Indicator system optimization model for evaluating resilience of regional agricultural soil – water resource composite system

Resilience is an important indicator for measuring regional sustainable development capacity. The construction of a suitable evaluation indicator system is the premise of evaluating regional sustainable development. In this study, taking the Jiansanjiang Administration of Heilongjiang Province in China as an example, a preliminary selection library of the evaluation indicator system for the resilience of a regional agricultural soil – water resource composite system covering seven subsystems and 59 indicators was established. Selection criteria such as the Dale indicator criteria, subjective and objective combination weighting and principal component analysis were introduced to construct an optimization model for the resilience evaluation indicator system for the ASWRS. First, 14 indicators that were incomplete or incapablewereremoved. Then,theDaleindicatorselectioncriteriawereusedtoensurethat 14indicators were selected. The binary fuzzy comparison method and criteria importance through interference correlation method were used to calculate the combination weight. Finally, an indicator system optimizationmodelwasestablished.Theindicatorsystemwasoptimizedfrom59to35indicators,andthe completeness of the indicator system reached 85.75%. The proposed method had obvious advantages in termsofindicatoridenti ﬁ cationandelimination,anditmaytrulyachievethegoalofindicatoroptimization.


INTRODUCTION
In ecosystems, soil and water resources are among the most widely affected resources, but water and land resources are not inexhaustible. Under the combined actions of the lithosphere, biosphere, atmosphere, hydrosphere, exosphere and humanity, the ecological environment is becoming severely damaged (Faiz et al. ). The uncertainty in regional agricultural soil and water resource systems has become increasingly clear, and the contradiction between supply and demand is becoming increasingly acute. Today, given the deteriorating ecological environment, the study of resilience is particularly important (Maleksaeidi et al. ). The establishment of a resilience evaluation indicator system has become an urgent need to maintain sustainable agricultural development. Therefore, it is very important to conduct research on the resilience of the agricultural soil-water resource composite system (ASWRS) to understand its status, predict its future development trends and achieve green environmental sustainability for its rational use (Selenica et al. ).
Resilience originated from the Latin word 'resilio', and is annotated in Webster's dictionary as 'the ability to recover its original shape and size after being subjected to a contraction deformation when subjected to pressure' (Merriam-Webster ). Holling () introduced resilience to the study of ecosystem stability in 1973, and the establishment of the Resilience Alliance, a famous international academic organization led by Holling, in 1999 (Thompson et al. ), the resilience of ASWRS can be understood as a system of agricultural soil-water resources undergoing significant changes in structure and function when subjected to external stress. After the removal of the external stress and the return to conditions similar to those in the original state, the combined effects of its own forces and external forces enable the system to restore its original structure, function, and capabilities. That is, the system can absorb the disturbance by adjusting the influencing factor in the system while its own structure remains unchanged.
International scholars have actively researched a resilience indicator system and produced useful results. They used information substitutability to select 12 indicators for evaluating resilience. An MTS-GRA-TOPSIS model was used to evaluate the resilience rating of a combined regional agricultural water and soil resource system.
These studies show that current research on resilience focuses primarily on river basins or administrative districts; few studies have focused on core areas of grain production.
There have been many studies on soil resources or water resources and related disasters. However, there have been few research projects on agricultural soil-water resource composite systems. Furthermore, a reasonable, complete and fixed indicator evaluation system has not been established. However, the lack of a strong principle for selection impacts the identification of resilience factors (Mnisi & Dlamini ). It is still necessary to construct a stronger and more complete model for the selection of The binary fuzzy comparison method (BFCM) is a relatively mature method for determining the weight of indicators, and this method has a good ability to eliminate the differences in values reported by different researchers (Luo ). The BFCM allows quantification through the matrix transformation of interconnected and differentiated indicators, extracts and summarizes information, and finds the fuzzy scale of linear changes so that comparisons can be made at a glance for complex systems (Zhang ). The objective weighting methods determine the weight from actual data and use objective information reflected by the indicator value. The CRITIC method considers the influence of differences in the indicators on the weight and considers conflict between the indicators. Among the various objective weighting methods, the CRITIC method is considered to be a calculation method that can reflect the objective weight of the indicators (Wang & Song ). The combination of subjective and objective weights reflects not only the preference of policymakers but also the objective attributes of the indicators themselves. Combining weights not only incorporates the advantages of the two weighting methods but also avoids their inadequacies to determine the final combined weight.
The Jiansanjiang Administration is an important commodity grain production base in China. It is mainly planted with rice and has a reputation as 'the hometown of green rice in China'. In this area, due to the excessive pursuit of economic growth in recent years, the long-term, largescale, inappropriate reclamation of marsh wetlands, woodlands, and grasslands in the reclamation area has resulted in the long-term, excessive and unreasonable use of chemical fertilizers and pesticides by local farmers in pursuit of higher yields (Zhang et al. ). Unsustainable agricultural development models and resource allocation models have generally resulted in effects such as declines in groundwater levels, increased soil erosion, aggravation of agricultural pollution, depletion of soil, shrinkage of wetland areas, and inadequate defence capabilities against agricultural floods and droughts. Therefore, it is particularly important to study the resilience evaluation indicator for the ASWRS in this area. Based on the above research, an agricultural soil resource system and water resource system are considered an organic composite environmental system. The primary selection pool of indicators affecting resilience was chosen according to the characteristics and definition of resilience for the ASWRS in the study area. Next, the indicators were screened to identify the decisive indicators, the indicator system framework was designed, and the indicator selection model was constructed. In this process, the Dale indicator inclusion criteria were introduced to provide theoretical support for the optimization model. When combining the BFCM and CRITIC in the indicator optimization model, the use of the main and objective weight calculation method alone is not sufficient or useful. The criterion defining indicator completeness as a cumulative contribution rate of !85% determined with the PCA method was selected as a constraint, and the evaluation indicators were selected and optimized. Finally, a relatively complete assessment indicator system was constructed for the resilience of the ASWRS.
The main objectives of this paper are as follows: (1) explore the connotation for the resilience of ASWRS, build a preliminary selection database of evaluation indicators, and determine the evaluation indicator levels; (2) determine the framework structure of the evaluation indicator system according to the logical relationship

