Water quality fuzzy comprehensive evaluation method and system based on game theory and empowerment

Abstract

The invention provides a water quality fuzzy comprehensive evaluation method and system based on the game theory and empowerment, and relates to the technical field of water quality comprehensive evaluation, and the method comprises the steps: obtaining a plurality of water quality indexes of a to-be-evaluated water sample; performing correlation analysis on each water quality index; according to a correlation analysis result, under the condition that highly-collinear water quality indexes exist, principal component analysis is carried out on all the water quality indexes, and a water quality evaluation index set is determined; dividing water quality grades according to a surface water quality evaluation standard; calculating a membership degree matrix of each evaluation index; determining a subjective weight value of each evaluation index in combination with a single pollution index algorithm and an analytic hierarchy process algorithm; determining an objective weight value of each evaluation index through an entropy weight algorithm; calculating a fusion weight matrix of each evaluation index relative to different water quality levels in the water quality evaluation index set by taking Nash equilibrium as a target based on a game theory; and generating the water quality grade of the to-be-evaluated water sample in combination with the membership matrix and the fusion weight matrix.

Description

Technical Field

[0001] The present invention relates to the technical field of comprehensive water quality evaluation, and in particular to a fuzzy comprehensive water quality evaluation method and system based on game theory and weighting. Background Art

[0002] Game theory is a mathematical theory that studies how multiple decision makers (usually called "players") make strategic choices under mutual influence. Weighting refers to assigning weights to different indicators based on certain principles or algorithms. The fuzzy comprehensive evaluation method of water quality is a method that comprehensively judges the water quality level through membership degree and weight coefficient based on fuzzy mathematics theory. In the specific water quality evaluation process, the selection of appropriate evaluation indicators and indicator weights has a greater impact on the accuracy of the evaluation results.

[0003] Water quality evaluation is one of the important measures for river and lake water environment management. Therefore, objectively evaluating water quality with appropriate water quality evaluation methods plays an important role in improving the quality of river and lake water environment. It is of great significance for determining water quality types, identifying major pollution factors, and analyzing the evolution of water environment.

[0004] Current research usually selects indicators that play a major role in water pollution based on experience when selecting evaluation indicators, which is subjective and arbitrary. In addition, weight assignment is the most critical process in the fuzzy comprehensive evaluation method and has the greatest impact on the evaluation results. However, in the process of determining the weights of evaluation indicators, a single weight assignment method is somewhat one-sided, and the evaluation process is prone to data loss. For example, the weights given by the hierarchical analysis method depend on the subjective judgment and preference of decision makers, and the entropy weight method does not consider the differences in the indicators themselves. The weights obtained may not be consistent with the importance of the actual indicators, resulting in inaccurate water quality evaluation results, low water quality evaluation efficiency, and difficulty in meeting the needs of complex water quality evaluation, resulting in reduced stability and credibility of the evaluation results. Summary of the invention

[0005] In order to solve the technical problems existing in the prior art that when selecting evaluation indicators, the indicators that play a major role in water environment pollution are usually selected based on experience, which has a certain degree of subjectivity and arbitrariness; in the process of determining the weights of evaluation indicators, a single weight assignment method has a certain one-sidedness, and the evaluation process is prone to data loss, resulting in inaccurate water quality evaluation results, low water quality evaluation efficiency, and difficulty in meeting the needs of complex water quality evaluation, resulting in reduced stability and credibility of the evaluation results, the present invention provides a water quality fuzzy comprehensive evaluation method and system based on game theory and empowerment.

[0006] The technical solution provided by the embodiment of the present invention is as follows:

[0007] First aspect

[0008] The embodiment of the present invention provides a fuzzy comprehensive evaluation method of water quality based on game theory and weighting, comprising:

[0009] S1: Obtain multiple water quality indicators of the water sample to be evaluated;

[0010] S2: Conduct correlation analysis on various water quality indicators;

[0011] S3: Based on the results of the correlation analysis, in the case of highly collinear water quality indicators, principal component analysis is performed on all water quality indicators to determine the water quality evaluation indicator set;

[0012] S4: Classify water quality levels according to surface water quality evaluation standards;

[0013] S5: Calculate the membership matrix of each evaluation index relative to each water quality level through the distribution function of the semi-trapezoidal index;

[0014] S6: Combine the single pollution index algorithm and the hierarchical analysis algorithm to determine the subjective weight value of each evaluation index in the water quality evaluation index set;

[0015] S7: Determine the objective weight value of each evaluation index in the water quality evaluation index set through the entropy weight algorithm;

[0016] S8: Based on game theory, with Nash equilibrium as the goal, combining subjective weight values ​​and objective weight values, calculate the fusion weight matrix of each evaluation index in the water quality evaluation index set relative to different water quality levels;

[0017] S9: Combine the membership matrix and the fusion weight matrix to generate the water quality grade of the water sample to be evaluated.

[0018] Second aspect

[0019] The embodiment of the present invention provides a fuzzy comprehensive evaluation system for water quality based on game theory and weighting, comprising:

[0020] processor;

[0021] A memory having computer-readable instructions stored therein, which, when executed by a processor, implements the fuzzy comprehensive evaluation method for water quality based on game theory and weighting as in the first aspect.

