/4	1	1	0.08069
CR = 0.00589

Table 12.

The judgment matrix of criteria under B1.

B1	B2	B3	B4	Alternatives	Weight
B2	1	1/2	1/2	2	0.18906
B3	2	1	1	3	0.35091
B4	2	1	1	3	0.35091
Alternatives	1/2	1/3	1/3	1	0.10911
CR = 0.00388

Table 13.

The judgment matrix of criteria under B2.

B2	B4	Alternatives	Weight
B4	1	2	0.6667
Alternatives	1/2	1	0.3333
CR = 0

Table 14.

The judgment matrix of criteria under B3.

B3	B4	Alternatives	Weight
B4	1	1/3	0.25
Alternatives	3	1	0.75
CR = 0

Table 15.

The judgment matrix of criteria under B5.

B5	B4	Alternatives	Weight
B4	1	1	0.5
Alternatives	1	1	0.5
CR = 0

Table 16.

ANP unweighted super matrix.

	OWT1	OWT2	OWT3	OWT4	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16	C17	C18	C19	C20	C21	C22
OWT1	0.000	0.000	0.000	0.000	0.333	0.167	0.250	0.424	0.250	0.273	0.125	0.200	0.333	0.133	0.250	0.273	0.250	0.222	0.188	0.286	0.182	0.351	0.250	0.185	0.188	0.250
OWT2	0.000	0.000	0.000	0.000	0.167	0.500	0.250	0.122	0.125	0.545	0.125	0.200	0.167	0.400	0.250	0.091	0.250	0.111	0.063	0.071	0.091	0.351	0.250	0.185	0.375	0.250
OWT3	0.000	0.000	0.000	0.000	0.167	0.167	0.250	0.227	0.500	0.091	0.125	0.200	0.333	0.400	0.250	0.545	0.250	0.444	0.375	0.571	0.182	0.109	0.250	0.097	0.063	0.250
OWT4	0.000	0.000	0.000	0.000	0.333	0.167	0.250	0.227	0.125	0.091	0.625	0.400	0.167	0.067	0.250	0.091	0.250	0.222	0.375	0.071	0.545	0.189	0.250	0.532	0.375	0.250
C1	0.121	0.174	0.174	0.174	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C2	0.255	0.087	0.174	0.174	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C3	0.081	0.174	0.087	0.087	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C4	0.184	0.174	0.174	0.174	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C5	0.104	0.043	0.174	0.174	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C6	0.046	0.174	0.043	0.043	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C7	0.210	0.174	0.174	0.174	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C8	0.262	0.258	0.261	0.200	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C9	0.065	0.258	0.121	0.200	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C10	0.164	0.093	0.261	0.200	0.000	1.000	1.000	1.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C11	0.459	0.110	0.261	0.200	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C12	0.051	0.280	0.095	0.200	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C13	0.241	0.183	0.260	0.136	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.333	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C14	0.112	0.121	0.260	0.273	1.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C15	0.090	0.298	0.260	0.273	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.667	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C16	0.137	0.101	0.138	0.273	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C17	0.420	0.298	0.082	0.045	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C18	0.200	0.750	0.333	0.250	0.333	0.667	0.500	0.750	0.667	0.500	0.250	0.833	0.500	0.250	0.333	0.500	0.800	0.200	0.667	0.500	0.500	0.000	0.000	0.250	0.750	0.333
C19	0.800	0.250	0.667	0.750	0.667	0.333	0.500	0.250	0.333	0.500	0.750	0.167	0.500	0.750	0.667	0.500	0.200	0.800	0.333	0.500	0.500	0.000	0.000	0.750	0.250	0.667
C20	0.200	0.300	0.692	0.200	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C21	0.400	0.100	0.231	0.400	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C22	0.400	0.600	0.077	0.400	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000

Table 17.

ANP weighted super matrix.

