Application of MCDA to Rural Spatial Sustainability Evaluation

Application of MCDA to Rural Spatial Sustainability Evaluation: Comparison

Please note this is a comparison between Version 1 by Zheng Yuan and Version 2 by Zheng Yuan.

The rational allocation of spatial resources is an important factor to ensure the sustainable development of rural areas, and effective pre-emptive spatial evaluation is the空间资源的合理配置是保障农村资源的可持续发展，有效评估先人的空间资源配置是农村资源配置的重要指标。在研究的各个方面，已经证明了利用多维度评估结果的评估结果的更新研究。框架评估框架步骤的研究，研究。在统计和研究内容中进行回顾，并根据程序标准制定、权利分配、设备和三个常用操作进行比较和横向比较。通过结果确定了 prerequisite for identifying the predicament of rural resource allocation. Multi-criteria decision-making analysis has advantages in solving multi-attribute and multi-objective decision-making problems, and has been used in sustainability evaluation research in various disciplines in recent years.MC 方法在相关研究中的应用现状和特点，提出了未来的 5 个研究热点。

multi-criteria decision-making
rural areas
spatial evaluation
sustainability

一、简介

1.1。背景概述

Driven by the global evaluation of rnvironmental crisis, sustainability has gradually become the focus of rural development. The ultimate goal of sustainability can be seen as a balance between society, the economy, and the environment [1]. Rural sustainable developatial susment can be considered as a process of “sustainable governance of resources” [2]. Based on the urgent needs of sustainability refers t, the rational allocation of production, living, and ecological resources is of great significance to promoting sustainable rural development [3]. As the provider the claof these resources, space is the most important resource to support sustainable rural development [4]. Therefore, scientific sifipatial evaluation is a prerequisite for ensuring the rational allocation of rese other rural resources.

乡村空间可持续性评价是指研究问题的分类。即以可持续发展的目标和农村地区的空间资源为评价对象，旨在通过识别甚至改善空间布局来提高农村可持续发展的一个或多个方面。一般来说，现有的农村空间评价与“空间决策”一词密切相关，进而指导后续方案或策略的选择[ 5 ]。现有的乡村空间评价以可持续性为目标，涉及自然资源[ 6、7 ] 、公共设施[ 8 ]、能源服务[ 9 ]、规划设计[10 , 11 ]。先前的研究表明，与农村相关的空间评估或决策是一项复杂的任务 [ 12 ]。因此，实现可持续发展目标还需要基于知识生产的新决策方法 [ 13 ]。在过去的二十年中，多准则决策分析方法已应用于相关领域，以协助决策者。多标准决策分析可能是解决此类问题的有效选择。

1.2. 多标准决策

多准则决策（或多准则决策分析，以下简称 MCDA）是一种基本的科学方法，用于选择最佳备选方案、对备选方案进行分类或按优先顺序排列备选方案[ 14、15 ]。MCDM 一词用于涉及决策者用来推导偏好的多个相互冲突的标准的所有方法和技术 [ 14 ]。MCDA起源于运筹学领域。经过演进和发展， MCDA已广泛应用于管理科学[ 16、17 ] 、环境科学[ 18、19 ] 、地理学[ 18、20 ]、材料科学[21 ]、能源[ 22 ]、数学[ 23 ]、信息与计算机科学[ 24 ]等。近年来，MCDA方法已被用于辅助与可持续性相关的决策[ 25 ]。迄今为止，已有 100 多种 MCDA 方法在实践中得到应用，包括原始方法、派生方法和组合方法 [ 26 ]，但只有少数 MCDA 方法用于解决农村空间评价问题。

1.3. 文献综述

表 1 总结了与本研究具有相似性和相关性的两篇评论的详细信息。

Gebre et al. [27] provided a quantitative and desch problems. That is, with the goal of sustainable development andriptive review of the application of the MCDA approach to solving sustainable land allocation problems in rural areas. The study screened 69 articles from Web of Science, Science Direct, and Google Scholar for review. Quantitative and qualitative overviews were carried out on the basis of the categorized research problems. This review only focused on the research field of land use. It was not a comprehensive review of all disciplines. Secondly, some of the literature in this review dealt with policy decisions, and not all of them focused on the spatial issue of land allocation.

Mudashiru est al. [28] provided a qurces of rantitative and narrative review of the application of MCDA, statistics, and machine learning methods in sustainable planning and management to identify flood hazard-prone areas in rural areas as the evaluation object, it aims to improve . The review screened 84 articles from Science Direct and Scopus, of which 46 used the MCDA method. This review provided an overview of the application of different kinds of quantitative or semi-quantitative methods using a cluster analysis approach. However, the review only focused on the planning and management of flood hazards. Secondly, the review did not take into account the huge amount of data in the Web of Science database, and the duplication of Science Direct and Scopus may not be conducive to expanding the relevant literature. Finally, the study only summarized the application of MCDA with a descriptive narrative.

After reviewing the limitations and distinctions of the or more aspeabove reviews, we believe that a comprehensive review of the literature related to the topic of this study is warranted to provide detailed insights.

1.4. Research Purpose

In view of the fact that the application of the MCDA method to solve the problem of rural spatial sustainability evaluation is not clear, this review aims to:

(1)

Provide an up-to-date overview of the application of the MCDA method to the issue of rural spatial sustainability idevaluation;

(2)

Determintifying ande the specific research topic or unit ranges for which these MCDA methods are commonly used;

(3)

Identify theven improv criteria aspects most commonly considered in the MCDA process;

(4)

Determinge the spatial feature and distribution of MCDA methods in each operation stage in terms of time and research topics;

(5)

Clarifyout the focus of future research work.

This Greview will be usenerally, existing rural spatial evaluations ful in terms of the following aspects. Firstly, this review will help researchers and practitioners gain a detailed understanding of this research topic. Secondly, it introduces the commonly used MCDA methods in the research field, and provides guidance on the selection tendency of these methods.