[0022] The third aspect

[0023] An embodiment of the present invention provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the fuzzy comprehensive evaluation method for water quality based on game theory and weighting as in the first aspect is implemented.

[0024] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0025] In the present invention, a plurality of water quality indicators of a water sample to be evaluated are obtained, and correlation analysis is performed on each water quality indicator. In the presence of high collinearity, principal component analysis is performed on the water quality indicators to determine a water quality evaluation indicator set. Water quality grades are divided according to surface water quality evaluation standards. Then, through the distribution function of the semi-trapezoidal indicator, the membership matrix of each evaluation indicator is calculated. The subjective weight value of each evaluation indicator in the water quality evaluation indicator set is determined by combining the single pollution index algorithm and the hierarchical analysis algorithm. The objective weight value of each evaluation indicator in the water quality evaluation indicator set is determined by the entropy weight algorithm. Based on game theory and with Nash equilibrium as the goal, the fusion weight matrix of each evaluation indicator in the water quality evaluation indicator set relative to different water quality grades is calculated by combining the subjective weight value and the objective weight value. The water quality grade of the water sample to be evaluated is generated by combining the membership matrix and the fusion weight matrix. The problem of selecting evaluation indicators and determining the weight of evaluation indicators in the process of fuzzy comprehensive evaluation of water quality is effectively solved, and its limitations are effectively avoided, so that the water quality evaluation result is more objective and reasonable, and the weight accuracy and the efficiency and accuracy of water quality evaluation are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0027] Figure 1 A flow chart of a fuzzy comprehensive evaluation method for water quality based on game theory and weighting provided in an embodiment of the present invention;

[0028] Figure 2 A schematic diagram of the structure of a fuzzy comprehensive evaluation system for water quality based on game theory and weighting provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The technical solution of the present invention is described below in conjunction with the accompanying drawings.

[0030] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design described as "example" in the present invention should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of the word "example" is intended to present the concept in a specific way. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or it can be either of the two.

[0031] In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0032] Reference Manual Attached Figure 1 , showing a flow chart of a fuzzy comprehensive evaluation method for water quality based on game theory and empowerment provided by an embodiment of the present invention.

[0033] The embodiment of the present invention provides a fuzzy comprehensive evaluation method for water quality based on game theory and weighting, which can be implemented by a fuzzy comprehensive evaluation device for water quality based on game theory and weighting, and the fuzzy comprehensive evaluation device for water quality based on game theory and weighting can be a terminal or a server. The processing flow of the fuzzy comprehensive evaluation method for water quality based on game theory and weighting can include the following steps:

[0034] S1: Obtain multiple water quality indicators of the water sample to be evaluated.

[0035] Among them, the water sample to be evaluated refers to the water sample that needs to be evaluated for water quality, which can be a river, lake, groundwater or other surface water body. The water quality index is the parameter used to measure the quality of the water body, including physical, chemical and biological indicators.

[0036] It should be noted that by obtaining multiple water quality indicators of the water samples to be evaluated, the main factors affecting water quality are comprehensively covered, which can provide a complete data basis for subsequent analysis.

[0037] In a possible implementation, the water quality indicators specifically include: water temperature, pH, dissolved oxygen, permanganate index, chemical oxygen demand, five-day biochemical oxygen demand, ammonia nitrogen, total phosphorus, total nitrogen, fluoride, copper, zinc, selenium, arsenic, mercury, cadmium, hexavalent chromium, lead, cyanide, volatile phenols, petroleum, and anionic synthetic detergents and sulfides.

[0038] S2: Conduct correlation analysis on various water quality indicators.

[0039] It should be noted that correlation analysis of water quality indicators helps to identify redundant or repeated information between indicators, reduce data redundancy, and thus optimize the evaluation indicator set, which not only improves the accuracy of the evaluation results, but also reduces computational complexity, ensuring that subsequent analysis is more efficient.

[0040] S3: Based on the results of correlation analysis, in the presence of highly collinear water quality indicators, principal component analysis is performed on all water quality indicators to determine the water quality evaluation indicator set.

[0041] Among them, principal component analysis is a dimensionality reduction technology that converts original high-dimensional data into a few comprehensive variables (principal components) through linear transformation to explain the main variations of the data. The water quality evaluation index set is a set of key indicators selected based on correlation analysis and principal component analysis, which is used to comprehensively evaluate water quality.

[0042] It should be noted that the principal component analysis method can scientifically extract the most important evaluation indicators from complex water quality indicators, reduce data redundancy and collinearity problems, which not only reduces the computational complexity but also improves the stability and reliability of the evaluation model.

[0043] In a possible implementation, S3 specifically includes:

[0044] S301: Conduct principal component analysis on water quality indicators.

[0045] S302: Calculate the eigenvalue of each principal component and determine whether the eigenvalue is greater than a preset eigenvalue. If so, retain the principal component; otherwise, discard the principal component.

