A refined evaluation and diagnosis method for the state of regional systems based on subtraction sets and Moran's exponent.

Abstract

This invention discloses a method for refined evaluation and diagnosis of regional system status based on subtractive set pair potential and Moran's index, belonging to the technical field of regional system evaluation. The method includes: constructing a multi-level evaluation index system and determining the grading standards for each evaluation index; calculating the weight coefficients of the evaluation indicators; calculating the connection number of each evaluation sample and determining the evaluation level of each sample; coupling the subtractive set pair potential with Moran's index to identify the refined spatial clustering type of each evaluation sample; and spatial mapping the refined spatial clustering type of each evaluation sample. This invention couples the set pair potential, which reflects the internal structural characteristics of the connection number, with the traditional Moran's index spatial clustering framework, achieving a leap from "spatial pattern identification" to "spatial pattern identification and collaborative diagnosis of future development trends" in assessing the status of regional systems, providing a more scientific decision-making basis for refined regional management and cross-regional collaborative development.

Description

Technical Field

[0001] This invention belongs to the technical field of regional system evaluation, specifically relating to a method for refined evaluation and diagnosis of the state of regional systems based on subtraction set potential and Moran index. Background Technology

[0002] In the interdisciplinary field of water resources science, environmental science, and ecology, comprehensive evaluations of the systemic status of water resources, including carrying capacity, spatial balance, high-quality development of water conservancy, and the ecological environment, are crucial foundations for supporting regional resource integration development and utilization planning and scientific decision-making. Traditional comprehensive system evaluations often focus on a single study area or conduct independent evaluations of each sub-region within the study area, paying insufficient attention to the spatial relationships between these sub-regions. Currently, most studies still rely on Geographic Information Systems (GIS) tools, using color-coding to visualize evaluation results and perform qualitative comparative analysis, making it difficult to quantitatively characterize the spatial interactions and dependencies between regions. However, the spatial correlations and differences between regions are crucial for revealing the allocation patterns, coordination mechanisms, and potential game-theoretic relationships of resources across regions.

[0003] To further explore the spatial correlation and clustering characteristics among evaluation samples, existing techniques typically introduce Moran's index and Theil index for spatial correlation analysis. Moran's index, by calculating the global and local Moran's indices, uses a single numerical indicator to measure the degree of spatial clustering across the entire study area and local regions. In local Moran's index analysis, the spatial correlation patterns of each evaluation sample can be classified into four basic types: high-high (HH, high-value areas surrounded by high-value areas), low-low (LL, low-value areas surrounded by low-value areas), high-low (HL, high-value areas surrounded by low-value areas), and low-high (LH, low-value areas surrounded by high-value areas). This classification method provides an effective tool for identifying spatial hotspots and cold zones.

[0004] However, in practical applications, this traditional spatial clustering method has the following drawbacks: (1) It masks the differences in internal structure within the same spatial cluster type. This method can only identify spatial relationships between regions, but it cannot reveal the differences in the development status of each sample within the same spatial cluster type. For example, two regions belonging to the same "high-high" cluster may have different development levels. One region may have a high level of development and a stable internal structure, with each subsystem developing in synergy. The other region may have a high current level, but its internal structure may fluctuate drastically or face significant competitive pressure (such as the two regions relying on a single resource and having a certain degree of competitiveness). Traditional methods use a general "high-high" label to mask these two very different internal states, making it impossible for decision-makers to conduct refined management of their inherent stability.

[0005] (2) Lack of diagnostic capability for the dynamic evolution trend of the system. Traditional Moran index analysis is based on a final comprehensive evaluation value (such as a single score, level characteristic value, etc.), which is usually static and deterministic. It cannot reflect the uncertainty information behind the evaluation results, such as the fluctuation trend of the evaluation results between "meeting the standard" and "not meeting the standard", or the potential to transform into "better" or "worse". Therefore, traditional methods are difficult to effectively diagnose and predict the potential risks, vulnerabilities and future evolution trends of the system.