The papere closely related to the term “spatial decision-making”, which in turn guides the selec consists of five sections as follows. In the “Methods and Data Sources” section, the classification of MCDA methods, the structure of the study, the sources of data, and the screening methods are introduced. In the “Primary Review Analysis and Results” section, the overview and trends of the literature are introduced, and several research topics and scopes are clarified. In “Detail Review Analysis and Results”, the application of MCDA methods in three stages of operation is analyzed. In “Discussion”, the results of the above two sections are further refined and fully discussed. The last section is the “Conclusion” of the research.

2. Methods and Data Sources

2.1. Classification of MCDA Methods

As a comprehensive evaluation methof subsequent programs or d, MCDA is suitable for solving complex problems characterized by uncertainty, conflicting goals, information heterogeneity, and diversity of interests or viewpoints, in addition to explaining dynamic development systems under the influence of multiple factors [27]. In contrast to the trategieditional single-criteria analysis method, the MCDA method has advantages because it can obtain the comprehens^{[ 1 ]}ive score or the ranking of the objects under the influence of multiple criteria [29]. TFrom the existing evaluation operspective of the attribute of the judgment subject, MCDA methods can be divided into three categories: multi-objective decision-making analysis (MODA), multi-attribute decision-making analysis (MADA), and comprehensive MCDA [30]. From the perspective of the operuation process and system composition, Figure 1 clearly shows the six operational space, aiteps and the three sub-systems of the MCDA method. At present, there is no unified classification standard for the criteria, but evaluation research aiming at sustainability, in usually divides the criteria into three categories: society, the economy, and the environment [31,32]. The index is used as a quantitative basis folves r measuring the quality of the criteria. From the perspective of using functions, Table 2 divides the MCDA methods commonly used in sustany aspectsinability evaluation into weighting methods and ranking methods, and some methods have both functions [14,25,30,31,33,34]. The weighting methodsuch as natural resou can be divided into the subjective weighting method and objective weighting method. The subjective weighting method depends only on the preference of the decision maker, and not on the quantitative measured data of the evaluation target. In contrast, the objective weighting method is obtained mathematically through the analysis of the initial data [31,35]. Both methods have their advantages and disadvantages. Subjeces, public facilities, energtive weighting is more explanatory and misleading, and objective weighting is resistant to interference, but sometimes exceeds the limits of research assumptions. Usually, in a complete multi-criteria decision-making process, at least one weighting method and ranking method are required.

2.2. Research Structure

Figure 2 presents the five main parts of this study and the services, and planning and design. Previouub-steps in each part. After the literature data were obtained and the research sample was determined, primary and detailed review analysis were carried out. Bibliometric methods have been widely and commonly used to evaluate and review existing research, and the analysis scope includes publication pattern research, bibliographic compilation, bibliographic coupling (co-citation and co-occurrence), and citation analysis (scientific papers and patents) [64]. This study used VOSvies have demonstrated that rural-relatewer 1.6.17 as an auxiliary tool for data processing in the primary review. Finally, according to the three operating procedures of criteria and index, weight and priority, and ranking and verification, the detailed review of the sample was analyzed from the vertical and horizontal perspectives, including a key literature commentary.

2.3. Bibliographic Search Engine Databases

This study spatiaelected five potential databases and identified their basic information [27,65,66,67]. Web of Science core collections evaluation or decision making is a complex task ^{[ 2 ]}(WOS), Scopus, Science Direct (SD), and Google Scholar (GS) are currently widely used literature databases. In addition, China’s rural area in 2021 is 8,868,577 square meters, and the rural population is 544 million, accounting for 7.93% and 16% of the world, and ranking second and third in the world, respectively. Its cereal production land comprises more than 100 million hectares, ranking first in the world [68]. Therefore, as the most important agrichievingultural country in the world, the research progress of China’s rural spatial sustainability goals aevaluation deserves attention. As the largest academic database in China, China National Knowledge Infrastructure (CNKI) was considered for this review. Table 3 clearly illuso requitrates the characteristics of each database for better understanding.

Through thes new approaches to decision ma above comparison, WOS, Scopus, and CNKI were selected as the final data sources for this study because of their relatively large database capacity and powerful search function. Science Direct was abandoned due to poor search functionality and high overlap with Scopus data. Google Scholar was excluded due to the singularity of the search function, the lack of categorical tags, and imprecise search results [69,70].

2.4. Data Extraction and Procedures

This study used the PRISMA framework to ing based on knowledge dentify the target literature for analysis. Previous studies have demonstrated the usefulness of the PRISMA framework for literature or data screening and further meta-analysis [71,72]. In terms of operoductioation steps, it is mainly divided into four steps: Identification, Screening, Eligibility, and In^{[ 3 ]}cluded [71].

Step O1—Identification: This study used “rural” + “spatial” + “evaluation” + “sustainable”, and the combination between them: “rural sustainability” + “spatial evaluation” or “rural” + “spatial sustainability” + “ever the pasaluation”, as topics and keywords in CNKI, Scopus, and Web of Science (WOS) Core Collection to search academic journals and conference papers before 31 December 2021.

Step 2—Screening: two decades, After removing duplicates, the above databases yielded 741, 186, and 113 articles, respectively. Then, the results were refined by “multi-criteria decision-making”, “multi-criteria decision-making analysis me”, and the names of MCDA methods in Table 2 to filter the evaluavtion literature using MCDA methods. This search resulted in 186 entries.

Step been applied in relate3—Eligibility: Further screening was based on the following principles to eliminate irrelevant entries:

(1)

The definition fields to assist decision makersof the keyword “rural” includes documents that take the suburban, urban–rural border, township, and rural areas as the research scope, and the documents that take the city as the research object alone were not included.

(2)

The Mu“space” referred to in this articlti-criteria decision-making analysis may be an effective and efficient option for solve is the concept of physical space in the category of geography, so the “space” of abstract content involving the universe, network, cogitation, and mathematics is not included in the scope of consideration. Furthermore, the space must be the evaluation object of the research, and the relevant literature must take the exploration of the spatial characteristics as the main purpose. If a study only referred to the research area of the geospatial attribute, and did not make space the evaluation object, it was not included.

