# Industrial Land Performance Assessment Based on Fuzzy Analytic Hierarchy Process

Authors: Jing Lv; Sijia Ge
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The use of industrial land tends to be standardized and rational, but the total amount of developed industrial land has reached its limit in many places. Under such circumstances, industrial transformation and upgrading are difficult, and how to improve the quality and efficiency of the stock space must become the key to the problem. Therefore, this paper proposes to take X city industrial land as the research object, with the help of multidimensional feature analysis of spatial performance evaluation, and apply the method of Fuzzy analytic hierarchy process to explore the refined utilization of industrial land promoted by spatial calculation. Through example analysis, the results of site-specific spatial performance evaluation are derived by using various weighted evaluation factors.


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## Body

## 1. Introduction

With the acceleration of global industrial reform and urbanization, the “bottom-up” process of rural industrialization has led to a low threshold for industrial land access, which is reflected in a high degree of spatial fragmentation and wasteful allocation of resources. Although the intensive industrial land development model of “farmers in the city, industry in the park” has been the mainstream of planning since the 1990s, the complex entanglement of property rights and the redistribution of differential land rent have made this model unsustainable. With the advent of the new economic norm, land is bound to undergo a functional transformation. How to find a balance in the reform and how to scientifically judge the reorganization function of urban and rural land is an urgent issue for local governments in the Pearl River Delta. The spatial performance of land use is a reflection of the comprehensive effectiveness of urban land use function. The systematic study of “urban spatial performance” according to the law of urban space operation is conducive to improving the effectiveness and relevance of planning disciplines and planning practices. Only by meeting the development needs of various urban functions to the maximum extent and allocating various spatial resources reasonably can we effectively improve the comprehensive benefits of cities. Therefore, the establishment of a spatial performance assessment system for industrial land can help the government scientifically formulate public policy tools, including urban planning, and facilitate the effective operation of the land market. Currently, China’s industrial economy is moving toward a new normal of slow speed and good structure, facing problems such as industrial structure adjustment and stable growth rate, development of high-tech industries, and the tightening of resource and environmental constraints [1].Development zone construction includes regional development such as economic and technological development zones, high-tech development zones, bonded zones, border economic cooperation zones, tourist resorts, and similar regional development projects such as industrial parks. With the rapid development of various development activities, the demand for land in China is increasing at this stage and land development has to be expanded to land that was previously considered unsuitable for development. The construction of development zones is bound to occupy a certain amount of agricultural land, thus making the conflict between industrial land and agricultural land increasingly acute. According to statistics, in 2000, China had 128 million hm2 of agricultural land with 0.101 hm2 of agricultural land per capita, less than half of the world’s per capita agricultural land. In 2000, various kinds of construction occupied 163,000 hm2 of agricultural land, according to which, the situation of land resources in China is very serious. Moreover, from the total natural productivity of land in 2000, the annual biological production is about 32 × 108 tons of dry matter, and the reasonable carrying capacity of the population is 950 million. Land resource conservation and rational development and utilization of land resources are the urgent problems facing the sustainable use of land in China.As an important carrier of industrial undertaking, China’s industrial land has maintained rapid growth and has undergone changes from scattered layout to park agglomeration. At the same time, due to the dual effects of urbanization and post-industrialization, the overlap between industrial land and urban land, lack of planning, duplication of structure, and confusion about the layout of industrial land have become increasingly acute. Ensuring the rational layout and effective supply of industrial land and promoting the safe integration of production cities have become bottlenecks in the development of many cities. Space security for industrial land will be directly related to the socio-economic and ecological security of the region and the scientific assessment of the space security of industrial land will be conducive to optimizing the allocation of land resources. Realizing the “win-win” between industrial development and land space security finally realized the integration development of town, people, and industry in function and space, that is, the integration of production city [2].In regional natural resources, land resources are non-renewable resources on which the regional economy depends. It has become an important part of urban ecosystems through various construction activities, such as regional infrastructure land, corresponding supporting facilities in parks, etc. However, if the land to be exploited and the whole natural environment are not clearly understood, the capacity of natural environment and the appropriateness of land use are ignored, the overexploitation will lead to the occurrence of natural disasters, ecosystem damage, and other serious ecological negative effects.Economic development will lead to the destruction of the ecological environment. But as the population grows and the demand for consumption increases, there is also an urgent need to develop the economy to improve people’s lives [3]. To coordinate the relationship between the two in the face of the contradiction between economic development and ecological protection, a win-win situation is an important task [4]. History has told us that the path to pollution and then management is not feasible. Therefore, according to the principle of ecological priority, the quality of the ecological environment can be reasonably evaluated to determine whether it is suitable for industrial development. To put forward, reasonable environmental protection measures for existing problems will play a fundamental role in regional sustainable development and ecological environment management. Therefore, for urban land resources, cherish every inch of urban land, we should develop and utilize land resources scientifically and rationally.Theoretical studies on the ecological safety of industrial land have always accompanied the stages of industrial development. At the early stage of industrialization, the ecological safety of industrial land mainly focused on suitability evaluation [5], and the scope of research ranged from individual industrial parks to cities [6] and larger regions [7]. With the explosive growth of industrial parks, intensive and economical utilization within the industrial land has gradually become the focus of research [8], and scholars have combined different scales to propose various evaluation indexes [9], mainly involving the degree of land development, the degree of land input, land use intensity, land use efficiency, and land structure. With the advent of post-industrialization and comprehensive urbanization era, scholars mostly start from the urban construction land as a whole and conduct research on the evolution of urban spatial structure [10], urban land scale boundary [11], and optimization of land use pattern [12] to provide technical support for the safe and efficient use of urban land [13]. In contrast, there are few studies on the relationship between the layout of industrial land and other land and the performance evaluation of industrial land layout.After reform and opening up, the development of both local and foreign industries is based on cheap resources, including land, labor, environmental costs, etc., and with the process of the localized economy, many small industrialized towns are formed, becoming the main areas carrying primary processing industries. However, after the rapid development of these small towns in the early stages, the characteristics of inadequate land use and inefficient land use gradually emerged. On the one hand, the proportion of industrial land has long exceeded reasonable limits. For example, in some small towns in the Yangtze River Delta and the Pearl River Delta, the built-up area covers not only the entire town area but also the proportion of industrial land far exceeds the standard. On the other hand, the industrial structure is unreasonable, used inefficiently, and occupies a large amount of land. Related research reveals the fragmentation and inefficient utilization of industrial land at different levels and gives the countermeasures in combination with the forming reasons, but it is limited to qualitative research whether it is an integrated layout or optimized configuration. The land use performance evaluation can be traced to the land rent theory of classical political economy at the earliest. However, in China, due to the restriction of industrial land data acquisition, the performance evaluation can be carried out gradually after 2000. The content of the evaluation usually focuses on the intensity of industrial land development, input and output, and economic benefits, and different methods are used for industrial land performance evaluation (1) to strengthen the intensive use of industrial land by evaluating the intensity of land use, the degree of input, the efficiency of use, and other core elements [14], and to propose ways and measures for intensive use of industrial land; (2) to explore ways and systems for the supply of industrial land, to study the performance of industrial land use using an industrial land renewal benefit reduction mechanism or an industrial land use based on liability positioning method [15]. A quantitative evaluation study on the performance of industrial land supply, and according to the development process and characteristics of industrial land in China, explore the path of innovation evaluation [16]; (3) to update the stock of industrial land, quantify it with indicators such as location, plot ratio, production efficiency, property rights, etc., performance evaluation of inefficient industrial land through hierarchical analysis and to explore the application in planning control [17]. These studies are gradually establishing methods for evaluating the performance of industrial land in different dimensions. The evaluation, however, ignores businesses that are land users. This is the core element of the current industrial development and transformation period.The regional land ecological environment is a complex giant system containing many factors. Only by reasonably selecting the evaluation factors, establishing a hierarchical index system, and assigning reasonable weight values to each index can, we ensure the reasonableness of the evaluation results. Since the evaluation of regional ecological environment quality involves not only a large number of complex phenomena and the interaction of many factors, there are a lot of fuzzy phenomena and fuzzy concepts in the evaluation, which requires a clear quantitative concept to reflect the severity of ecological damage, but also requires that the quantitative index can appropriately reflect the inherent criteria of environmental quality classification and the continuity of environmental quality changes. The fuzzy theory is an effective tool to deal with the problem of ambiguity. Therefore, in this study, the Fuzzy analytic hierarchy process (FAHP) was considered for the evaluation of industrial land performance indicators. The specific technical route is described in Figure1.Figure 1
Schematic diagram of the basic research route.