[0046] The eigenvalue of the principal component indicates the proportion of the total variance of the original data that can be explained by the principal component, and the preset eigenvalue is the threshold set in the analysis, which is used to screen the principal component.

[0047] It should be noted that those skilled in the art can set the size of the preset characteristic value according to actual conditions, and the present invention does not limit this.

[0048] S303: Calculate the correlation value between each water quality index in the retained principal component, and determine whether the correlation value is greater than a preset correlation value. If so, retain the water quality index; otherwise, discard the water quality index.

[0049] Among them, the correlation value refers to the degree of correlation between the water quality index and the retained principal component, which is usually expressed by the correlation coefficient. The preset correlation value refers to the water quality index that has a significant correlation with the retained principal component, which is considered to be a key indicator and is used for subsequent analysis.

[0050] It should be noted that those skilled in the art can set the size of the preset correlation value according to actual conditions, and the present invention does not limit this.

[0051] S304: Determine a water quality evaluation index set based on the retained water quality index:

[0052] U={u1,u2,…,u i ,…,u n}

[0053] Among them, U represents the water quality evaluation index set, u i represents the i-th water quality evaluation index, i=1,…,n, and n represents the total number of water quality evaluation indexes.

[0054] It should be noted that principal component analysis provides an objective data screening method, which avoids the arbitrariness of artificially selected indicators, makes water quality evaluation more accurate and efficient, and also improves the versatility and adaptability of the method.

[0055] S4: Water quality is divided into grades according to surface water quality evaluation standards.

[0056] Among them, the surface water quality evaluation standard is a set of normative standards for classifying and evaluating surface water quality. Water quality is usually divided into multiple grades (such as Class I to Class V), and each grade represents different water body functions and pollution levels. Water quality grades are categories divided according to water quality evaluation standards and are used to describe the quality status of water bodies, such as "clean", "lightly polluted", "heavily polluted", etc.

[0057] It should be noted that the classification of water quality grades through surface water quality evaluation standards provides a scientific and unified reference framework to ensure the standardization and comparability of evaluation results. This classification method can intuitively reflect the quality of water and facilitate decision makers to quickly understand the water status and take corresponding management measures.

[0058] S5: Calculate the membership matrix of each evaluation index relative to each water quality level through the distribution function of the semi-trapezoidal index.

[0059] Among them, the distribution function of the semi-trapezoidal index is a fuzzy mathematical tool used to describe the membership relationship between water quality index values ​​in different water quality grades. The membership matrix is ​​a two-dimensional matrix, in which each element represents the membership of a certain water quality index value to a certain water quality grade. It quantifies the relationship between the index value and the water quality grade.

[0060] It should be noted that by calculating the membership of water quality index values ​​to different water quality levels and constructing a membership matrix, the matching degree of each indicator to each water quality level can be fully reflected. This method avoids the over-simplification problem caused by a single standard division, retains the ambiguity and continuity of the data, and improves the accuracy of the evaluation.

[0061] In a possible implementation, S5 specifically includes:

[0062] S501: According to the water quality membership function, the membership of each evaluation index relative to each water quality level is calculated:

[0063] When j=1, the first-level (primary) water quality membership function is specifically:

[0064]

[0065] When j = 2, ..., 4, the water quality membership functions from level II to IV are as follows:

[0066]

[0067] When j = 5, the Vth level water quality membership function is specifically:

[0068]

[0069] Among them, r i1 represents the membership of the i-th water quality evaluation index to the first-level water quality, x i represents the measured value of the i-th water quality evaluation index, S ij represents the standard value of the j-th water quality corresponding to the i-th water quality evaluation index, S i,j+1 represents the standard value of the j+1th level of water quality corresponding to the i-th water quality evaluation index, r ij represents the membership of the i-th water quality evaluation index to the j-th water quality, S i,j-1 It represents the standard value of the j-1th level of water quality corresponding to the ith water quality evaluation index.

[0070] S502: Determine a membership matrix according to the membership.

[0071] It should be noted that the membership matrix provides a scientific basis for the subsequent comprehensive weight calculation and water quality grade determination, and enhances the flexibility and applicability of the overall evaluation.

[0072] S6: Combine the single pollution index algorithm and the hierarchical analysis algorithm to determine the subjective weight value of each evaluation index in the water quality evaluation index set.

[0073] Among them, the single pollution index algorithm is an algorithm used to measure the pollution degree of a single water quality indicator. The ratio of the actual measured value to the standard value reflects the contribution of the indicator to the water quality. The hierarchical analysis algorithm is a multi-indicator evaluation method used for decision analysis. By constructing a hierarchical structure model and a pairwise comparison matrix, the relative importance weight of each indicator is calculated. The subjective weight value is the importance weight given to the water quality evaluation indicator based on expert experience and decision maker judgment, reflecting the relative importance of the indicator.

[0074] It should be noted that by combining the hierarchical analysis algorithm and the single pollution index algorithm, the relative importance of water quality indicators and the degree of pollution are comprehensively considered to calculate the subjective weight value. This method takes into account the scientific nature of expert experience and the characteristics of the indicators themselves, making the weight assignment more reasonable and targeted.