(3)

Sustainability should be the research targ such problemset of the considered literature. These studies should identify or improve one or more aspects of rural sustainability through spatial evaluation using the MCDA approach.

Step 4—Inclulded: After ti-criteria dehe above screening, 103 documents were identified as the final sample for qualitative and quantitative analysis in this study.

3. Primary Review Analysis and Results

3.1. Journal and Publication Year

The amount of research on rural spatision making (or mal sustainability evaluation using the MCDA method has increased over time. Figure 3a shows that the number of relti-criteria decevant publications surged in 2015 and 2018, and showed a steady upward trend in other years. In terms of publication years, the overall trend has increased since 2002. Figure 3b shows the publicationsion-makin and citations of all journals. The number of related papers published in Land Use Policy is the largest. aThrough statistical analysis, hereafte of the published journals of the sample literature, it was found that the Land Use Policy journal referred to apublished seven related publications. By calculating the total citations of the journals to which the sample papers belonged, it can be found that Land Use Policy still MCDA) is a bashas the highest number, i.e., 334, so it can be considered to be an important journal for this theme.

3.2. Author, Organization and Country/Area

The geographical scientific method used to select the best alternative, classifdistribution of the study area is characterized by a greater number of studies in the Eastern Hemisphere, fewer in the Western Hemisphere, more in the Northern Hemisphere, and fewer in the Southern Hemisphere. The research institutions and personnel are mainly concentrated in Asia and Europe. Since the CNKI database mainly includes research documents of authors and institutions in China, in order to objectively show the global distribution of the research areas in the relevant literature related to the research topic, the global distribution statistics of the 67 English documents from WOS and Scopus were determined. The global distribution of the relevant literature is shown below (Figure 4). It can be seen that China, Turkey, alternatives,nd Italy are the top three countries in terms of quantity; Iran and Spain are close behind. According to the number of publications and citations, Table 4 shows that six impor rank alterntant authors and four research institutions in related fields were identified.

3.3. Keywords and Research Area

The 103 artives in ocles covered 26 research areas, four categories of keywords, and six research topics. Figure 5 shows all the research areas coverede by the sample and the number of preference ^{[ 4 ]}ublications in each field. Environmental Sciences and Ecology is the category having the most publications. Through the term MCDMco-occurrence analysis of the keywords, it can be seen that the most common keywords in the rural spatial evaluation research using the MCDA method are “Environmental science”, “GIS”, and “Science & Technology”. In order to compare the sample horizontally, it is a common to categorize topics according to the research field, content, problem, and goal [27,73]. Using VOSvis used for aewer 1.6.17 software to perform cluster analysis on keywords having a frequency of at least four, four categories were obtained (Figure 6). According to the content of keywords in the clustering, the above four categories can be defined as domain, target, probl em, and methods and techniq. In order to further determine the research focus, the above four categories of keywords and their related literature were screened, and six research topics were finally determined. Table 5 shows the names of the six research topics and the number of studies t in each topic.

3.4. Unit Range

From the perspective of the unit rat involve multnge delineated by the rural space evaluation, all articles could be divided into four scale categories: Regional scale (36.89%), District/county area (44.66%), Community/village (13.59%), and Architecture (2.91%). Figure 7 shows the correlation characteristics between ple conflicting criteria used by decision makers to derive preferences ^{[ 6 ]}ublication year, unit range, and research topic. The number of the related studies in Regional scale was relatively even in the past 10 years, whereas the studies involving District/county area and Community/village increased significantly in the past five years. With the exception of Habitat, which had the lowest number, and the Land use subject, which had the highest number, the Regional scale research had a relatively even distribution among the other four types of topic. With the exception of Conservation and Habitat, the distribution in District/county area is relatively even in the other four categories. Community/village research is involved in all six types of research topic, of which Habitat is the most distributed. Architecture research is only related to Conservation and Habitat.

3.5. MCDA Methods

Compared with other MCDA originated methods, AHP is the most commonly used. In this study, the clustering statistics along the time axis were carried out by the MCDA methods used in the fthree stages of the sample documents. Figure 8 shows that SAW was the earliest used MCDA method. Subsequentld of operations researcy, the AHP method was introduced for the first time in the sustainable evaluation of rural space in 2005, and the number of related publications has increased over time, especially in the past five years. PCM is ranked second, and Delph^[7]i and TOPSIS follow. Several other MCDAfter evolution and development, methods have been gradually applied in rural spatial sustainability evaluation research in the past 10 years. In particular, in the last four years, qualitative analysis methods such as SWOT and TOWS have also begun to emerge, in addition to the traditional MCDA has methods that rely on statistics for quantitative analysis.

4. Detail Review Analysis and Results

4.1. Criteria and Index

According to the ultimate goal of sustainability [1], the criten widely used in managementria system of most rural spatial sustainability evaluation studies includes the three categories of social, economic, and environmental content. In order to analyze the criteria components of the sample literature, the following equations were used to calculate the number of criteria in the evaluation system for the relevant literature in each year and each research topic.

Step 1: Calculate the resciencepective proportions of social, economic, environmental sc, or other criteria in a single article:

(1)

In Equation (1), is thence, geogr number of criteria for society, economy, environment, or other in a single article, and is the total number of criteria in a single article.

Step 2: Calculate the arithmetic mean of the phy, materialroportion of social, economic, environmental, or other criteria in the total n literature in the jth year:

(2)

Step 3: Calculate the proportion of socience, energyal, economic, environmental, or other criteria in the total m articles in a single research topic:

(3)

In Equation (3), is mathematicthe total criteria number of all studies in the corresponding research topic.

4.1.1. The Formulation of Criteria

Quantitative Analysis of Criteria

Although the earliest published literature in the sample is from 2002, information and cosince the literature before 2010 was mainly based on theoretical research and did not include empirical research on specific criteria data, 2010 was considered the starting year.

Figure 9 indicates that the number of criteria for the three categories of society, economy, and environment has generally exputer science, etc. In recent years, MCDA meterienced a slightly fluctuating upward trend since 2010. The overall number of environmental criteria is larger than that of social and economic criteria, and the number of social criteria is slightly higher than that of economic criteria. However, with the enrichment in research topics, the difference in research focus has led to subsequent fluctuations in the distribution of social, economic, and environmental criteria.