[0006] In summary, existing evaluation methods have significant limitations in "diagnosing the internal structure of spatial patterns" and "diagnosing development trends," making it difficult to provide the key support needed for refined evaluation of the status of water resources, environment, ecology, and other systems, as well as differentiated regulation and management for regional coordinated development. Summary of the Invention

[0007] The purpose of this invention is to address the aforementioned shortcomings in the prior art by providing a refined evaluation and diagnosis method for the state of regional systems based on subtraction set potential and Moran's index. This method solves the problem that the prior art, which uses a single numerical index for spatial autocorrelation analysis, cannot distinguish the structural differences in stability, volatility, and competitiveness among evaluation samples within the same spatial cluster type, thereby masking the heterogeneity and dynamic evolution characteristics within the region.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for refined evaluation and diagnosis of the state of a regional system based on subtraction sets and Moran's index includes the following steps: S1. Construct a multi-level evaluation index system that includes a target layer, a criterion layer, and an indicator layer, and determine the grading standards for each evaluation index; S2. Obtain the relative importance ranking of each evaluation indicator and calculate the weight coefficient of the evaluation indicator; S3. Based on the multi-level evaluation index system, grading standards and weight coefficients, calculate the connection number of each evaluation sample index layer, criterion layer and target layer in sequence, and finally determine the evaluation level of each evaluation sample target layer. S4. Calculate the subtraction set pair potential based on the connection components of the target layer calculated in S3; S5. Couple the subtraction set potential with the Moran index to identify the refined spatial clustering type of each evaluation sample; S6. Based on the geographic information system platform, spatial mapping is performed on the refined spatial clustering types of each evaluation sample, and countermeasure analysis is carried out for each refined spatial clustering type.

[0009] Furthermore, S2 specifically refers to: The relative importance ranking of each evaluation indicator was obtained by using expert consultation or questionnaire survey, and the weight coefficient of each evaluation indicator was calculated by using the analytic hierarchy process.

[0010] Furthermore, in S3, the correlation coefficients of the indicator layer, criterion layer, and target layer for each evaluation sample are calculated, including the following steps: S31, Number of Sample Connections for a Single Indicator at the Indicator Layer u ijd calculate; Constructing single-index sample values x ijd ( i =1, 2,…, n i ; j =1, 2,…, n j ; d =1, 2,…, n d The number of single-indicator correlations between ) and evaluation criteria u ijd ， If we take the evaluation standard level f =3, with levels 1-3 corresponding to excellent, average, and poor, respectively. x ijd Connection number components μ ijdf The calculation formulas are as follows: In the formula, sample value x ijd middle i , j , d These are the serial numbers of the evaluation sample, the criterion layer, and the evaluation index, respectively. n i、 n j、 n d These represent the number of evaluation samples, the criterion layer, and their respective evaluation indicators; S 1jd 、S 2jd、 S 3jd The threshold values ​​for Level 1, Level 2, and Level 3 evaluation standards are respectively. S 0jd This is the left endpoint value of the Level 1 evaluation standard; Sample value x ijdRelative to rating level f relative membership degree v * ijdf Represented as: relative membership v * ijdf Normalization is performed to obtain the normalized connection components of the evaluation index sample values. v ijdf : S32, Criterion Layer Sample Connection Component v ijf calculate: In the formula, w jd For the first j The first criterion level d The weight of each indicator; S33, Target Layer Sample Connection Component v if calculate: In the formula, w j For the first j The weights of each criterion layer; make v i1 = a , v i2 = b , v i3 = c Then the number of connections at the target layer u Represented as: u = a + bI + cJ in: a + b + c =1 In the formula, a To the same degree; b For the degree of difference; c The degree of opposition; I The coefficient of difference. J The degree of opposition; v i1、 vi2、 v i3 These are the connection number components of the target layer corresponding to f=1, 2, and 3, respectively.

[0011] Furthermore, in S3, level feature values ​​are introduced. h Determine the evaluation level of the target layer for each evaluation sample; Among them, level feature values h Represented as: h = a +2 b +3 c Based on level characteristic values h The value of determines the final evaluation level of each evaluation sample's target layer. Assuming there are three evaluation levels, the specific division is as follows: When 1≤ h A score <1.5 corresponds to a rating of 1, indicating excellent performance. When 1.5≤ h A score of <2.5 corresponds to a rating of level 2, indicating a moderate level. when h A score of ≥2.5 corresponds to an evaluation sample of level 3, indicating poor performance.

