# Fuzzy Comprehensive Evaluation of Maritime Boundary Delimitation Schemes Based on AHP-Entropy Weight Method

Authors: Degang Wang; Dongling Li; Yujuan Dou; Yonghua Tan; Zhenke Zhang; Dui’an Lv; Jie Cheng
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The basic science region of marine management boundary lines among different provinces within the extent at least of the territorial sea is of great means to promote the sustainable growth of China's marine economy. There are 11 provinces along the coastal regions of the Chinese Mainland, and the scientific division of marine management boundaries among different provinces within the extents of the territorial sea is of great importance in promoting the sustainability of China's marine economy. We conducted a case study of maritime boundary demarcation between Jiangsu and Shandong Provinces, and a fuzzy evaluation index system with 14 indices in three subsets was developed to evaluate the benefits and drawbacks of maritime boundary delimitation, determine the optimal scheme, and address shortages in the current evaluation indicators and evaluation methods. The analytic hierarchy process (AHP) and the entropy weight method were used to calculate the combined weights of indices. Three maritime border delimitation schemes, namely, the historical boundary delimitation scheme, angle bisector delimitation scheme, and equidistance delimitation scheme, were evaluated using the comprehensive evaluation indices. Results show that the equidistance delimitation scheme is relatively superior to the two other schemes. The evaluation index is 0.504761, and the evaluation grade is “good.” The second best delimitation scheme is the angle bisector. The grade is “moderate,” and the evaluation index is 0.361641. The most ineffective boundary delimitation scheme is the historical one. The grade is “bad,” and the evaluation index is 0.135345. More consideration should be given to people's livelihoods and the safeguarding of national marine rights and interests in the late optimization of maritime boundary delimitation schemes. The fuzzy comprehensive evaluation technique based on AHP-entropy weight can help decision-makers choose the optimum scheme by providing a quantitative top-down sequence of schemes in terms of quality and solving estimate difficulties in maritime boundary delimitation schemes. As a result, it has a wide range of applications.


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## Body

## 1. Introduction

A total of 71% of the area on the Earth is covered by marine resources. The rich natural resources (e.g., minerals, fishing industry, and renewable energy sources) and extensive space in marine resources have also attracted the concern of countries in coastal areas. With marine exploration and development, improving the status of maritime strategy, and the awakening and strengthening of awareness on maritime rights, coastal countries are fighting for more maritime rights and interests, which inevitably leads to many disputes on the sea. Disputes on the sea have been occurring and developing continuously throughout the human exploration of marine resources. Specifically, disputes over maritime boundary delimitation are the core [1, 2]. The maritime boundary delimitation among countries is very important. For China, the maritime boundary delimitation among 11 coastal provinces is equally important. Although the sea areas in China’s territorial sea are owned by the country, coastal provinces have the right to use and jurisdiction of the sea areas. Adjacent provinces often have conflicts because of disputes over the management of sea areas. Hence, a reasonable maritime boundary delimitation among the 11 coastal provinces in China is of important significance to ensuring the sustainable development of the marine economy and social stability in China’s coastal regions.The problem of maritime boundary delimitation has attracted a global concern since its proposal. It is often a hot topic in many international conferences organized by governments of different countries and international organizations. Many scholars and experts have also studied maritime boundary delimitation from the perspectives of principles, influencing factors, formulation and evaluation, and policies of delimitation [3, 4]. The creation and assessment of maritime boundary delimitation schemes are a fundamental and relatively major aspect of studies on marine management in the studies mentioned above. The scientificity of maritime border delimitation schemes, as well as their direct influence on subsequent marine exploitation and the formation of management policies, has been determined through relevant study. At present, many methods to formulate maritime boundary delimitation schemes have been proposed, including the equidistance delimitation method, angle bisector delimitation method, latitude delimitation method, and longitude delimitation method [5, 6]. Among these methods, the equidistance delimitation method, angle bisector delimitation method, and historical habit delimitation method are relatively classical delimitation methods. These three methods were used in this study to formulate the maritime boundary delimitation scheme between Jiangsu and Shandong Provinces. Proportional fairness validation is the first choice to evaluate maritime boundary delimitation schemes because the comparison system of different maritime boundary delimitation schemes is mature [7]. Although proportional fairness validation is easy to use, it still can be used as a reference for evaluation results of delimitation schemes only for nonobjective judgment standards, single evaluation indices, and difficulties in quality assessment. Some scholars have also discussed new evaluation methods for maritime boundary delimitation schemes. For example, the sea area loss of two or more countries after maritime boundary delimitation was calculated automatically based on GIS, and results were used to evaluate the maritime boundary delimitation schemes [8]. Some scholars have evaluated the reasonability of maritime boundary delimitation schemes through the traditional division of fishing areas [9]. Some scholars also have divided the middle line of sea areas automatically among all provinces in a region based on the Voronoi diagram to eliminate limitations that previous maritime boundaries were drawn mainly by cartographers or GIS experts and realized the function of maritime boundary delimitation under noninterference of users [10]. Although studies on the evaluation of maritime boundary delimitation schemes have achieved some progress, they are still limited within the proportional fairness validation of schemes, making it difficult to meet the current requirements of maritime boundary delimitation scheme evaluation on integrity, comprehensiveness, reasonability, and scientificity.Introducing a more comprehensive evaluation method is necessary to address existing problems in current maritime boundary delimitation schemes. Many common evaluation methods for maritime boundary delimitation schemes have been proposed, and they can generally be divided into subjective weighting methods and objective weighting methods. The subjective weighting methods include the analytic hierarchy process (AHP), which is used to obtain the weights of different indices based on the subjective experiences of experts. The objective weighting methods, which include the correlation coefficient method, gray correlation method, TOPSIS method, and entropy weight method, determine the weights of indices according to their relations or the coefficient of variation [11–14]. Having errors in weights of indices is inevitable if only subjective weighting methods (e.g., AHP) [15–17] or objective weighting methods (e.g., entropy weight method) are used [18, 19], thereby influencing the final evaluation results greatly. Other methods, such as the fuzzy evaluation or principal component analysis (PCA), can choose subjective or objective weights or comprehensive weights and realize a comprehensive evaluation of maritime boundary delimitation schemes. These methods have been widely applied in practice for their good applicability and reliability.To sum up, a comprehensive evaluation of maritime boundary delimitation schemes has become a concern among academic circles, and some research progress has been achieved. To solve problems of the current proportional fairness validation, such as single index and poor accuracy of index weights determined by only AHP or entropy weight method, this study will adopt the fuzzy comprehensive evaluation method based on AHP-entropy weight. This method can not only reflect the correlations of evaluation indices and avoid errors caused by single subjective or objective weighting methods, but also explore the contributions of evaluation indices to delimitation schemes to some extent and determine the advantages and disadvantages of maritime boundary delimitation schemes intuitively. In this study, the fuzzy comprehensive evaluation method of the maritime boundary delimitation schemes based on the AHP-entropy weight method has important practical value in the evaluation and perfection of maritime boundary delimitation schemes.The remainder of this study is organized as follows. Section2 describes the conditions of study areas for maritime boundary delimitation between Jiangsu and Shandong Provinces, data sources, and three preliminary maritime boundary delimitation schemes. Section 3 analyzes the fuzzy evaluation model of maritime boundary delimitation schemes and establishes evaluation indices, such as natural resources, social economy, and expected effect of sea areas. Moreover, the calculating method of comprehensive weights of indices and the determination method of comprehensive evaluation indices are introduced. Section 4 provides comprehensive evaluation results of the maritime boundary delimitation schemes between Jiangsu and Shandong Provinces. In addition, the maritime boundary delimitation schemes between Jiangsu and Shandong Provinces are analyzed and discussed from the perspectives of natural resource factor evaluation, social-economic factor evaluation, expected effect evaluation, and comprehensive evaluation. Section 5 provides the conclusions.


## 2. Study Areas and Data

### 2.1. Study Areas

The study areas were determined at the bordering sea areas between Jiangsu Province and Shandong Province, China (see Figure1), which is located in the west of Haizhou Bay (34°N–36°N) and the border between the Lianyungang City of Jiangsu Province and Rizhao City of Shandong Province. The total sea area in the study area is about 2,500 km2, and the overall submarine topographical features are manifested by the increasing water depth from banks to the sea, with a gentle slope. The maximum water depth in the sea area near the external boundary line is about 28 m. In this study area, there are 10 islands including Ping Island, Dashan Island, and Cheniushan Island, covering an area of about 0.35 km2.Figure 1
Geographic locations of the study area.The bordering sea areas between Jiangsu and Shandong Provinces have high water depth, good water qualities, and good water exchange conditions. This sea area is applicable for not only the construction of large ports, but also the development of marine aquaculture activities. The Rizhao Port in Shandong Province and Lianyungang Port in Jiangsu Province, which are among the large ports in China, can also be found in the adjacent bordering areas. The cargo throughput of Rizhao Port reached 0.46 billion tons in 2019, ranking 8th on China’s Port List. The cargo throughput of Lianyungang Port was 0.23 billion tons in 2019, ranking 19th on the China Port List. By 2019, Jiangsu and Shandong Provinces had large-scaled aquaculture activities of precious marine products, such as sea cucumbers and abalones in the study area. The aquaculture area reached 15,000 ha, which brought considerable economic benefits. The current dispute between the Jiangsu and Shandong Provinces focuses on the affiliation of 10 islands and surrounding sea areas. At present, Jiangsu Province has local police stations on the islands, while many fishermen from Shandong Province have aquaculture activities in the surrounding sea areas of the islands. With the rapid marine economic developments in the Lianyungang City of Jiangsu Province and the Rizhao City of Shandong Province, the intentions of these two provinces in developing the bordering sea areas and further deepening resource exploitation in local sea areas are strengthened, which cause larger conflicts and trigger larger-scale conflicts. The disputes between the Jiangsu and Shandong Provinces oversea areas have influenced the social stability in the Lianyungang City of Jiangsu Province and the Rizhao City of Shandong Province to some extent. Therefore, it is very necessary to formulate a scientific and reasonable maritime boundary between Jiangsu and Shandong Provinces.