## 2. Fuzzy Analytic Hierarchy Process

### 2.1. Fuzzy Set Theory

Fuzzy mathematics is based on the theory of fuzzy sets. The concept of fuzzy sets corresponds to the classical notion of either/or sets, describing sets without clear and well-defined boundaries. It emerged in the 1960s as a mathematical approach to the study and treatment of “fuzzy” phenomena. The so-called fuzziness refers to the indistinctness and uncertainty of objective things, which is rooted in the existence of a mid-valve transition between objective differences, such as “good and bad” in the evaluation of environmental quality. In daily life “Early and late,” “more and less,” etc., are difficult to draw a clear line. Auxiliary mathematics is based on set theory. According to the requirements of set theory, an object either belongs to a set or not. There are no ambiguous cases of belonging and not belonging at the same time. This precision of set theory greatly limits its scope of application. It makes it unable to deal with the ambiguities of everyday life. Faced with this situation, in 1965, the American cybernetics expert Zadeh [18] published his famous paper marking the birth of the new discipline of fuzzy mathematics. Although only 40 years have passed, the development of fuzzy mathematics has been exceptionally rapid, and its application has involved almost all fields and sectors of the national economy. Fuzzy mathematics has been widely and successfully used in agriculture, forestry, meteorology, environment, geological survey, military, and other fields.The theory and method of fuzzy mathematics show its superiority when the object cannot be accurately described by classical mathematics. The appropriateness of industrial supervisory land is determined by various factors. When evaluating the suitability of industrial land at the location of the development zone, it is impossible to get a very precise result. The main problems that need to be determined by the evaluation of fuzzy mathematical theory are the determination of factor weight, the establishment of affiliation dispersion, and the selection of the evaluation model.The main difference between fuzzy sets and ordinary sets is that there are only two relations between elements in the domain and ordinary sets. There are many relationships between fuzzy sets and elements, which can be represented by any value on [0, 1]. Taking “0” means that the element does not belong to the fuzzy set, taking “1” means that the element belongs entirely to the fuzzy set, taking “0.3” means that the element belongs to the fuzzy set to a degree of 0.3, and so on. The number taken is called the affiliation of the element to the fuzzy set. Affiliation is an indicator of the fuzziness of characterization factors. It can be said to be the cornerstone of fuzzy sets is applied to practical problems. If this affiliation varies with a variable, the affiliation function needs to be established. The membership function is generally denoted byA(x).To solve a practical problem, generally, is to determine the degree of affiliation function scatter. However, the affiliation function is often not declared and given, and its determination is generally approximated by using the method of inference. Its determination process is objective in nature. However, a certain amount of artificial skill is allowed, and sometimes the artificial skill plays a decisive role in the solution of the problem. It is worth noting that the artificial skill should be reasonable and not contrary to the objective reality. It can be given by fuzzy statistical tests or by the typical function method summarized by practical experience.The weight coefficient is a quantitative description of the importance of each factor in the evaluation domain, which can be regarded as the affiliation of each factor in the evaluation domain with respect to the “importance.” The assigned weights in common evaluation problems are generally subjective based on experience and are highly subjective. In some cases, the subjective determination of weights has an objective aspect and reflects the actual situation to a certain extent. However, in most cases, the evaluation results of the subjective determination method are usually seriously distorted and may lead to misjudgment of decision makers. As a rule, mathematical methods should be used more often to determine weights, although they are also subjective in nature. However, due to the strict logic of mathematical methods, the determined weights can be processed, thus eliminating as much subjective components as possible and conforming to objective facts.There are various methods for determining the weights, such as expert empirical estimation, survey statistics, hierarchical analysis, fuzzy inverse equation method, and sequential synthesis method. The literature points out that the accuracy of the hierarchical analysis method in weight calculation is relatively better [19]. Moreover, the hierarchical analysis method requires less data, takes less time to score, has less computational effort, and is easy to understand and master. In view of the advantages of the hierarchical analysis method, and considering the popularity and relative objectivity of the expert empirical estimation method in practice, this study uses the combination of the hierarchical analysis method and the expert scoring method to determine the weights of each index affecting the suitability of the industrial land.The analytic hierarchy process (AHP) is essentially a way of thinking about decision-making, that is, decomposing a complex problem into component factors, grouping these factors into an orderly hierarchical structure according to the dominant relationship, determining the relative importance of each factor in the hierarchy through a two-by-two comparison, and then integrating human judgment to determine the total relative importance of each factor. This is a reasonable way to solve the process of quantifying qualitative problems. The basic steps of using hierarchical analysis to solve the intrusion problem are as follows: (1) clarify the problem and establish the hierarchical structure; (2) construct a two-by-two judgment matrix; (3) calculate the relative weights of the elements being compared; (4) calculate the combined weights of the elements in each hierarchy.Defining the problem and establishing the hierarchy is the most important step of AHP. First, the complex problem is decomposed into component elements, and these elements are divided into groups according to different attributes to form different levels. The elements of the same level act as a criterion to dominate some elements of the next level, and at the same time, it is dominated by the elements of the previous level. This top-down dominance relationship forms a hierarchy. A typical hierarchy can be represented in Figure2. In a recursive hierarchy, the number of levels generally depends on the complexity of the intrusion and the level of detail required for the analysis. The number of elements contained in the same hierarchy is usually no more than 9. The number of elements included is too large, which can make it difficult to compare two comparisons. The index system established in this study is a recursive hierarchy, including three levels, target level, criterion level, and sub-criterion level, in which the regional industrial land suitability level is the target of evaluation.Figure 2
Schematic diagram of the recursive hierarchy.The hierarchical analysis method is also based on expert survey scoring, but the method of comparing grading and calculating weight coefficient is different. The experiments show that when people compare the different important degrees of multiple factors, they cannot compare and judge too much. Usually, the number of factors a person can compare simultaneously cannot exceed 9. However, a comparison of the degree of importance difference between the two factors. Man is perfectly competent. Therefore, the “two-two comparison method” can be used for multi-factor weight analysis, and only two factors are of relative importance to each other inn factors. A measure of relative importance between factors is called a judgment scale.