Figure 10 shodws have been used to assist decision makthat the number of criteria at the environmental category still accounts for a large proportion. With the exception of Tourism, the remaining five categories of topics all exceed 30%. The overall proportion of criteria at the economic category is still relatively low, especially in terms of Site selection, Tourism, Conservation, and Habitat. The social criteria accounted for the highest proportion in Habitat; Site selection and Tourism ranked second.

Content Analysis of Criteria

Firstly, the measuremeng related to sustainability. To date, more than 100 MCDA methods hat angle of environmental criteria is the most multi-dimensional factor. The element composition of the environment can be divided into atmosphere, water, soil, geological, and biological environments. The inherent characteristics of the environment can be classified into three types: capacity, stability, and complexity. Therefore, necessity and diversity lead to dominance of environmental criteria. Secondly, a number of studies do not strictly distinguish the three categories of society, economy, and environment to construct a criteria system. One of the most common approaches is to combine social and economic criteria [78,89,95,116,144,149,160]. Finally, the evaluation steps of crite ria are not single. Some studies regarding Site selection set up a multi-stage index system [20,110,158], by seen used in practicetting one or more constraint criteria systems as the access rules for screening samples before the spatial sustainability evaluation. The content involved in other criteria of each topic are shown in Table 6. In addition, Rahmoun et al. [138], starting from the cluding original oncept of “peaceful tourism”, selected criteria related to war or refugees to discuss the comprehensive planning and reorganization of tourism space in the coastal areas of Syria. Zhou et al. [76] aimed athods, derived methods helping China to overcome poverty, and selected indicators related to household livelihoods to explore the evolution of the mechanism of remediation policies and measures among different stakeholders in the process of land governance. In the research on the spatial sustainability of agriculture [74,156] and forestry [153], some schomlars have also considered the impact of household livelihood capacity.

4.1.2. Measurement of the Index

Equations (1)–(3) were used to calculate the distributined methods, but onon of the sample literature index measurement method from the perspectives of time and topic, respectively. According to the meaning and dimensions of the index, it can be summarized in terms of Proportion, Quantity, Area, Distance, and Others.

Quantitative Analysis of Criteria

Figure 11 indicates several indices have shown a slightly a few MCDA methodfluctuating upward trend and have maintained a relatively stable ratio in the past five years. The ratio of the Proportion index is the highest, and the Distance index ranks the second. The Area and Quantity indices have been apobvious alternations in some years, and the overall number is comparable.

Figure 12 shows that the ratio of Proportion is relied to solving rural spatial evaluation problematively high in Habitat and is the lowest in Site selection. The index of Quantity is the highest in Tourism, whereas it is lower in Site selection and Habitat. The Area index has the lowest overall proportion. The Distance index accounts for the largest proportion in Site selection, reaching 46%, whereas it is lower in other topics.

Content Analysis of Criteria

Table 7 shows the mea comprehensive evaluationsurement content of the four types of indices in each topic. In addition to the above objective quantitative measurement method, MCDA is suitable for solving complex problems chars, subjective and qualitative index measurement methods are also common. The use of a sociological questionnaire is one of the common ways to try to quantify the subjective wishes of respondents. In contrast to the Delphi method, the consultation objects are senior experts in the relevant professional fields. The objects of such questionnaires are usually the stakeholders. In Tourism, some scholars [132,139] conducted a questionnaire survey regarding the attracterized by unciveness, value, attention, and satisfaction of tourism resources, and finally obtained quantitative values of 1–10 or 0–1. In Habitat, some scholars [170,172] used a questionnairtaine to evaluate the accessibility, conflicting goals, informatimfort, safety, and multivalences of space with scores in the range of 0–1. The qualitative analysis methods based on SWOT and TOWS are different from the common enrichment data collection process, and mainly construct a conditional descriptive comparison matrix [86,138] or a simple pairwise comparison hetematrix with no more than three levels [146] to measure the evaluation objectives.

4.2. Weight and Priority

Figure 13 shows that the number of studies using theneity, and diversity subjective weighting method has grown steadily since 2011, and increased significantly since 2018, whereas the number of studies using the objective weighting method has gradually increased since 2017 and increased significantly in 2020.

Figure 14 shows the distribution of interests or viewpoints, in addition to explaining dynamic deveall methods in different topics. Due to the characteristics of the AHP operating process, the combination of AHP and PCM is the most common in the topics of Site selection, Tourism, and Habitat. The number using subjective weighting methods is also significantly higher than that using objective weighting methods, and 34% of the studies used a comprehensive weighting method; only three studies used a combination of subjective and objective comprehensive weighting methods. Table 8 shows the classificatiopment sn of comprehensive weighting methods.

4.2.1. Subjective Weight

Various typestems under the influence o of subjective weighting methods are used in the sample literature. The weighting methods not only include the more traditional relative comparison methods, such as AHP, Delphi, PCM, and fuzzy approaches, but also the network methods represented by ANP and BWM. Combinations of multiple fsubjective weighting methods are common. Although Delphi is used in combination with PCM, the relative importance of factors . In contrastin the pairwise comparison weight scale is determined by a group of experts related to the research topic. In Site selection, considering the practical significance of several level factors [105,110], AHP, ANP, fuzzy, Delphi, and DEMATEL meto the trahods have been used to assign weights to different factors at each level.

Karasan et al. [107] used DEMATEL to itional sidentify the most effective criteria and their internal and external dependencies. Boyaci et al. [112] examined the problem of epidemiologle-criteria analyical hospital site selection in the context of COVID-19 and used the PFN-enhanced AHP method combined with GIS to determine the weight of criteria for the first time. Regarding Land use, Cui et al. [93], based on the combis method, the MCDAnation of Delphi and PCM or AHP to determine the weights, introduced the fuzzy method has advantageto establish a semantic fuzzy judgment matrix, and finally used the fuzzy operator to comprehensively evaluate the degree of rural industry–city integration. Regarding Tourism, Zheng et al. [143] used because it can obtain the Delphi by combining experts, field interviews, and website scoring to determine the weights among the factors in the directional ANP network of rural tourism transformation and development. Jeong et al. [11] proposed a comprehensive deciscore or tion-making framework named MC-SDSS based on a web platform and several MCDA methods. Fuzzy-DAMATEL, PCM, and WLC were combined to ensure the relative objectivity and accuracy of weights.