	OWT1	OWT2	OWT3	OWT4	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16	C17	C18	C19	C20	C21	C22
OWT1	0.000	0.000	0.000	0.000	0.188	0.107	0.160	0.271	0.211	0.231	0.106	0.171	0.286	0.114	0.214	0.234	0.214	0.133	0.161	0.245	0.156	0.351	0.250	0.159	0.161	0.214
OWT2	0.000	0.000	0.000	0.000	0.094	0.320	0.160	0.078	0.106	0.461	0.106	0.171	0.143	0.343	0.214	0.078	0.214	0.067	0.054	0.061	0.078	0.351	0.250	0.159	0.321	0.214
OWT3	0.000	0.000	0.000	0.000	0.094	0.107	0.160	0.145	0.423	0.077	0.106	0.171	0.286	0.343	0.214	0.468	0.214	0.267	0.321	0.490	0.156	0.109	0.250	0.083	0.054	0.214
OWT4	0.000	0.000	0.000	0.000	0.188	0.107	0.160	0.145	0.106	0.077	0.529	0.343	0.143	0.057	0.214	0.078	0.214	0.133	0.321	0.061	0.468	0.189	0.250	0.456	0.321	0.214
C1	0.032	0.047	0.047	0.047	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C2	0.068	0.023	0.047	0.047	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C3	0.022	0.047	0.023	0.023	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C4	0.049	0.047	0.047	0.047	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C5	0.028	0.012	0.047	0.047	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C6	0.012	0.047	0.012	0.012	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C7	0.056	0.047	0.047	0.047	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C8	0.052	0.051	0.052	0.040	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C9	0.013	0.051	0.024	0.040	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C10	0.032	0.018	0.052	0.040	0.000	0.244	0.244	0.244	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C11	0.091	0.022	0.052	0.040	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C12	0.010	0.055	0.019	0.040	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C13	0.055	0.042	0.059	0.031	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.100	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C14	0.026	0.028	0.059	0.062	0.335	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C15	0.021	0.068	0.059	0.062	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.200	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C16	0.031	0.023	0.032	0.062	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C17	0.096	0.068	0.019	0.010	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C18	0.031	0.115	0.051	0.038	0.034	0.078	0.058	0.087	0.103	0.077	0.039	0.119	0.071	0.036	0.048	0.071	0.114	0.020	0.095	0.071	0.071	0.000	0.000	0.036	0.107	0.048
C19	0.123	0.038	0.102	0.115	0.068	0.039	0.058	0.029	0.051	0.077	0.116	0.024	0.071	0.107	0.095	0.071	0.029	0.080	0.048	0.071	0.071	0.000	0.000	0.107	0.036	0.095
C20	0.031	0.046	0.106	0.031	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C21	0.061	0.015	0.035	0.061	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
C22	0.061	0.092	0.012	0.061	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000

Table 18.

ANP limit super matrix.

	OWT1	OWT2	OWT3	OWT4	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16	C17	C18	C19	C20	C21	C22
OWT1	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112	0.112
OWT2	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107	0.107
OWT3	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115	0.115
OWT4	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124	0.124
C1	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020
C2	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021
C3	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013
C4	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022
C5	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015
C6	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009	0.009
C7	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022
C8	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022	0.022
C9	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015
C10	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.030
C11	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023	0.023
C12	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014	0.014
C13	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024
C14	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027	0.027
C15	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029	0.029
C16	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017	0.017
C17	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021	0.021
C18	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054	0.054
C19	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072	0.072
C20	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024	0.024
C21	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020	0.020
C22	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026	0.026

Table 19.

The weights of criteria that only consider the opinion of Expert X.

Criteria	Sub-criteria	ANP weights $φ_{1}$	EWM weights $φ_{2}$	Comprehensive weights $φ$
B1	C1	0.0363	0.0286	0.0326	0.2299
	C2	0.0391	0.0432	0.0411
	C3	0.0239	0.0432	0.0331
	C4	0.0398	0.0198	0.0302
	C5	0.0285	0.0385	0.0333
	C6	0.0168	0.0251	0.0208
	C7	0.0412	0.0361	0.0388
B2	C8	0.0407	0.0476	0.0440	0.1898
	C9	0.0268	0.0427	0.0344
	C10	0.0553	0.0338	0.0450
	C11	0.0430	0.0435	0.0432
	C12	0.0260	0.0201	0.0232
B3	C13	0.0442	0.0625	0.0530	0.2220
	C14	0.0496	0.0518	0.0507
	C15	0.0543	0.0427	0.0488
	C16	0.0319	0.0213	0.0268
	C17	0.0396	0.0462	0.0427
B4	C18	0.1003	0.0882	0.0945	0.2279
	C19	0.1331	0.1337	0.1334	0.2279
B5	C20	0.0449	0.0471	0.0460	0.1304
	C21	0.0372	0.0589	0.0476
	C22	0.0474	0.0254	0.0368

Table 20.