Study area
The Jiansanjiang Administration is in the hinterland of the Sanjiang Plain on the northern border of China, and the area is adjacent to Fujin, Tongjiang, Ruyuan and Raohe and two counties. It is part of the confluence zone of the Heilongjiang River, the Ussuri River and the Songhua River. The geographic coordinates are between 132 31 0 26″ ∼ 134 22 0 26″E and 46 49 0 42″ ∼ 48 13 0 58″N, and the annual average temperature is 1-2 C. With a total area of 12,400 km 2 , 15 farms are located within the jurisdiction, accounting for 22% of the total area of the entire Heilongjiang reclamation area. With fertile land, flat terrain and abundant resources, this area with abundant rainfall, heat, and hours of sunshine is a highly productive zone in which rice, beans, and other cash crops grow. It is famous for producing high-quality green rice, and its annual grain production capacity exceeds 150 billion kg, with a commodity grain rate as high as 80%. It is also the core area of grain production in Heilongjiang Province (Liu et al. ). The specific location of the study area is shown in Figure 1.

Data sources
The Statistical Yearbook of Heilongjiang State Farms

Data extension
The explanatory variable data set was determined according to the definitions, influencing factors, and factors related to three interpreted variables: surface water environmental quality, groundwater quality, and soil quality. The data for each explanatory variable were collected in 2016 and used to calculate the water environmental quality comprehensive index and soil environmental quality index. SPSS software was used to perform multiple linear regression analysis (He ) on the above data to obtain multiple regression  Table 1.  Table 2.

Weight determination methods
The calculation steps are as follows: ① Determine the qualitative ordering matrix F of each indicator about importance.
② According to the ordering of importance of matrix F and establishing a binary comparison matrix on the degree of importance, If the condition is satisfied, the matrix F is called an ordered binary comparison matrix about importance, where f kl is the importance fuzzy scale of indicator k on l.
③ Determine the value of f kl by using the relationship between the tone operator and the fuzzy scale. The nonnormalized weight vector of the indicator is represented by the sum of the fuzzy scale value f kl of each row of the square matrix F, and the weight vector of the indicator is: The formula for calculating the amount of information G j  contained in the jth indicator is as follows: where S j represents the standard deviation of the jth indicator; X ij is the correlation coefficient between indicator i and indicator j; and P m i¼1 (1 À X ij ) is a quantitative indicator of the conflict between the jth indicator and the other indicators. A larger G j value indicates a greater amount of information contained in the jth evaluation indicator and the greater relative importance of the indicator; thus, the objective weight w of the jth indicator is: Combined weights determine the weight coefficients. The weight combination method combines the respective advantages of the subjective weights and objective weights and improves the reliability of the weight selection. The calculation method is as follows: where W yi is the combined weight; w B is the weight of the BFCM; and w C is the weight calculated by the CRITIC method.
Analytic hierarchy process. The aim of the analytic hierarchy process (AHP) is to decompose the elements related to decision-making into goals, criteria, and programmes; this process is used for qualitative and quantitative analyses in decision-making (Gao & Su ).
The calculation steps are as follows: ① Analyse the relationships between various factors in the system. Compare the importance of the elements at the same level with respect to a criterion at the previous level. Construct the judgement matrix for the pairwise comparison.
② The relative weight of the elements compared with the criterion is calculated by decision matrix A. The calculation should satisfy: where λ max is the maximum characteristic root of judgement matrix A; and W is the normalized eigenvector corresponding to λ max . The component W i of W is the weighted value of the corresponding single-order element.
③ Conduct a consistency test of the judgement matrix.
The specific calculation process is as follows: where CI represents the consistency indicator of the total hierarchical ordering; W aj represents the total rank weight of element A j at the A level; CI j refers to the consistency indicator of the judgement matrix at the next layer corresponding to A j ; RI represents the random consistency indicator of the total hierarchical ordering; RI j represents the random consistency indicator of the judgement matrix at the next level corresponding to A j ; and CR represents the random consistency ratio of the total hierarchical ordering.
If CR < 0.1, the total rank consistency test is considered to have been passed. Otherwise, it is necessary to adjust the judgement matrix of this level so that the total order of the level has satisfactory consistency.
④ Calculate the total ranking weights of the systems for each level and sort them.

