# Online Evaluation Method of Water Resources Recycling Effect in Urban Landscaping Using Fuzzy Approach

Authors: Hengji Zhang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The common perception of people about recycling involves reusage of aluminum cans, glass bottles, and newspapers, whereas recycling of water resources is a most important aspect nowadays. Water recycling is known to reuse cleaned wastewater for beneficial applications including agricultural and landscape irrigation, industrial activities, and replenishing a groundwater using the latest technologies. The current methods have some flaws in the evaluations of water resources’ recycling systems such as large mean square error, time complexity, and low-evaluation efficiency; therefore, this paper proposes an online evaluation method for the recycling process of water resources in urban landscaping. The health model of water resources recycling in urban landscaping has been analyzed using fuzzy-based approach. Second, the evaluation index system of water resources’ recycling is also analyzed using the ecological water-level analysis results, water resource quality, water resource abundance, and water resource utilization rate. Then, the extension of analytic hierarchy process (AHP) is utilized to calculate the weight of water recycling evaluation index. Then a fuzzy-based comprehensive evaluation method is used to find the online evaluation model of the water recycling. Eventually, the evaluation of the effect of water recycling in urban landscaping is performed and analysis is made for decision-making. The results prove that the proposed AHP and fuzzy method has a low mean square error and high accuracy.


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## Body

## 1. Introduction

The integration of urban and rural areas promotes the development of urban and rural planning industrial layout which leads to the rapid growth of water consumption. The shortage of water resources is one of the critical problems in the world [1]. The design of the garden city in the new era retains the advantages of traditional gardens. It combines with the country's development needs and even the world so that the city has high green coverage and advanced new landscape design [2, 3]. Based on the ecological environment, the new garden city has lofty social and practical significance [4]. Water supply and drainage are an important part of urban landscaping water which directly determines the utilization efficiency of water resources. The evaluation of the water resources recycling utilization rate of urban landscaping is to improve its recycling utilization rate. Therefore, it is important to optimize and improve the evaluation method of water resources recycling utilization [5].In [6], the authors proposed a method for evaluating the effect of water resources recycling utilization by combining chromatography analysis and data envelopment analysis. Five input indexes and eight output indexes were selected from agriculture, industry, life, ecology, and society. The analytical water use efficiency model was established through the improved analytic hierarchy process and data envelopment analysis. The evaluation index system of water use efficiency was constructed, evaluating the effect of water resources recycling. However, this method ignored the circulation characteristics of water resources in urban landscaping. Moreover, the calculation index weight error was large, and the mean square error of evaluation results was large. In [7], the author proposed an evaluation method of the water resources recycling effect based on the iterative idea. This method adopted the mean, Copeland, and fuzzy methods to combine the single evaluation. Thus, the evaluation model of the water resources recycling effect based on iterative thinking was established. Finally, the evaluation of water resources recycling was completed. However, this method took a long time to select indicators, and the evaluation efficiency was low.In [8], the authors proposed the evaluation method of water resources recycling utilization effect based on critical TOPSIS gray correlation degree. In this method, the weight of each index in the evaluation index system was determined by the critical method. The TOPSIS method and gray correlation analysis method were combined to calculate the relative closeness degree of Huai He River Basin. According to the calculation results, the CRITIC-TOPSIS gray correlation evaluation model was used to evaluate the effect of water resources recycling. However, the evaluation indexes selected by this method cannot express the circulation characteristics of water resources in detail, leading to a large error between the evaluation results and the actual results, and the mean square error of the evaluation results was also large [9]. All the methods discussed above have certain limitation such as noninclusion of circulation characteristics of the water resources in urban and rural places. Evaluation efficiency of some previous methods is low, and they are time-consuming as well.Many methods proposed earlier have a large mean square error. In this regard, this paper proposes an online evaluation method for the recycling impact of water resources in urban landscaping. Multicriteria decision-making (MCDM) approach is used to evaluate water resources in urban landscaping. The analytical hierarchal process (AHP), TOPSIS, data envelopment analysis (DEA), the analytical network process (ANP), and fuzzy decision-making are some of the MCDM methodologies accessible.The highlights of the proposed fuzzy based method are as follows:(i)
The proposed method is based on AHP to find out weights of parameters impacting the water recycling(ii)
The circulation characteristics of water resources in urban landscaping are analyzed, and the evaluation index system of the recycling effect of water resources is established(iii)
The extension of AHP and comprehensive fuzzy evaluation method are introduced to construct the online evaluation model of the water recycling to preserve natural resources such as water(iv)
According to the mean square error and evaluation efficiency, the effectiveness of the proposed method has been verified for its efficacyThe paper is organized as follows: Section2 evaluates the index system of water recycling. Section 3 discusses the proposed model using a fuzzy approach. Section 4 is experiment and discussion, and at last in Section 5 a summary and related future work are presented.