The weights of alternatives that only consider the opinion of Expert X.

Alternatives	ANP	EWM	ANP-EWM
OWT1	0.2449	0.2504	0.2475
OWT2	0.2340	0.2338	0.2339
OWT3	0.2511	0.2873	0.2684
OWT4	0.2699	0.2285	0.2501

For the calculation of EWM, Expert X needs to grade the qualitative criteria in Table 10. After inputting the original data for quantitative criteria, the weight of each criterion can be obtained according to the process of EWM in chapter 2.2. The weights of criteria are shown in Table 19 and the weights of alternatives are shown in Table 20.

Next, we calculate the distribution coefficients of ANP and EWM according to Section 2.3. The distribution coefficients $α = 0.5211$ and $β = 0.4789$ , according to formula 16.

{\begin{matrix} {(α - β)}^{2} = 0.00178 \\ α + β = 1 \end{matrix}

(16)

Therefore, the comprehensive weights $φ$ are calculated by formula 17 as listed in Table 19.

φ = 0.5211 φ_{1} + 0.4789 φ_{2}

(17)

Similarly, we can get the weights of alternatives for ANP-EWM in Table 20. For example, the weight of OWT1 is computed as follows:

OWT 1 = 0.5211 \times 0.2449 + 0.4789 \times 0.2504 = 0.2475

(18)

Decision results of Expert Y

The calculation process of ANP and EWM by Expert Y are the same as those of Expert X. The distribution coefficients are α = 0.5336 and β = 0.4664. The weights of criteria and alternatives obtained by the three methods are shown in Tables 21 and 22.

Table 21.

The weights of criteria that only consider the opinion of Expert Y.

Criteria	Sub-criteria	ANP weights $φ_{1}$	EWM weights $φ_{2}$	Comprehensive weights $φ$
B1	C1	0.0363	0.0415	0.0387	0.2183
	C2	0.0302	0.0332	0.0316
	C3	0.0319	0.0413	0.0363
	C4	0.0245	0.0191	0.0220
	C5	0.0385	0.0301	0.0346
	C6	0.0198	0.0302	0.0247
	C7	0.0252	0.0365	0.0305
B2	C8	0.0628	0.0448	0.0544	0.2069
	C9	0.0317	0.0385	0.0349
	C10	0.0483	0.0336	0.0415
	C11	0.0432	0.0281	0.0362
	C12	0.0475	0.0316	0.0401
B3	C13	0.0441	0.0508	0.0472	0.1937
	C14	0.0492	0.0398	0.0448
	C15	0.0293	0.0573	0.0424
	C16	0.0119	0.0316	0.0211
	C17	0.0388	0.0374	0.0382
B4	C18	0.0967	0.1534	0.1231	0.2261
	C19	0.1263	0.0762	0.1029	0.2261
B5	C20	0.0631	0.0423	0.0534	0.1550
	C21	0.0518	0.0478	0.0499
	C22	0.0488	0.0549	0.0516

Table 22.

The weights of alternatives that only consider the opinion of Expert Y.

Alternatives	ANP	EWM	ANP-EWM
OWT1	0.2328	0.2578	0.2445
OWT2	0.2373	0.2727	0.2538
OWT3	0.2717	0.2496	0.2614
OWT4	0.2582	0.2199	0.2403

Decision results of Expert Z

The calculation process of ANP and EWM is the same as above, which will not be repeated for Expert Z. The distribution coefficients are α = 0.5334 and β = 0.4666. The weights of criteria and alternatives obtained by the three methods are shown in Tables 23 and 24.

Table 23.

The weights of criteria that only consider the opinion of Expert Z.