4.2.2. Objective Weight

The objective weights used in the sample aranking ofe only used in Entropy, DEA, and BP networks. Regarding Land use, some scholars [77,85,87] introduced the Entrobjects unpy method mainly to revise the weights determined by existing research or the mathematical models used. In Tourism, researchers [132,136] used ther the influence of mu Entropy method to assign weights to the spatial factors affecting the accessibility and attractiveness of tourist destinations. In Urban–rural planning, some researchers used it to determine the weight of traffic accessibility indicators in rural mountainous areas [113,118], the spatial factipors affecting eco-agricultural development [115], or the spatiale criteriafactors that influence the orientation ^[8]of landscape functions [127]. From the perspective of the use of cross-step methods, the combinattribute of the judion of Entropy as a weighting method and TOPSIS as a ranking method is the most commonly used approach [79,80,113,118,127,164]. In addition, as an existing linear programment subject, MCDA methods cing model, the DEA method does not involve artificial weight distribution or calculations in the operation process, and is mainly used in the evaluation of tourism industry productivity [137], leisure agriculture efficien becy and driving factor evaluation [141], andivi the evaluation of the efficiency of tourism industry poverty alleviation [133]. According to thed into th advantages of the BP network in dealing with uncertain nonlinear complex relationships, Kong et al. [123] proposee categories: multi-d an improved PSO-BP network, which modifies the weights of neurons in each layer through machine learning to reduce the error signal, to determine the sorting potential of rural settlements in poor mountainous areas by continuous learning and tuning.

4.2.3. Comprehensive Weight

The number of studies using the comprehensive weight method combining subjective decisioand objective weights is still insufficient. Zhou et al. [78] used Entropy combin-ed with Delphi and PCM to determaking analysis (MOine the rate of contribution of government support, environmental pressure, resource endowment, and quality of life to the spatial differences in rural eco-development in arid regions of China. In Urban–rural planning, scholars [114,119] combined Entropy with Delphi and A), multi-attribute decisHP, and finally took the average of expert scores and entropy values as the weight of multiple factors affecting the quality or potential of sustainable development in villages and towns.

4.3. Ranking and Verification

4.3.1. Ranking and Aggregation

Quantitative Analysis of Ranking and Aggregation

Figure 15 and Figure 16 show that AHP remains the mon-making analysis (MADA), and comprehensive MCDAst commonly used ranking method, both in total and in each research topic, and its use has continued to rise over the past five years. After AHP, TOPSIS and ANP are the second and third most frequently used, respectively. TOPSIS is the most widely used method, after AHP, ^[9]in Site selection and Urban–rural planning. FANP is the most popular method in Habitat.

Aggregatiom the perspective of the opn is the final step to determine alternatives after sorting, and can be divided into the Hard Mathematical method, Soft Mathematical method, and Voting method, according to [31]. Table 9 shows the usage frequency of all aggregation process and system composition, Figure 1 methods. The usage frequency of the Hard Mathematical method is 75.73%, and this is the most commonly used aggregation method. Both the Soft Mathematical method and Voting method are at lower levels, accounting for 14.48% and 3.88%, respectively.

Content Analysis of Ranking and Aggregation

The TOPSIS method in Site selection or Urbarly shows tn–rural planning is widely used to deal with site suitability [9,98,102,103,107,112], scheme scomparison [115,118], traffixc accessibility [113,118], and influencing factoprs [79,80] by calculating the Euclidean distance between alternational steps anve projects and the optimal and worst solutions. ANP is used to solve system problems with a feedback mechanism in villages [116,143,162,169]. The fuzzy method is used the three sub-systems of theo solve the dilemma that a clear mathematical model cannot be established in the whole process of MCDA or in a certain link, so is often combined with other MCDA methods [75,102,104,106].

Figure 1. Operation process and system composition of MCDA.

DEA is used t present, there is no o assess the characteristics or influencing factors of tourism development by calculating the ratio between inputs and outputs [133,137,141].

In the aggregation calculationified classification standard for the crit stage after ranking, the Hard Mathematical method selects the optimal result by calculating the sum and average of the values (or scores) of all or specific alternatives. Based on the Hard Mathematical method, the Soft Mathematical method adds the human intervention of decision makers, and is used to solve the research problems of public participation [108,128,146,147] and conflicts of views [86,126,138,152]. The voting method determia, but evaluationnes the optimal result by selecting a number of stakeholders involved in the research problem to vote on the alternatives, and is mainly used to solve research aimin problems of public participation and community co-governance [93,122,145,157].

4.3.2. Verification of Data

Quantitative Analysis of Verification

According to the review of the sat sustainample, the verification methods can be divided into Empirical data, Previous research, Comparison between methods, SA, Monte Carlo, and some combinations of these. Figure 17 shows the distributility usually dion of all verification methods in different topics. Due to forecasts or lack of data, most of the studies did not verify the results. The usage rate of Empirical data ranked second; SA was used more frequently in Land use and Site selection.

Content Analysis of Verification

As one of the more commonly used verides the fication methods, SA is used 11 times in the sample [11,82,91,92,94,95,100,109,110,112,158], and is mainly used to test the standard score (oriteria into three categori performance measure) of the effectiveness of alternative ranking. Empirical data are verified by comparing the results of MCDA with the follow-up data of existing research objects or the existing situation of the implemented program. This approach is widely used to deal with regularity [86,90,120,155], the mechanis:m [87,149,156], and suitability [84,96,98,99,103,106] in Conservation, Land use, and Site seleciety, the economytion. The comparison between methods achieves the purpose of testing by comparing the results of multiple MCDA methods [85,104,109]. The operand the envition principle of previous research is based on the data or results of similar previous research as a reference for data verification [89,167].