[0012] Furthermore, in S4, the subtraction set pair potential of each evaluation sample's evaluation target layer is calculated, which is expressed as: S ( u )= a - c + ba - bc =( a - c (1+) b ) In the formula, S ( u ) is the subtraction set pair potential.

[0013] Furthermore, step S5 includes the following sub-steps: S51, Based on Level Feature Values h The global Moran index of the target layer of all evaluation samples is calculated to test the significance of its spatial clustering. The local Moran index is then calculated, and each evaluation sample is divided into four spatial clusters based on the local Moran index. S52. Calculate the global Moran index corresponding to the subtraction set potential, test the significance of its spatial clustering, and further calculate the local Moran index corresponding to the subtraction set potential. Based on the local Moran index, divide each evaluation sample into four spatial clusters. S53, Based on level feature values hCoupled with four spatial clustering types obtained from the local Moran index based on the subtraction set potential, 16 refined spatial clustering types are formed.

[0014] Furthermore, in S51, based on the local Moran index of each evaluation sample... The numerical value determines the spatial clustering of each evaluation sample into four types, including: Gao Gao: >0, h i > and h ik > ; Low: >0, h i < and h ik < ; High and low: <0, h i > and h ik < ; Low High: <0, h i < and h ik > ; In the formula, hi For the first i The level feature values ​​of each evaluation sample, h ik In order to be with the first i The evaluation sample is adjacent to the first k ( k =1,2,…, n k , i ≠ k The level feature values ​​of ) evaluation samples; This is the mean of the level feature values ​​for all evaluation samples. Furthermore, S52 specifically includes: Based on the potential of the subtraction set, its local Moran exponent is calculated as follows: In the formula, For the first i The evaluation sample subtraction set is related to the potential. S ( u ) iThe local Moran index, S (u) ik In order to be with the first i The evaluation sample is adjacent to the first k The subtraction set of each evaluation sample is a pair of potentials; The mean of the potential of the subtraction set of all evaluation samples; The sample variance of the potential for all evaluation sample subtraction sets; n k In order to be with the first i The total number of neighboring evaluation samples of each evaluation sample. q ik For spatial weights, if the first... i The evaluation sample and the first k Each evaluation sample is adjacent. q ik =1, otherwise, q ik =0.

[0015] Furthermore, in S53, the 16 refined spatial clustering types include: High-altitude spatial patterns specifically include: High-high-dual-high synergistic type, high-high-core radiation type, high-high-potential catch-up type, and high-high-dual-weak early warning type; Low-rise spatial layout types specifically include: Low-low-high potential type, low-low-high value collapse type, low-low-strong neighbor and weak type, and low-low-low-lagging type; The types of spatial layouts with varying elevations include: High-low-double-high driven type, high-low-strong isolated type, high-low-art-crisis type, and high-low-double-low recession type; Low-rise spatial pattern types, specifically including: Low-high-double-high radiation type, low-high-potential depression type, low-high-non-equilibrium suppression type, and low-high-double-low lag type.

[0016] The method for refined evaluation and diagnosis of the state of regional systems based on subtraction set potential and Moran's index provided by this invention has the following beneficial effects: 1. This invention achieves a refined leap from "spatial pattern identification" to "spatial pattern identification and collaborative diagnosis of future development trends." It overcomes the limitation of traditional Moran's index analysis, which can only identify spatial clustering patterns. Firstly, based on level eigenvalues... h The traditional local Moran index is calculated to obtain the spatial clustering type of each sample (high-high HH, low-low LL, high-low HL, low-high LH). Based on this, the connection number components of each evaluation sample are analyzed. a , b , cThe method calculates the subtraction set pair potential. Substituting this subtraction set pair potential as a comprehensive index into the local Moran index model, it further subdivides each spatial clustering type based on the strength of the sample's own set pair potential and the potential of its neighboring set pairs, resulting in 16 refined types (e.g., the high-high spatial pattern is subdivided into "high-high-dual-high collaborative type, high-high-core radiation type, high-high-potential catch-up type, and high-high-dual-weak early warning type," etc.). This method not only identifies spatial clustering patterns between regions but also reveals the potential and future trends of collaborative development between regions, providing decision-makers with insights far exceeding those of traditional methods.