### 2.2. Fuzzy Integrated Evaluation

Here, it is assumed that the upper-level element C is the criterion or sub-criterion, and the elements governing the next level areu1,u2,…,un. The judgment matrix is the basic information of the hierarchical analysis method, and it is also an important basis for the relative importance calculation of each factor in this study. The judgment matrix is a two-by-two comparison of the elements of this level to determine the elements in the matrix with the upper-level element C as the evaluation criterion, and the judgment matrix with n factors with C as the evaluation criterion is as follows in Table 1.Table 1
Form judgment matrix.
Cu1u2…uj…unu1a11a12…a1ja1nu2a21a22…a2ja2n…………………uiai1ai1…aij…ain…………………unan1an1…anj…annSo the judgment matrixA could be expressed as equation (1):(1)A=aijn×n.In the general evaluation problem, the evaluator cannot judge the value of the weight indicatorwi/wj very precisely, but can only estimate it. If there is an error in the estimation, it will inevitably lead to deviations in the eigenvalues of the judgment matrix as well. This means that the judgment matrix obtained by the two-by-two comparison method may have inconsistent judgments, so a consistency test is required. By consistency, it means that when X1 is more important than X2 and X2 is more important than X3, then X1 must be considered more important than X3. When the judgments are in complete agreement, there should be λmax=n. Consistency indicators, CI, can be written as equation (2):(2)CI=λmax−nn−1.When consistent, CI = 0, andCI>0 when non-consistent. Regarding how to measure the acceptability of CI values, Saaty [20, 21] constructed the most inconsistent case by taking 1/9,1/7,1/5,…,5,7,9 randomly taken values of elements in the judgment matrix for different n, and used 100 to 500 subsamples for different n to calculate their consistency indexes, and then found the average value, noted as RI.Fuzzy synthesis evaluation is a proven decision-making method to solve multi-factor and multi-indicator synthesis problems. It applies the characteristics of fuzzy relationship synthesis and makes a comprehensive evaluation of the affiliation level of the evaluated thing from multiple indicators according to the given evaluation criteria and the measured values. It divides the change interval of the evaluated thing and analyzes the degree of the thing belonging to each level, which makes the description of the thing more in-depth and objective, and the analysis result more accurate. The operation process of fuzzy comprehensive evaluation is shown in Figure3.Figure 3
Fuzzy comprehensive evaluation flow diagram.One-level evaluation is the basis of multi-level evaluation. Generally speaking, the first-level fuzzy comprehensive evaluation is carried out mainly in the following steps.(1)
Determine the set of factors and the set of comments to establish the set of factors and the set of comments is the first step of evaluation. A fuzzy comprehensive evaluation is a comprehensive evaluation that considers all factors related to the evaluated thing, and its focus is on all relevant factors to be considered. Therefore, a factor set is created. To clearly describe the evaluation results, it is necessary to classify the evaluation results into certain levels, so it is necessary to establish a set of comments at the same time.(2)
Determining the affiliation function based on the evaluation criteria. The affiliation function is based on the established evaluation criteria, and the purpose is to evaluate the affiliation level by dividing the evaluation factors through certain function operations to make the original ambiguous mathematical concept intuitive. At present, the affiliation function is widely used in a variety of affiliation functions, and I used the actual frequency of the current ascending semi-trapezoidal affiliation function and descending semi-trapezoidal affiliation function. The ascending semi-trapezoidal affiliation function is applied to those negative effect indicators that are less applicable to industrial sites with higher values. The descending semi-trapezoidal affiliation function is applied to those positive indicators whose larger values indicate better suitability of industrial land. In practical application, the affiliation function should be selected scientifically according to the focus of evaluation work and the change rule of factors.(3)
Determine the affiliation degree of each indicator. Based on the affiliation function constructed in step 2, the affiliation degree ofui on the rubric vj level can be solved - denoted by γij. The affiliation degree of each factor for each evaluation level constitutes a vector Ri=γi1,γi2,γi3,…,γin. It is a fuzzy subset on the decision rubric V.(4)
Determine the weights of the factors. In the comprehensive evaluation, it is necessary to know the relative importance of each factor with respect toC, i.e., the weight of each factor. To do this, we can find the eigenvector W of the judgment matrix A and then normalize it to find the relative importance (weight) of each factor with respect to C.(5)
The fuzzy matrix composite operation is to synthesize the weight setA and the affiliation set R rows according to a certain algorithm, such as equation (3).(3)B=A⋅R=b1,b2,…,bn=a1,a2,…,an⋅γ11γ21…γ21γ22…………γm1γm2…γ1nγ2n…γmn.B is the rank fuzzy subset on the set of decision rubrics V, and bjj=1,2,3,…,n is the affiliation of rank Vi to the set of rank fuzzy subsets obtained from the composite rubric.(6)
Draw the conclusion.Ifbj=maxb1,b2,…,bn, then make a comment on the judged object vj.In the more complex system, when many factors need to be considered and the evaluation elements have a mutual influence on each other, it is inevitable that each factor is assigned a small weight, and it is not easy to determine. At this time, the first level of comprehensive evaluation may be that too small weights do not work and lose a lot of useful information, so the results should not be obtained. However, we can divide all the factors into several categories to determine the relative importance of the factors in a smaller range more accurately, set the weight vector, and then preform the comprehensive evaluation.