5. Discussion

5.1. Discussion of the Results in Primary Review Analysis

5.1.1. Overview of Research Trends

The results in Section 3.1 show that 2015 anmentd 2018 were the years in which the related research increased rapidly. In 2015, with the signing of the Paris Agreement, ^[10]a unified global system of sustainability goals was established. Then, index is 2018, the Central Committee of the Communist Party of China incorporated the concept of green development into the new rural construction plan [174], which fusrther promoted as a quantitative bas the attention of Chinese academia on the spatial sustainability of rural areas. Driven by international events and national policies, the academic community began to reach a consensus [175,176], realizing that cons for measuideration of several factors and systems in rural areas is an important way to promote sustainable development.

The results in Section 3.2 show that the research areas are mainly concentrated in developing counthe quality ories or developing regions in developed countries. Because urban and rural development and its sustainability in developed countries have entered the era of the inventory update [177], and developing countriteria. Fres are still in the process of continuous urban and rural construction [178,179], global scientific research institutions and universities are paying m the perspore attention to the spatial sustainability research in rural areas.

5.1.2. Research Topic and Unit Range

The results in Section 3.3 show that the literature ctive of using functian be divided into six research topics. It can also be seen that related research has been widely focused on Environmental Sciences and Ecology, and the combination with the GIS platform has matured in the past 20 years via the use of clustering analysis [180]. From the results ins, Table 27, we can further see that dexivides the MCDA methods commsting studies are closely related to society, the economy, and the environment in the six topics. However, culture, as mentioned in “Culture: at the heart of SDGs”, proposed by the United Nations Educational, Scientific, and Cultural Organization [181], only involves Urban–rused in sustainability evaluation into weigral planning, Tourism, and Habitat. The number of relevant studies is still insufficient. Under the influence of frequent urban renewal, geopolitics, and boundary replacement, the preservation of cultural heritage is as important as the protection of the ecological environment.

The resultins in Section 3.4 show that a large methods and ranking methods, and some methods have both functions . The amount of existing research is focused on the macroscopic scale. The number of studies regarding Community/village is lower, and studies of Architecture are particularly scarce in the existing research, compared to the large-scale data acquisition that relies on satellites, remote sensing, monitoring, and even access to existing databases and data platforms. Extensive reliance on field surveys greatly increases the difficulty of data acquisition in small- and medium-scale research. The lack of specific data may have contributed to the scarcity of relevant studies.

The results in Section 3.5 show that theighting sample is dominated by traditional quantitative methods can be divfor enriching data. As shown by the frequency ranking of the MCDA method shown in Figure 8, the simple MCDA methoded into is used often in each research topic [31,73]. Most of the subjective weighting method and otudies using AHP in the weighting stage still continue to use it in the ranking step because of its versatility. Due to the convenience of mathematical model establishment and the existence of current software (such as Yaahp, EvaGear, and Super Decisions), Delphi, PCM, TOPSIS, and ANP are more frequently used. In recent years, the qualitative MCDA method has also begun to emerge gradually due to its simple operation and convenience; however, the number, depth, and accuracy of related studies are still insufficient.

5.2. Discussion of the Results in Detail Review Analysis

5.2.1. Criteria Aspects

The results in Section 4.1.1 show that the numbjer of environmective weighting method. The subjntal criteria dominates, whereas social criteria contribute more to Habitat, and economic criteria need to be considered in Land use and Urban–rural planning. In the context of the current global environmental crisis, from the multi-dimensional perspective weighting method deof elements and characteristics, focusing on a comprehensive evaluation of the status quo and potential of the environment has become an overall trend in the research on the sustainability of rural spaces around the world.

The results in Section 4.1.2 show that Proportion is thends only on the preference o most commonly used index. Since most of the statistical data in yearbooks and government websites are presented in the form of proportions, the convenient access channels have led to the dominance of the decision maker, and not on the quantitProportion index. In Site selection, measuring the distance between candidate addresses and the sensitive locations of the research question has been verified as the most effective approach by many studies [97,103,110]. However, compared tivo using straight-line distance measureement, in many cases [9,20,103,104,107,110,111] using distance datato measure may be more rigorous and scientific. The insufficient application of the eArea index in the evaluation target. In contraof rural spatial sustainability and few measurable factors are the weak points of the current research.

5.2.2. Feature and Distribution of MCDA Methods

The result,s in Section 4.2 show that the cobmbined use of subjective weighting method is obtained mathematically through the analysiss has dominated during the past 10 years due to the superiority of subjective weighting over objective weighting in terms of operational convenience. On this basis, PCM and Delphi are widely used for their simplicity and compatibility. The practical significance of criteria is considered in the formulation process in subjective weighting, but is greatly affected by the knowledge background and the existing cognitive structure of the initial dataresearcher establishing the criteria. The objective weighting eliminates human interference, but does not consider the actual meaning of ^[11]the indicator representation. Few Both methods have their advantexisting studies have used the combination of subjective and objective weights, but such a practice is very common in the fields of computer and management science [182,183]. The results in Section 4.2.2 shows that 12 of the 14 studies usinges and disadvantages. Su objective weights were conducted by scholars in the Chinese region, and only two are from other countries. Chinese scholars and their related research tend to use the method of objective weighting is more explanator. At present, no existing literature or data can explain the reasons for this phenomenon. According to the experience of the research team working in the countryside for many years, the complexity and misleading, and ocontradiction of multiple stakeholders in rural China is one of the possible reasons for the unconvincing use of subjective weighting.

The results in Section 4.3 shows that resistant to interAHP and TOPSIS are still the mainstream ranking methods; this finding is also in line with Gebre et al. [27]. Secondly, the effective application of TOPSIS to Site selerence, but sometimes exceeds the limction and Urban–rural planning has been demonstrated. The Hard Mathematical method is a widely used data aggregation method. The Soft Mathematical and Voting methods provide a more democratic aggregation process for public research problems that may cause multi-stakeholder conflicts [31]. The exists of research assumptions. Usually, in a completing research generally lacks a verification process. It is common to compare and verify the MCDA evaluation results through the existing empirical data, whereas the evaluation research of the prediction type is often unable to verify the results due to the lack of effective follow-up data. In this case, mathematical verification models such as SA and Monte Carlo may help to verify the validity of the results.