### 2.2. Research Data

The original data in this study include mainly the coastline data, sea area, and ocean development data, coastline and area data of islands, and so on (Table1). Among them, data on the coastline and ocean development came mainly from field surveys and investigation, while data on islands were mainly from remote-sensing imagery interpretation. Other socioeconomic data were collected from the Statistical Yearbook of Rizhao City in 2019 and the Statistical Yearbook of Lianyungang City in 2019.Table 1
Datasets used in the present study.
CategoriesData sourceData specificationsSea area dataMeasured data2500 km2Coastline dataMeasured data200 kmMarine development dataMarine aquaculture area data of Jiangsu and Shandong Province198 recordsSocioeconomic data of Jiangsu ProvinceStatistical Yearbook of Lianyungang city in 2019—Socioeconomic data of Shandong ProvinceStatistical Yearbook of Rizhao city in 2019—Island dataRemote-sensing satellite dataResolution = 0.5 m


### 2.3. Preliminary Schemes

Based on principles of maritime boundary delimitation in terms of fairness and natural extension, several delimitation technological methods, which use the historical habit delimitation method, equidistance delimitation method, angle bisector delimitation method, trough centerline delimitation method, latitude delimitation method, and longitude delimitation method as beneficial supplementations, have been formed [20, 21] (Table 2). With consideration of natural geographic features of bordering sea areas between Jiangsu Province and Shandong Province, three maritime boundary delimitation schemes between these two provinces were formulated by using the historical habit delimitation method (Scheme 1), angle bisector delimitation method (Scheme 2), and equidistance delimitation method (Scheme 3) (Figure 2).Table 2
Common technological methods to formulate delimitation schemes.
No.Name of methodsIntroduction of methods1Equidistance delimitation methodThe involved parties advocated the generation of a line in the overlapping sea areas that the distances from every point on this line to the estimated nearest points on the baselines of each party’s territorial seas are equal. The line is used as the preliminary maritime boundary delimitation2Historical habit delimitation methodThe historical habit line accepted by involved parties is used as the preliminary line for maritime boundary delimitation3Angle bisector delimitation methodAdjacent coastal countries or provinces make a straight from the land administration boundary point along the extension directions or main body of their coasts to form an angle. The bisector of this angle is made and used as the preliminary line for maritime boundary delimitation4Bearing line delimitation methodThe two parties involved formed a bearing line after negotiation and use it as the preliminary line for maritime boundary delimitation5Latitude parallel line delimitation methodBased on negotiation, the involved parties agreed to use latitude or longitude lines that run through the overlapping sea areas as the preliminary line for maritime boundary delimitation6Overlapping bisector delimitation methodThe involved parties agree to make a straight line or curve in the overlapping sea area according to the principle of equal areas between two sides of the line and use it as the preliminary line for maritime boundary delimitation7Trough centerline delimitation methodIn disputing regions with deep troughs or evident topographical changes, the topographic centerline can be used as the preliminary line for maritime boundary delimitation among involved partiesFigure 2
Sketch map of three delimitation schemes.


## 2.1. Study Areas

The study areas were determined at the bordering sea areas between Jiangsu Province and Shandong Province, China (see Figure1), which is located in the west of Haizhou Bay (34°N–36°N) and the border between the Lianyungang City of Jiangsu Province and Rizhao City of Shandong Province. The total sea area in the study area is about 2,500 km2, and the overall submarine topographical features are manifested by the increasing water depth from banks to the sea, with a gentle slope. The maximum water depth in the sea area near the external boundary line is about 28 m. In this study area, there are 10 islands including Ping Island, Dashan Island, and Cheniushan Island, covering an area of about 0.35 km2.Figure 1
Geographic locations of the study area.The bordering sea areas between Jiangsu and Shandong Provinces have high water depth, good water qualities, and good water exchange conditions. This sea area is applicable for not only the construction of large ports, but also the development of marine aquaculture activities. The Rizhao Port in Shandong Province and Lianyungang Port in Jiangsu Province, which are among the large ports in China, can also be found in the adjacent bordering areas. The cargo throughput of Rizhao Port reached 0.46 billion tons in 2019, ranking 8th on China’s Port List. The cargo throughput of Lianyungang Port was 0.23 billion tons in 2019, ranking 19th on the China Port List. By 2019, Jiangsu and Shandong Provinces had large-scaled aquaculture activities of precious marine products, such as sea cucumbers and abalones in the study area. The aquaculture area reached 15,000 ha, which brought considerable economic benefits. The current dispute between the Jiangsu and Shandong Provinces focuses on the affiliation of 10 islands and surrounding sea areas. At present, Jiangsu Province has local police stations on the islands, while many fishermen from Shandong Province have aquaculture activities in the surrounding sea areas of the islands. With the rapid marine economic developments in the Lianyungang City of Jiangsu Province and the Rizhao City of Shandong Province, the intentions of these two provinces in developing the bordering sea areas and further deepening resource exploitation in local sea areas are strengthened, which cause larger conflicts and trigger larger-scale conflicts. The disputes between the Jiangsu and Shandong Provinces oversea areas have influenced the social stability in the Lianyungang City of Jiangsu Province and the Rizhao City of Shandong Province to some extent. Therefore, it is very necessary to formulate a scientific and reasonable maritime boundary between Jiangsu and Shandong Provinces.


## 2.2. Research Data

The original data in this study include mainly the coastline data, sea area, and ocean development data, coastline and area data of islands, and so on (Table1). Among them, data on the coastline and ocean development came mainly from field surveys and investigation, while data on islands were mainly from remote-sensing imagery interpretation. Other socioeconomic data were collected from the Statistical Yearbook of Rizhao City in 2019 and the Statistical Yearbook of Lianyungang City in 2019.Table 1
Datasets used in the present study.
CategoriesData sourceData specificationsSea area dataMeasured data2500 km2Coastline dataMeasured data200 kmMarine development dataMarine aquaculture area data of Jiangsu and Shandong Province198 recordsSocioeconomic data of Jiangsu ProvinceStatistical Yearbook of Lianyungang city in 2019—Socioeconomic data of Shandong ProvinceStatistical Yearbook of Rizhao city in 2019—Island dataRemote-sensing satellite dataResolution = 0.5 m


## 2.3. Preliminary Schemes

Based on principles of maritime boundary delimitation in terms of fairness and natural extension, several delimitation technological methods, which use the historical habit delimitation method, equidistance delimitation method, angle bisector delimitation method, trough centerline delimitation method, latitude delimitation method, and longitude delimitation method as beneficial supplementations, have been formed [20, 21] (Table 2). With consideration of natural geographic features of bordering sea areas between Jiangsu Province and Shandong Province, three maritime boundary delimitation schemes between these two provinces were formulated by using the historical habit delimitation method (Scheme 1), angle bisector delimitation method (Scheme 2), and equidistance delimitation method (Scheme 3) (Figure 2).Table 2
Common technological methods to formulate delimitation schemes.
No.Name of methodsIntroduction of methods1Equidistance delimitation methodThe involved parties advocated the generation of a line in the overlapping sea areas that the distances from every point on this line to the estimated nearest points on the baselines of each party’s territorial seas are equal. The line is used as the preliminary maritime boundary delimitation2Historical habit delimitation methodThe historical habit line accepted by involved parties is used as the preliminary line for maritime boundary delimitation3Angle bisector delimitation methodAdjacent coastal countries or provinces make a straight from the land administration boundary point along the extension directions or main body of their coasts to form an angle. The bisector of this angle is made and used as the preliminary line for maritime boundary delimitation4Bearing line delimitation methodThe two parties involved formed a bearing line after negotiation and use it as the preliminary line for maritime boundary delimitation5Latitude parallel line delimitation methodBased on negotiation, the involved parties agreed to use latitude or longitude lines that run through the overlapping sea areas as the preliminary line for maritime boundary delimitation6Overlapping bisector delimitation methodThe involved parties agree to make a straight line or curve in the overlapping sea area according to the principle of equal areas between two sides of the line and use it as the preliminary line for maritime boundary delimitation7Trough centerline delimitation methodIn disputing regions with deep troughs or evident topographical changes, the topographic centerline can be used as the preliminary line for maritime boundary delimitation among involved partiesFigure 2
Sketch map of three delimitation schemes.


## 3. Methods and Models

### 3.1. Principle of the Fuzzy Evaluation Model

In the practical world, many fuzzy concepts, such as “beautiful or ugly,” “good or bad,” and “effective or ineffective,” can be found. Everyone has uncertain evaluations. The development of fuzzy mathematics can solve this problem well. A fuzzy comprehensive evaluation is a comprehensive evaluation method based on fuzzy mathematics. It transforms qualitative evaluations into quantitative indices according to the membership theory of fuzzy mathematics. In other words, a fuzzy comprehensive evaluation is an evaluation method proposed by fuzzy mathematics and it makes an overall evaluation on the thing or object restricted by various factors. With characteristics of explicit outcomes and strong systematicness, fuzzy comprehensive evaluation can solve fuzzy, ambiguous, and difficult-to-quantify problems. It is applicable for solving various uncertainty problems [22].


#### 3.1.1. List the Set of Evaluation Indices

According to the evaluation goal, the set ofn indices for the evaluation objects P=p1,p2,p3,…,pn is listed, where n is determined according to specific evaluation contents.


#### 3.1.2. Propose the Set of Evaluation Index Grades

The set of evaluation index gradesQ=q1,q2,q3,…,qm is proposed, and the number of evaluation grades of indices is m, which generally ranges 3∼5.


#### 3.1.3. Determine Weights of Evaluation Indices

According to the importance of indices in the general evaluation objective, a weight fuzzy subset (B) is established based on P: B=b1,b2,b3,…,bn, where bi≥0 and ∑i=1nbi=1.