### 2.3. One-Level Comprehensive Evaluation for Spatial Performance

The purpose of spatial performance evaluation is to grasp the status of industrial land use and provide a basis for formulating land use and industrial development strategies. In addition to the selection of indicators for the industrial land itself, the indicator system also needs to consider the spatial characteristics of the hosted industrial enterprises. Moreover, the use of industrial land in small towns not only affects the development of towns but also directly affects the interests of grassroots communities in the case of collective industrial land in villages. Therefore, the evaluation indicators need to consider the multidimensional characteristics of spatial attributes in the hierarchical framework, including four aspects of social benefits, economic benefits, environmental benefits, and development potential, specifically divided into six positive indicators of average number of employees, average rent, average production value, innovation capacity, industrial relevance [22] and industrial aggregation [23], and two negative indicators of energy consumption and pollution intensity (see Table 2).Table 2
Spatial performance evaluation index system for industrial land.
ObjectiveClassificationIndicatorRelevancyRemarkEffective use of industrial landSocial benefitsU1Number of employees per landu11PositivelyEconomic benefitsU2Average land rentu21PositivelyAverage land valueu22PositivelyEnvironmental benefitsU3Energy consumptionu31NegativelyPer unit industrial landPollution intensityu32NegativelyPer unit industrial landPotential benefitsU4Industrial correlationu41PositivelyThe degree of correlation between industriesIndustrial aggregationu42PositivelyLocation entropy of leading industriesInnovation capacityu43PositivelyR&D (research and development) investment intensityConsidering the availability and authenticity of data and the sustainability of evaluation, the basic data in this paper are obtained through the mutual support of enterprise census data and geographic information data. Among them, industrial land use status is based on town planning and is combined with on-site research to obtain relevant data; industrial enterprises’ spatial distribution, output value scale, pollution and energy consumption, innovation input, and industry type data are based on enterprise surveys [24], including enterprises’ spatial positioning, statistical yearbooks, and communication interviews [25]. These processing methods can clearly and effectively reflect the use status of industrial land and help to more clearly understand the characteristics of each index of spatial performance.According to the weight of each indicator, the weighted superposition is carried out to obtain a comprehensive evaluation score. Comprehensive evaluation score calculation adopts the weighted summation method of factor scores, and its calculation formula is shown in equation (4).(4)S=∑i=1,j=1nviuijwj=S1,S2,S3,S4=NSPL,LSPL,MSPL,HSPL,where S is the comprehensive evaluation score; vi is the weight of the ith evaluation index, which is determined by the 6th process in the last section; n is the total number of impact factors. Here, uij is the present value of the characteristic evaluation index, which is the data acquired from geographic information, and wj is the corresponding weight. The NSPL,LSPL,MSPL,HSPL stand for No Space Performance Land, Low Space Performance Land, Mid Space Performance Land, and High Space Performance Land.