[0075] In a possible implementation, S6 specifically includes:

[0076] S601: Calculate the relative importance of each water quality evaluation index through the hierarchical analysis algorithm.

[0077] Among them, relative importance refers to the comparison result of the importance between water quality evaluation indicators in the hierarchical analysis algorithm, reflecting the importance of an indicator relative to other indicators in the entire evaluation system.

[0078] S602: Construct a discriminant matrix based on relative importance:

[0079]

[0080] Among them, A represents the discriminant matrix, a ij It represents the importance of the i-th water quality evaluation index relative to the j-th water quality evaluation index, i = 1,…,n, j = 1,…,m, n and m both represent the total number of water quality evaluation indicators.

[0081] S603: According to the discriminant matrix, the scale value of each water quality evaluation index is calculated by a single pollution index algorithm:

[0082]

[0083] Among them, d i represents the scale value of the i-th water quality evaluation index, c i represents the measured concentration of the i-th water quality evaluation index, c oi Represents the concentration standard value of the i-th water quality evaluation index.

[0084] It should be noted that there are usually two methods for determining the standard concentration value, using the water quality index limit of Class III surface water or the average value of the standard limit of Class V water. However, the range of variation between the standard limits of different water quality grades is different. In the present invention, the weighted average method is used to determine the standard concentration value.

[0085] S604: Combine the discriminant matrix and the scale value to calculate the subjective weight value of each water quality evaluation index:

[0086]

[0087] Among them, λ max represents the maximum eigenvalue of the discriminant matrix, w i represents the importance weight of the i-th water quality evaluation index in the lower layer relative to the water quality evaluation index in the upper layer, represents the subjective weight value of the i-th water quality evaluation index, and g represents the normalization coefficient.

[0088] It should be noted that the introduction of subjective weights can reflect the priority indicators in specific evaluation scenarios, and provide a qualitative and quantitative basis for subsequent weight fusion and comprehensive evaluation, thereby improving the reliability and practicality of water quality evaluation results.

[0089] S7: Determine the objective weight value of each evaluation index in the water quality evaluation index set through the entropy weight algorithm.

[0090] Among them, the entropy weight algorithm is an objective weighting method. The weight is calculated according to the degree of variation of water quality indicators. The greater the fluctuation of indicator data and the more information, the higher the weight. The objective weight value is a weight calculated entirely based on the data, which avoids the influence of human factors and reflects the actual contribution of the indicator to the evaluation results.

[0091] It should be noted that the entropy weight algorithm is used to objectively calculate the weights of water quality evaluation indicators. Based on data fluctuations and conflicts, the weight distribution is ensured to be more scientific and data-driven. This method can effectively reduce subjective bias, especially in complex multi-indicator evaluations, and can more accurately reflect the independent information of each indicator.

[0092] In a possible implementation, S7 specifically includes:

[0093] S701: Calculate the conflicts among various water quality evaluation indicators through entropy weight algorithm:

[0094]

[0095] Among them, r ij Represents the correlation coefficient between the i-th water quality evaluation index and the j-th water quality evaluation index.

[0096] S702: Determine the relative strength of each water quality evaluation index based on the conflict:

[0097]

[0098] Among them, C i represents the relative strength of the i-th water quality evaluation index, δ i Represents the variance of the i-th water quality evaluation index.

[0099] S703: Calculate the subjective weight value of each water quality evaluation index by combining conflict and relative strength:

[0100]

[0101] in, represents the objective weight value of the i-th water quality evaluation index, and m represents the total number of water quality evaluation indicators.

[0102] It should be noted that by combining relative strength, the rationality of weight distribution is further enhanced, making the evaluation results more objective and credible, while adapting to the needs of different water quality evaluation scenarios.

[0103] S8: Based on game theory, with Nash equilibrium as the goal, combined with subjective weight values ​​and objective weight values, the fusion weight matrix of each evaluation indicator in the water quality evaluation index set relative to different water quality levels is calculated.

[0104] Among them, game theory studies the optimal strategy selection of multiple subjects in interaction. The goal is to achieve a balance state in the weight combination (such as Nash equilibrium) to ensure the stability and rationality of the results. Nash equilibrium means that in the game, the choices of all subjects (or strategies) are optimal, and any single change in strategy will not bring better results. The fusion weight matrix is ​​a comprehensive weight matrix generated by combining subjective and objective weights and optimized through game theory, which is used for final evaluation.

[0105] It should be noted that through game theory, subjective weights and objective weights are organically integrated to seek a balance between the two and generate a scientific and reasonable fusion weight matrix. This method takes into account the rationality of expert experience and the objectivity of data-driven, and avoids the one-sidedness of a single weighting method.

[0106] In a possible implementation, S8 specifically includes:

[0107] S801: Assign weights to each water quality evaluation index in different ways to generate a weight set:

[0108]

[0109] Among them, S k represents the weight set, represents the weight value assigned by the kth method to the nth water quality evaluation index, S represents the combined weight, l represents the total number of methods, and a k represents the linear combination coefficient.