## 2. Evaluation Index System for Water Recycling

Traditionally, the concept of a healthy water cycle emphasizes the objective law that human social activities do not affect the natural water cycle [10]. In this way, the water cycle can be maintained in its original state [11]. With the development of the urbanization, the connotation of a healthy water cycle should be considered including climate change and human activities [12]. Climate change causes the change in regional water resources which affect the evolution of the water cycle at its source [13]. The utilization of water resources by human activities has changed the natural structure of the water cycle [14]. In addition, the efficiency of water use can directly reflect economic and social development [15]. This can reflect the service function of water resources to human society. In order to ensure the health of the water cycle, we must ensure the normalization of water ecological function and water body function at first [16]. Second, we need sufficient water resources to meet the demands of social and economic development. Finally, we need to design an efficient water utilization mode. The concept of a healthy water cycle is shown in Figure 1.Figure 1
Connotation of healthy water cycle.According to a healthy water cycle concept, the ecological water level is the primary level for evaluating the water resource recycling utilization effect. In addition, water resource quality is also an important factor in water cycle health [17, 18]. A healthy water cycle mode has a natural function and needs to have a social service function [19]. In densely populated areas with fierce water competition, it is necessary to use water resource abundance and utilization rate to characterize the healthy level of water cycle social services [20]. Therefore, the evaluation index system of the water recycling utilization effect will be built from four dimensions: ecological water level, water resource quality, water resource abundance, and water resource utilization rate.


### 2.1. Water Ecological Level

The water ecology dimension represents the level of the water ecological civilization construction which is a very important part of a healthy water cycle system. It also reflects the natural attribute of the water cycle [14]. The guaranteed rate of ecological water demand reflects the guaranteed degree of environmental water demand [15]. The coverage rate of evaluation system represents the greening level of the built-up area. The variation of groundwater depth and groundwater exploitation coefficient reflects the regional groundwater exploitation situation and dynamic trend. These indicators have a stronger characterization for the areas relying on groundwater.(i)
Guarantee rate of ecological water demandEco is given by(1)Eco=RepDe,whereRep is the ecological water replenishment and De is the ecological water demand.(ii)
Coverage rateCov of landscape area is given by(2)Cov=GaTa,whereGa is the green area and Ta is the built-up area.(iii)
Variation of depth to ground water in plain areaΔDep is given by(3)ΔDep=Di+1−Di,whereDi+1 is the depth to ground water in the i+1 th year and Di is the depth to ground water in the i th year.(iv)
Coefficient of groundwater exploitationExp is given by(4)Exp=ExCex,whereEx is the exploitation amount of groundwater and Cex is the exploitable amount of underground water.


### 2.2. Water Environment Quality

The dimension of water environment quality is an indispensable part of evaluating a healthy water cycle system which can reflect the water quality in the researched area and the social attributes of the water cycle [15]. Four indexes are used to characterize the water quality. The standard-reaching rate of river length and water function area reflects the water quality status of natural rivers as well as the standard-reaching status of five functional areas. The water function area involves the development, utilization, conservation, and protection of water resources. The qualified rate of water in pipe network and the standard-reaching rate of drinking water sources reflect the safety level of human drinking water from the aspects of water supply and water source.(i)
The proportionQua of river length whose water quality to reach the standard is given by(5)Qua=stdS,wherestd is the standard river length and S is the length of river with water.(ii)
The rate of reaching the standard of water function areaFuc is given by(6)Fuc=numNum,wherenum is the number of water functional areas up to standard and Num is the total number of water functional areas.(iii)
Qualification ratePip of water in pipe network is shown in(7)Pip=tT,wheret is the time to pass the test and T is the total time.(iv)
Standard-reaching rate of the drinking water sourceDri is given by (8)Dri=timTim,wheretim is the time to pass the test and Tim is the total time.


### 2.3. Abundance of Water Resources

The water resource abundance has distinct regional characteristics. The water resource richness benchmarks differ in different regions mainly caused by the different climates, geographical locations, and other factors between regions [17]. Four indexes have been used to characterize the water resource abundance. The indexes of per capita water resources can indicate the situation of the carrying capacity of regional water resources to some extent. The excessive population is not suitable for the small water resources. The utilization rate of water resources reflects the degree of regional economic and social development to the local water resource exploitation. The high utilization rate of water resources leads to the pathological condition of water circulation. The proportion index of groundwater supply emphasizes the dependence of water supply on groundwater, and excessive utilization of groundwater will destroy the benign circulation of the groundwater system.(i)
Per capita water resourcePer is shownas follows:(9)Per=TolPou,whereTol is the total water resource and Pou is the population.(ii)
Utilization rateUti of water resource is given by(10)Uti=Sur+GrdTol,whereSur is the surface water consumption and Grd is the underground water consumption.(iii)
Average water resources per muAcre is shown as follows:(11)Acre=TolArea,whereArea is the irrigated area.(iv)
ProportionDsup of groundwater to water supply is given by(12)Dsup=aTsup,wherea is the groundwater supply and Tsup is the total water supply.


