**4. Case Study**

#### *4.1. Study Area*

In the "Marine Renewable Energy Development Plan" in China, Shandong Province is positioned as a key area for marine renewable energy development [51,58,81]. It borders the Bohai Sea and the Yellow Sea, with a coastline of approximately 3345.41 km, rich in wave energy resources. It has a developed marine economy, and there is a huge demand for energy due to busy marine activities along the coast. At the same time, Shandong Province has gathered many powerful marine science research institutes and related enterprises in China, which is an important condition for the development and utilization of wave energy [82].

Shandong Province has jurisdiction over 589 islands, among which 32 are inhabited. Given the distance from the mainland, the economic activities of the inhabited islands are severely restricted by power dilemmas [83]. In addition, traditional power-generation modes are costly and cause serious pollution. Clean wave energy can be easily obtained around islands, which will not cause pollution and can greatly alleviate the power-shortage problems in the islands [84].

This study investigated site selection for wave power plants for the inhabited islands of Shandong Province. Based on locations and development conditions, the latitude and longitude of the study area (Figure 3) are selected from 34◦24 N to 38◦58 N and 117◦34 E to 123◦37 E. Considering the requirements for the accuracy of the results, the evaluation units in the study area are divided into 100 m × 100 m grids. Table 2 shows the data description and source of each criterion.

**Figure 3.** Study area.


#### **Table 2.** Data descriptions and sources of criteria.

#### *4.2. Exclusion of Unfeasible Areas*

In this study, unfeasible marine areas are excluded by three exclusion criteria. The MERL of Shandong Province includes 10 types of areas: marine nature reserves; special marine protected areas; important estuarine ecosystems; important coastal wetlands; important fishery waters; special protected islands; natural landscape and historical and cultural heritage areas; important coastal tourist areas; important sandy shorelines; and sand source protected sea area [85,86]. All of these areas should be excluded. The Simulating Waves Nearshore (SWAN) model is used to simulate the wave field, and the 39-year average WPD distribution in the study area could be obtained by calculation [87,88]. WPD data are point feature data with an accuracy of 1 × 1 . Considering the existing wave-energy-generation devices and the data for Shandong Province, marine areas with a WPD lower than 1 kW/m are regarded as undeveloped sea areas [87]. WD data are point-feature data with an accuracy of 0.1◦ × 0.1◦. Considering currently available technology and installation types, areas with a WD greater than 50 m are excluded. The exclusion range of each criterion is shown in Table 3.

**Table 3.** Exclusion range of each criterion.


ArcGIS software is used for overlay analysis. The thematic map of unfeasible areas is obtained by superimposing the respective maps of these three criteria. Figure 4 shows a different thematic map for each exclusion criterion. Figure 5 shows the unfeasible and feasible marine areas determined by the combination of the three maps.

**Figure 4.** Unfeasible areas based on the three exclusion criteria.

**Figure 5.** Unfeasible areas and feasible areas.

### *4.3. Feasible Islands Identification and Data Acquisition*

After excluding the unfeasible parts of the study area, thirteen inhabited islands that can feasibly develop wave energy are identified: South Changshan, North Changshan, Temple, Daheishan, Xiaoheishan, Jiming, Nanhuang, East Little Qingdao, Zhucha, Muguan, Daguan, Xiaoguan, and Zhaitang, which constitute alternative set *A* = {*A*1, *A*2, ··· *A*13}. *A*1, *A*2, *A*3, *A*4, *A*<sup>5</sup> are located in the northern part of Yantai. *A*6, *A*7, *A*<sup>8</sup> belong to Weihai, and the other five islands are located in the east and south of Qingdao. Figure 6 shows the distribution of the thirteen island alternatives for constructing wave power plants.

**Figure 6.** Thirteen island alternatives for constructing wave power plants.

Through data investigation, on-site observation, and numerical simulation, the at tribute values of the evaluation criteria of each alternative are obtained, as shown in Table 4.