[0110] S802: Based on game theory, with Nash equilibrium as the goal, calculate the combination weight by minimizing the objective function:

[0111]

[0112]

[0113] Among them, min means taking the minimum value, s j represents the weight value of the i-th method, represents the transpose of the weight vector of the jth method, The transpose of the weight vector of the ith method, T represents the transpose, ||||2 represents the two-norm, represents the linear combination coefficient after normalization processing, w * Represents the combined weight.

[0114] S803: Generate a fusion weight matrix of each water quality evaluation index at different levels according to the combined weights:

[0115]

[0116] Among them, W represents the fusion weight matrix, Represents the combined weight of the i-th water quality evaluation index.

[0117] It should be noted that the introduction of game theory ensures the stability and optimality of weight distribution, making the evaluation model more adaptable and accurate. In addition, the fusion weight matrix provides more comprehensive support for complex multi-indicator water quality evaluation, making the results more credible and scientific.

[0118] S9: Combine the membership matrix and the fusion weight matrix to generate the water quality grade of the water sample to be evaluated.

[0119] It should be noted that by combining the fusion weight matrix and the membership matrix and using the weighted average principle to generate water quality grades, the scientific and precise comprehensive evaluation of multiple indicators is achieved. This method can fully integrate the importance and fuzzy characteristics of the indicators to ensure that the evaluation results are both data-driven and practical.

[0120] In a possible implementation, S9 specifically includes:

[0121] Through the weighted average principle, the fusion weight matrix and the membership matrix are compounded to obtain the water quality grade:

[0122]

[0123] Among them, B T Indicates water quality level, b j It represents the membership matrix of the indicator relative to the j-th level of water quality, β represents the weighting coefficient, and j represents the index of the indicator.

[0124] Among them, the weighted average principle is a mathematical calculation method that multiplies the weight and the corresponding value and sums them up to comprehensively consider the influence of multiple factors.

[0125] It should be noted that the output of water quality levels provides managers with an intuitive and specific reference, facilitating quick decision-making. At the same time, compound operations avoid the problem of over-reliance on a single standard in the evaluation process, enhance the versatility and flexibility of the method, and adapt to the needs of complex and diverse water quality scenarios.

[0126] In a specific implementation case, the water quality index data comes from a section of Dianchi Lake, with a total of 21 months of data on 24 water quality indicators, namely water temperature (WT, ℃), pH, dissolved oxygen (DO, mg / L), permanganate index (CODMn, mg / L), five-day biochemical oxygen demand (BOD5, mg / L), ammonia nitrogen (NH3-N, mg / L), volatile phenol (mg / L), cyanide (CN-, mg / L), mercury (Hg, mg / L), lead (Pb, mg / L), cadmium (Cd, mg / L), and iodine (I2O, mg / L). g / L), arsenic (As, mg / L), hexavalent chromium (Cr6+, mg / L), petroleum (PET, mg / L), electrical conductivity (EC, ms / m), fluoride (F, mg / L), total nitrogen (TN, mg / L), total phosphorus (TP, mg / L), chemical oxygen demand (COD, mg / L), copper (Cu, mg / L), zinc (Zn, mg / L), tetravalent selenium (Se4+, mg / L), sulfide (S, mg / L), anionic surfactant (LAS, mg / L).

[0127] Pearson correlation analysis of the above index data shows that there is a very significant positive correlation or negative correlation between the above 22 indicators (p < 0.001), especially the correlation between metal ions is very high, so it is necessary to perform principal component analysis on the above indicators to screen the indicators.

[0128] According to the criterion that the principal component is greater than 1, there are 6 principal components selected, which explain 74.4% of the original variable information. The first principal component PC1 has higher loading values, such as pH, DO, BOD5, NH3-N, Hg, Pb, As, Cr, EC, TN, TP, Cu, Se, which represent chemical pollution indicators such as heavy metals and human activities in water bodies. However, there is a significant correlation (r>0.7) between pH, Hg, Pb, As, Cr, EC, Cu, Se and other indicators, and the metal element index values ​​in PC1 are extremely low (far less than Class I indicators), which has almost no effect on the final water quality category. Therefore, DO, BOD5, NH3-N, EC, TN and TP are retained on the first principal component. The second principal component has the largest loading values, WT, CODMn, volatile phenols, PET, F and COD. This principal component mainly represents the pollution status of organic matter in water bodies. WT has no clear water quality classification, so this indicator is removed. The third principal component contains toxic pollution indicators such as Cd, Zn and S. The correlation between the indicators is not significant, so all of them can be retained. The fourth principal component contains CN and LAS. LAS has only two classification standard values ​​in the classification standard of surface water standards, so it is not considered for the time being. CN is retained. There are no specific water quality indicators with high load values ​​worthy of retention on the fifth and sixth principal components.

[0129] According to the results of principal component analysis and the pollution types represented by each principal component, after simplifying the correlation between indicators within the same principal component, the water quality indicators that need to be evaluated are finally determined to be DO, BOD5, NH3-N, TN, TP, CODMn, volatile phenols, PET, F, COD, Zn, S and CN.