[0017] 2. Enhanced the scientific content and decision-making guidance value of evaluation results. Traditional evaluation results provide decision-makers with a single spatial label (such as "HH type"), while the 16 refined types provided by this invention can intuitively reflect the region's inherent stability, development potential, and potential risks, as well as the spatial transmission characteristics of fluctuations and risks. For example, for "HHL..." S -L S In the "High-High-Double Weak Early Warning Type" region, it can be identified that the region itself and its neighboring regions may develop in a negative direction in the future, and the risk of synchronous decline between advantageous regions needs to be guarded against. For the "(LL-Ls-Ls) (Low-Low-Double Low Lagging Type)" region, it can be identified that the region itself and its neighboring regions may face the risk of coordinated decline in the future. This provides a direct scientific basis for formulating differentiated and precise regional regulation policies.

[0018] 3. The method is highly versatile and can be widely applied to evaluations in multiple fields. The core step of this invention is to combine the potential of the subtraction set of evaluation results with the Moran index, which has extremely strong universality. By simply adjusting the evaluation index system and grading standards in step one, this method can be seamlessly applied to multiple fields such as water resource carrying capacity evaluation, water resource spatial balance diagnosis, "four waters and four determinations" scheme formulation, new quality productivity assessment, and ecological environment vulnerability assessment, achieving the unification and innovation of evaluation methodology.

[0019] 4. It provides quantitative support for establishing cross-regional coordination mechanisms. By identifying 16 refined spatial relationships, this invention can more accurately characterize the interactions between regions (coordination, radiation, catching up, etc.), thus providing a scientific quantitative tool for establishing more effective cross-regional resource and ecological compensation mechanisms, collaborative development strategies, and resource optimization allocation schemes. Attached Figure Description

[0020] Figure 1 This is a flowchart of a method for refined evaluation and diagnosis of the state of a regional system based on the subtraction set and Moran's index, as described in the embodiment. Detailed Implementation

[0021] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0022] This embodiment provides a refined evaluation and diagnosis method for the state of regional systems based on subtractive set-pair potential and Moran's index. The invention uses a three-level classification standard (i.e., ternary connection number) as an example for method illustration, but the core idea is not limited to a three-level classification. For evaluation systems with more classification standards such as four-level and five-level, simply replace the ternary connection number with the connection number of the corresponding number of elements (e.g., the five-element connection number) and use the corresponding set-pair potential calculation formula; the remaining steps (such as indicator system construction, weight determination, Moran's index coupling, etc.) are completely identical. Therefore, the method of this invention has universality and can be flexibly applied to evaluation scenarios with any classification standard; see reference. Figure 1 Specifically, it includes the following: S1. Construct a multi-level evaluation index system that includes a target layer, a criterion layer, and an indicator layer, and determine the grading standards for each evaluation index; In some embodiments, a multi-level evaluation index system comprising a target layer, a criterion layer, and an indicator layer is constructed based on the connotation and characteristics of the object to be evaluated (such as water resource carrying capacity, water resource spatial balance, etc.). At the same time, the grading standards for each evaluation indicator are determined with reference to relevant plans, norms, or industry standards (for example, divided into three levels: "Level 1 (Excellent)", "Level 2 (Medium)" and "Level 3 (Poor)").

[0023] S2. Obtain the relative importance ranking of each evaluation indicator and calculate the weight coefficient of the evaluation indicator; In some embodiments, the relative importance ranking of each evaluation indicator is obtained by means of expert consultation or questionnaire survey, and the weight coefficients of each level of evaluation indicator are calculated by means of analytic hierarchy process or other subjective and objective weighting methods.