#### 3.1.4. Determine Membership of Factors

Theith factor (pi) of the single index is evaluated, and the jth membership in the evaluation set is vij. Therefore, the single index evaluation set pi can be gained: Vi=vi1,vi2,vi3,⋯,vim.After all indices are evaluated independently, the fuzzy relation matrix (V) from P to Q can be gained:(1)V=v11⋯v1m⋮⋱⋯v1n⋯vnm.


#### 3.1.5. Comprehensive Evaluation of Maritime Boundary Delimitation Schemes

Based onB and V, the fuzzy comprehensive evaluation vector R=r1,r2,r3,⋯,rm is calculated from the fuzzy comprehensive evaluation model R=B×V. Later, R∗ is calculated from the weighted averaging principle of R, and the grades of maritime boundary delimitation schemes are determined as follows:(2)R=B×V=r1,r2,r3,⋯rm,R∗=∑j=1mri×j∑j=1mrj,where j denotes evaluation grades (j=1,2,…,m). The vector rj refers to the membership of subsets to different evaluation grades, which are r1,r2,r3,…,rm in a comprehensive vector. The symbol R∗ is the comprehensive evaluation values of maritime boundary delimitation schemes, which refer to evaluation grades. In this study, the grade of each maritime boundary delimitation scheme can be determined, which provides intuitive data support for the comparative analysis of different schemes.


### 3.2. Establishment, Grading, and Assignment of Valuation Indices

The evaluation index system can be established by observing the principles of systematicness, scientificity, comparability, easy availability, and perceptiveness due to the complexity and macroscopic features of maritime boundary delimitation schemes. In the present study, evaluation indices were selected according to maritime boundary delimitation cases in the International Court of Justice and Arbitration Courts as well as associated studies, other determined interprovincial maritime boundaries in China and relevant studies, relevant China laws and regulations including the Sea Area Utilization and Administrative Laws, Island Protective Laws and Marine Environmental Protection Laws, and the collected marine economic statistical data in Jiangsu Province and Shandong Province. Based on the above principles and methods, the evaluation index system for maritime boundary delimitation between Jiangsu and Shandong Provinces was composed of the target, criterion, and index layers. The criterion layer consists of natural resource factors, socioeconomic factors, and expected delimitation effects of the sea areas. These three types can be further divided into 14 specific evaluation indices that form the hierarchical evaluation system for maritime boundary delimitation schemes (Table3).Table 3
Evaluation index system for maritime boundary delimitation schemes.
Target layerCriterion layerIndex layerIndex descriptionsA comprehensive evaluation of maritime boundary delimitation schemes (C)Natural resource factors of the sea area (C1)Sea area ratio between the two provinces (C11)Fairness of sea area divisionIsland quantity ratio between the two provinces (C12)Fairness of island quantity divisionIsland area ratio between the two provinces (C13)Fairness of island area divisionLength ratio of island deep-water shorelines between two provinces (C14)Fairness of deep-water shoreline divisionSocioeconomic factors of the sea area (C2)Disputing aquaculture sea area ratio between two provinces (C21)Fairness of aquaculture-oriented sea area divisionDisputing harbor and shipping sea area ratio between two provinces (C22)Fairness of harbor and shipping-oriented sea area divisionDisputing aquaculture fisherman quantity ratio between two provinces (C23)Livelihood index of aquaculture fishermenSocial stability in counties and cities near disputing sea areas in two provinces (C24)Social stability in adjacent counties and citiesExpected delimitation effects (C3)Protection conditions of territorial sea base points in Dashan island (C31)Maritime rights and interests maintenance indexNational maritime rights and interests guarantee capability (C32)Maritime rights and interests maintenance indexSustainable development capability of disputing sea areas (C33)Sustainable development indexes of sea areasManagement difficulties of disputing sea areas (C34)Sea area management indexesAcceptance of both parties to the delimitation schemes (C35)Acceptance index of schemesFairness verification index of maritime boundary delimitation outcome (C36)Sea area/shoreline length ratioThe grades of corresponding indexes of the historical boundary delimitation scheme (Scheme 1), angle bisector delimitation scheme (Scheme 2), and equidistance delimitation scheme (Scheme 3) were gained through the normalization of 14 evaluation indices and consultation with experts (Table4). Meanwhile, the membership vectors of the 14 indices of the three schemes were calculated from Equations (3)–(5) (Table 5).Table 4
Grades of evaluation indices of three maritime boundary delimitation schemes.
IndicesScheme 1Scheme 2Scheme 3Sea area ratio between two provinces (C11)0.910.020.74Island quantity ratio between two provinces (C12)0.150.250.55Island area ratio between two provinces (C13)0.300.500.70Length ratio of island deep-water shorelines between two provinces (C14)0.420.300.60Disputing aquaculture sea area ratio between two provinces (C21)0.120.000.03Disputing harbor and shipping sea area ratio between two provinces (C22)0.600.800.90Disputing aquaculture fisherman quantity ratio between two provinces (C23)0.500.000.55Social stability in counties and cities near disputing sea areas in two provinces (C24)0.700.500.30Protection conditions of territorial sea base points in Dashan island (C31)0.100.400.70National maritime rights and interests guarantee capability (C31)0.100.300.20Sustainable development capability of disputing sea areas (C33)0.150.250.350Management difficulties of disputing sea areas (C34)0.500.600.80Acceptance of both parties to the delimitation schemes (C35)0.250.450.55Fairness verification index of maritime boundary delimitation outcome (C36)1.000.980.99Table 5
Memberships of evaluation indices of three schemes.
Index layerMembership vector of Scheme 1Membership vector of Scheme 2Membership vector of Scheme 3Sea area ratio between two provinces (C11)(0,0,0,0,1)(1,0,0,0,0)(0,0,0,0.8,0.2)Island quantity ratio between two provinces (C12)(0.75,0.25,0,0,0)(0.25,0.75,0,0,0)(0,0,0.75,0.25,0)Island area ratio between two provinces (C13)(0,1,0,0,0)(0,0,1,0,0)(0,0,0,1,0)Length ratio of island deep-water shorelines between two provinces (C14)(0,0.4,0.6,0,0)(0,1,0,0,0)(0,0,0.5,0.5,0)Disputing aquaculture sea area ratio between two provinces (C21)(0.9,0.1,0,0,0)(1,0,0,0,0)(1,0,0,0,0)Disputing harbor and shipping sea area ratio between two provinces (C22)(0,0,0.5,0.5,0)(0,0,0,0.5,0.5)(0,0,0,0,1)Disputing aquaculture fisherman quantity ratio between two provinces (C23)(0,0,0,1,0)(1,0,0,0,0)(0,0,0.3,0.7,0)Social stability in counties and cities near disputing sea areas in two provinces (C24)(0,0,0,1,0)(0,0,1,0,0)(0,1,0,0,0)Protection conditions of territorial sea base points in Dashan island (C31)(1,0,0,0,0)(0,0.5,0.5,0,0)(0,0,0,1,0)National maritime rights and interests guarantee capability (C31)(1,0,0,0,0)(0,1,0,0,0)(0.5,0.5,0,0,0)Sustainable development capability of disputing sea areas (C33)(0.75,0.25,0,0,0)(0.25,0.75,0,0,0)(0,0.75,0.25,0,0)Management difficulties of disputing sea areas (C34)(0,0,1,0,0)(0,0,0.5,0.5,0)(0,0,0,0.5,0.5)Acceptance of both parties to the delimitation schemes (C35)(0.25,0.75,0,0,0)(0,0.25,0.75,0,0)(0,0,0.3,0.7,0)Fairness verification index of maritime boundary delimitation outcome (C36)(0,0,0,0,1)(0,0,0,0,1)(0,0,0,0,1)


### 3.3. Establishment of a Fuzzy Relation Matrix

Matrix (V) expresses the fuzzy relations between P and Q and is expressed as V=vijn×m, where vij refers to the possibility for the numerical value of the index i being evaluated as the Grade j, that is, the membership of Pi to the grade Qi. In this study, the membership was calculated with the triangle membership function: a key point in each grade interval is used as the demarcation point. When the index is at the midpoint of the interval, the membership of the index to the current grade is 1. When the index is at the midpoint of the adjacent interval, the membership to the current grade is 0. A total of five evaluation grades of maritime boundary delimitation schemes were determined.For indices that are safer under the smaller numerical values, the membership function to Grade 1 is as follows:(3)V1j=1x≤c1c1−xc2−c1c1<x0x≥c2<c2.The memberships of these indices to Grades 2, 3, and 4 are as follows:(4)Vkj=1x≤ck−1ck−1−xck−1−ckck−1<x<ckck+1−xck+1−ckck≤x<ck+10x≥ck+1k=2,3,4.The membership of these indices to Grade 5 is as follows:(5)V5j=0x≤c4c4−xc4−c5c4<x1x≥c5<c5,where vij is the membership of index j to Grade i. The symbol ck is the standard value of Grade k of the index j. For indices that are safer under larger numerical values, memberships can be calculated by changing the “ ≤ ” in Equations (3)–(5) into “ ≥ ”.According to equations (3)–(5) and Table 4, the membership vectors of the indices of three maritime boundary delimitation schemes could be gained (Table 5).


### 3.4. Determination of Comprehensive Weights of Indexes

Index weight has very important effects on the evaluation results of maritime boundary delimitation schemes. The main methods to determine the weights of the indices include AHP, correlation coefficient method, PCA, and entropy weight method. These methods can be divided into subjective weighting methods represented by AHP and objective weighting method represented by entropy weight method according to the weighting mode. In the practical evaluation process, the evaluation conclusions of schemes might be too subjective or objective if the weights of the indices are determined by one of the above methods, thereby showing a certain bias to practical situations. Hence, the comprehensive weights of indices are calculated by the AHP-entropy weight method, which can solve the above problems effectively.