[0130] After determining the evaluation factor set, objective weights and subjective weights are assigned to each water quality indicator that needs to be evaluated.

[0131] Firstly, the subjective weights of the above fourteen indicators were calculated by using the improved analytic hierarchy process with single factor evaluation method replacing the nine-scale method. Secondly, the objective weights of each indicator were determined by the CRITIC weighting method. Finally, the comprehensive weights were determined by game theory. The combination coefficient of subjective weights was 0.69958, and the combination coefficient of objective weights was 0.30042. The results showed that compared with the weighting results of the AHP subjective weighting method and the CRITIC objective weighting method, the value of the combined weighting method was more comprehensive and could coordinate the subjective and objective weight values. The weights of ammonia nitrogen and total phosphorus in water quality evaluation were higher than those of other indicators, indicating that ammonia nitrogen and total phosphorus were the main indicators of limit water quality, and PET and permanganate index had little influence on the final water quality evaluation results.

[0132] Based on the above different weighting methods combined with game theory, a fuzzy comprehensive evaluation was conducted on the water quality of the evaluated section of Dianchi Lake, and the water quality grade was quantified using the weighted average comprehensive evaluation index to obtain the water quality grade.

[0133] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0134] In the present invention, a plurality of water quality indicators of a water sample to be evaluated are obtained, and correlation analysis is performed on each water quality indicator. In the presence of high collinearity, principal component analysis is performed on the water quality indicators to determine a water quality evaluation indicator set. Water quality grades are divided according to surface water quality evaluation standards. Then, through the distribution function of the semi-trapezoidal indicator, the membership matrix of each evaluation indicator is calculated. The subjective weight value of each evaluation indicator in the water quality evaluation indicator set is determined by combining the single pollution index algorithm and the hierarchical analysis algorithm. The objective weight value of each evaluation indicator in the water quality evaluation indicator set is determined by the entropy weight algorithm. Based on game theory and with Nash equilibrium as the goal, the fusion weight matrix of each evaluation indicator in the water quality evaluation indicator set relative to different water quality grades is calculated by combining the subjective weight value and the objective weight value. The water quality grade of the water sample to be evaluated is generated by combining the membership matrix and the fusion weight matrix. The problem of selecting evaluation indicators and determining the weight of evaluation indicators in the process of fuzzy comprehensive evaluation of water quality is effectively solved, and its limitations are effectively avoided, so that the water quality evaluation result is more objective and reasonable, and the weight accuracy and the efficiency and accuracy of water quality evaluation are improved.

[0135] Reference Manual Attached Figure 2 , showing a structural schematic diagram of a water quality fuzzy comprehensive evaluation system based on game theory and empowerment provided by the present invention.

[0136] The present invention also provides a water quality fuzzy comprehensive evaluation system 20 based on game theory and weighting, which is applied to the above-mentioned water quality fuzzy comprehensive evaluation method based on game theory and weighting, and comprises:

[0137] Processor 201.

[0138] The memory 202 stores computer-readable instructions. When the computer-readable instructions are executed by the processor 201, the fuzzy comprehensive evaluation method for water quality based on game theory and weighting as in the method embodiment is implemented.

[0139] The water quality fuzzy comprehensive evaluation system 20 based on game theory and weighting provided by the present invention can execute the above-mentioned water quality fuzzy comprehensive evaluation method based on game theory and weighting, and achieve the same or similar technical effects. To avoid repetition, the present invention will not go into details.

[0140] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0141] In the present invention, a plurality of water quality indicators of a water sample to be evaluated are obtained, and correlation analysis is performed on each water quality indicator. In the presence of high collinearity, principal component analysis is performed on the water quality indicators to determine a water quality evaluation indicator set. Water quality grades are divided according to surface water quality evaluation standards. Then, through the distribution function of the semi-trapezoidal indicator, the membership matrix of each evaluation indicator is calculated. The subjective weight value of each evaluation indicator in the water quality evaluation indicator set is determined by combining the single pollution index algorithm and the hierarchical analysis algorithm. The objective weight value of each evaluation indicator in the water quality evaluation indicator set is determined by the entropy weight algorithm. Based on game theory and with Nash equilibrium as the goal, the fusion weight matrix of each evaluation indicator in the water quality evaluation indicator set relative to different water quality grades is calculated by combining the subjective weight value and the objective weight value. The water quality grade of the water sample to be evaluated is generated by combining the membership matrix and the fusion weight matrix. The problem of selecting evaluation indicators and determining the weight of evaluation indicators in the process of fuzzy comprehensive evaluation of water quality is effectively solved, and its limitations are effectively avoided, so that the water quality evaluation result is more objective and reasonable, and the weight accuracy and the efficiency and accuracy of water quality evaluation are improved.

[0142] It should be understood that the processor in the embodiment of the present invention may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0143] It should also be understood that the memory in the embodiments of the present invention may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous link DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0144] The above embodiments can be implemented in whole or in part by software, hardware (such as circuits), firmware or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When a computer instruction or computer program is loaded or executed on a computer, a process or function according to an embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. Computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center by wired (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that contains one or more available media sets. The available medium can be a magnetic medium (for example, a floppy disk, a hard disk, a tape), an optical medium (for example, a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state hard disk.