### 2.4. Utilization of Water Resource

The level of water resources utilization mainly involves the subprocesses of the water cycle such as centralized water supply, water use efficiency, water-saving level, and drainage system. This dimension reflects the social attribute of the water cycle [19]. Seven indexes are used to represent the water resources utilization. The centralized water supply rate and leakage rate of the water-supply network reflect the operation state of the water supply system from the aspects of water supply and water delivery efficiency respectively. The water consumption rate of domestic water, agricultural irrigation water quota, and industrial usage reflect the efficiency of the regional water resource utilization in the perspective of life, agriculture, and industry. The centralized sewage treatment rate reflects the regional water resources utilization efficiency. The centralized sewage treatment rate reflects the state of urban sewage treatment. If the industrial wastewater is directly discharged into the environment, it will cause continuous water pollution and water ecological environment damage. It is characterized by the ratio of industrial wastewater discharged into the environment [20]. The mathematical model is presented below.(i)
Centralized water supply rateCen is given by(13)Cen=CTsup,whereC is the centralized water supply.(ii)
Leakage rateLea of water supply network is given by(14)Lea=UC,whereU is the leakage.(iii)
Agricultural irrigation water quotaQuo is given by(15)Quo=AgiArea,whereAgi is agricultural water consumption.(iv)
Quantity of water intake of industrial added valuelavw (10000 Yuan) is given by(16)lavw=IwcIav,whereIwc is the industrial water consumption and Iav is the industrial added value.(v)
Centralized processing rateSctr is given by(17)Sctr=StcSq,whereStc is the sewage treatment capacity and Sq is the total wastewater.Based on the above analysis, the online evaluation method constructs the evaluation index system as shown in Figure2.Figure 2
Evaluation index system of cyclic utilization effect of water resource.


## 2.1. Water Ecological Level

The water ecology dimension represents the level of the water ecological civilization construction which is a very important part of a healthy water cycle system. It also reflects the natural attribute of the water cycle [14]. The guaranteed rate of ecological water demand reflects the guaranteed degree of environmental water demand [15]. The coverage rate of evaluation system represents the greening level of the built-up area. The variation of groundwater depth and groundwater exploitation coefficient reflects the regional groundwater exploitation situation and dynamic trend. These indicators have a stronger characterization for the areas relying on groundwater.(i)
Guarantee rate of ecological water demandEco is given by(1)Eco=RepDe,whereRep is the ecological water replenishment and De is the ecological water demand.(ii)
Coverage rateCov of landscape area is given by(2)Cov=GaTa,whereGa is the green area and Ta is the built-up area.(iii)
Variation of depth to ground water in plain areaΔDep is given by(3)ΔDep=Di+1−Di,whereDi+1 is the depth to ground water in the i+1 th year and Di is the depth to ground water in the i th year.(iv)
Coefficient of groundwater exploitationExp is given by(4)Exp=ExCex,whereEx is the exploitation amount of groundwater and Cex is the exploitable amount of underground water.


## 2.2. Water Environment Quality

The dimension of water environment quality is an indispensable part of evaluating a healthy water cycle system which can reflect the water quality in the researched area and the social attributes of the water cycle [15]. Four indexes are used to characterize the water quality. The standard-reaching rate of river length and water function area reflects the water quality status of natural rivers as well as the standard-reaching status of five functional areas. The water function area involves the development, utilization, conservation, and protection of water resources. The qualified rate of water in pipe network and the standard-reaching rate of drinking water sources reflect the safety level of human drinking water from the aspects of water supply and water source.(i)
The proportionQua of river length whose water quality to reach the standard is given by(5)Qua=stdS,wherestd is the standard river length and S is the length of river with water.(ii)
The rate of reaching the standard of water function areaFuc is given by(6)Fuc=numNum,wherenum is the number of water functional areas up to standard and Num is the total number of water functional areas.(iii)
Qualification ratePip of water in pipe network is shown in(7)Pip=tT,wheret is the time to pass the test and T is the total time.(iv)
Standard-reaching rate of the drinking water sourceDri is given by (8)Dri=timTim,wheretim is the time to pass the test and Tim is the total time.


## 2.3. Abundance of Water Resources

The water resource abundance has distinct regional characteristics. The water resource richness benchmarks differ in different regions mainly caused by the different climates, geographical locations, and other factors between regions [17]. Four indexes have been used to characterize the water resource abundance. The indexes of per capita water resources can indicate the situation of the carrying capacity of regional water resources to some extent. The excessive population is not suitable for the small water resources. The utilization rate of water resources reflects the degree of regional economic and social development to the local water resource exploitation. The high utilization rate of water resources leads to the pathological condition of water circulation. The proportion index of groundwater supply emphasizes the dependence of water supply on groundwater, and excessive utilization of groundwater will destroy the benign circulation of the groundwater system.(i)
Per capita water resourcePer is shownas follows:(9)Per=TolPou,whereTol is the total water resource and Pou is the population.(ii)
Utilization rateUti of water resource is given by(10)Uti=Sur+GrdTol,whereSur is the surface water consumption and Grd is the underground water consumption.(iii)
Average water resources per muAcre is shown as follows:(11)Acre=TolArea,whereArea is the irrigated area.(iv)
ProportionDsup of groundwater to water supply is given by(12)Dsup=aTsup,wherea is the groundwater supply and Tsup is the total water supply.