[0024] S3. Based on the multi-level evaluation index system, grading standards and weight coefficients, calculate the connection number of each evaluation sample (such as a certain administrative region or a certain watershed) in turn, and determine the evaluation level of each evaluation sample. First, calculate the connection components of each individual indicator, and then weight them to obtain the connection numbers of each subsystem and the overall system. u The number of connections between the indicator layer, criterion layer, and target layer of each evaluation sample. u The calculation steps are as follows: S31, Number of Sample Connections for a Single Indicator at the Indicator Layer u ijd Calculation; Constructing single-index sample values x ijd ( i =1, 2,…, n i ; j =1, 2,…, n j ; d =1, 2,…, n d The number of single-indicator correlations between ) and evaluation criteria u ijd If the evaluation standard level is adopted f =3, levels 1-3 represent excellent, average, and poor respectively, sample value x ijd Connection number components μ ijdf The calculation formulas are as follows: In the formula, sample value x ijd middle i , j , d These are the serial numbers of the evaluation sample, the criterion layer, and the evaluation index, respectively. n i、 n j、 n d These represent the number of evaluation samples, the criterion layer, and their respective evaluation indicators; S 1jd 、S 2jd、 S 3jd The threshold values ​​for Level 1, Level 2, and Level 3 evaluation standards are respectively. S 0jd The left endpoint value of the Level 1 evaluation standard; sample value x ijd Compared to "rating level" f The relative membership degree of " v * ijdf Represented as: right v * ijdf Normalization is performed to obtain the normalized connection number components of the evaluation index samples. v ijdf S32, Criterion Layer Sample Connection Component v ijf calculate; No. j The formulas for calculating the number of connection components in each criterion layer are as follows: In the formula, w jd For the first j The first criterion level i The weights of the indicators satisfy the following conditions: ; S33, Target Layer Sample Connection Component v if calculate; The calculation formula is as follows: In the formula, w j For the first j The weights of each criterion layer satisfy... For ease of expression, let v i1 = a , v i2 = b , v i3 = c Then the number of connections at the target layer u Represented as: u = a + bI + cJ in: a + b + c =1 In the formula, a To the same degree; b For the degree of difference; c The degree of opposition; I The coefficient of difference. J This is the coefficient of contrast.

[0025] Secondly, level eigenvalues ​​are introduced. h Determine the evaluation level of each evaluation sample; Among them, level feature values h Represented as: h = a +2 b +3 c Based on level characteristic values h The value of determines the final evaluation level of the target layer for each evaluation sample. Assuming there are three evaluation levels, the specific division is as follows: When 1≤ h A score <1.5 corresponds to a rating of 1, indicating excellent performance. When 1.5≤ h A score of <2.5 corresponds to a rating of level 2, indicating a moderate level. when h A score of ≥2.5 corresponds to an evaluation sample of level 3, indicating poor performance.

[0026] S4. Calculate the subtraction set pair potential of the connection number components of the target layer; Among them, the subtraction set is related to the potential. S ( u ) is represented as: S ( u )= a - c + ba - bc =( a - c (1+) b ) S5. Couple the subtraction set potential with the Moran index to identify the refined spatial clustering type of each evaluation sample. This includes the following steps: S51, Based on Level Feature Values h Traditional Moran space clustering analysis; Calculate the global Moran index for all evaluation samples. I h and local Moran index And based on the local Moran index, each evaluation sample is divided into four spatial clusters; Among them, the global Moran index I h and local Moran index They are represented as follows: In the formula, h i For the first i The level feature values ​​of each evaluation sample, h ik In order to be with the first i The evaluation sample is adjacent to the first k ( k =1,2,…, n k , i ≠ kThe level feature values ​​of ) evaluation samples. The mean of all evaluation sample-level feature values. S h 2 The sample variance of all evaluation sample-level feature values; n k In order to be with the first i The total number of neighboring evaluation samples of each evaluation sample. q ik For spatial weights, if the first... i The evaluation sample and the first k Each evaluation sample is adjacent. q ik =1, otherwise, q ik =0.