## 2.1. Fuzzy Set Theory

Fuzzy mathematics is based on the theory of fuzzy sets. The concept of fuzzy sets corresponds to the classical notion of either/or sets, describing sets without clear and well-defined boundaries. It emerged in the 1960s as a mathematical approach to the study and treatment of “fuzzy” phenomena. The so-called fuzziness refers to the indistinctness and uncertainty of objective things, which is rooted in the existence of a mid-valve transition between objective differences, such as “good and bad” in the evaluation of environmental quality. In daily life “Early and late,” “more and less,” etc., are difficult to draw a clear line. Auxiliary mathematics is based on set theory. According to the requirements of set theory, an object either belongs to a set or not. There are no ambiguous cases of belonging and not belonging at the same time. This precision of set theory greatly limits its scope of application. It makes it unable to deal with the ambiguities of everyday life. Faced with this situation, in 1965, the American cybernetics expert Zadeh [18] published his famous paper marking the birth of the new discipline of fuzzy mathematics. Although only 40 years have passed, the development of fuzzy mathematics has been exceptionally rapid, and its application has involved almost all fields and sectors of the national economy. Fuzzy mathematics has been widely and successfully used in agriculture, forestry, meteorology, environment, geological survey, military, and other fields.The theory and method of fuzzy mathematics show its superiority when the object cannot be accurately described by classical mathematics. The appropriateness of industrial supervisory land is determined by various factors. When evaluating the suitability of industrial land at the location of the development zone, it is impossible to get a very precise result. The main problems that need to be determined by the evaluation of fuzzy mathematical theory are the determination of factor weight, the establishment of affiliation dispersion, and the selection of the evaluation model.The main difference between fuzzy sets and ordinary sets is that there are only two relations between elements in the domain and ordinary sets. There are many relationships between fuzzy sets and elements, which can be represented by any value on [0, 1]. Taking “0” means that the element does not belong to the fuzzy set, taking “1” means that the element belongs entirely to the fuzzy set, taking “0.3” means that the element belongs to the fuzzy set to a degree of 0.3, and so on. The number taken is called the affiliation of the element to the fuzzy set. Affiliation is an indicator of the fuzziness of characterization factors. It can be said to be the cornerstone of fuzzy sets is applied to practical problems. If this affiliation varies with a variable, the affiliation function needs to be established. The membership function is generally denoted byA(x).To solve a practical problem, generally, is to determine the degree of affiliation function scatter. However, the affiliation function is often not declared and given, and its determination is generally approximated by using the method of inference. Its determination process is objective in nature. However, a certain amount of artificial skill is allowed, and sometimes the artificial skill plays a decisive role in the solution of the problem. It is worth noting that the artificial skill should be reasonable and not contrary to the objective reality. It can be given by fuzzy statistical tests or by the typical function method summarized by practical experience.The weight coefficient is a quantitative description of the importance of each factor in the evaluation domain, which can be regarded as the affiliation of each factor in the evaluation domain with respect to the “importance.” The assigned weights in common evaluation problems are generally subjective based on experience and are highly subjective. In some cases, the subjective determination of weights has an objective aspect and reflects the actual situation to a certain extent. However, in most cases, the evaluation results of the subjective determination method are usually seriously distorted and may lead to misjudgment of decision makers. As a rule, mathematical methods should be used more often to determine weights, although they are also subjective in nature. However, due to the strict logic of mathematical methods, the determined weights can be processed, thus eliminating as much subjective components as possible and conforming to objective facts.There are various methods for determining the weights, such as expert empirical estimation, survey statistics, hierarchical analysis, fuzzy inverse equation method, and sequential synthesis method. The literature points out that the accuracy of the hierarchical analysis method in weight calculation is relatively better [19]. Moreover, the hierarchical analysis method requires less data, takes less time to score, has less computational effort, and is easy to understand and master. In view of the advantages of the hierarchical analysis method, and considering the popularity and relative objectivity of the expert empirical estimation method in practice, this study uses the combination of the hierarchical analysis method and the expert scoring method to determine the weights of each index affecting the suitability of the industrial land.The analytic hierarchy process (AHP) is essentially a way of thinking about decision-making, that is, decomposing a complex problem into component factors, grouping these factors into an orderly hierarchical structure according to the dominant relationship, determining the relative importance of each factor in the hierarchy through a two-by-two comparison, and then integrating human judgment to determine the total relative importance of each factor. This is a reasonable way to solve the process of quantifying qualitative problems. The basic steps of using hierarchical analysis to solve the intrusion problem are as follows: (1) clarify the problem and establish the hierarchical structure; (2) construct a two-by-two judgment matrix; (3) calculate the relative weights of the elements being compared; (4) calculate the combined weights of the elements in each hierarchy.Defining the problem and establishing the hierarchy is the most important step of AHP. First, the complex problem is decomposed into component elements, and these elements are divided into groups according to different attributes to form different levels. The elements of the same level act as a criterion to dominate some elements of the next level, and at the same time, it is dominated by the elements of the previous level. This top-down dominance relationship forms a hierarchy. A typical hierarchy can be represented in Figure2. In a recursive hierarchy, the number of levels generally depends on the complexity of the intrusion and the level of detail required for the analysis. The number of elements contained in the same hierarchy is usually no more than 9. The number of elements included is too large, which can make it difficult to compare two comparisons. The index system established in this study is a recursive hierarchy, including three levels, target level, criterion level, and sub-criterion level, in which the regional industrial land suitability level is the target of evaluation.Figure 2
Schematic diagram of the recursive hierarchy.The hierarchical analysis method is also based on expert survey scoring, but the method of comparing grading and calculating weight coefficient is different. The experiments show that when people compare the different important degrees of multiple factors, they cannot compare and judge too much. Usually, the number of factors a person can compare simultaneously cannot exceed 9. However, a comparison of the degree of importance difference between the two factors. Man is perfectly competent. Therefore, the “two-two comparison method” can be used for multi-factor weight analysis, and only two factors are of relative importance to each other inn factors. A measure of relative importance between factors is called a judgment scale.