## 2.4. Utilization of Water Resource

The level of water resources utilization mainly involves the subprocesses of the water cycle such as centralized water supply, water use efficiency, water-saving level, and drainage system. This dimension reflects the social attribute of the water cycle [19]. Seven indexes are used to represent the water resources utilization. The centralized water supply rate and leakage rate of the water-supply network reflect the operation state of the water supply system from the aspects of water supply and water delivery efficiency respectively. The water consumption rate of domestic water, agricultural irrigation water quota, and industrial usage reflect the efficiency of the regional water resource utilization in the perspective of life, agriculture, and industry. The centralized sewage treatment rate reflects the regional water resources utilization efficiency. The centralized sewage treatment rate reflects the state of urban sewage treatment. If the industrial wastewater is directly discharged into the environment, it will cause continuous water pollution and water ecological environment damage. It is characterized by the ratio of industrial wastewater discharged into the environment [20]. The mathematical model is presented below.(i)
Centralized water supply rateCen is given by(13)Cen=CTsup,whereC is the centralized water supply.(ii)
Leakage rateLea of water supply network is given by(14)Lea=UC,whereU is the leakage.(iii)
Agricultural irrigation water quotaQuo is given by(15)Quo=AgiArea,whereAgi is agricultural water consumption.(iv)
Quantity of water intake of industrial added valuelavw (10000 Yuan) is given by(16)lavw=IwcIav,whereIwc is the industrial water consumption and Iav is the industrial added value.(v)
Centralized processing rateSctr is given by(17)Sctr=StcSq,whereStc is the sewage treatment capacity and Sq is the total wastewater.Based on the above analysis, the online evaluation method constructs the evaluation index system as shown in Figure2.Figure 2
Evaluation index system of cyclic utilization effect of water resource.


## 3. Online Evaluation Method of Water Recycling

The fuzzy approach is devised to determine the weights of the criteria, an extension of AHP is used. The model is constructed to evaluate the cyclic utilization effect of water resources in urban landscaping with an online evaluation method of the cyclic utilization effect of water resources.The fuzzy approach in combination to AHP model is mainly composed of the AHP and fuzzy comprehensive evaluation system. The fuzzy comprehensive evaluation is based on the advantages of two approaches, one is AHP which is MCDM approach and second is Fuzzy which is a soft computing-based approach to evaluate the water recycling system. The two methods complement each other, and the reliability and effectiveness of evaluation are improved. The technology roadmap is shown in Figure3.Figure 3
Technical roadmap of comprehensive fuzzy evaluation method.


### 3.1. Use of Extension of AHP to Determine the Weights

#### 3.1.1. Constructing Extension Judgment Matrix

After constructing the evaluation index system of water recycling, many experts and scholars use the pairwise comparison the relative importance of the lower-level elements dominated by the elements of the upper layer [21, 22], and then construct the extension interval judgment matrix A=aijn×n, i,j=1,2,3,⋯,n to measure the importance of different criteria. The 1 to 9 scale method shown in Table 1 is used for the assignment of weights.aij=aij−,aij+ is an extension interval number, aij− and aij+ are the upper and lower end points of the extension interval elements in the ith row and jth column of the judgment matrix. In order to quantify each element in the extension judgment matrix, the median value of the extension interval number must be the integer in the scaling method.Table 1
1–9 evaluation scale.
Relative scaleMeaning1Elementx and element y are equally important3Elementx is slightly more important than y5Elementx is more important than element y7Elementx is obviously more important than element y9Elementx is absolutely important2,4,6,8The importance of elementx relative to element y is between the two values1,1/2, …, 1/9The unimportant degree elementx and element y


#### 3.1.2. Obtaining the Eigenvector for Judgment Matrix

The eigenvector is obtained after pairwise comparison of one criterion over another criterion. The purpose is to check the impact of levels of elements on the decision-making. The square root method can be used to calculate the eigenvector. The specific calculation steps are shown from equations (18)–(20).(18)Fi+=∏j=1naij+,(19)x¯i+=Fi+n,(20)xi+=x¯i−∑i=1nx¯i+.Finally, the eigenvectorx+=x1+,x2+,⋯,xn+T is obtained. Then, the eigenvectors corresponding to the extension judgment matrix A=aijn×n are calculated. k and m are solved in (21) and (22), respectively. When 0≤k≤1≤m, the judgment matrix A of extension interval number meets the consistency requirements.(21)k=∑j=1n1∑i=1naij+,(22)m=∑j=1n1∑i=1naij−.