[0027] Subsequently, based on the local Moran index The numerical value determines the spatial clustering of each evaluation sample into four types, including: Gao Gao (HH): >0, h i > and h ik > (High skill level of the user and high skill level of neighboring regions); Low Low (LL): >0, h i < and h ik < (Their own level is low, and the level of neighboring areas is also low). High / Low (HL): <0, h i > and h ik < (High skill level itself, low skill level in neighboring areas); Low High (LH): <0, h i < and h ik > (Low skill level itself, high skill level in neighboring areas); S52. Based on the number of components, including the same degree. a Difference b degree of opposition c The numerical value is used to calculate the subtraction set of the evaluation target layer for each evaluation sample, and the potential is calculated.S ( u ); S ( u )= a - c + ba - bc =( a - c (1+) b ) Calculate the global and local Moran exponents corresponding to the potential of the subtraction set; specifically: In the formula, The global Moran index of the potential for all evaluation sample subtraction sets. For the first i Evaluation of the subtraction set of the sample to potential The local Moran index, The mean of the potential of the subtraction set of all evaluation samples; The sample variance of the potential for all evaluation sample subtraction sets; q ik For spatial weights, if the first... i The evaluation sample and the first k Each evaluation sample is adjacent. q ik =1, otherwise, q ik =0.

[0028] S53, Based on level feature values h With subtraction set-based potential S ( u The four spatial clustering types obtained from the local Moran index are coupled to form comprehensive diagnostic information. The final diagnostic result for each evaluation region includes: based on Spatial clustering types based on The spatial clustering types are coupled.

[0029] A total of 16 refined spatial clustering types were formed, including: High-altitude spatial patterns specifically include: High-high-dual-high synergistic type, high-high-core radiation type, high-high-potential catch-up type, and high-high-dual-weak early warning type; Low-rise spatial layout types specifically include: Low-low-high potential type, low-low-high value collapse type, low-low-strong neighbor and weak type, and low-low-low-lagging type; The types of spatial layouts with varying elevations include: High-low-double-high driven type, high-low-strong isolated type, high-low-art-crisis type, and high-low-double-low recession type; Low-rise spatial pattern types, specifically including: Low-high-double-high radiation type, low-high-potential depression type, low-high-non-equilibrium suppression type, and low-high-double-low lag type.

[0030] See Table 1 for specific classifications.

[0031] Table 1. Sixteen refined spatial clustering types based on the coupling of subtraction set potential and Moran's index. S6. Based on the geographic information system platform, spatial mapping is performed on the refined spatial clustering types of each evaluation sample, and countermeasure analysis is carried out for each refined spatial clustering type.

[0032] Specifically, based on a Geographic Information System (GIS) platform, spatial mapping is performed on the 16 refined spatial clustering types identified in step four, generating refined spatial clustering distribution maps. For each refined type, strategy analysis is conducted based on its spatial location and spatial relationships. For example: (1) Regarding "HHH" S -H S The "High-High-Double-High Collaborative" region (where both the region itself and its neighboring regions are at a high level and the future development trend of both is positive) can be regarded as the core area for regional development, and it can be encouraged to play a radiating and driving role while maintaining its stability advantage.

[0033] (2) Regarding "LHH" S -H S The "low-high-double-high radiation zone" area (which is itself at a low level but has a positive future development trend, and the adjacent area is at a high level and has a positive future development trend) should strengthen infrastructure interconnection, create favorable conditions to undertake the allocation of resources from the core area and the joint control of risks between regions, and at the same time pay attention to its internal volatility to avoid instability caused by external influences.

[0034] (3) For the “HH-Ls-Ls (high-high-double-weak early warning type)” region (both itself and the adjacent region are at a high level, but the future development trend of both is weak and the risk of decline needs to be guarded against), the early warning mechanism should be activated immediately, the dominant factors that lead to the weak development trend (such as resource shortage and environmental degradation) should be analyzed in depth, and targeted measures should be taken to block the risk transmission path and prevent the risk from spreading between advantageous regions.