#### 3.4.1. Weight Calculation Based on AHP

Analytic hierarchy process (AHP) was proposed by T.L. Saaty, a famous mathematical scientist from the University of Pittsburgh in the 1970s.AHP is essentially a decision thinking mode, and it decomposes a complicated problem into several factors. These factors are grouped according to memberships and form an ordered hierarchical structure [23, 24]. Pairwise comparisons of the importance of the indices are performed through the experiences of experts to determine the sequence of the importance of factors to the decision-making goal (weights). Classical AHP is performed in five steps, including establishing a hierarchical structure, building an importance judgment matrix, a single hierarchical arrangement of indices, consistency check, and the overall ranking of indices [25, 26].


#### 3.4.2. Weight Calculation Based on Entropy Weight Method

The concept of entropy was proposed by Rudolf Clausius, a German physicist, in 1850. In 1948, Shannon, an American mathematician, introduced entropy into the theory of information and proposed the concept of “information entropy” to describe the probability or uncertainty of occurrence of signals in information source [27, 28]. Information entropy is the measurement of the uncertainty of random variables. The higher the information entropy is, the larger the uncertainty will be; otherwise, the certainty is smaller. This can be expressed as follows:(6)Hp1,p2,…,pn=−∑i=1npilog2pi,where Hp1,p2,…,pn is the information entropy, and pi refers to the probability of occurrence of an event i.The dispersion degree of an evaluation index can be judged from the entropy value. The index with the smaller entropy value provides larger information size and has a higher dispersion degree, and thus, it can influence the overall goal more and has higher weights. Hence, the entropy weight method, which is a classical objective weighting tool, can be used to determine the weights of the indices and delete indices that have small contributions to evaluation results. Later, the weights of indices are corrected by entropy weight. Finally, objective weights of indices are gained [29], which can provide references for multi-index comprehensive evaluation.Them evaluating objects and n specific evaluation indices were taken as examples. The initial data factor matrix B=bijm×n was formed:(7)B=bijm×n=b11…b1n⋮⋱⋮bm1⋯bmn,where bij is the evaluation values of the Object i under the index j. Then, the steps to calculate the weight of each index are introduced as follows:(1)
Calculatepij , which is the proportion of the value of the evaluation index j under the index i.(8)pij=bij∑j=1nbiji=1,2,3,⋯,n;j=1,2,3,⋯,m.Ifpij=0, it defines that(9)limpij⟶0pijlnpij=0.(2)
Calculate entropy value (Ei) of an index i:(10)Ei=−∑j=1npijlnpijlnni=1,2,3,⋯,n.(3)
According toEi , calculate the entropy value (objective weight) of an index i (vi).(11)vi=1−Ei∑i=1m1−Eii=1,2,3,⋯,n.


#### 3.4.3. Calculation Methods of Comprehensive Weights

Generally, the comprehensive weights of indices (zi) are gained by combining the proportional method, simple multiplication averaging method, and minimum relative information entropy method with the subjective weight of AHP (wi) and the objective weight of entropy weight method (vi). With comprehensive consideration as to scientific preciseness and operation convenience, the simple multiplication averaging method was chosen to calculate the comprehensive weights of ecological safety indices of water resources.(12)zi=wivi∑j=1nwivi.Based on the processing and analysis of research data, subjective weights were calculated by AHP, and objective weights were gained through the entropy weight method. Next, the comprehensive weights of evaluation indices for maritime boundary delimitation schemes were calculated according to (12) (Table 6).Table 6
Subjective, objective, and comprehensive weights of evaluation indices for maritime boundary delimitation schemes.
Indices of the index layerSubjective weightwiObjective weightviComprehensive weightziSea area ratio between two provinces (C11)0.195800.036700.06980Island quantity ratio between two provinces (C12)0.024400.001400.00030Island area ratio between two provinces (C13)0.095800.005600.00520Length ratio of island deep-water shorelines between two provinces (C14)0.028600.158100.04390Disputing aquaculture sea area ratio between two provinces (C21)0.035500.051600.01780Disputing harbor and shipping sea area ratio between two provinces (C22)0.005400.011700.00060Disputing aquaculture fisherman quantity ratio between two provinces (C23)0.011100.003100.00030Social stability in counties and cities near disputing sea areas in two provinces (C24)0.056500.075000.04120Protection conditions of territorial sea base points in Dashan island (C31)0.155400.288200.43530National maritime rights and interests guarantee capability (C31)0.25200.119200.29200Sustainable development capability of disputing sea areas (C33)0.042700.119200.04950Management difficulties of disputing sea areas (C34)0.019100.026100.00480Acceptance of both parties to the delimitation schemes (C35)0.055500.051600.02780Fairness verification index of maritime boundary delimitation outcome (C36)0.022100.052600.01130


### 3.5. Grading of Maritime Boundary Delimitation Schemes

The grading of maritime boundary delimitation schemes is performed to reflect the advantages and disadvantages of schemes. Because the comprehensive evaluation values of maritime boundary delimitation schemes cannot reflect the state of the scheme directly, grading maritime boundary delimitation schemes is necessary to connect evaluation values and grades of schemes. The maritime boundary delimitation schemes are graded based on a consultation with experts and existing delimitation cases, combined with natural conditions and social development conditions in the study area (Table7).Table 7
Grades of maritime boundary delimitation schemes between Jiangsu Province and Shandong Province.
Grades of indicesIIIIIIIVVWeights0∼0.10.1∼0.30.3∼0.50.5∼0.70.7∼1MeaningsExtremely poorPoorModerateGoodExcellent


## 3.1. Principle of the Fuzzy Evaluation Model

In the practical world, many fuzzy concepts, such as “beautiful or ugly,” “good or bad,” and “effective or ineffective,” can be found. Everyone has uncertain evaluations. The development of fuzzy mathematics can solve this problem well. A fuzzy comprehensive evaluation is a comprehensive evaluation method based on fuzzy mathematics. It transforms qualitative evaluations into quantitative indices according to the membership theory of fuzzy mathematics. In other words, a fuzzy comprehensive evaluation is an evaluation method proposed by fuzzy mathematics and it makes an overall evaluation on the thing or object restricted by various factors. With characteristics of explicit outcomes and strong systematicness, fuzzy comprehensive evaluation can solve fuzzy, ambiguous, and difficult-to-quantify problems. It is applicable for solving various uncertainty problems [22].


### 3.1.1. List the Set of Evaluation Indices

According to the evaluation goal, the set ofn indices for the evaluation objects P=p1,p2,p3,…,pn is listed, where n is determined according to specific evaluation contents.


### 3.1.2. Propose the Set of Evaluation Index Grades

The set of evaluation index gradesQ=q1,q2,q3,…,qm is proposed, and the number of evaluation grades of indices is m, which generally ranges 3∼5.


### 3.1.3. Determine Weights of Evaluation Indices

According to the importance of indices in the general evaluation objective, a weight fuzzy subset (B) is established based on P: B=b1,b2,b3,…,bn, where bi≥0 and ∑i=1nbi=1.


### 3.1.4. Determine Membership of Factors

Theith factor (pi) of the single index is evaluated, and the jth membership in the evaluation set is vij. Therefore, the single index evaluation set pi can be gained: Vi=vi1,vi2,vi3,⋯,vim.After all indices are evaluated independently, the fuzzy relation matrix (V) from P to Q can be gained:(1)V=v11⋯v1m⋮⋱⋯v1n⋯vnm.


### 3.1.5. Comprehensive Evaluation of Maritime Boundary Delimitation Schemes

Based onB and V, the fuzzy comprehensive evaluation vector R=r1,r2,r3,⋯,rm is calculated from the fuzzy comprehensive evaluation model R=B×V. Later, R∗ is calculated from the weighted averaging principle of R, and the grades of maritime boundary delimitation schemes are determined as follows:(2)R=B×V=r1,r2,r3,⋯rm,R∗=∑j=1mri×j∑j=1mrj,where j denotes evaluation grades (j=1,2,…,m). The vector rj refers to the membership of subsets to different evaluation grades, which are r1,r2,r3,…,rm in a comprehensive vector. The symbol R∗ is the comprehensive evaluation values of maritime boundary delimitation schemes, which refer to evaluation grades. In this study, the grade of each maritime boundary delimitation scheme can be determined, which provides intuitive data support for the comparative analysis of different schemes.


## 3.1.1. List the Set of Evaluation Indices

According to the evaluation goal, the set ofn indices for the evaluation objects P=p1,p2,p3,…,pn is listed, where n is determined according to specific evaluation contents.


## 3.1.2. Propose the Set of Evaluation Index Grades

The set of evaluation index gradesQ=q1,q2,q3,…,qm is proposed, and the number of evaluation grades of indices is m, which generally ranges 3∼5.


## 3.1.3. Determine Weights of Evaluation Indices

According to the importance of indices in the general evaluation objective, a weight fuzzy subset (B) is established based on P: B=b1,b2,b3,…,bn, where bi≥0 and ∑i=1nbi=1.


## 3.1.4. Determine Membership of Factors

Theith factor (pi) of the single index is evaluated, and the jth membership in the evaluation set is vij. Therefore, the single index evaluation set pi can be gained: Vi=vi1,vi2,vi3,⋯,vim.After all indices are evaluated independently, the fuzzy relation matrix (V) from P to Q can be gained:(1)V=v11⋯v1m⋮⋱⋯v1n⋯vnm.


## 3.1.5. Comprehensive Evaluation of Maritime Boundary Delimitation Schemes

Based onB and V, the fuzzy comprehensive evaluation vector R=r1,r2,r3,⋯,rm is calculated from the fuzzy comprehensive evaluation model R=B×V. Later, R∗ is calculated from the weighted averaging principle of R, and the grades of maritime boundary delimitation schemes are determined as follows:(2)R=B×V=r1,r2,r3,⋯rm,R∗=∑j=1mri×j∑j=1mrj,where j denotes evaluation grades (j=1,2,…,m). The vector rj refers to the membership of subsets to different evaluation grades, which are r1,r2,r3,…,rm in a comprehensive vector. The symbol R∗ is the comprehensive evaluation values of maritime boundary delimitation schemes, which refer to evaluation grades. In this study, the grade of each maritime boundary delimitation scheme can be determined, which provides intuitive data support for the comparative analysis of different schemes.