Indicator system optimization model
The Structuring the relationship matrix Z (i×j) . The relationship matrix Z is constructed according to the hierarchical framework of the evaluation indicator system. It is used to determine the interaction between layers. Z represents the relationship between the nth layer and the n À 1 layer, that is, the relationship between the indicator layer and the middle layer. In the matrix Z (i×j) , i represents the ith indicator of the n À 1 layer, and j represents the jth indicator of the nth layer. If j is related to i, then Z ij ¼ 1; otherwise, Z ij ¼ 0. If the first indicator of the indicator layer has a relationship with the first system in the middle layer, then Z 11 ¼ 1. If the second indicator of the indicator layer is not related to the third system in the middle layer, then Z 32 ¼ 0.
Constructing the inclusion criteria matrix Y ( j×7) . According to Dale's eight single-indicator selection principles, the overall principle covers the entire indicator system, and thus, the overall principle is not considered. Therefore, a matrix of j rows and seven columns is constructed to select and optimize the individual indicators.
where j represents the indicator number of the nth floor and 7 represents the seven selection conditions. When the indicator meets the selection condition g, Y gj ¼ 1; otherwise, Y gj ¼ 0.
To achieve a complete indicator system, select the five principles of measurable, vulnerable, typical, controllable, and stable to form the selection condition g. The indicators that meet the selection condition g are directly selected; otherwise, they are determined. Based on the above principles, a vector P that satisfies the selection criteria of these five principles is established. The selection criteria of these five principles are set to 1, and the remaining pending conditions are 0; that is, P ¼ [1, 1, 0, 1, 1, 0, 1].
Optimizing the indicator system. The target function optimized by the selected matrix to the indicator can be set as follows: and must meet the following constraints: when the evalu- where W yi ¼ (w y1 , w y2 , Á Á Á , w yj ) is a matrix composed of all specific indicator weights.
The specific steps are shown in Figure 2. The reader can refer to the Supplementary Material for more detail regarding how we set the experimental scheme and data extension methods framework design for agricultural soil-water resource.  Table 3.

Indicator screening
The selection principle for individual indicators was combined with the data for the study area and considered with reference to expert advice and a large number of documents. After comprehensive consideration, the conformity of the indicator standard was determined, and the correlation between indicators and system resilience was determined (' þ ' indicates a positive correlation, and 'À' indicates a negative correlation). The results are shown in Table 3.
Due to imperfect data collection in the study area, no long-term monitoring data existed, and the indicators WRS 10 , WRS 11 , WRS 12 , SRS 7 , AS 9 , EES 7 , EES 8 , and EES 9 were excluded. There is a high degree of local land levelling, and the terrain is flat; thus, the indicator SRS 8 was excluded. The study area is located at high latitudes and experiences cold weather. The crop growing period is one year, and there is no option for multiple cropping (Han et al. ). Therefore, the indicator SRS 9 was excluded. Because there is no accurate measurement standard that can be counted and quantified, the indicators MS 5 , MS 6 , and MS 7 were excluded.
Because no change occurred throughout the year, the indicator weight could not be calculated; thus, the indicator EES 10 was excluded. Therefore, following the principles of a scientific, complete and accessible indicator system, a total of 14 indicators were eliminated, leaving 45 indicators.