**Table 4.** Attribute value matrix.

#### *4.4. Determination of Criteria Weights*

The evaluation criteria weights are determined by the combined weighting method. First-level criteria weights can be solved based on the fuzzy GDM-AHP method. Secondlevel criteria weights are calculated based on the entropy method.

#### (1) Determination of first-level criteria weights

The first-level criteria weights are calculated by Equations (2)–(4). Matrices of pairwise comparisons are created based on five experts in the fields of economics, marine energy technology, and the social sciences, using a fuzzy scale from (1,1,1) to (8,9,9). Expert weights are specified as (0.3, 0.3, 0.2, 0.1, 0.1). Appendix A shows the fuzzy pairwise comparison matrix generated by the five experts. Table 5 shows the fuzzy values of the first-level criteria weights. Through defuzzification and normalization, the weights calculated by Equation (6) are (0.4896, 0.1779, 0.1286, 0.2038).

**Table 5.** Fuzzy values of the first-level criteria weights.


The calculation results show that resource criteria account for almost 50% of the weight. It means resource criteria are the most important and should be considered more in the site-selection process. Resource criteria have always been the most important criteria in decision making for renewable energy power plant site selection [23,25,28,29]. The weight of social/environmental criteria is the second largest at 20.38%, indicating that the external conditions of social/environmental criteria can restrict or promote site selection to a certain extent. The weights of natural criteria and economic criteria are 17.79% and 12.86%, respectively, indicating slightly less importance.

#### (2) Determination of second-level criteria weights

The second-level criteria weights are calculated by Equations (7)–(10). Figure 7 shows the calculation results. From the calculation results, it can be seen that the weight of WPD under resource criteria is much larger than that of WH, indicating that WPD has a greater impact on site selection. The weight of PS under economic criteria accounts for 70.69%, indicating its high importance among economic criteria.

#### (3) Determination of combined criteria weights

Figure 8 shows the combined weights based on Equation (11). According to the calculation results, the weight of WPD is the largest at 39.14%. As a resource criterion, WPD plays a vital role in the process of site selection. The criteria weights of WD and population served are close to 10%, indicating that these two criteria also have a relatively large impact on site selection. At the same time, the weights of other criteria are relatively small, and the impact on overall decision making is relatively small, but their role in the process of site selection should not be ignored.

#### **Figure 8.** Criteria weights.

#### *4.5. Evaluation of Feasible Islands*

The 13 identified inhabited islands of Shandong Province are evaluated and ranked using TOPSIS-GRA to determine the precedence sequences for development. Table 6 shows the final results and rankings of the 13 islands, obtained on the basis of Section 3.4.

Based on the complete assessment results obtained by the proposed decision framework, the top five optimal islands are Daguan, South Changshan, Xiaoguan, Zhucha, and

**Figure 7.** Weights of second-level criteria.

Zhaitang, respectively. Daguan is found to be the best site for establishing a wave power plant owing to its optimal wave energy conditions and good other features. The National Ocean Technology Center established a hybrid solar–wind–wave independent power system on Daguan in 2010 [89]. To some extent, this also shows that the resources and social environmental conditions of Daguan are suitable for wave energy development.

**Table 6.** Ranking of site alternatives.


South Changshan ranks second. It has the largest population served and the best social and environmental conditions. Given the large number of residents, the island is in urgent need of developing wave power plants to alleviate power pressures. Xiaoguan has the second-largest WPD and the smallest WD, leading it to the third place. Ranking fourth, Zhucha has the smallest distance to ports, and it performs relatively well for WPD and wave height. Finally, Zhaitang ranks fifth, performing best for distance to the shore and performing relatively well for WPD and population served.

#### *4.6. Sensitivity Analysis*

In decision making, various uncertain issues affect decision accuracy, such as the different risk attitudes of DMs, different weights of evaluation criteria, and different MCDM methods for the final ranking. Hence, it is necessary to test the sensitivity of the ranking results.