## 3.2. Establishment, Grading, and Assignment of Valuation Indices

The evaluation index system can be established by observing the principles of systematicness, scientificity, comparability, easy availability, and perceptiveness due to the complexity and macroscopic features of maritime boundary delimitation schemes. In the present study, evaluation indices were selected according to maritime boundary delimitation cases in the International Court of Justice and Arbitration Courts as well as associated studies, other determined interprovincial maritime boundaries in China and relevant studies, relevant China laws and regulations including the Sea Area Utilization and Administrative Laws, Island Protective Laws and Marine Environmental Protection Laws, and the collected marine economic statistical data in Jiangsu Province and Shandong Province. Based on the above principles and methods, the evaluation index system for maritime boundary delimitation between Jiangsu and Shandong Provinces was composed of the target, criterion, and index layers. The criterion layer consists of natural resource factors, socioeconomic factors, and expected delimitation effects of the sea areas. These three types can be further divided into 14 specific evaluation indices that form the hierarchical evaluation system for maritime boundary delimitation schemes (Table3).Table 3
Evaluation index system for maritime boundary delimitation schemes.
Target layerCriterion layerIndex layerIndex descriptionsA comprehensive evaluation of maritime boundary delimitation schemes (C)Natural resource factors of the sea area (C1)Sea area ratio between the two provinces (C11)Fairness of sea area divisionIsland quantity ratio between the two provinces (C12)Fairness of island quantity divisionIsland area ratio between the two provinces (C13)Fairness of island area divisionLength ratio of island deep-water shorelines between two provinces (C14)Fairness of deep-water shoreline divisionSocioeconomic factors of the sea area (C2)Disputing aquaculture sea area ratio between two provinces (C21)Fairness of aquaculture-oriented sea area divisionDisputing harbor and shipping sea area ratio between two provinces (C22)Fairness of harbor and shipping-oriented sea area divisionDisputing aquaculture fisherman quantity ratio between two provinces (C23)Livelihood index of aquaculture fishermenSocial stability in counties and cities near disputing sea areas in two provinces (C24)Social stability in adjacent counties and citiesExpected delimitation effects (C3)Protection conditions of territorial sea base points in Dashan island (C31)Maritime rights and interests maintenance indexNational maritime rights and interests guarantee capability (C32)Maritime rights and interests maintenance indexSustainable development capability of disputing sea areas (C33)Sustainable development indexes of sea areasManagement difficulties of disputing sea areas (C34)Sea area management indexesAcceptance of both parties to the delimitation schemes (C35)Acceptance index of schemesFairness verification index of maritime boundary delimitation outcome (C36)Sea area/shoreline length ratioThe grades of corresponding indexes of the historical boundary delimitation scheme (Scheme 1), angle bisector delimitation scheme (Scheme 2), and equidistance delimitation scheme (Scheme 3) were gained through the normalization of 14 evaluation indices and consultation with experts (Table4). Meanwhile, the membership vectors of the 14 indices of the three schemes were calculated from Equations (3)–(5) (Table 5).Table 4
Grades of evaluation indices of three maritime boundary delimitation schemes.
IndicesScheme 1Scheme 2Scheme 3Sea area ratio between two provinces (C11)0.910.020.74Island quantity ratio between two provinces (C12)0.150.250.55Island area ratio between two provinces (C13)0.300.500.70Length ratio of island deep-water shorelines between two provinces (C14)0.420.300.60Disputing aquaculture sea area ratio between two provinces (C21)0.120.000.03Disputing harbor and shipping sea area ratio between two provinces (C22)0.600.800.90Disputing aquaculture fisherman quantity ratio between two provinces (C23)0.500.000.55Social stability in counties and cities near disputing sea areas in two provinces (C24)0.700.500.30Protection conditions of territorial sea base points in Dashan island (C31)0.100.400.70National maritime rights and interests guarantee capability (C31)0.100.300.20Sustainable development capability of disputing sea areas (C33)0.150.250.350Management difficulties of disputing sea areas (C34)0.500.600.80Acceptance of both parties to the delimitation schemes (C35)0.250.450.55Fairness verification index of maritime boundary delimitation outcome (C36)1.000.980.99Table 5
Memberships of evaluation indices of three schemes.
Index layerMembership vector of Scheme 1Membership vector of Scheme 2Membership vector of Scheme 3Sea area ratio between two provinces (C11)(0,0,0,0,1)(1,0,0,0,0)(0,0,0,0.8,0.2)Island quantity ratio between two provinces (C12)(0.75,0.25,0,0,0)(0.25,0.75,0,0,0)(0,0,0.75,0.25,0)Island area ratio between two provinces (C13)(0,1,0,0,0)(0,0,1,0,0)(0,0,0,1,0)Length ratio of island deep-water shorelines between two provinces (C14)(0,0.4,0.6,0,0)(0,1,0,0,0)(0,0,0.5,0.5,0)Disputing aquaculture sea area ratio between two provinces (C21)(0.9,0.1,0,0,0)(1,0,0,0,0)(1,0,0,0,0)Disputing harbor and shipping sea area ratio between two provinces (C22)(0,0,0.5,0.5,0)(0,0,0,0.5,0.5)(0,0,0,0,1)Disputing aquaculture fisherman quantity ratio between two provinces (C23)(0,0,0,1,0)(1,0,0,0,0)(0,0,0.3,0.7,0)Social stability in counties and cities near disputing sea areas in two provinces (C24)(0,0,0,1,0)(0,0,1,0,0)(0,1,0,0,0)Protection conditions of territorial sea base points in Dashan island (C31)(1,0,0,0,0)(0,0.5,0.5,0,0)(0,0,0,1,0)National maritime rights and interests guarantee capability (C31)(1,0,0,0,0)(0,1,0,0,0)(0.5,0.5,0,0,0)Sustainable development capability of disputing sea areas (C33)(0.75,0.25,0,0,0)(0.25,0.75,0,0,0)(0,0.75,0.25,0,0)Management difficulties of disputing sea areas (C34)(0,0,1,0,0)(0,0,0.5,0.5,0)(0,0,0,0.5,0.5)Acceptance of both parties to the delimitation schemes (C35)(0.25,0.75,0,0,0)(0,0.25,0.75,0,0)(0,0,0.3,0.7,0)Fairness verification index of maritime boundary delimitation outcome (C36)(0,0,0,0,1)(0,0,0,0,1)(0,0,0,0,1)


## 3.3. Establishment of a Fuzzy Relation Matrix

Matrix (V) expresses the fuzzy relations between P and Q and is expressed as V=vijn×m, where vij refers to the possibility for the numerical value of the index i being evaluated as the Grade j, that is, the membership of Pi to the grade Qi. In this study, the membership was calculated with the triangle membership function: a key point in each grade interval is used as the demarcation point. When the index is at the midpoint of the interval, the membership of the index to the current grade is 1. When the index is at the midpoint of the adjacent interval, the membership to the current grade is 0. A total of five evaluation grades of maritime boundary delimitation schemes were determined.For indices that are safer under the smaller numerical values, the membership function to Grade 1 is as follows:(3)V1j=1x≤c1c1−xc2−c1c1<x0x≥c2<c2.The memberships of these indices to Grades 2, 3, and 4 are as follows:(4)Vkj=1x≤ck−1ck−1−xck−1−ckck−1<x<ckck+1−xck+1−ckck≤x<ck+10x≥ck+1k=2,3,4.The membership of these indices to Grade 5 is as follows:(5)V5j=0x≤c4c4−xc4−c5c4<x1x≥c5<c5,where vij is the membership of index j to Grade i. The symbol ck is the standard value of Grade k of the index j. For indices that are safer under larger numerical values, memberships can be calculated by changing the “ ≤ ” in Equations (3)–(5) into “ ≥ ”.According to equations (3)–(5) and Table 4, the membership vectors of the indices of three maritime boundary delimitation schemes could be gained (Table 5).


## 3.4. Determination of Comprehensive Weights of Indexes

Index weight has very important effects on the evaluation results of maritime boundary delimitation schemes. The main methods to determine the weights of the indices include AHP, correlation coefficient method, PCA, and entropy weight method. These methods can be divided into subjective weighting methods represented by AHP and objective weighting method represented by entropy weight method according to the weighting mode. In the practical evaluation process, the evaluation conclusions of schemes might be too subjective or objective if the weights of the indices are determined by one of the above methods, thereby showing a certain bias to practical situations. Hence, the comprehensive weights of indices are calculated by the AHP-entropy weight method, which can solve the above problems effectively.


### 3.4.1. Weight Calculation Based on AHP

Analytic hierarchy process (AHP) was proposed by T.L. Saaty, a famous mathematical scientist from the University of Pittsburgh in the 1970s.AHP is essentially a decision thinking mode, and it decomposes a complicated problem into several factors. These factors are grouped according to memberships and form an ordered hierarchical structure [23, 24]. Pairwise comparisons of the importance of the indices are performed through the experiences of experts to determine the sequence of the importance of factors to the decision-making goal (weights). Classical AHP is performed in five steps, including establishing a hierarchical structure, building an importance judgment matrix, a single hierarchical arrangement of indices, consistency check, and the overall ranking of indices [25, 26].