5.3. Limitations

The literature reviewed multi-criteria decision-makin this study is limited to the WOS, Scopus, and CNKI databases. Because the bibliometric analysis of the database generated by only relying on a string search may produce misleading results, the manual screening process, at least one weight of the team was added on the basis of an automatic search. Although the researchers tried their best to screen out the literature that contains all relevant keywords, some literature may have been missed due to some unique keywords. Therefore, establishing a literature capture or cleaning method and ranking method are requiredbased on advanced algorithms is an important technical path to more accurately determine the relevant literature in the future.

Table 2. Classification of MCDA methods based on functional perspective.

Method	Function	Introduction
AHP	Subjective weight ranking	AHP was first developed by Saaty (1980). It consists of a pairwise comparison, using relative values of criteria (weights) and a score scale on alternatives against criteria. Typically, eigenvalue techniques or regression analysis are used to determine the ordering. AHP is one of the most common MCDA methods.
ANP	Subjective weight ranking	The analysis process of ANP and AHP is roughly the same, but in contrast to the one-way process of AHP, ANP has a feedback mechanism.
BP network	Objective weight ranking	BP network is a type of supervised network based on error back-propagation. Through the calculation and feedback of input information, output information, and the error, the weights of neurons in each layer of the BP network can be modified to obtain the minimum error signal and form the final network model. The learning process of the neural network is mainly the updating process of weights.
BWM	Subjective weight ranking	BWM can obtain weights for different criteria based on pairwise comparisons, requiring less comparison data. Quite differently from AHP, BWM only performs reference comparisons, which means it only needs to use numbers between 1 and 9 to determine the preference of the best criterion over all other criteria and the preference of all criteria over the worst criterion. This process is easier, more accurate, and less redundant because it does not perform quadratic comparisons.
DEA	Objective weight ranking	DEA is a nonparametric productivity measure for multiple-input and multiple-output operations. The method combines and converts multiple inputs and outputs into a single efficiency metric. This approach first establishes an “efficient frontier” formed by a set of decision-making units (DMUs) exhibiting best practices, and then assigns efficiency levels to other non-boundary units based on their distances to the efficient frontier. Finally, the efficiency level of each object is obtained.
Delphi	Objective weight	The Delphi method is a systematic, interactive method that relies on a group of independent experts. Based on this principle, Delphi uses carefully selected experts to answer questionnaires to determine weights. After each round, the summary of the previous round of expert selection and the reasons for their judgment will be fed back to the experts. During this process, the floating range of the weights will shrink and gradually converge towards the “correct” weights. Finally, the process is stopped according to predefined rules.
DEMATEL	Ranking	DEMATEL is considered for an effective method for identifying the components of the causal chain of complex systems. It handles the interdependencies among the evaluation factors and finds the key factors through a visual structural model. The DEMATEL technique can convert the interrelationships between factors into an understandable structural model of the system and divide it into cause and effect groups. Its operation consists of four steps: 1. establish an influence matrix; 2. create a normalized matrix; 3. build a total influence matrix; 4. generate an influence graph.
ELECTRE	Ranking	ELECTRE is a technique for selecting the best alternative from a given set of alternatives. It uses pairwise comparisons of alternatives and sets ranking relationships on them. For example, if a is at least as good as b for criterion i, then alternative a is ranked higher than the alternative b. The ELECTRE tool has evolved over time into different sequential versions, such as ELECTRE I, II, III, IV, and ELECTRE TRI.
Entropy	Objective weight	Information entropy is a measure of the degree of disorder in a system. It can measure the amount of useful information with the data provided. When the value difference between the evaluation objects of the same indicator is large, but the entropy is small, it means that the indicator provides more useful information, and the weight of the indicator should be set correspondingly high.
Fuzzy	Subjective weight Ranking	Due to the availability and uncertainty of information, as well as the ambiguity of human perception and cognition, most selection parameters cannot be given accurately. The fuzzy set provides a mathematical model to determine the membership degree of each element to the set, so that the applicability evaluation data of various subjective standards and the weight of the standard are converted into numerical values by the language of the decision maker.
Grey relation	Ranking	The grey relational method is a branch of grey system theory developed in 1980. The method is similar to TOPSIS, which defines the grey relational degree to represent the closeness between the alternatives. Typically, ideal scenarios are defined and the degree of relevance of alternatives to them is calculated. The most relevant alternative has the shortest distance from the ideal solution and the longest distance from the worst solution.
MAVT (MAUT)	Ranking	MAUT is a systematic approach that takes into account decision makers’ preferences in the form of a utility function defined over a set of attributes. Its functional form is determined by applying preference validation and setting certain utility-independent conditions. The formula is extended to derive a multi-attribute utility function. In the case of MAVT, the difference between utility and value is that the function uses attribute values instead of quantitative attribute measures in a cardinal scale.
OWA	Ranking	The OWA method is similar to WLC, but considers two sets of weights. The first set of weights controls the relative contributions of specific criteria, and the second set of weights controls the order in which the weighted criteria are aggregated. The advantage of OWA is that a variety of different solutions and forecast scenarios can be generated by reordering and changing standard parameters.
PCA	Objective weight	The modeling properties of PCA are largely rooted in regression thinking: variation explained by principal components. After introducing the idea of linear combination of variables, the change in principal components is emphasized. When there is a certain correlation between the two variables, it can be explained that the information of the two variables reflecting the subject overlaps to a certain extent. Principal component analysis is to delete duplicate or irrelevant variables for all the variables originally proposed, and establish as few new variables as possible, so that these new variables are unrelated to each other. Finally, the importance of the variable is obtained.
PCM	Subjective weight	In the pairwise comparison method, participants are presented with a worksheet and asked to compare the importance of two criteria at a time. The scoring scale can be varied, for example, an odd scale of 1 to 9 is often used. Results are combined by adding the scores obtained for each criterion, when the preferred criterion is compared with the criterion to which it is compared. The results are then normalized to a total of 1.0. This weighting method provides a framework for comparing each criterion to all others and helps to show differences in importance between criteria.
Regime	Ranking	The regime method is a discrete multiple evaluation method suitable for evaluating projects and policies by processing qualitative and quantitative information. It uses pairwise comparisons to evaluate the performance of alternatives and establishes ranking relationships among alternatives. The framework of the method is based on two kinds of input data: an influence matrix and a set of weights.
SAW	Ranking	The SAW method, originally applied by Charles (1954), is one of the most commonly used MCDM techniques. The method performs a simple multi-product summation of each criterion score through the corresponding attribute weights to find an overall performance measure for each alternative.
SWOT	Ranking	SWOT analysis is a common tool for strategic planning and a form of brainstorming. It helps organizations better understand their internal and external business environment when making strategic plans and decisions by analyzing and locating their resources and environments in terms of four areas: strengths, weaknesses, opportunities, and threats.
TOPSIS	Ranking	TOPSIS means that the optimal selection scheme has the shortest Euclidean distance from the ideal solution and the largest distance from the negative ideal solution. Intuitively, based on the distance from the ideal solution, the method can take any number of attributes as input. However, TOPSIS can produce unreliable results, and it also does not account for the uncertainty of the weights.
TOWS	Ranking	TOWS matrix is a derivative type of SWOT. In contrast to the SWOT method, TOWS focuses more on the solution strategy obtained through the situation analysis. The matrix includes four strategies: WT, WO, ST, and SO.
VIKOR	Ranking	The VIKOR method is similar to the TOPSIS method in that both are based on distance measurements. In contrast to the strict sorting of TOPSIS, VIKOR seeks a compromise solution. The VIKOR method can also provide clustering capabilities when faced with alternatives.
WASPAS	Ranking	The WASPAS method combines the historical data and current data, and adds the weighted sum model (WSM) and the weighted product model (WPM) to determine the decision target under the corresponding decision criterion.
WLC	Ranking	WLC is an evaluation function method, and is a method of solving multi-objective/attribute programming problems by assigning corresponding weight coefficients to each objective according to its importance, and then optimizing its linear combination.