## 2.2. Fuzzy Integrated Evaluation

Here, it is assumed that the upper-level element C is the criterion or sub-criterion, and the elements governing the next level areu1,u2,…,un. The judgment matrix is the basic information of the hierarchical analysis method, and it is also an important basis for the relative importance calculation of each factor in this study. The judgment matrix is a two-by-two comparison of the elements of this level to determine the elements in the matrix with the upper-level element C as the evaluation criterion, and the judgment matrix with n factors with C as the evaluation criterion is as follows in Table 1.Table 1
Form judgment matrix.
Cu1u2…uj…unu1a11a12…a1ja1nu2a21a22…a2ja2n…………………uiai1ai1…aij…ain…………………unan1an1…anj…annSo the judgment matrixA could be expressed as equation (1):(1)A=aijn×n.In the general evaluation problem, the evaluator cannot judge the value of the weight indicatorwi/wj very precisely, but can only estimate it. If there is an error in the estimation, it will inevitably lead to deviations in the eigenvalues of the judgment matrix as well. This means that the judgment matrix obtained by the two-by-two comparison method may have inconsistent judgments, so a consistency test is required. By consistency, it means that when X1 is more important than X2 and X2 is more important than X3, then X1 must be considered more important than X3. When the judgments are in complete agreement, there should be λmax=n. Consistency indicators, CI, can be written as equation (2):(2)CI=λmax−nn−1.When consistent, CI = 0, andCI>0 when non-consistent. Regarding how to measure the acceptability of CI values, Saaty [20, 21] constructed the most inconsistent case by taking 1/9,1/7,1/5,…,5,7,9 randomly taken values of elements in the judgment matrix for different n, and used 100 to 500 subsamples for different n to calculate their consistency indexes, and then found the average value, noted as RI.Fuzzy synthesis evaluation is a proven decision-making method to solve multi-factor and multi-indicator synthesis problems. It applies the characteristics of fuzzy relationship synthesis and makes a comprehensive evaluation of the affiliation level of the evaluated thing from multiple indicators according to the given evaluation criteria and the measured values. It divides the change interval of the evaluated thing and analyzes the degree of the thing belonging to each level, which makes the description of the thing more in-depth and objective, and the analysis result more accurate. The operation process of fuzzy comprehensive evaluation is shown in Figure3.Figure 3
Fuzzy comprehensive evaluation flow diagram.One-level evaluation is the basis of multi-level evaluation. Generally speaking, the first-level fuzzy comprehensive evaluation is carried out mainly in the following steps.(1)
Determine the set of factors and the set of comments to establish the set of factors and the set of comments is the first step of evaluation. A fuzzy comprehensive evaluation is a comprehensive evaluation that considers all factors related to the evaluated thing, and its focus is on all relevant factors to be considered. Therefore, a factor set is created. To clearly describe the evaluation results, it is necessary to classify the evaluation results into certain levels, so it is necessary to establish a set of comments at the same time.(2)
Determining the affiliation function based on the evaluation criteria. The affiliation function is based on the established evaluation criteria, and the purpose is to evaluate the affiliation level by dividing the evaluation factors through certain function operations to make the original ambiguous mathematical concept intuitive. At present, the affiliation function is widely used in a variety of affiliation functions, and I used the actual frequency of the current ascending semi-trapezoidal affiliation function and descending semi-trapezoidal affiliation function. The ascending semi-trapezoidal affiliation function is applied to those negative effect indicators that are less applicable to industrial sites with higher values. The descending semi-trapezoidal affiliation function is applied to those positive indicators whose larger values indicate better suitability of industrial land. In practical application, the affiliation function should be selected scientifically according to the focus of evaluation work and the change rule of factors.(3)
Determine the affiliation degree of each indicator. Based on the affiliation function constructed in step 2, the affiliation degree ofui on the rubric vj level can be solved - denoted by γij. The affiliation degree of each factor for each evaluation level constitutes a vector Ri=γi1,γi2,γi3,…,γin. It is a fuzzy subset on the decision rubric V.(4)
Determine the weights of the factors. In the comprehensive evaluation, it is necessary to know the relative importance of each factor with respect toC, i.e., the weight of each factor. To do this, we can find the eigenvector W of the judgment matrix A and then normalize it to find the relative importance (weight) of each factor with respect to C.(5)
The fuzzy matrix composite operation is to synthesize the weight setA and the affiliation set R rows according to a certain algorithm, such as equation (3).(3)B=A⋅R=b1,b2,…,bn=a1,a2,…,an⋅γ11γ21…γ21γ22…………γm1γm2…γ1nγ2n…γmn.B is the rank fuzzy subset on the set of decision rubrics V, and bjj=1,2,3,…,n is the affiliation of rank Vi to the set of rank fuzzy subsets obtained from the composite rubric.(6)
Draw the conclusion.Ifbj=maxb1,b2,…,bn, then make a comment on the judged object vj.In the more complex system, when many factors need to be considered and the evaluation elements have a mutual influence on each other, it is inevitable that each factor is assigned a small weight, and it is not easy to determine. At this time, the first level of comprehensive evaluation may be that too small weights do not work and lose a lot of useful information, so the results should not be obtained. However, we can divide all the factors into several categories to determine the relative importance of the factors in a smaller range more accurately, set the weight vector, and then preform the comprehensive evaluation.


## 2.3. One-Level Comprehensive Evaluation for Spatial Performance

The purpose of spatial performance evaluation is to grasp the status of industrial land use and provide a basis for formulating land use and industrial development strategies. In addition to the selection of indicators for the industrial land itself, the indicator system also needs to consider the spatial characteristics of the hosted industrial enterprises. Moreover, the use of industrial land in small towns not only affects the development of towns but also directly affects the interests of grassroots communities in the case of collective industrial land in villages. Therefore, the evaluation indicators need to consider the multidimensional characteristics of spatial attributes in the hierarchical framework, including four aspects of social benefits, economic benefits, environmental benefits, and development potential, specifically divided into six positive indicators of average number of employees, average rent, average production value, innovation capacity, industrial relevance [22] and industrial aggregation [23], and two negative indicators of energy consumption and pollution intensity (see Table 2).Table 2
Spatial performance evaluation index system for industrial land.
ObjectiveClassificationIndicatorRelevancyRemarkEffective use of industrial landSocial benefitsU1Number of employees per landu11PositivelyEconomic benefitsU2Average land rentu21PositivelyAverage land valueu22PositivelyEnvironmental benefitsU3Energy consumptionu31NegativelyPer unit industrial landPollution intensityu32NegativelyPer unit industrial landPotential benefitsU4Industrial correlationu41PositivelyThe degree of correlation between industriesIndustrial aggregationu42PositivelyLocation entropy of leading industriesInnovation capacityu43PositivelyR&D (research and development) investment intensityConsidering the availability and authenticity of data and the sustainability of evaluation, the basic data in this paper are obtained through the mutual support of enterprise census data and geographic information data. Among them, industrial land use status is based on town planning and is combined with on-site research to obtain relevant data; industrial enterprises’ spatial distribution, output value scale, pollution and energy consumption, innovation input, and industry type data are based on enterprise surveys [24], including enterprises’ spatial positioning, statistical yearbooks, and communication interviews [25]. These processing methods can clearly and effectively reflect the use status of industrial land and help to more clearly understand the characteristics of each index of spatial performance.According to the weight of each indicator, the weighted superposition is carried out to obtain a comprehensive evaluation score. Comprehensive evaluation score calculation adopts the weighted summation method of factor scores, and its calculation formula is shown in equation (4).(4)S=∑i=1,j=1nviuijwj=S1,S2,S3,S4=NSPL,LSPL,MSPL,HSPL,where S is the comprehensive evaluation score; vi is the weight of the ith evaluation index, which is determined by the 6th process in the last section; n is the total number of impact factors. Here, uij is the present value of the characteristic evaluation index, which is the data acquired from geographic information, and wj is the corresponding weight. The NSPL,LSPL,MSPL,HSPL stand for No Space Performance Land, Low Space Performance Land, Mid Space Performance Land, and High Space Performance Land.