### 3.4.2. Weight Calculation Based on Entropy Weight Method

The concept of entropy was proposed by Rudolf Clausius, a German physicist, in 1850. In 1948, Shannon, an American mathematician, introduced entropy into the theory of information and proposed the concept of “information entropy” to describe the probability or uncertainty of occurrence of signals in information source [27, 28]. Information entropy is the measurement of the uncertainty of random variables. The higher the information entropy is, the larger the uncertainty will be; otherwise, the certainty is smaller. This can be expressed as follows:(6)Hp1,p2,…,pn=−∑i=1npilog2pi,where Hp1,p2,…,pn is the information entropy, and pi refers to the probability of occurrence of an event i.The dispersion degree of an evaluation index can be judged from the entropy value. The index with the smaller entropy value provides larger information size and has a higher dispersion degree, and thus, it can influence the overall goal more and has higher weights. Hence, the entropy weight method, which is a classical objective weighting tool, can be used to determine the weights of the indices and delete indices that have small contributions to evaluation results. Later, the weights of indices are corrected by entropy weight. Finally, objective weights of indices are gained [29], which can provide references for multi-index comprehensive evaluation.Them evaluating objects and n specific evaluation indices were taken as examples. The initial data factor matrix B=bijm×n was formed:(7)B=bijm×n=b11…b1n⋮⋱⋮bm1⋯bmn,where bij is the evaluation values of the Object i under the index j. Then, the steps to calculate the weight of each index are introduced as follows:(1)
Calculatepij , which is the proportion of the value of the evaluation index j under the index i.(8)pij=bij∑j=1nbiji=1,2,3,⋯,n;j=1,2,3,⋯,m.Ifpij=0, it defines that(9)limpij⟶0pijlnpij=0.(2)
Calculate entropy value (Ei) of an index i:(10)Ei=−∑j=1npijlnpijlnni=1,2,3,⋯,n.(3)
According toEi , calculate the entropy value (objective weight) of an index i (vi).(11)vi=1−Ei∑i=1m1−Eii=1,2,3,⋯,n.


### 3.4.3. Calculation Methods of Comprehensive Weights

Generally, the comprehensive weights of indices (zi) are gained by combining the proportional method, simple multiplication averaging method, and minimum relative information entropy method with the subjective weight of AHP (wi) and the objective weight of entropy weight method (vi). With comprehensive consideration as to scientific preciseness and operation convenience, the simple multiplication averaging method was chosen to calculate the comprehensive weights of ecological safety indices of water resources.(12)zi=wivi∑j=1nwivi.Based on the processing and analysis of research data, subjective weights were calculated by AHP, and objective weights were gained through the entropy weight method. Next, the comprehensive weights of evaluation indices for maritime boundary delimitation schemes were calculated according to (12) (Table 6).Table 6
Subjective, objective, and comprehensive weights of evaluation indices for maritime boundary delimitation schemes.
Indices of the index layerSubjective weightwiObjective weightviComprehensive weightziSea area ratio between two provinces (C11)0.195800.036700.06980Island quantity ratio between two provinces (C12)0.024400.001400.00030Island area ratio between two provinces (C13)0.095800.005600.00520Length ratio of island deep-water shorelines between two provinces (C14)0.028600.158100.04390Disputing aquaculture sea area ratio between two provinces (C21)0.035500.051600.01780Disputing harbor and shipping sea area ratio between two provinces (C22)0.005400.011700.00060Disputing aquaculture fisherman quantity ratio between two provinces (C23)0.011100.003100.00030Social stability in counties and cities near disputing sea areas in two provinces (C24)0.056500.075000.04120Protection conditions of territorial sea base points in Dashan island (C31)0.155400.288200.43530National maritime rights and interests guarantee capability (C31)0.25200.119200.29200Sustainable development capability of disputing sea areas (C33)0.042700.119200.04950Management difficulties of disputing sea areas (C34)0.019100.026100.00480Acceptance of both parties to the delimitation schemes (C35)0.055500.051600.02780Fairness verification index of maritime boundary delimitation outcome (C36)0.022100.052600.01130


## 3.4.1. Weight Calculation Based on AHP

Analytic hierarchy process (AHP) was proposed by T.L. Saaty, a famous mathematical scientist from the University of Pittsburgh in the 1970s.AHP is essentially a decision thinking mode, and it decomposes a complicated problem into several factors. These factors are grouped according to memberships and form an ordered hierarchical structure [23, 24]. Pairwise comparisons of the importance of the indices are performed through the experiences of experts to determine the sequence of the importance of factors to the decision-making goal (weights). Classical AHP is performed in five steps, including establishing a hierarchical structure, building an importance judgment matrix, a single hierarchical arrangement of indices, consistency check, and the overall ranking of indices [25, 26].


## 3.4.2. Weight Calculation Based on Entropy Weight Method

The concept of entropy was proposed by Rudolf Clausius, a German physicist, in 1850. In 1948, Shannon, an American mathematician, introduced entropy into the theory of information and proposed the concept of “information entropy” to describe the probability or uncertainty of occurrence of signals in information source [27, 28]. Information entropy is the measurement of the uncertainty of random variables. The higher the information entropy is, the larger the uncertainty will be; otherwise, the certainty is smaller. This can be expressed as follows:(6)Hp1,p2,…,pn=−∑i=1npilog2pi,where Hp1,p2,…,pn is the information entropy, and pi refers to the probability of occurrence of an event i.The dispersion degree of an evaluation index can be judged from the entropy value. The index with the smaller entropy value provides larger information size and has a higher dispersion degree, and thus, it can influence the overall goal more and has higher weights. Hence, the entropy weight method, which is a classical objective weighting tool, can be used to determine the weights of the indices and delete indices that have small contributions to evaluation results. Later, the weights of indices are corrected by entropy weight. Finally, objective weights of indices are gained [29], which can provide references for multi-index comprehensive evaluation.Them evaluating objects and n specific evaluation indices were taken as examples. The initial data factor matrix B=bijm×n was formed:(7)B=bijm×n=b11…b1n⋮⋱⋮bm1⋯bmn,where bij is the evaluation values of the Object i under the index j. Then, the steps to calculate the weight of each index are introduced as follows:(1)
Calculatepij , which is the proportion of the value of the evaluation index j under the index i.(8)pij=bij∑j=1nbiji=1,2,3,⋯,n;j=1,2,3,⋯,m.Ifpij=0, it defines that(9)limpij⟶0pijlnpij=0.(2)
Calculate entropy value (Ei) of an index i:(10)Ei=−∑j=1npijlnpijlnni=1,2,3,⋯,n.(3)
According toEi , calculate the entropy value (objective weight) of an index i (vi).(11)vi=1−Ei∑i=1m1−Eii=1,2,3,⋯,n.


## 3.4.3. Calculation Methods of Comprehensive Weights

Generally, the comprehensive weights of indices (zi) are gained by combining the proportional method, simple multiplication averaging method, and minimum relative information entropy method with the subjective weight of AHP (wi) and the objective weight of entropy weight method (vi). With comprehensive consideration as to scientific preciseness and operation convenience, the simple multiplication averaging method was chosen to calculate the comprehensive weights of ecological safety indices of water resources.(12)zi=wivi∑j=1nwivi.Based on the processing and analysis of research data, subjective weights were calculated by AHP, and objective weights were gained through the entropy weight method. Next, the comprehensive weights of evaluation indices for maritime boundary delimitation schemes were calculated according to (12) (Table 6).Table 6
Subjective, objective, and comprehensive weights of evaluation indices for maritime boundary delimitation schemes.
Indices of the index layerSubjective weightwiObjective weightviComprehensive weightziSea area ratio between two provinces (C11)0.195800.036700.06980Island quantity ratio between two provinces (C12)0.024400.001400.00030Island area ratio between two provinces (C13)0.095800.005600.00520Length ratio of island deep-water shorelines between two provinces (C14)0.028600.158100.04390Disputing aquaculture sea area ratio between two provinces (C21)0.035500.051600.01780Disputing harbor and shipping sea area ratio between two provinces (C22)0.005400.011700.00060Disputing aquaculture fisherman quantity ratio between two provinces (C23)0.011100.003100.00030Social stability in counties and cities near disputing sea areas in two provinces (C24)0.056500.075000.04120Protection conditions of territorial sea base points in Dashan island (C31)0.155400.288200.43530National maritime rights and interests guarantee capability (C31)0.25200.119200.29200Sustainable development capability of disputing sea areas (C33)0.042700.119200.04950Management difficulties of disputing sea areas (C34)0.019100.026100.00480Acceptance of both parties to the delimitation schemes (C35)0.055500.051600.02780Fairness verification index of maritime boundary delimitation outcome (C36)0.022100.052600.01130


## 3.5. Grading of Maritime Boundary Delimitation Schemes

The grading of maritime boundary delimitation schemes is performed to reflect the advantages and disadvantages of schemes. Because the comprehensive evaluation values of maritime boundary delimitation schemes cannot reflect the state of the scheme directly, grading maritime boundary delimitation schemes is necessary to connect evaluation values and grades of schemes. The maritime boundary delimitation schemes are graded based on a consultation with experts and existing delimitation cases, combined with natural conditions and social development conditions in the study area (Table7).Table 7
Grades of maritime boundary delimitation schemes between Jiangsu Province and Shandong Province.
Grades of indicesIIIIIIIVVWeights0∼0.10.1∼0.30.3∼0.50.5∼0.70.7∼1MeaningsExtremely poorPoorModerateGoodExcellent


## 4. Results and Discussion

### 4.1. Research Results

The comprehensive evaluation values of three delimitation schemes in Shandong and Jiangsu Provinces were calculated according to (2). Next, the grades of the three schemes were determined according to Table 7. The results are shown in Table 8.Table 8
Evaluation results of the three schemes.
SchemesEvaluation valuesComprehensive evaluation grades of schemesEvaluation values of natural resource factors in the sea areaEvaluation values of socioeconomic factors in the sea areaEvaluation values of expected effect factorsComprehensive evaluation valuesScheme 1 (historical boundary delimitation scheme)0.695150.526640.121450.13534PoorScheme 2 (angle bisector delimitation scheme)0.191480.382130.365120.36164ModerateScheme 3 (equidistance delimitation scheme)0.686210.248280.502290.50476Good


### 4.2. Results Discussion

#### 4.2.1. Evaluation of Natural Resource Factors in the Sea Area

Disputes over maritime areas are caused by competition for marine resources. In this study, four factors were added to the index system: sea area, island quantity, island area, and deep-water shoreline resources of islands. Other natural resource components of sea areas, such as marine biological resources, marine energy resources, and marine mineral resources, were left out since they were difficult to determine. According to research results (Table8 and Figure 3), Scheme 2 achieved the lowest evaluation value (only 0.191485) of natural resource factors of sea areas and is graded “Poor.” Schemes 1 and 3 achieved similar grades of natural resource factors, and the evaluation values are close to 0.7, which corresponds to “Good” and approaches “Excellent.” Such difference is related to the great gap in the sea area between Shandong and Jiangsu Provinces (520 km2) in Scheme 2, but similar sea areas of two provinces in Schemes 1 and 3. Moreover, the deep-water shoreline lengths of Shandong and Jiangsu Provinces differ to some extent (about more than 800 m) in Scheme 2, which accounts for about 10% of the total shoreline length. The evaluation values of natural resource elements in three schemes show that sea area division plays an essential role in maritime boundary delimitation schemes.Figure 3
Variations of evaluation values of the subsets of different schemes.


