CN114331053A - Shallow lake eutrophication evaluation method based on fuzzy hierarchical evaluation model - Google Patents

Shallow lake eutrophication evaluation method based on fuzzy hierarchical evaluation model Download PDF

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CN114331053A
CN114331053A CN202111524448.XA CN202111524448A CN114331053A CN 114331053 A CN114331053 A CN 114331053A CN 202111524448 A CN202111524448 A CN 202111524448A CN 114331053 A CN114331053 A CN 114331053A
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王策
唐利
肖冰
吴昊
孟祥鑫
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Shanghai Jianyuan Water Ecological Environment Engineering Co ltd
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Abstract

The invention discloses a shallow lake eutrophication evaluation method based on a fuzzy hierarchical evaluation model, which comprises the following steps: step one, determining an evaluation standard of a model; step two, constructing a fuzzy hierarchical evaluation model; step three, establishing a judgment matrix of each level; step four, establishing a fuzzy relation matrix of the evaluation factors and the evaluation grades; and step five, comprehensively evaluating result expression. The method constructs a comprehensive evaluation model of the water quality of the shallow lake based on fuzzy hierarchy evaluation, applies an Analytic Hierarchy Process (AHP) to a fuzzy mathematical evaluation method to construct an ordered hierarchical structure to obtain the index weight, overcomes the defects that the determination of the weight set of the traditional fuzzy mathematical evaluation method has large subjective factor influence, lacks the consideration of the interaction influence among indexes and the like, and realizes the reliable evaluation of the eutrophication state of the shallow lake.