[0145] It should be understood that the term "and / or" in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. A and B can be singular or plural. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship, but it may also indicate an "and / or" relationship. Please refer to the context for specific understanding.

[0146] In the present invention, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can be represented by: a, b, c, ab, ac, bc, or abc, where a, b, c can be single or multiple.

[0147] It should be understood that in various embodiments of the present invention, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0148] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0149] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described equipment, devices and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0150] In the several embodiments provided by the present invention, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other ways. For example, the device embodiments described above are only schematic, for example, the division of units is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0151] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0152] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0153] If the function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods of various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, etc., various media that can store program codes.

[0154] An embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, a fuzzy comprehensive evaluation method for water quality based on game theory and weighting is implemented as in the method embodiment.

[0155] A computer-readable storage medium provided by the present invention can implement the steps and effects of the fuzzy comprehensive evaluation method for water quality based on game theory and empowerment in the above-mentioned method embodiment. To avoid repetition, the present invention will not go into details.

[0156] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0157] In the present invention, a plurality of water quality indicators of a water sample to be evaluated are obtained, and correlation analysis is performed on each water quality indicator. In the presence of high collinearity, principal component analysis is performed on the water quality indicators to determine a water quality evaluation indicator set. Water quality grades are divided according to surface water quality evaluation standards. Then, through the distribution function of the semi-trapezoidal indicator, the membership matrix of each evaluation indicator is calculated. The subjective weight value of each evaluation indicator in the water quality evaluation indicator set is determined by combining the single pollution index algorithm and the hierarchical analysis algorithm. The objective weight value of each evaluation indicator in the water quality evaluation indicator set is determined by the entropy weight algorithm. Based on game theory and with Nash equilibrium as the goal, the fusion weight matrix of each evaluation indicator in the water quality evaluation indicator set relative to different water quality grades is calculated by combining the subjective weight value and the objective weight value. The water quality grade of the water sample to be evaluated is generated by combining the membership matrix and the fusion weight matrix. The problem of selecting evaluation indicators and determining the weight of evaluation indicators in the process of fuzzy comprehensive evaluation of water quality is effectively solved, and its limitations are effectively avoided, so that the water quality evaluation result is more objective and reasonable, and the weight accuracy and the efficiency and accuracy of water quality evaluation are improved.

[0158] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

[0159] There are a few points to note:

[0160] (1) The drawings of the embodiments of the present invention only relate to the structures related to the embodiments of the present invention, and other structures may refer to the general design.

[0161] (2) For the sake of clarity, in the drawings used to describe the embodiments of the present invention, the thickness of the layers or regions is exaggerated or reduced, that is, these drawings are not drawn according to the actual scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element may be "directly" "on" or "under" the other element or there may be intermediate elements.

[0162] (3) In the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other to obtain new embodiments.

[0163] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A fuzzy comprehensive evaluation method for water quality based on game theory and weighting, characterized in that: include: S1: Obtain multiple water quality indicators of the water sample to be evaluated; S2: Conduct correlation analysis on various water quality indicators; S3: Based on the results of the correlation analysis, in the case of highly collinear water quality indicators, principal component analysis is performed on all water quality indicators to determine the water quality evaluation indicator set; S4: Classify water quality levels according to surface water quality evaluation standards; S5: Calculate the membership matrix of each evaluation index relative to each water quality level through the distribution function of the semi-trapezoidal index; S6: Determine the subjective weight value of each evaluation index in the water quality evaluation index set by combining the single pollution index algorithm and the hierarchical analysis algorithm; S7: Determine the objective weight value of each evaluation index in the water quality evaluation index set by using an entropy weight algorithm; S8: Based on game theory and with Nash equilibrium as the goal, the subjective weight value and the objective weight value are combined to calculate a fusion weight matrix of each evaluation index in the water quality evaluation index set relative to different water quality levels; S9: Combining the membership matrix and the fusion weight matrix, generating the water quality grade of the water sample to be evaluated.

2. The fuzzy comprehensive evaluation method of water quality based on game theory and weighting according to claim 1 is characterized in that: The water quality indicators specifically include: water temperature, pH, dissolved oxygen, permanganate index, chemical oxygen demand, five-day biochemical oxygen demand, ammonia nitrogen, total phosphorus, total nitrogen, fluoride, copper, zinc, selenium, arsenic, mercury, cadmium, hexavalent chromium, lead, cyanide, volatile phenols, petroleum, and anionic synthetic detergents and sulfides.

3. The fuzzy comprehensive evaluation method of water quality based on game theory and weighting according to claim 1 is characterized in that: The S3 specifically includes: S301: performing principal component analysis on the water quality index; S302: Calculate the eigenvalue of each principal component and determine whether the eigenvalue is greater than a preset eigenvalue. If so, retain the principal component; otherwise, discard the principal component. S303: Calculate the correlation value between each water quality index in the retained principal component, and determine whether the correlation value is greater than a preset correlation value. If so, retain the water quality index; otherwise, discard the water quality index; S304: Determine the water quality evaluation index set according to the retained water quality index: U={u1,u2,…,u i ,…,u n } Among them, U represents the water quality evaluation index set, u i represents the i-th water quality evaluation index, i=1,…,n, and n represents the total number of water quality evaluation indexes.