#### 4.2.2. Evaluation of Socioeconomic Factors in the Sea Area

Socioeconomic factors are important attributes of marine resources. Aquaculture-oriented sea area, harbor, and shipping-oriented sea areas, number of aquaculture fishermen, and social stability that affect socioeconomic development in involved counties and cities were chosen as indices because the disputing sea areas between Shandong and Jiangsu Provinces have good conditions for aquaculture, harbor, and shipping development. Scheme 3 received the lowest socioeconomic factor evaluation score (only 0.24828) and was evaluated “Poor” based on the research findings (Table8 and Figure 3). Scheme 2 achieved the second-lowest evaluation value of socioeconomic factors (only 0.382137) and is graded “Moderate.” Scheme 1 is relatively superior, and the evaluation value is 0.526644, which is graded “Good.” These results can be interpreted from the following aspects. First, sea areas that are suitable for aquaculture in the study area are in the south, and a certain gap can be observed between the two provinces in terms of such aquaculture sea areas. Specifically, the gap in Scheme 3 is the largest, in which Jiangsu Province has 3000 ha (20% of total areas) more aquaculture-oriented sea areas than Shandong Province. Second, in Shandong Province’s Rizhao City, more fishermen are involved in marine aquaculture than in Jiangsu Province’s Lianyungang City. Shandong Province, on the other hand, has a lesser proportion of aquaculture-oriented sea waters in Scheme 3, which has an impact on social stability following the delimitation.


#### 4.2.3. Evaluation of Expected Effect Factors

The expected effect refers to the expectations in resource protection and utilization in the disputing sea areas and socioeconomic development in involved counties and cities after maritime boundary delimitation. Territorial sea base points can be found in the Dashan Island in the disputing sea areas between Jiangsu and Shandong Provinces. According to the Measures for the Selection and Delineation of the Scope of Protection and the Protection of Territorial Sea Base Points, which are issued by the State Oceanic Administration, a certain sea area has been determined as the protection zone of territorial sea base points, which is inappropriate for segmentation. Strategic significance is superior. Although the proportional fairness validation index of maritime boundary delimitation cannot evaluate the quality of delimitation schemes, it can be used as reference data to determine the fairness of the delimitation schemes. Therefore, six indexes were chosen to evaluate the expected effect, including protection conditions of territorial sea base points in Dashan Island (C31), national maritime rights and interests guarantee capability (C32), sustainable development capability of disputing sea areas (C33), management difficulties of disputing sea areas (C34), acceptance of both parties to the delimitation schemes (C35), and fairness verification index of maritime boundary delimitation outcome (C36). According to the research results (Table8 and Figure 3), Scheme 1 had the lowest evaluation value (0.121451) of expected effect factors and is graded “Poor.” Scheme 2 shows the second-lowest evaluation value (0.365121) of expected effect factors and is graded “Moderate.” Scheme 3 is relatively better (0.502299) and is graded “Good.” This is because the evaluation of expected effect factors focuses on the integrity of 10 islands in the study area, and Scheme 1 divides islands more thoroughly, which can affect the maintenance of China’s national maritime rights and interests to some extent.


#### 4.2.4. Comprehensive Evaluation of Delimitation Schemes

Research results (Table8 and Figure 4) show that Scheme 1 is inferior to the two other Schemes in terms of comprehensive evaluation values (0.135345) and is graded “Poor.” Scheme 2 is better (0.361641) and is graded “Moderate.” Scheme 3 is the best, but the comprehensive evaluation value is only 0.504761 and is graded as “Good.” All three schemes have some disadvantages and divide 10 islands, which affect China’s national maritime rights and interests to some extent. Experts are also concerned about the preservation of national marine rights and interests. In C31, it weighed 0.4353 while in C32, it weighed 0.2920. Furthermore, while having the lowest assessment values in sea area socioeconomic aspects, Scheme 3 has significantly higher evaluation values in expected effect factors. Scheme 3 is the best because the weights of natural resource factors, socioeconomic factors, and expected effect factors of sea areas are 0.1192, 0.0599, and 0.8207. Scheme 3, on the other hand, which has the highest overall assessment value, is only given a “Good” rather than an “Excellent” rating. From the standpoint of protecting territorial sea base points and optimizing the maritime boundary delimitation scheme, it is vital to maintain the integrity of 10 islands.Figure 4
Comprehensive evaluation values of the three schemes.


## 4.1. Research Results

The comprehensive evaluation values of three delimitation schemes in Shandong and Jiangsu Provinces were calculated according to (2). Next, the grades of the three schemes were determined according to Table 7. The results are shown in Table 8.Table 8
Evaluation results of the three schemes.
SchemesEvaluation valuesComprehensive evaluation grades of schemesEvaluation values of natural resource factors in the sea areaEvaluation values of socioeconomic factors in the sea areaEvaluation values of expected effect factorsComprehensive evaluation valuesScheme 1 (historical boundary delimitation scheme)0.695150.526640.121450.13534PoorScheme 2 (angle bisector delimitation scheme)0.191480.382130.365120.36164ModerateScheme 3 (equidistance delimitation scheme)0.686210.248280.502290.50476Good


## 4.2. Results Discussion

### 4.2.1. Evaluation of Natural Resource Factors in the Sea Area

Disputes over maritime areas are caused by competition for marine resources. In this study, four factors were added to the index system: sea area, island quantity, island area, and deep-water shoreline resources of islands. Other natural resource components of sea areas, such as marine biological resources, marine energy resources, and marine mineral resources, were left out since they were difficult to determine. According to research results (Table8 and Figure 3), Scheme 2 achieved the lowest evaluation value (only 0.191485) of natural resource factors of sea areas and is graded “Poor.” Schemes 1 and 3 achieved similar grades of natural resource factors, and the evaluation values are close to 0.7, which corresponds to “Good” and approaches “Excellent.” Such difference is related to the great gap in the sea area between Shandong and Jiangsu Provinces (520 km2) in Scheme 2, but similar sea areas of two provinces in Schemes 1 and 3. Moreover, the deep-water shoreline lengths of Shandong and Jiangsu Provinces differ to some extent (about more than 800 m) in Scheme 2, which accounts for about 10% of the total shoreline length. The evaluation values of natural resource elements in three schemes show that sea area division plays an essential role in maritime boundary delimitation schemes.Figure 3
Variations of evaluation values of the subsets of different schemes.


### 4.2.2. Evaluation of Socioeconomic Factors in the Sea Area

Socioeconomic factors are important attributes of marine resources. Aquaculture-oriented sea area, harbor, and shipping-oriented sea areas, number of aquaculture fishermen, and social stability that affect socioeconomic development in involved counties and cities were chosen as indices because the disputing sea areas between Shandong and Jiangsu Provinces have good conditions for aquaculture, harbor, and shipping development. Scheme 3 received the lowest socioeconomic factor evaluation score (only 0.24828) and was evaluated “Poor” based on the research findings (Table8 and Figure 3). Scheme 2 achieved the second-lowest evaluation value of socioeconomic factors (only 0.382137) and is graded “Moderate.” Scheme 1 is relatively superior, and the evaluation value is 0.526644, which is graded “Good.” These results can be interpreted from the following aspects. First, sea areas that are suitable for aquaculture in the study area are in the south, and a certain gap can be observed between the two provinces in terms of such aquaculture sea areas. Specifically, the gap in Scheme 3 is the largest, in which Jiangsu Province has 3000 ha (20% of total areas) more aquaculture-oriented sea areas than Shandong Province. Second, in Shandong Province’s Rizhao City, more fishermen are involved in marine aquaculture than in Jiangsu Province’s Lianyungang City. Shandong Province, on the other hand, has a lesser proportion of aquaculture-oriented sea waters in Scheme 3, which has an impact on social stability following the delimitation.


### 4.2.3. Evaluation of Expected Effect Factors

The expected effect refers to the expectations in resource protection and utilization in the disputing sea areas and socioeconomic development in involved counties and cities after maritime boundary delimitation. Territorial sea base points can be found in the Dashan Island in the disputing sea areas between Jiangsu and Shandong Provinces. According to the Measures for the Selection and Delineation of the Scope of Protection and the Protection of Territorial Sea Base Points, which are issued by the State Oceanic Administration, a certain sea area has been determined as the protection zone of territorial sea base points, which is inappropriate for segmentation. Strategic significance is superior. Although the proportional fairness validation index of maritime boundary delimitation cannot evaluate the quality of delimitation schemes, it can be used as reference data to determine the fairness of the delimitation schemes. Therefore, six indexes were chosen to evaluate the expected effect, including protection conditions of territorial sea base points in Dashan Island (C31), national maritime rights and interests guarantee capability (C32), sustainable development capability of disputing sea areas (C33), management difficulties of disputing sea areas (C34), acceptance of both parties to the delimitation schemes (C35), and fairness verification index of maritime boundary delimitation outcome (C36). According to the research results (Table8 and Figure 3), Scheme 1 had the lowest evaluation value (0.121451) of expected effect factors and is graded “Poor.” Scheme 2 shows the second-lowest evaluation value (0.365121) of expected effect factors and is graded “Moderate.” Scheme 3 is relatively better (0.502299) and is graded “Good.” This is because the evaluation of expected effect factors focuses on the integrity of 10 islands in the study area, and Scheme 1 divides islands more thoroughly, which can affect the maintenance of China’s national maritime rights and interests to some extent.