[0035] (4) For the “LL-Ls-Ls (low-low-double low lagging type)” region (both itself and the adjacent regions are at a low level, and the future development trend of both is weak, a typical lagging and declining region, which urgently needs external assistance and coordinated transformation), we should focus on the reasons for the decline in development trend, prevent long-term low-level lock-in due to coordinated lag, and explore the possibility of coordinated transformation with surrounding regions and external assistance.

[0036] This invention uses a three-level standard, so it uses ternary contact numbers, but it is not limited to a three-level standard. If the level standard is four-level or five-level or other levels, there are corresponding quaternary and quinary contact numbers or corresponding multi-level contact numbers, and the method of this invention can also be used. Obviously, the method corresponding to the level standard of four-level or five-level or other levels is also within the scope of protection of this invention.

[0037] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.

Claims

1. A method for refined evaluation and diagnosis of the state of a regional system based on subtraction sets and Moran's exponent, characterized in that, Includes the following steps: S1. Construct a multi-level evaluation index system that includes a target layer, a criterion layer, and an indicator layer, and determine the grading standards for each evaluation index; S2. Obtain the relative importance ranking of each evaluation indicator and calculate the weight coefficient of the evaluation indicator; S3. Based on the multi-level evaluation index system, grading standards and weight coefficients, calculate the connection number of each evaluation sample index layer, criterion layer and target layer in sequence, and finally determine the evaluation level of each evaluation sample target layer. S4. Calculate the subtraction set pair potential based on the connection components of the target layer calculated in S3; S5. Couple the subtraction set potential with the Moran index to identify the refined spatial clustering type of each evaluation sample; S6. Based on the geographic information system platform, spatial mapping is performed on the refined spatial clustering types of each evaluation sample, and countermeasure analysis is carried out for each refined spatial clustering type.

2. The method for refined evaluation and diagnosis of the state of a regional system based on the subtraction set and Moran's index as described in claim 1, characterized in that, Specifically, S2 is: The relative importance ranking of each evaluation indicator was obtained by using expert consultation or questionnaire survey, and the weight coefficient of each evaluation indicator was calculated by using the analytic hierarchy process.

3. The method for refined evaluation and diagnosis of the state of a regional system based on the subtraction set and Moran's index as described in claim 1, characterized in that, In step S3, the correlation coefficients of the indicator layer, criterion layer, and target layer for each evaluation sample are calculated, including the following steps: S31, Number of Sample Connections for a Single Indicator at the Indicator Layer u ijd calculate; Constructing single-index sample values x ijd Single indicator correlation number with evaluation criteria u ijd If the evaluation standard level is adopted f =3, with levels 1-3 corresponding to excellent, average, and poor, respectively. x ijd Connection number components μ ijdf The calculation formulas are as follows: In the formula, sample value x ijd middle i , j , d These are the serial numbers of the evaluation sample, the criterion layer, and the evaluation index, respectively. n i、 n j、 n d These represent the number of evaluation samples, the criterion layer, and their respective evaluation indicators; S 1jd 、S 2jd、 S 3jd The threshold values ​​for Level 1, Level 2, and Level 3 evaluation standards are respectively. S 0jd This is the left endpoint value of the Level 1 evaluation standard; Sample value x ijd Relative to rating level f relative membership degree v * ijdf Represented as: relative membership v * ijdf Normalization is performed to obtain the normalized connection components of the evaluation index sample values. v ijdf : S32, Criterion Layer Sample Connection Component v ijf calculate: In the formula, w jd For the first j The first criterion level d The weight of each indicator; S33, Target Layer Sample Connection Component v if calculate: In the formula, w j For the first j The weights of each criterion layer; make v i1 = a , v i2 = b , v i3 = c Then the number of connections at the target layer u Represented as: u = a + bI + cJ in: a + b + c =1 In the formula, a To the same degree; b For the degree of difference; c The degree of opposition; I The coefficient of difference. J The degree of opposition; v i1、 v i2、 v i3 They are respectively f =1, 2, 3 correspond to the contact number components of the target layer.