4. The fuzzy comprehensive evaluation method of water quality based on game theory and weighting according to claim 1 is characterized in that: The S5 specifically includes: S501: According to the water quality membership function, the membership of each evaluation index relative to each water quality level is calculated: When j=1, the first-level (primary) water quality membership function is specifically: When j = 2, ..., 4, the water quality membership functions from level II to IV are as follows: When j = 5, the Vth level water quality membership function is specifically: Among them, r i1 represents the membership of the i-th water quality evaluation index to the first-level water quality, x i represents the measured value of the i-th water quality evaluation index, S ij represents the standard value of the j-th water quality corresponding to the i-th water quality evaluation index, S i,j+1 represents the standard value of the j+1th level of water quality corresponding to the i-th water quality evaluation index, r ij represents the membership of the i-th water quality evaluation index to the j-th water quality, S i,j-1 It represents the standard value of the j-1th level of water quality corresponding to the i-th water quality evaluation index; S502: Determine the membership matrix according to the membership.

5. The fuzzy comprehensive evaluation method of water quality based on game theory and weighting according to claim 1 is characterized in that: The S6 specifically includes: S601: Calculating the relative importance of each water quality evaluation index through the hierarchical analysis algorithm; S602: Construct a discriminant matrix according to the relative importance: Among them, A represents the discriminant matrix, a ij represents the importance of the i-th water quality evaluation index relative to the j-th water quality evaluation index, i = 1, ..., n, j = 1, ..., m, n and m both represent the total number of water quality evaluation indicators; S603: According to the discriminant matrix, the scale value of each water quality evaluation index is calculated by a single pollution index algorithm: Among them, d i represents the scale value of the i-th water quality evaluation index, c i represents the measured concentration of the i-th water quality evaluation index, c oi represents the concentration standard value of the i-th water quality evaluation index; S604: Calculate the subjective weight value of each water quality evaluation index by combining the discriminant matrix and the scale value: Among them, λ max represents the maximum eigenvalue of the discriminant matrix, w i It represents the importance weight of the i-th water quality evaluation index in the lower layer relative to the water quality evaluation index in the upper layer, represents the subjective weight value of the i-th water quality evaluation index, and g represents the normalization coefficient.

6. The fuzzy comprehensive evaluation method of water quality based on game theory and weighting according to claim 1 is characterized in that: The S7 specifically includes: S701: Calculate the conflicts among various water quality evaluation indicators through the entropy weight algorithm: Among them, r ij represents the correlation coefficient between the i-th water quality evaluation index and the j-th water quality evaluation index; S702: According to the conflict, determine the relative strengths of the various water quality evaluation indicators: Among them, C i represents the relative strength of the i-th water quality evaluation index, δ i represents the variance of the i-th water quality evaluation index; S703: Calculate the subjective weight value of each water quality evaluation index by combining the conflict and the relative strength: in, represents the objective weight value of the i-th water quality evaluation index, and m represents the total number of water quality evaluation indicators.

7. The fuzzy comprehensive evaluation method of water quality based on game theory and weighting according to claim 1 is characterized in that: The S8 specifically includes: S801: Assign weights to each water quality evaluation index in different ways to generate a weight set: Among them, S k represents the weight set, represents the weight value assigned by the kth method to the nth water quality evaluation index, S represents the combined weight, l represents the total number of methods, and a k represents the linear combination coefficient; S802: Based on game theory, with Nash equilibrium as the goal, calculate the combination weight by minimizing the objective function: Among them, min means taking the minimum value, s j represents the weight value of the i-th method, represents the transpose of the weight vector of the jth method, The transpose of the weight vector of the ith method, T represents transpose, ||||2 represents the two-norm, represents the linear combination coefficient after normalization processing, w * represents the combined weight; S803: Generate a fusion weight matrix of each water quality evaluation index at different levels according to the combined weights: Among them, W represents the fusion weight matrix, Represents the combined weight of the i-th water quality evaluation index.

8. The fuzzy comprehensive evaluation method of water quality based on game theory and weighting according to claim 1 is characterized in that: The S9 is specifically: By using the weighted average principle, the fusion weight matrix and the membership matrix are compounded to obtain the water quality grade: Among them, B T Indicates water quality level, b j It represents the membership matrix of the indicator relative to the j-th level of water quality, β represents the weighting coefficient, and j represents the index of the indicator.

9. A fuzzy comprehensive evaluation system for water quality based on game theory and weighting, characterized in that: include: processor; A memory having computer-readable instructions stored thereon, wherein when the computer-readable instructions are executed by the processor, the fuzzy comprehensive evaluation method for water quality based on game theory and weighting as described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the fuzzy comprehensive evaluation method for water quality based on game theory and weighting as described in any one of claims 1 to 8 is implemented.

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