#### 3.1.3. Solving the Single Ranking Weight Vector of Factor

Different elements in each layer correspond to respective weight vector of interval number are analyzed [23, 24], that is ωi=kxi−,mxi+=ωi−,ωi+T. Equation (23)–(25) collaboratively solve the possible degree whether ωi is greater than ωj:(23)Vωi≥ωj=2ωi+−ωj−Lωi+Lωj,(24)Lωi=ωi+−ωi−,(25)Lωj=ωj+−ωj−.For∀, if any i,j=1,2,⋯,n and i≠j, Vωi≥ωj≥0, then Pj and Pi is given by(26)Pj=1,Pi=V.In (26), Pi is the single ranking vector of the ith element in this layer with respect to an element in the upper layer. After further normalization, the single ranking weight of all elements in this layer with respect to an element in upper layer can be obtained by equation: (27)P=P1,P2,⋯,PnT.


#### 3.1.4. Solving the Total Ranking Weight Vector of Factor

Let us assume that the single-order weight vectors ofnk elements in the k th layer corresponding to each element in the upper layer are phk=p1hk,p2hk,⋯,pnkhkT . k denotes the kth layer. h denotes the hth element in the upper layer. When h=1,2,⋯,nk−1, the matrix can be obtained as follows:(28)phk=p1hk,p2hk,⋯,pnkhkT=p11kp12k⋯p1nk−1kp21kp22k⋯p2nk−1k⋯⋯⋯⋯pnk1kpnk2k⋯pnknk−1k.If the single ranking weight of elements in thek−1th layer with respect to the final goal is set as ωk−1=ω1k−1,ω2k−1,⋯,ωnk−1k−1T, the total ranking weight ωk of all elements in the k th layer with respect to the final goal can be obtained by(29)ωk=pkpk−1⋯p3ω2,where ω2 is the single ordering weight.


### 3.2. Using Fuzzy Comprehensive Evaluation to Determine the Evaluation Grade

The steps of fuzzy comprehensive evaluation method to determine the evaluation grade are described below:


#### 3.2.1. Determining the Set of Rank Assessing Criteria

The comment set is a set of evaluation results that may be made by the evaluation object [25] which can be expressed by(30)V=v1,v2,⋯,vm,where vi is the rank assessing criterion and m is the number of elements. It is the grade or the number of comments.


#### 3.2.2. Constructing Fuzzy Evaluation Matrix

After the quantitative evaluation indexes are substituted into the membership formula, the membership degreerij of each evaluation index belonging to each evaluation grade can be obtained. Thus, the evaluation matrix R can be obtained as (31)R=R1R2⋮Rn=r11r12⋯r1mr21r22⋯r2m⋯⋯⋯⋯rn1rn2⋯rnm.The online evaluation method of cyclic utilization effect of water resource in urban landscaping uses the fold-line membership function to determine the membership degree.The membership degree of positive index is calculated by equations (32)–(34):(32)ri1=0.51+ki1−Ciki2−Ci,Ci≤ki1,0.51−Ci−ki1ki2−ki1,ki1Ciki2,0,Ci≥ki2,(33)ri2=0.51−ki1−Ciki2−Ci,Ci≤ki1,0.51+Ci−ki1ki2−ki1,ki1≤Ciki2,0.51+ki3−Ciki3−ki2,ki2≤Ciki3,0.51+Ci−ki3Ci−ki2,Ci≥ki3,(34)ri3=0,Ci≤ki2,0.51−Ci−ki3ki3−ki2,ki2Ciki3,0.51+Ci−ki3Ci−ki2,Ci≥ki3.In equations (32)–(34), rij is the fuzzy membership degree of the jth evaluation-level corresponding to evaluation index Ci.


#### 3.2.3. Fuzzy Operation

The fuzzy evaluation matrix and the weight vector of factor are adopted for fuzzy operation so that the comprehensive result of fuzzy evaluation can be obtained. After determining the weight set and evaluation matrix, the online evaluation model of cyclic utilization effect of water resource is built and given by(35)B=W⋅R.Based on the evaluation model, the online evaluation of cyclic utilization effect of water resource is completed.