Criteria	Sub-criteria	ANP weights $φ_{1}$	EWM weights $φ_{2}$	Comprehensive weights $φ$
B1	C1	0.0397	0.0321	0.0362	0.2364
	C2	0.0381	0.0379	0.0380
	C3	0.0432	0.0291	0.0366
	C4	0.0328	0.0201	0.0269
	C5	0.0272	0.0372	0.0319
	C6	0.0306	0.0330	0.0317
	C7	0.0202	0.0522	0.0351
B2	C8	0.0592	0.0401	0.0503	0.1426
	C9	0.0317	0.0184	0.0255
	C10	0.0365	0.0117	0.0249
	C11	0.0138	0.0120	0.0130
	C12	0.0351	0.0219	0.0289
B3	C13	0.0624	0.0517	0.0574	0.2271
	C14	0.0484	0.0385	0.0438
	C15	0.0614	0.0573	0.0595
	C16	0.0252	0.0318	0.0283
	C17	0.0388	0.0374	0.0382
B4	C18	0.0967	0.1519	0.1225	0.2233
	C19	0.1171	0.0823	0.1009	0.2233
B5	C20	0.0510	0.0668	0.0584	0.1706
	C21	0.0492	0.0613	0.0548
	C22	0.0417	0.0753	0.0574

Table 24.

The weights of alternatives that only consider the opinion of Expert Z.

Alternatives	ANP	EWM	ANP-EWM
OWT1	0.2420	0.2679	0.2541
OWT2	0.2146	0.2389	0.2259
OWT3	0.2614	0.2436	0.2531
OWT4	0.2820	0.2496	0.2669

Comprehensive decision results

What we finally need is the comprehensive weight of the three experts on the alternative wind turbines. The offshore wind turbine with the largest comprehensive weight is considered to be the best choice. Based on the information in Tables 7, 20, 22, and 24, the weights after combining the opinions of the three experts are calculated as presented in Table 25 and Figure 8. For example, the comprehensive weight of $C_{1}$ , $B_{1}$ , and $OWT 1$ is computed as follows:

\begin{matrix} C_{1} = 0.32 \times 0.0326 + 0.38 \times 0.0387 + 0.3 \times 0.0362 = 0.0360 \\ B_{1} = 0.32 \times 0.2299 + 0.38 \times 0.2183 + 0.3 \times 0.2364 = 0.2274 \\ OWT 1 = 0.32 \times 0.2475 + 0.38 \times 0.2445 + 0.3 \times 0.2541 = 0.2484 \end{matrix}

(19)

Table 25.

The weights of criteria that consider opinions of three experts.

Criteria	Sub-criteria	ANP weights $φ_{1}$	EWM weights $φ_{2}$	Comprehensive weights $φ$
B1	C1	0.0373	0.0346	0.0360	0.2274
	C2	0.0354	0.0378	0.0366
	C3	0.0327	0.0382	0.0354
	C4	0.0319	0.0196	0.0261
	C5	0.0319	0.0349	0.0333
	C6	0.0221	0.0294	0.0255
	C7	0.0289	0.0411	0.0345
B2	C8	0.0546	0.0443	0.0498	0.1821
	C9	0.0301	0.0338	0.0319
	C10	0.0470	0.0271	0.0376
	C11	0.0343	0.0282	0.0315
	C12	0.0369	0.0250	0.0313
B3	C13	0.0497	0.0548	0.0521	0.2128
	C14	0.0491	0.0433	0.0464
	C15	0.0470	0.0526	0.0496
	C16	0.0223	0.0284	0.0251
	C17	0.0391	0.0402	0.0396
B4	C18	0.0979	0.1321	0.1138	0.2258
	C19	0.1257	0.0964	0.1121	0.2258
B5	C20	0.0537	0.0512	0.0525	0.1518
	C21	0.0463	0.0554	0.0507
	C22	0.0462	0.0516	0.0486

Figure 8.

Weights of alternatives based on the opinions of three experts.

It can be seen from Figure 8 that B1 and B4 have the highest weight, 0.2274 and 0.2258 respectively, B2 and B5 have the lowest weights, 0.1821 and 0.1518, respectively. This means that, based on the ideas of the experts, the technology of offshore wind turbine is more significant for this alternative. Offshore wind turbines are faced with more complex and risky operation environment. Only advanced and mature technology can ensure the efficiency and safety of power generation. Moreover, the maintenance of wind turbines on the sea is more inconvenient than on land. In the event of a failure, the later maintenance costs are also very expensive, but advanced technology can effectively reduce the failure rate of the wind turbine and worries. Therefore, the B1 has the highest weight in the selection model. The historical performance of wind turbine B4 is an important criterion for judging the overall level of wind turbine. It is obviously reasonable to evaluate the competitiveness of wind turbines based on sales volume and the actual conditions of operation in wind farms. Although the weight of B2 is not dominant in this decision, it does not mean that it is not important. In fact, a good match between wind turbines and wind resources is a major premise to ensure the normal and efficient operation of wind turbine. In this case, the alternative wind turbines that have been preliminarily screened can well meet the requirements of matching with the wind resources, and the matching difference is small. Therefore, B2 take on relatively small weight. On the other hand, the investment of offshore wind farm is relatively high, the cost of wind turbines usually account for about 40% to 50% of the total investment. Therefore, the importance of B3 is self-evident. But in the long run, the power generation benefits of wind turbines with advanced technology are more important than the cost savings at the time of purchase. Therefore, the weight of B3 is less than the weight of B1. The well-known wind turbine manufacturers have little difference in after-sales service, so B5 has the smallest impact on the selection.