### 4.2.4. Comprehensive Evaluation of Delimitation Schemes

Research results (Table8 and Figure 4) show that Scheme 1 is inferior to the two other Schemes in terms of comprehensive evaluation values (0.135345) and is graded “Poor.” Scheme 2 is better (0.361641) and is graded “Moderate.” Scheme 3 is the best, but the comprehensive evaluation value is only 0.504761 and is graded as “Good.” All three schemes have some disadvantages and divide 10 islands, which affect China’s national maritime rights and interests to some extent. Experts are also concerned about the preservation of national marine rights and interests. In C31, it weighed 0.4353 while in C32, it weighed 0.2920. Furthermore, while having the lowest assessment values in sea area socioeconomic aspects, Scheme 3 has significantly higher evaluation values in expected effect factors. Scheme 3 is the best because the weights of natural resource factors, socioeconomic factors, and expected effect factors of sea areas are 0.1192, 0.0599, and 0.8207. Scheme 3, on the other hand, which has the highest overall assessment value, is only given a “Good” rather than an “Excellent” rating. From the standpoint of protecting territorial sea base points and optimizing the maritime boundary delimitation scheme, it is vital to maintain the integrity of 10 islands.Figure 4
Comprehensive evaluation values of the three schemes.


## 4.2.1. Evaluation of Natural Resource Factors in the Sea Area

Disputes over maritime areas are caused by competition for marine resources. In this study, four factors were added to the index system: sea area, island quantity, island area, and deep-water shoreline resources of islands. Other natural resource components of sea areas, such as marine biological resources, marine energy resources, and marine mineral resources, were left out since they were difficult to determine. According to research results (Table8 and Figure 3), Scheme 2 achieved the lowest evaluation value (only 0.191485) of natural resource factors of sea areas and is graded “Poor.” Schemes 1 and 3 achieved similar grades of natural resource factors, and the evaluation values are close to 0.7, which corresponds to “Good” and approaches “Excellent.” Such difference is related to the great gap in the sea area between Shandong and Jiangsu Provinces (520 km2) in Scheme 2, but similar sea areas of two provinces in Schemes 1 and 3. Moreover, the deep-water shoreline lengths of Shandong and Jiangsu Provinces differ to some extent (about more than 800 m) in Scheme 2, which accounts for about 10% of the total shoreline length. The evaluation values of natural resource elements in three schemes show that sea area division plays an essential role in maritime boundary delimitation schemes.Figure 3
Variations of evaluation values of the subsets of different schemes.


## 4.2.2. Evaluation of Socioeconomic Factors in the Sea Area

Socioeconomic factors are important attributes of marine resources. Aquaculture-oriented sea area, harbor, and shipping-oriented sea areas, number of aquaculture fishermen, and social stability that affect socioeconomic development in involved counties and cities were chosen as indices because the disputing sea areas between Shandong and Jiangsu Provinces have good conditions for aquaculture, harbor, and shipping development. Scheme 3 received the lowest socioeconomic factor evaluation score (only 0.24828) and was evaluated “Poor” based on the research findings (Table8 and Figure 3). Scheme 2 achieved the second-lowest evaluation value of socioeconomic factors (only 0.382137) and is graded “Moderate.” Scheme 1 is relatively superior, and the evaluation value is 0.526644, which is graded “Good.” These results can be interpreted from the following aspects. First, sea areas that are suitable for aquaculture in the study area are in the south, and a certain gap can be observed between the two provinces in terms of such aquaculture sea areas. Specifically, the gap in Scheme 3 is the largest, in which Jiangsu Province has 3000 ha (20% of total areas) more aquaculture-oriented sea areas than Shandong Province. Second, in Shandong Province’s Rizhao City, more fishermen are involved in marine aquaculture than in Jiangsu Province’s Lianyungang City. Shandong Province, on the other hand, has a lesser proportion of aquaculture-oriented sea waters in Scheme 3, which has an impact on social stability following the delimitation.


## 4.2.3. Evaluation of Expected Effect Factors

The expected effect refers to the expectations in resource protection and utilization in the disputing sea areas and socioeconomic development in involved counties and cities after maritime boundary delimitation. Territorial sea base points can be found in the Dashan Island in the disputing sea areas between Jiangsu and Shandong Provinces. According to the Measures for the Selection and Delineation of the Scope of Protection and the Protection of Territorial Sea Base Points, which are issued by the State Oceanic Administration, a certain sea area has been determined as the protection zone of territorial sea base points, which is inappropriate for segmentation. Strategic significance is superior. Although the proportional fairness validation index of maritime boundary delimitation cannot evaluate the quality of delimitation schemes, it can be used as reference data to determine the fairness of the delimitation schemes. Therefore, six indexes were chosen to evaluate the expected effect, including protection conditions of territorial sea base points in Dashan Island (C31), national maritime rights and interests guarantee capability (C32), sustainable development capability of disputing sea areas (C33), management difficulties of disputing sea areas (C34), acceptance of both parties to the delimitation schemes (C35), and fairness verification index of maritime boundary delimitation outcome (C36). According to the research results (Table8 and Figure 3), Scheme 1 had the lowest evaluation value (0.121451) of expected effect factors and is graded “Poor.” Scheme 2 shows the second-lowest evaluation value (0.365121) of expected effect factors and is graded “Moderate.” Scheme 3 is relatively better (0.502299) and is graded “Good.” This is because the evaluation of expected effect factors focuses on the integrity of 10 islands in the study area, and Scheme 1 divides islands more thoroughly, which can affect the maintenance of China’s national maritime rights and interests to some extent.


## 4.2.4. Comprehensive Evaluation of Delimitation Schemes

Research results (Table8 and Figure 4) show that Scheme 1 is inferior to the two other Schemes in terms of comprehensive evaluation values (0.135345) and is graded “Poor.” Scheme 2 is better (0.361641) and is graded “Moderate.” Scheme 3 is the best, but the comprehensive evaluation value is only 0.504761 and is graded as “Good.” All three schemes have some disadvantages and divide 10 islands, which affect China’s national maritime rights and interests to some extent. Experts are also concerned about the preservation of national marine rights and interests. In C31, it weighed 0.4353 while in C32, it weighed 0.2920. Furthermore, while having the lowest assessment values in sea area socioeconomic aspects, Scheme 3 has significantly higher evaluation values in expected effect factors. Scheme 3 is the best because the weights of natural resource factors, socioeconomic factors, and expected effect factors of sea areas are 0.1192, 0.0599, and 0.8207. Scheme 3, on the other hand, which has the highest overall assessment value, is only given a “Good” rather than an “Excellent” rating. From the standpoint of protecting territorial sea base points and optimizing the maritime boundary delimitation scheme, it is vital to maintain the integrity of 10 islands.Figure 4
Comprehensive evaluation values of the three schemes.


## 5. Conclusions

Comprehensive weights of different evaluation indices for maritime boundary delimitation schemes between Jiangsu Province and Shandong Province are calculated through the AHP-entropy weight method based on the established evaluation index system to identify the effects of natural resource, socioeconomic, and expected effect factors on maritime boundary delimitation schemes and relations among these factors. A fuzzy evaluation model is used to examine the influence of various factors on maritime boundary delimitation strategies. Historical border delimitation, angle bisector delimitation, and equidistance delimitation systems are explored for their benefits and drawbacks. Some measures to optimize the maritime boundary delimitation scheme are proposed. Some major conclusions can be drawn:(1)
According to the evaluation results of the historical boundary delimitation, angle bisector delimitation, and equidistance delimitation schemes, the fuzzy evaluation model fully considers the various factors, including natural resources, social economy, and expected effect. It can not only avoid a single factor's incompleteness, but also accurately express relationships between different factors. Furthermore, it can provide a full evaluation of maritime boundary delimitation strategies that is satisfactory.(2)
On the one hand, the weight calculation method based on the combination of AHP and entropy weight method avoids subjective influences caused by individual preferences. On the other hand, it offsets nonconformance to practical conditions in the entropy weight method caused by data variability bias. Hence, it provides a good solution to determine the weights of indices in marine boundary delimitation schemes.(3)
According to the analysis of various subsystems, “protection conditions of territorial sea base points in Dashan Island” and “national maritime rights and interests guarantee capability” in the expected effect factors are two important influencing indices. Their weights reach 0.4353 and 0.292, respectively, and also point out the direction for continuous optimization of the current equidistance delimitation scheme. In other words, the formulation of a maritime boundary delimitation scheme should consider the integrity of islands in bordering sea areas with the aim of increasing the comprehensive evaluation values and grades of maritime boundary delimitation schemes.The fuzzy evaluation model based on the AHP-entropy weight approach is used to evaluate the interprovincial marine boundary delimitation schemes in China. Natural resources, socioeconomic factors, and projected consequences on the quality of marine boundary delimitation systems are investigated. The correlation analysis of different factors provides theoretical references to evaluate the status of interprovincial maritime boundary delimitation schemes and formulate optimization measures. Because national marine rights and interests are an important direction for optimization of maritime boundary delimitation schemes, future studies should deepen further the overall protection and utilization of interprovincial sea areas. Furthermore, to increase the reasonability and scientificity of the evaluation outputs of maritime border delimitation schemes, the evaluation index system for maritime boundary delimitation schemes might include marine ecological indices.



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*Source: 2757779-2022-05-18.xml*