## 3. Case Study Based on X City

The case chosen for this paper is X city in Guangdong Province, which, as a national economic powerhouse and a central town in Guangdong Province, has a tradition of doing business, and is a typical representative of small-town development in the Pearl River Delta region. Since the reform and opening up, the modern industry in X city developed rapidly and the industrial output value increased more than ten times in just a few years in the 1990s, and the corresponding industrial land also expanded rapidly. By 1996, the industrial land area reached 603.9 hm2, accounting for 18% of the total urban and rural construction land area, including 244.0 hm2 of rural industrial land. By the beginning of this century, only the rural industrial land had increased by 446.5 hm2, and the total industrial land reached 1318.9 hm2 in 2002, accounting for 36.5% of the rural construction land. Although the total industrial output value in the same period was as high as 14.3 billion yuan, the layout of industrial land was confusing and the efficiency of the land was not high.For this reason, X city focused on industrial restructuring and industrial zone construction in the recent plan (2001–2005). Since then, the total industrial output value is continuously increasing, but the industrial land development is well controlled, and by 2015, the industrial land area only rose to 1,320 hm2. During this period, due to a series of regulatory policies, the industrial land layout tends to be rationalized, and different industrial zones are intentionally specialized and networked to create industrial clusters. However, in general, the inefficiency of land use still exists, and the more problematic issue is that there is no more incremental industrial land, and these have become obstacles to industrial transformation and upgrading.Since this study focuses on industrial land and the bearing industrial enterprises, it is necessary to analyze the spatial association of the enterprises in a certain range, so the industrial land is divided into eight zones according to the existing division of industrial land and its proximity in space, combined with the administrative boundary of the town community. For simplicity, they are referred to as 1–8 in this study.At present, X city has nearly 10,000 industrial enterprises, mostly small, medium, and micro enterprises, and this paper selects 337 of the state-listed enterprises for statistical analysis [26], shown in Figure 4. In general, X city has formed an industrial spatial pattern with technology-intensive industries in the southern industrial zone, technology- and capital-intensive industries in the east, and labor- and technology-intensive industries in the rest of the industrial zone. The statistical results show that the manufacturing sector of X city is complete, but the layout of different manufacturing sectors is more arbitrary. Among them, the total industrial output value of the southern district 3 is the largest and the industrial categories are the most numerous, and the technology-intensive electronic equipment manufacturing is the pillar industry of this district; the eastern district 7 is mainly dominated by capital-intensive daily chemical and beverage enterprises, while the labor-intensive plastic products and paper products, in addition to the technology-intensive electronic equipment manufacturing, also occupy the majority in district 1, but lack the core industry; similar to the situation in district 1, there are also several other districts. This is different from the industrial layout plan of X city and may cause internal competition among industrial zones to attract advantageous industries to move in.Figure 4
X city Industrial land and industrial enterprises spatial distribution map.X city is guiding the construction of “big project - industrial chain - industrial cluster - industrial base” development model to strengthen the industrial clustering effect of different industrial zones, but due to differences in economic base, land conditions, and traffic factors, the development of each industrial zone is increasingly uneven. However, due to the differences in economic base, land conditions and transportation factors, the development imbalance among industrial zones has become increasingly prominent. To analyze the characteristics of industrial land use in X city, this study calculates the index values of eight industrial zones based on the basic data of industrial land, and by comparing the advantages and disadvantages of the indexes and combining the essential characteristics of the clustering economy of the zones, the eight zones are shown in Figure5.Figure 5
X city space performance indicators radar chart.Based on the original data, we analyzed the elements of external scale development, internal scale development, area homogeneous development, and lagging loose development of each district from the radar chart. The above preliminary analysis shows that District 3 has obvious advantages in terms of industrial spatial correlation, innovation capacity, and the number of employees per place; in terms of the output value per place and industrial aggregation, District 7 has obvious advantages, but pollution and energy consumption are also the most prominent. The rest of the industrial zones have their own characteristics, except for District 8, which has obvious disadvantages. It is difficult to judge their spatial performance from a single level, and further comprehensive evaluation will be conducted on this basis.The sub-study of comprehensive evaluation indexes of spatial performance helps to objectively understand the real characteristics of industrial land use so that effective development strategies can be formulated. However, if the spatial performance of industrial zones is evaluated by the virtue of a single indicator only, it is one-sided to a certain extent. Therefore, the study further calculates the evaluation indicators and weights of each indicator according to formulae (1) and (2), and then calculates the indicator values and ranks the scores of eight industrial zones in X city according to formulae (3) and (4), and then carries out a comprehensive evaluation. Details are shown in Tables 3 and 4.Table 3
Weighting of each indicator.
indicatoru11u21u22u31u32u41u42u43Weight (wj)0.09780.05210.16960.04160.03790.19140.35260.1270Table 4
Comprehensive evaluation score of industry zoning space performance.
DistrictComprehensive evaluation score (S)Ranking144.054251.902366.011439.007541.325640.516749.243838.588Among the index weights, the industrial agglomerationu42 has the largest weight, while the weights of industrial association u41, average land value u22, and innovation capacity u43 are at the second level. From the magnitude of the weights, it can be seen that the spatial aggregation of industries in the area has the largest weight in spatial performance, followed by spatial correlation and industrial scale, reflecting that the selection and leading of leading industries is the basis of spatial performance of industrial land, and industrial chain, industrial scale, and innovation capacity are the driving factors and potential factors of industrial land development. Special attention is paid to the fact that the high or low innovation capacity is not only a potential factor for the development of industrial enterprises, but also a side reflection of the number of regional investments.Since the infrastructure of industrial land is relatively homogeneous and the layout of industrial zones is relatively close, the weights of the average number of employeesu11 and the average rent u21 are smaller. However, for industrial zones with poor spatial performance, the lack of industrial land development planning and weak human resources are also important reasons for their difficulties in further development.