## 3.1. Use of Extension of AHP to Determine the Weights

### 3.1.1. Constructing Extension Judgment Matrix

After constructing the evaluation index system of water recycling, many experts and scholars use the pairwise comparison the relative importance of the lower-level elements dominated by the elements of the upper layer [21, 22], and then construct the extension interval judgment matrix A=aijn×n, i,j=1,2,3,⋯,n to measure the importance of different criteria. The 1 to 9 scale method shown in Table 1 is used for the assignment of weights.aij=aij−,aij+ is an extension interval number, aij− and aij+ are the upper and lower end points of the extension interval elements in the ith row and jth column of the judgment matrix. In order to quantify each element in the extension judgment matrix, the median value of the extension interval number must be the integer in the scaling method.Table 1
1–9 evaluation scale.
Relative scaleMeaning1Elementx and element y are equally important3Elementx is slightly more important than y5Elementx is more important than element y7Elementx is obviously more important than element y9Elementx is absolutely important2,4,6,8The importance of elementx relative to element y is between the two values1,1/2, …, 1/9The unimportant degree elementx and element y


### 3.1.2. Obtaining the Eigenvector for Judgment Matrix

The eigenvector is obtained after pairwise comparison of one criterion over another criterion. The purpose is to check the impact of levels of elements on the decision-making. The square root method can be used to calculate the eigenvector. The specific calculation steps are shown from equations (18)–(20).(18)Fi+=∏j=1naij+,(19)x¯i+=Fi+n,(20)xi+=x¯i−∑i=1nx¯i+.Finally, the eigenvectorx+=x1+,x2+,⋯,xn+T is obtained. Then, the eigenvectors corresponding to the extension judgment matrix A=aijn×n are calculated. k and m are solved in (21) and (22), respectively. When 0≤k≤1≤m, the judgment matrix A of extension interval number meets the consistency requirements.(21)k=∑j=1n1∑i=1naij+,(22)m=∑j=1n1∑i=1naij−.


### 3.1.3. Solving the Single Ranking Weight Vector of Factor

Different elements in each layer correspond to respective weight vector of interval number are analyzed [23, 24], that is ωi=kxi−,mxi+=ωi−,ωi+T. Equation (23)–(25) collaboratively solve the possible degree whether ωi is greater than ωj:(23)Vωi≥ωj=2ωi+−ωj−Lωi+Lωj,(24)Lωi=ωi+−ωi−,(25)Lωj=ωj+−ωj−.For∀, if any i,j=1,2,⋯,n and i≠j, Vωi≥ωj≥0, then Pj and Pi is given by(26)Pj=1,Pi=V.In (26), Pi is the single ranking vector of the ith element in this layer with respect to an element in the upper layer. After further normalization, the single ranking weight of all elements in this layer with respect to an element in upper layer can be obtained by equation: (27)P=P1,P2,⋯,PnT.


### 3.1.4. Solving the Total Ranking Weight Vector of Factor

Let us assume that the single-order weight vectors ofnk elements in the k th layer corresponding to each element in the upper layer are phk=p1hk,p2hk,⋯,pnkhkT . k denotes the kth layer. h denotes the hth element in the upper layer. When h=1,2,⋯,nk−1, the matrix can be obtained as follows:(28)phk=p1hk,p2hk,⋯,pnkhkT=p11kp12k⋯p1nk−1kp21kp22k⋯p2nk−1k⋯⋯⋯⋯pnk1kpnk2k⋯pnknk−1k.If the single ranking weight of elements in thek−1th layer with respect to the final goal is set as ωk−1=ω1k−1,ω2k−1,⋯,ωnk−1k−1T, the total ranking weight ωk of all elements in the k th layer with respect to the final goal can be obtained by(29)ωk=pkpk−1⋯p3ω2,where ω2 is the single ordering weight.


## 3.1.1. Constructing Extension Judgment Matrix

After constructing the evaluation index system of water recycling, many experts and scholars use the pairwise comparison the relative importance of the lower-level elements dominated by the elements of the upper layer [21, 22], and then construct the extension interval judgment matrix A=aijn×n, i,j=1,2,3,⋯,n to measure the importance of different criteria. The 1 to 9 scale method shown in Table 1 is used for the assignment of weights.aij=aij−,aij+ is an extension interval number, aij− and aij+ are the upper and lower end points of the extension interval elements in the ith row and jth column of the judgment matrix. In order to quantify each element in the extension judgment matrix, the median value of the extension interval number must be the integer in the scaling method.Table 1
1–9 evaluation scale.
Relative scaleMeaning1Elementx and element y are equally important3Elementx is slightly more important than y5Elementx is more important than element y7Elementx is obviously more important than element y9Elementx is absolutely important2,4,6,8The importance of elementx relative to element y is between the two values1,1/2, …, 1/9The unimportant degree elementx and element y


## 3.1.2. Obtaining the Eigenvector for Judgment Matrix

The eigenvector is obtained after pairwise comparison of one criterion over another criterion. The purpose is to check the impact of levels of elements on the decision-making. The square root method can be used to calculate the eigenvector. The specific calculation steps are shown from equations (18)–(20).(18)Fi+=∏j=1naij+,(19)x¯i+=Fi+n,(20)xi+=x¯i−∑i=1nx¯i+.Finally, the eigenvectorx+=x1+,x2+,⋯,xn+T is obtained. Then, the eigenvectors corresponding to the extension judgment matrix A=aijn×n are calculated. k and m are solved in (21) and (22), respectively. When 0≤k≤1≤m, the judgment matrix A of extension interval number meets the consistency requirements.(21)k=∑j=1n1∑i=1naij+,(22)m=∑j=1n1∑i=1naij−.