FIn this review, a detailed analysis om the existing research situation, there arf other software or tools used in conjunction with the MCDA method was not performed. The combination of the MCDA method with interdisciplinary software or tools has implications for improving the accuracy of rural spatial assessments. Therefore, its specific coupling usage rules need to be further explored in future research work.

6. Conclusions

Based the following characteristics and trends:

on the overall trends and research content, this study conducted a comprehensive review of 103 studies around the world according to the three common operation steps of the MCDA method and vertical and horizontal comparisons.

(1)

During the past 5–8 years, the evaluation of spatial sustainability in rural areas has gradually become a popular research topic due to the worldwide environmental crisis. More research has been published in the Eastern Hemisphere, less in the Western Hemisphere, more in the Northern Hemisphere, and less in the Southern Hemisphere. China, Turkey, and Italy are the three countries producing the most publications. Developing countries or developing regions in developed countries comprise an important zone for related research.

(2)

The literature can be divided into six research topics: Land use, Site selection, Urban–rural planning, Tourism, Conservation, and Habitat. The target area of the study consists of four scales: Regional scale, District/county area, Community/village, and Architecture. Macro-scale research is relatively mature, but that of Communities/villages and Architecture is still insufficient.

(3)

Due to the urgent needs of the environment, the impact of environmental indicators on research problems and goals should be first considered in the process of criteria formulation. Social and economic criteria are secondary considerations. The contents of other criteria can be formulated with reference to Table 6. Proportion is the most commonly used index type, and Distance is one of the most effective index types in Site selection. The content involved in the index can be formulated with reference to Table 7.

(4)

The subjective weighting method is still used in mainstream research, with AHP being the most prominently used approach. Delphi and PCM have excellent applicability in most research topics. For the problems in Site selection and Urban–rural planning, TOPSIS is a more effective MCDA method. Objective weighting is an ideal method for solving problems in Land use, Urban–rural planning, and Tourism. The evaluation of rural spatial sustainability is a very complex problem, and the use of only a single MCDA method has limitations. A hybrid MCDA approach is the preferred option. The Hard Mathematical method can handle most situations, but the Soft Mathematical and Voting methods are recommended for issues involving public participation. The comparative verification of empirical data is a more intuitive method, but when data are lacking, statistical models can be considered.

Based on the above analysis, the following points were identified for future research work:

(1)

This study found that, although there are fewer rural studies in developed countries, they are limited by the method and region. Hence, determining the difference in the focus of research on spatial sustainability assessment in developed and developing countries is one of the issues worthy of further study.

(2)

In the current research on the evaluation of the sustainability of rural space, the consideration of cultural factors is one of the research gaps. As the core of sustainable development goals, cultural factors need to be paid more attention. Therefore, the research of sustainable space evaluation related to rural cultural heritage will be an important topic for future work.

(3)

Against the background of a rapid marginal expansion of related research fields and frequent interdisciplinary penetration, establishing a relatively complete data collection and sharing mechanism within the scope of small- and medium-scale units is basic work that urgently needs to be undertaken in the research on rural spatial sustainability.

(4)

Important means to improve the accuracy of rural spatial sustainability evaluation include expanding the types of feasible measurement criteria and indices; increasing the combination of subjective and objective weights; further clarifying the boundary conditions for the use of the deterministic MCDA methods; and adding auxiliary verification for predictive evaluation.

(5)

Identifying different characteristics and orientations of rural spatial sustainability research issues, and adopting appropriate quantitative or qualitative MCDA methods, can provide a theoretical basis for formulating a scientific and reasonable evaluation system, so as to provide a decision-making reference for more active and effective promotion of rural sustainable development. The proposal of a scientific and comprehensive MCDA selection list according to research fields, topics, and goals is still an important challenge for future research.

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