#### 4.6.1. Varying Expert Weights

A sensitivity analysis based on equal expert weights is performed, as shown in Figure 9. The results obtained from equal expert weights are very similar to the original results. It is worth noting that the top nine islands remain unchanged, and only two islands have changed in development order. Therefore, the ranking results remain stable for variable expert weights.

**Figure 9.** Ranking results of the sensitivity analysis.

#### 4.6.2. Varying Criteria Weights

Because the criteria weights affect the final results, equal criteria weights are set to test its impact on the decision results. Figure 9 shows the final rankings. With the adjustment of the criteria weights, the ranking results change accordingly. The rankings of all alternatives fluctuate within five ranks. A1 performed best in population served; when the criteria weights are equal, it ranks first. A11, A1, A9, and A13 still perform fairly well, ranking among the top five. A5 is still last with equal criteria weights. When criteria weights are equal, the order of islands will inevitably change since resource conditions are the decisive criteria for site selection. A significant reduction in resource condition criteria will inevitably change the ranking results, reflecting the characteristics of sensitivity. Therefore, when the importance of criteria is quite different, it is necessary to find a suitable algorithm to solve the criteria weights.

#### 4.6.3. Varying the Ranking Method

Different MCDM methods have different calculation principles, and the obtained ranking results might also be different. TOPSIS is used to rank islands to test the universality of the results. Figure 9 shows that the ranking of islands is generally stable, and the top six optimal islands remain unchanged. The results under TOPSIS change only four alternatives; A2, A8, A4, and A6 are changed in the development order. This comparative analysis demonstrates the practicability of the proposed model.

## **5. Conclusions**

To address the problems of wave-power-plant site selection for islands in China, this study proposed a two-stage decision framework, including both large- and small-scale site selection, based on a combination of GIS, fuzzy GDM-AHP, entropy method and GRA-TOPSIS. This approach enabled us to identify feasible islands and determine priority order. The main contributions of this study were as follows:


The proposed methodology framework can be generally applied to other energy sources by changing the criteria system. Future research on wave power plants site selection can be conducted as follows: first, attribute values can be used in the fuzzy environment to improve the precision of the results. Second, while the fuzzy sets in this paper are TFNs, the trapezoidal fuzzy numbers, intuitionistic fuzzy sets and interval hesitant fuzzy sets can be used in subsequent research to improve the flexibility of fuzzy sets in dealing with fuzzy and uncertain problems.

**Author Contributions:** Conceptualization, M.S. and S.Z.; methodology, M.S.; software, S.Z.; validation, S.Z., J.S. and Z.H.; formal analysis, J.S.; investigation, S.Z. and J.S.; resources, M.S., Z.H. and Z.S.; data curation, Z.S.; writing—original draft preparation, S.Z.; writing—review and editing, M.S. and C.Y.; visualization, C.Y; funding acquisition, M.S. and J.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 51609224; Shandong Provincial Natural Science Foundation of China, grant numbers ZR2020QE297 and Qingdao Postdoctoral Application Research Project.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The research was financially supported by the National Natural Science Foundation of China (Grant No. 51609224), Shandong Provincial Natural Science Foundation of China (ZR2020QE297) and Qingdao Postdoctoral Application Research Project.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

**Table A1.** Fuzzy pairwise comparison matrix of expert 1 (Weight: 0.3).


**Table A2.** Fuzzy pairwise comparison matrix of expert 2 (Weight: 0.3).


**Table A3.** Fuzzy pairwise comparison matrix of expert 3 (Weight: 0.2).


**Table A4.** Fuzzy pairwise comparison matrix of expert 4 (Weight: 0.1).



**Table A5.** Fuzzy pairwise comparison matrix of expert 5 (Weight: 0.1).

**Table A6.** Fuzzy pairwise comparison matrix by GDM.