## 3.1.3. Solving the Single Ranking Weight Vector of Factor

Different elements in each layer correspond to respective weight vector of interval number are analyzed [23, 24], that is ωi=kxi−,mxi+=ωi−,ωi+T. Equation (23)–(25) collaboratively solve the possible degree whether ωi is greater than ωj:(23)Vωi≥ωj=2ωi+−ωj−Lωi+Lωj,(24)Lωi=ωi+−ωi−,(25)Lωj=ωj+−ωj−.For∀, if any i,j=1,2,⋯,n and i≠j, Vωi≥ωj≥0, then Pj and Pi is given by(26)Pj=1,Pi=V.In (26), Pi is the single ranking vector of the ith element in this layer with respect to an element in the upper layer. After further normalization, the single ranking weight of all elements in this layer with respect to an element in upper layer can be obtained by equation: (27)P=P1,P2,⋯,PnT.


## 3.1.4. Solving the Total Ranking Weight Vector of Factor

Let us assume that the single-order weight vectors ofnk elements in the k th layer corresponding to each element in the upper layer are phk=p1hk,p2hk,⋯,pnkhkT . k denotes the kth layer. h denotes the hth element in the upper layer. When h=1,2,⋯,nk−1, the matrix can be obtained as follows:(28)phk=p1hk,p2hk,⋯,pnkhkT=p11kp12k⋯p1nk−1kp21kp22k⋯p2nk−1k⋯⋯⋯⋯pnk1kpnk2k⋯pnknk−1k.If the single ranking weight of elements in thek−1th layer with respect to the final goal is set as ωk−1=ω1k−1,ω2k−1,⋯,ωnk−1k−1T, the total ranking weight ωk of all elements in the k th layer with respect to the final goal can be obtained by(29)ωk=pkpk−1⋯p3ω2,where ω2 is the single ordering weight.


## 3.2. Using Fuzzy Comprehensive Evaluation to Determine the Evaluation Grade

The steps of fuzzy comprehensive evaluation method to determine the evaluation grade are described below:


### 3.2.1. Determining the Set of Rank Assessing Criteria

The comment set is a set of evaluation results that may be made by the evaluation object [25] which can be expressed by(30)V=v1,v2,⋯,vm,where vi is the rank assessing criterion and m is the number of elements. It is the grade or the number of comments.


### 3.2.2. Constructing Fuzzy Evaluation Matrix

After the quantitative evaluation indexes are substituted into the membership formula, the membership degreerij of each evaluation index belonging to each evaluation grade can be obtained. Thus, the evaluation matrix R can be obtained as (31)R=R1R2⋮Rn=r11r12⋯r1mr21r22⋯r2m⋯⋯⋯⋯rn1rn2⋯rnm.The online evaluation method of cyclic utilization effect of water resource in urban landscaping uses the fold-line membership function to determine the membership degree.The membership degree of positive index is calculated by equations (32)–(34):(32)ri1=0.51+ki1−Ciki2−Ci,Ci≤ki1,0.51−Ci−ki1ki2−ki1,ki1Ciki2,0,Ci≥ki2,(33)ri2=0.51−ki1−Ciki2−Ci,Ci≤ki1,0.51+Ci−ki1ki2−ki1,ki1≤Ciki2,0.51+ki3−Ciki3−ki2,ki2≤Ciki3,0.51+Ci−ki3Ci−ki2,Ci≥ki3,(34)ri3=0,Ci≤ki2,0.51−Ci−ki3ki3−ki2,ki2Ciki3,0.51+Ci−ki3Ci−ki2,Ci≥ki3.In equations (32)–(34), rij is the fuzzy membership degree of the jth evaluation-level corresponding to evaluation index Ci.


### 3.2.3. Fuzzy Operation

The fuzzy evaluation matrix and the weight vector of factor are adopted for fuzzy operation so that the comprehensive result of fuzzy evaluation can be obtained. After determining the weight set and evaluation matrix, the online evaluation model of cyclic utilization effect of water resource is built and given by(35)B=W⋅R.Based on the evaluation model, the online evaluation of cyclic utilization effect of water resource is completed.


## 3.2.1. Determining the Set of Rank Assessing Criteria

The comment set is a set of evaluation results that may be made by the evaluation object [25] which can be expressed by(30)V=v1,v2,⋯,vm,where vi is the rank assessing criterion and m is the number of elements. It is the grade or the number of comments.