## 4. Discussion and Conclusion

This paper adopts a spatial performance evaluation method to conduct a more comprehensive analysis of the situation of industrial land in X city. The selection of spatial performance indicators in this study is based on the traditional performance evaluation index system, with more emphasis on the extraction of spatial element characteristics. Through spatial performance analysis, this study systematically understands the use status of industrial land in X city and calculates that the main factors affecting the performance of industrial land in X city are industrial spatial agglomeration, industrial spatial correlation, and industrial scale through the Fuzzy comprehensive evaluation method, which also reflects to a certain extent the future development direction of industrial land in X city. This also reflects to a certain extent the future development direction of industrial land in X city.Based on the evaluation results of spatial performance, we will fully consider the possible potential factors, promote the intensive development of industrial land in an orderly manner with enterprises as the core, and establish a long-term regulation and control mechanism, thus realizing the optimization and upgrading of industries under the dynamic adjustment of industrial land spatial structure. Specific recommendations include.(1)
In the industrial land, which is dominated by internal economies of scale, we should pay attention to industrial linkage development, increase industrial spatial correlation, and mobilize ecological restoration and improvement of the industrial system. We should consciously cultivate the leading role of core industries in surrounding industries, emphasize the relatively concentrated “clusters” and “nets” industrial spatial models, and then form a good industrial upgrading environment [27];(2)
Industrial land for the development of industry homogenization needs to promote the development of advantageous industries through the centralized space platform and increase the concentration of the industrial space and the scale of the industry. This requires industrial land to attach importance to the selection of industrial enterprises in development, to plan the industrial structure scientifically and rationally, and increase the scientific and technological support to the industry in a targeted manner, cultivate its independent innovation ability, and on this basis, to control the intensity of industrial land use and avoid uneconomical phenomena that are too scattered or concentrated.(3)
For the lagging development of industrial land, there are obvious defects in its industrial dynamics. In its own development, we should cultivate the “shared concept” and consolidate resources so as to proceed step by step. With the help of the transformation and upgrading of urban industries, full consideration is given to multifunctional embedding in production, circulation, and innovation. Promoting the renewal of industrial land and the improvement of the soft and hard environment [28]. Promote the full utilization of stock space and the concentration of higher efficiency.Urban space performance refers to the combined effect or effect of urban space. Only to maximize the development needs of the city’s functions and rationally allocate all kinds of space resources to promote balanced development of all elements, “Performance is a multidimensional structure. Different angles are observed and measured, and the results are different” [29]. The performance of urban spatial structure development refers to the internal effect and external effect of the change of spatial structure in the development process, namely, the shaping and tear change of urban spatial structure to the society of the city ontology and its radiation, economic, ecological, and other effects . These effects are manifested specifically in urban economic gains, social differentiation ecological control, urban form, and transportation network [30]. The evaluation of the performance of urban spatial development is the qualitative and attributive analysis of these changes.The hierarchical analysis–fuzzy evaluation method combines hierarchical analysis and fuzzy comprehensive evaluation method, which can not only establish a hierarchical index relationship tree, avoid information overlap and information loss among the indicators but also use fuzzy set and fuzzy logic to delineate the affiliation of each indicator to the evaluation level according to certain rules so that the evaluation result level value has continuity. In this paper, the factors affecting the spatial performance of industrial land in development zones are screened. The index system of spatial performance analysis of industrial land in the development zone is established by using the hierarchical analysis method. By using the combination of fuzzy evaluation model calculation and hierarchical analysis method, the spatial performance of industrial land in the development zone is analyzed. Thus, a complete analysis of whether the development zone is suitable for industrial construction is carried out. This paper is a new attempt to apply the hierarchical analysis-fuzzy evaluation method to the practical work of specific development zones, which makes the method more complete in practice and develops a practical method for spatial performance assessment of industrial parks.In this paper, the spatial performance study of X city is comprehensively analyzed by FAHP method, which can evaluate and grade the determination of individual impact factors as well as realize the overall spatial positioning and grade classification. The study shows that the hierarchical fuzzy object metamodel can also realize a comparative analysis of multiple evaluation objects, and should continue to innovate in terms of multi-regional comparison and evaluation index selection and rank classification in subsequent studies to make the evaluation results more valuable in practice.Overall, this study tries to explore the evaluation method of industrial land spatial performance at multiple levels, but the extension in vertical and horizontal directions is not yet very deep. Therefore, future research should include a longitudinal comparison of the time dimension while appropriately adding a horizontal comparative analysis of relevant indicators of neighboring towns, so as to reflect the use status of industrial land in more dimensions. The evaluation of the spatial performance of industrial land is an extremely complex task that involves a wide range of knowledge. This study has only developed and improved the evaluation method to a certain extent, but it is far from perfect. It needs to be further researched and improved continuously. On the other hand, in future development, we can try to use the method to conduct evaluation studies on regions of different sizes and different degrees of economic development and industrial structure.



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*Source: 1384583-2022-08-25.xml*