In the paper, the combination of ANP and EWM is applied to select the best offshore wind turbine. In order to further compare the application of different decision-making methods in selection of wind turbines. According to the opinions of experts, we further used AHP method to select the wind turbine for wind farm. The AHP is simpler than ANP because it does not consider the internal relationship between the criteria. The calculation results based on AHP are presented in Table 26. In addition, according to Tables 20, 22, and 24, the comprehensive weight of alternatives for ANP and EWM can be calculated. For example, the comprehensive weight of OWT1 for ANP method is computed by formula 20. The comprehensive weight of OWT2 for EWM is computed by formula 21. Table 26 shows the final weight of alternatives based on the five methods. In order to compare the results of different methods, the ranking of alternatives for different methods is shown in Figure 9.

OWT 1 = 0.32 \times 0.2449 + 0.38 \times 0.2328 + 0.3 \times 0.2420 = 0.2394

(20)

OWT 2 = 0.32 \times 0.2338 + 0.38 \times 0.2727 + 0.3 \times 0.2389 = 0.2501

(21)

Table 26.

The weights of alternatives for different methods.

Alternatives	AHP	ANP	EWM	AHP-EWM	ANP-EWM
OWT1	0.2682	0.2394	0.2585	0.2635	0.2484
OWT2	0.2179	0.2294	0.2501	0.2332	0.2391
OWT3	0.2727	0.2620	0.2599	0.2666	0.2612
OWT4	0.2412	0.2691	0.2316	0.2366	0.2514

Figure 9.

Rankings of the alternatives for different methods.

Overall, a glance at Figure 9 illustrates that the trend of curves for the five methods are very similar in such a way that there are four mutual choices about OWT3 as the best one and OWT2 at the fourth rank. For the ranking of OWT1 and OWT4, the compared results are quite different. Finally, the wind turbine rankings in Figure 9 are compared with the bid-winning result to verify the feasibility and superiority of different methods. In fact, the predictive rankings of alternatives based on ANP-EWM are most consistent with the actual bid-winning rankings that wind power development enterprise announces, and the result is: $OWT 3 > OWT 4 > OWT 1 > OWT 2$ . The selection results in this case study show that the proposed hybrid decision-making method can faithfully transfer the ideas of the participated experts to the results of the final decision.

After experiments, the small change for input data has little influence on weights and the rankings of alternatives are not changed, which reveals that the final weights of the method are determined by all criteria, and the method has good robustness.

Conclusion

In this research, a novel hybrid MCDM approach, which combined ANP and EWM, was proposed and applied to a case study where wind turbines were evaluated and selected. This decision-making method not only makes full use of the rich project experience of experts, but also modifies the subjectivity of ANP method through using entropy. In conclusion, through analyzing the engineering example, the paper provides a more accurate and practical method for the selection of offshore wind turbine among the five methods, which opens new perspectives for assisting utility companies in developing wind farms.

Research results show that the technology is the most important for the development of offshore wind power generation. Offshore wind power is not only the future development direction of wind power industry, but also an important support for the transformation of energy structure. Although the market for offshore wind power is large, the risk of uncertainty is also high. The harsh ecological environment at sea poses challenges to the operation and maintenance of wind turbines. Especially under the policy background of reducing subsidies, competitive bidding and the connection to grid at an equal price, advanced technology is the fundamental to reduce the cost of power generation and improve the efficiency of operation and maintenance. In the future, offshore wind power will develop in the direction of digitalization, intelligence and precision. Only by breaking through key technologies can the offshore wind power industry continue to move forward.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Nos. 11502141 and 11701359).

ORCID iD

Li Xu

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