## 3.2.2. Constructing Fuzzy Evaluation Matrix

After the quantitative evaluation indexes are substituted into the membership formula, the membership degreerij of each evaluation index belonging to each evaluation grade can be obtained. Thus, the evaluation matrix R can be obtained as (31)R=R1R2⋮Rn=r11r12⋯r1mr21r22⋯r2m⋯⋯⋯⋯rn1rn2⋯rnm.The online evaluation method of cyclic utilization effect of water resource in urban landscaping uses the fold-line membership function to determine the membership degree.The membership degree of positive index is calculated by equations (32)–(34):(32)ri1=0.51+ki1−Ciki2−Ci,Ci≤ki1,0.51−Ci−ki1ki2−ki1,ki1Ciki2,0,Ci≥ki2,(33)ri2=0.51−ki1−Ciki2−Ci,Ci≤ki1,0.51+Ci−ki1ki2−ki1,ki1≤Ciki2,0.51+ki3−Ciki3−ki2,ki2≤Ciki3,0.51+Ci−ki3Ci−ki2,Ci≥ki3,(34)ri3=0,Ci≤ki2,0.51−Ci−ki3ki3−ki2,ki2Ciki3,0.51+Ci−ki3Ci−ki2,Ci≥ki3.In equations (32)–(34), rij is the fuzzy membership degree of the jth evaluation-level corresponding to evaluation index Ci.


## 3.2.3. Fuzzy Operation

The fuzzy evaluation matrix and the weight vector of factor are adopted for fuzzy operation so that the comprehensive result of fuzzy evaluation can be obtained. After determining the weight set and evaluation matrix, the online evaluation model of cyclic utilization effect of water resource is built and given by(35)B=W⋅R.Based on the evaluation model, the online evaluation of cyclic utilization effect of water resource is completed.


## 4. Experimental Results and Discussion

In order to evaluate the effectiveness of the proposed method, it is necessary to test the online evaluation method of urban landscape water recycling. The testing is performed in real environment of Yantai province. The proposed fuzzy method and three reviewed methods are used to evaluate the effect of water recycling process. The performance evaluation metrics used for comparative study are mean square error (MSE) and evaluation time as the evaluation index. The proposed online evaluation method of water recycling system in urban landscaping is compared with the method presented in reference [6] method (2) using chromatography analysis and data envelopment analysis, second, it is compared with the method presented in reference [7] as method 3 based on critic-topsis-gray correlation degree and finally method 4 given in reference [8] is taken for comparative study. The experimental results are shown in Figure 4.Figure 4
The MSE score obtained by different methods.As shown in Figure4, the MSE score of method-1 is lower than that of other methods. In first iteration of experiment, the mean square error is obtained around 0.18 which is lower than that of the method 2, 3 and 4 which is around 0.45, 0.6, and 0.5, respectively. Same is observed in the next four iterations. Difference between method-1 and the highest MSE score from other three methods is 0.4, 0.5, 0.5, and 0.5 for iteration 2, 3, 4, and 5, respectively. The proposed or Method-1 has adopted the extension of analytic hierarchy process (AHP) in combination to Fuzzy methods to describe the relative importance of each evaluation index and to rank the water recycling resources. The proposed method can reduce the subjective impact and enhances the accuracy to calculate the weight of each evaluation element. Finally, the accuracy of the evaluation results is improved, and the MSE score of the proposed method is reduced. The test results of evaluation time of the four methods are shown in Figure 5.Figure 5
The evaluation time for different methods.Figure5 shows that the proposed method's evaluation time, that is, method-1 is far less than that of the other three methods presented in references [6–8]. In first iteration, the time taken to produce the solution is 17s which is lower than that of the methods method 2 (29s), 3 (33s), and 4 (28s), respectively. Same is observed in the next four iterations. Difference between method 1 and the highest evaluation time taken from other three methods are 25s, 20s, 20s, and 23s for iterations 2, 3, 4, and 5, respectively. Method 1 is analyzed for the connotation of the healthy water cycle. Through the analysis results, it is observed that the proposed method for the evaluation index of water recycling or water utilization has the lower time complexity to produce results and better evaluation system based on pairwise comparison and ranking.


## 5. Conclusion

The allocation of water resources determines the sustainable development of the nation. The recycling effect of water resources in the urban landscape has attracted widespread attention to preserve the natural resources. Therefore, this paper proposes an online evaluation method of the water recycling process to solve this environmental problem of preserving the natural resources like water. The proposed method is based on the advantages of AHP and fuzzy logic. The method proposed has a low MSE score than the other studied methods. The evaluation of the water resource recycling process can be completed in a short time via the introduction of an extended AHP and fuzzy comprehensive evaluation method by using the advantages of two methods. In future work, different methods can be utilized to test the efficacy of different methods for evaluating the water recycling systems. The existing approaches are compared with proposed method with respect to the accuracy of measuring the system and time complexity to produce the solutions. There is a need to optimize the industrial structure and to support the harmonious growth of the economy and the environment. The economy is the driving force behind the regional growth but it is also a significant supporter of environmental conservation in the water sector. Therefore, in future, this research might be linked to the economy of the world or a specific country to analyze the relationship between the economy and water recycling system of the country.



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*Source: 1811283-2022-05-19.xml*