Indicator weight determination
The evaluation indicator system for ASWRS resilience was determined based on statistical data from 1997 to 2016 for the study area. The weight of the middle tier was determined using the BFCM, and the weight of the indicator layer was determined by the CRITIC method. Finally, the combined weight was calculated. The results are shown in Table 4.

Indicator system optimization and selection
In accordance with the inclusion criteria matrix formula combined with the evaluation indicator system for ASWRS resilience, the selection criteria matrix Y (45×7) and the relationship matrix Z (7×45) were constructed.
According to the assessment model for the resilience indicator of the ASWRS and the Dale indicator selection criteria, the following can be calculated.  and to prevent the middle layers of the entire indicator system from being disconnected, YI Á Z > 0 should be satisfied.
Thus, this condition has been met.
According to the indicator system, the principles of selection and completeness are optimized and are simultaneously concise and operable. The PCA method with a cumulative contribution rate of 85% of the criteria was used for further selection and optimization of the indicators, using the formula YI Á W 0 yi ! 0:85 to ensure the completeness of the indicator.
At the same time, to ensure that the objective function had an optimal solution: Not all yi can be 0; thus, for the remaining 31 indicators to be determined, the ten indicators SS 4 , SS 2 , SS 1 , WRS 3 , WRS 4 , WRS 6 , ES 7 , ES 4 , ES 3 , and ES 6 , which had smaller weights, were discarded. The remaining indicators guaranteed the completeness of the indicator system at 85.75%, which met the optimization conditions.

Rationality analysis of algorithm results
To verify the reliability of the indicator selection process in this paper, three comparison methods were included. The The weight calculation results are shown in Table 5.
In addition, the above indicator optimization model was used to satisfy and ensure the following objective function: min Q ¼ P j m¼1 yi m ,YI Á Z > 0, YI Á W 0 yi ! 0:85. Finally, the AHP-CRITIC method was used to calculate the optimal solution for min Q ¼ 33 and YI Á W 0 yi ¼ 0:8534; the CRITIC method was used to calculate the optimal solution for min Q ¼ 38 and YI Á W 0 yi ¼ 0:8551; and the AHP method was used to calculate the optimal solution for min Q ¼ 30 and YI Á W 0 yi ¼ 0:8527. The AHP method was more suitable for weight calculation with fewer indicators.
For the 45 indicators in this paper, the calculation result using the AHP method was too subjective. The results excluded 15 indicators too often. Therefore, the accuracy of the indicator system was affected, and this method was not considered. The eliminated indicators for each method are shown in Figure 3.
Based on the three remaining weight determination methods, ES 3 and ES 6 were removed, and the indicators WRS 6 , SS 1 , SS 2 , SS 4 , ES 4 and ES 7 , which were removed by the BFCM-CRITIC method, were also eliminated by the AHP-CRITIC method. The BFCM-CRITIC method removed 80% of the same indicators, while the AHP-CRITIC method excluded indicators from the MS, ES, SS and EES. The main reason for these exclusions was that the middle-layer weight of the four systems determined by the AHP method was small. As a result, the combination weights of the indicators in the four systems were too small, and the indicators were in turn eliminated. The AHP method was more subjective,

Comparative analysis of evaluation results
To verify the rationality of the indicator system constructed in this paper, the similarities and differences in the indicators used to measure the resilience are compared and analysed in order to avoid the impact of regional and research content differences on the resulting analysis. By referring to the results and content of research in similar areas, a comparative analysis was carried out considering three aspects: the construction of the indicator system, the selection of initial indicators and the difference in the screening indicator layer (Perrings ). The results are shown in Table 6.
The initial indicator is the basis for optimizing the indi- for 80%, which indicates that the indicators screened in this paper are reasonable and comprehensive.

CONCLUSIONS
Regional agricultural soil-water resources represent a complex, large system, and resilience is a basic attribute that can be used to describe the operational status of such systems (Milman & Short ). Constructing a complete resilience evaluation indicator system is a primary task for the green environmental sustainable development of ASWRS. The selection of indicators plays an important role in research on resilience. The establishment of an evaluation indicator system also provides a good theoretical basis for calculating the next step of resilience.
( (2) Based on the current conditions in the research area, the BFCM is combined with the CRITIC method to determine the combination weights of the indicator (3) Notably, the use of multiple linear regression analysis extended the historical data that were missing environmental parameters. The use of a sum of indicator system weights !0.85 as an indicator of completeness may have had an impact on the preferred results for the indicators. In the future, to ensure the breadth of the evaluation indicators of the restoration capacity of regional ASWRSs, determining how to more accurately derive missing historical data for related indicators and how to more reasonably determine the completeness of the indicator system are worth further study.