4. The method for refined evaluation and diagnosis of the state of a regional system based on the subtraction set and Moran's index as described in claim 1, characterized in that, In S3, level feature values ​​are introduced. h Determine the evaluation level of the target layer for each evaluation sample; Among them, level feature values h Represented as: h = a +2 b +3 c Based on level characteristic values h The value of determines the final evaluation level of each evaluation sample's target layer. Assuming there are three evaluation levels, the specific division is as follows: When 1≤ h A score <1.5 corresponds to a rating of 1, indicating excellent performance. When 1.5≤ h A score of <2.5 corresponds to a rating of level 2, indicating a moderate level. when h A score of ≥2.5 corresponds to a rating of level 3, indicating poor performance.

5. The method for refined evaluation and diagnosis of the state of a regional system based on the subtraction set and Moran's index as described in claim 1, characterized in that, In step S4, the subtraction set pair potential of each evaluation sample's evaluation target layer is calculated, and it is expressed as: S ( u )= a - c + ba - bc =( a - c )(1+ b ) In the formula, S ( u ) is the subtraction set pair potential.

6. The method for refined evaluation and diagnosis of the state of a regional system based on the subtraction set and Moran's index as described in claim 1, characterized in that, S5 includes the following steps: S51, Based on Level Feature Values h The global Moran index of the target layer of all evaluation samples is calculated to test the significance of its spatial clustering. The local Moran index is then calculated, and each evaluation sample is divided into four spatial clusters based on the local Moran index. S52. Calculate the global Moran index corresponding to the subtraction set potential, test the significance of its spatial clustering, and further calculate the local Moran index corresponding to the subtraction set potential. Based on the local Moran index, divide each evaluation sample into four spatial clusters. S53, Based on level feature values h Coupled with four spatial clustering types obtained from the local Moran index based on the subtraction set potential, 16 refined spatial clustering types are formed.

7. The method for refined evaluation and diagnosis of the state of a regional system based on the subtraction set and Moran's index as described in claim 6, characterized in that, In S51, based on the local Moran index of each evaluation sample Based on the numerical value, each evaluation sample is divided into four spatial clusters. include: Gao Gao: >0, h i > and h ik > ; Low: >0, h i < and h ik < ; High and low: <0, h i > and h ik < ; Low High: <0, h i < and h ik > ; In the formula, h i For the first i The level feature values ​​of each evaluation sample, h ik In order to be with the first i The evaluation sample is adjacent to the first k The level feature values ​​of each evaluation sample, This is the mean of the level feature values ​​for all evaluation samples.

8. The method for refined evaluation and diagnosis of the state of a regional system based on the subtraction set and Moran's index as described in claim 6, characterized in that, Specifically, S52 includes: Based on the potential of the subtraction set, its local Moran exponent is calculated as follows: In the formula, For the first i The evaluation sample subtraction set is related to the potential. S ( u ) i The local Moran index, S (u) ik In order to be with the first i The evaluation sample is adjacent to the first k The subtraction set of each evaluation sample is a pair of potentials; The mean of the potential of the subtraction set of all evaluation samples; The sample variance of the potential for all evaluation sample subtraction sets; n k In order to be with the first i The total number of neighboring evaluation samples of each evaluation sample. q ik For spatial weights, if the first... i The evaluation sample and the first k Each evaluation sample is adjacent. q ik =1, otherwise, q ik =0.

9. The method for refined evaluation and diagnosis of the state of a regional system based on set-pair potential and Moran's index according to claim 6, characterized in that, In S53, the 16 refined spatial clustering types include: High-altitude spatial patterns specifically include: High-high-dual-high synergistic type, high-high-core radiation type, high-high-potential catch-up type, and high-high-dual-weak early warning type; Low-rise spatial layout types specifically include: Low-low-high potential type, low-low-high value collapse type, low-low-strong neighbor and weak type, and low-low-low-lagging type; The types of spatial layouts with varying elevations include: High-low-double-high driven type, high-low-strong isolated type, high-low-art-crisis type, and high-low-double-low recession type; Low-rise spatial pattern types, specifically including: Low-high-double-high radiation type, low-high-potential depression type, low-high-unbalanced suppression type, and low-high-double-low lag type.

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