Description

Shallow lake eutrophication evaluation method based on fuzzy hierarchical evaluation model
Technical Field
The invention belongs to the field of environmental evaluation, and particularly relates to a shallow lake eutrophication evaluation method based on a fuzzy hierarchical evaluation model.
Background
The water eutrophication evaluation is a quantitative description of the nutritional status of a certain stage in the water eutrophication development process, and the main purpose is to judge the nutritional status of the water, understand the eutrophication process and predict the development trend of the water through the investigation of the representative index of the water eutrophication, and provide scientific basis for water quality management and prevention and control of the eutrophication. In recent years, the blue algae bloom outbreak caused by eutrophication of many shallow lakes in China greatly affects the living environment of people and even threatens the health of people. Therefore, the evaluation of the eutrophication of the water body is particularly important.
Actually, certain relation exists among various evaluation factors in the shallow lake, and the evaluation factors influence each other. Therefore, only single-factor evaluation has one-sidedness, and the water quality condition of the shallow lake cannot be accurately reflected. The comprehensive evaluation of water eutrophication fully considers the interrelation among different indexes in the water through different mathematical methods, and formulates different classification standards, so that the real water quality condition of the water can be more clearly reflected, and the comprehensive evaluation is most widely applied in the current research on the evaluation of water eutrophication. The main water eutrophication comprehensive evaluation methods include a comprehensive nutrition state index method, a fuzzy mathematical method, a gray clustering method, an artificial neural network and the like, and the fuzzy mathematical evaluation method is relatively widely applied in a plurality of evaluation methods.
The fuzzy mathematical evaluation method quantizes all factors in the constructed index system based on the fuzzy mathematical theory and the membership function, and performs synthetic operation on the weight set and the fuzzy relation matrix to realize comprehensive evaluation of the target layer under the common influence of multiple factors. However, the determination of the weight set by the traditional fuzzy mathematical evaluation method has the defects of large subjective factor influence, lack of consideration on the interaction among all indexes and the like, so that the reliable evaluation on the eutrophication state of the water body cannot be realized.
Disclosure of Invention
Aiming at the problem that reliable evaluation on the water eutrophication state cannot be realized in the prior art, the invention provides the shallow lake eutrophication evaluation method based on the fuzzy hierarchical evaluation model, the hierarchical analysis method is applied to the fuzzy mathematical evaluation method to construct an ordered hierarchical structure to obtain the index weight, and the defects that the determination of the weight set of the traditional fuzzy mathematical evaluation method has large subjective factor influence, lacks consideration on the interaction influence among indexes and the like are overcome.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a shallow lake eutrophication evaluation method based on a fuzzy hierarchical evaluation model, which comprises the following steps:
step one, determining an evaluation standard of a model:
selecting a plurality of water body pollution indexes as evaluation indexes of the eutrophication degree of the shallow lake, and quantifying the relationship between each evaluation index and the eutrophication degree of the shallow lake so as to determine the evaluation standard of the eutrophication model of the shallow lake;
step two, constructing a fuzzy level evaluation model:
according to the mathematical principle of an Analytic Hierarchy Process (AHP), constructing an ordered hierarchical structure divided into a target layer V, a criterion layer A and a scheme layer B;
step three, establishing a judgment matrix of each level:
respectively establishing a V-A layer judgment matrix and an A-B layer judgment matrix, and calculating the maximum characteristic root lambda of each single-layer judgment matrix by using a square root methodmaxAnd the corresponding normalized feature vector W, and carrying out consistency check; then, utilizing all the single-level sequencing results in the same level to carry out total level sequencing, and simultaneously, checking the consistency; finally, a single-ordering weight set W ' of the layer A relative to the layer V and a single-ordering weight set W ' of the layer B relative to the layer A are obtained through calculation, and then a total-ordering weight set W ' of the layer B is obtained;
step four, establishing a fuzzy relation matrix of the evaluation factors and the evaluation grades:
using membership in fuzzy mathematics to describe hierarchical boundary, rootMonitoring value x according to evaluation factor iiStandard value d corresponding to evaluation gradeiLinear interpolation relationship therebetween to determine membership function rijThereby forming a fuzzy relation matrix of the evaluation factors and the evaluation grades
Figure BDA0003409560690000022
Step five, comprehensively evaluating result expression:
the weight set W and the fuzzy relation matrix corresponding to the weight set W
Figure BDA0003409560690000021
And (3) obtaining a fuzzy hierarchical evaluation model by adopting a weighted average method, obtaining the membership of the water quality of the shallow lake to each eutrophication level after completing fuzzy synthesis weighted linear transformation, and determining the eutrophication evaluation level of the evaluated object according to the maximum membership principle.
Further, the plurality of water body pollution indicators in the first step include a permanganate index (COD)Mn) Total phosphorus index (TP), total nitrogen index (TN) and chlorophyll a index (Chla), and the eutrophication degree of shallow lakes refers to poor nutrition, medium nutrition, rich nutrition, light rich nutrition, medium rich nutrition and heavy rich nutrition.
Further, in the second step, the target layer V refers to water quality evaluation factor weighting, and the criterion layer A refers to a factor monthly mean value A1And the maximum value of the sum factor2Scheme layer B refers to the permanganate index (COD)Mn) Value B1Total phosphorus index (TP) value B2Total nitrogen index (TN) value B3And chlorophyll a index (Chla) value B4。
Further, the method for establishing the V-a layer judgment matrix in step three is as follows:
the basis for establishing the V-A layer judgment matrix is as follows: considering the importance of the two factors of the layer A to the comprehensive evaluation of the water quality of the landscape water body, the monthly mean value A of the index is considered1Specific maximum value A2Obviously important, according to the contents and meanings of the matrix scales, if two factors are compared, one is obviously more important than the other, then the scale is 5, and V-A can be obtainedLayer judgment matrix:
Figure BDA0003409560690000031
further, the method for establishing the layer a-B judgment matrix in the third step is as follows:
determining the matrix element b of the layerst，
Each criterion A1、A2The sub-exponential formula beta is used for the monitoring values of all indexesij＝Cij/CsjStandardization of wherein CijIs aiMean (or maximum) of monitoring values of jth index under criterion, CsjIs the maximum allowable concentration value of the jth index,
for each of the criteria that are to be followed,
let betaki＝max{βij|j＝1,2,…,4}，
βli＝min{βij|j＝1,2,…,4}i＝1，2，
Calculating Deltai＝(βki-βli)/9，
Is provided with
Figure BDA0003409560690000032
For arbitrary betasAnd betatIn contrast, it determines the matrix element bstIs determined by:
Figure BDA0003409560690000033
the judgment matrix of 4X 4A-B layers can be obtained according to the formula.
Further, the single-rank weight set W' and the total-rank weight set W ″ in step three are calculated as follows:
W’＝(w1’，…，wj’，…，wn’)，
Figure BDA0003409560690000034
W”＝(w1”，w2”，w3”，w4”)，
Figure BDA0003409560690000035
in the formula: bijRepresenting a relative importance value; ciRepresenting the single rank weight of the A-layer relative to the V-layer; dijRepresenting the single rank weight of the B-layer relative to the a-layer.
Further, the consistency test method in the third step is as follows:
the maximum characteristic root of the matrix is judged,
Figure BDA0003409560690000041
the index of the consistency is that the consistency index,
Figure BDA0003409560690000042
in the formula: n represents the order of the decision matrix,
the proportion of the consistency is that,
Figure BDA0003409560690000043
in the formula, RI represents average random consistency index, and when CR is less than or equal to 0.1, the matrix is judged to meet the requirement of consistency test; otherwise, the matrix elements need to be compared two by two again until the consistency check is passed.
Further, the step four membership function rijIndicating the likelihood that the evaluation factor i can be rated as a jth evaluation level, r, based on the monitored value of the ith evaluation factorijAnd
Figure BDA0003409560690000044
the calculation formula of (a) is as follows:
Figure BDA0003409560690000045
Figure BDA0003409560690000046
Figure BDA0003409560690000047
further, the fuzzy hierarchical evaluation model establishing method in the fifth step is as follows:
Figure BDA0003409560690000048
Figure BDA0003409560690000049
represents the synthetic operation, i.e.:
Figure BDA00034095606900000410
Figure BDA00034095606900000411
the following results were obtained:
Figure BDA00034095606900000412
compared with the prior art, the invention has the beneficial effects that:
the method constructs a comprehensive evaluation model of the water quality of the shallow lake based on fuzzy hierarchy evaluation, applies an Analytic Hierarchy Process (AHP) to a fuzzy mathematical evaluation method to construct an ordered hierarchical structure to obtain the index weight, overcomes the defects that the determination of the weight set of the traditional fuzzy mathematical evaluation method has large subjective factor influence, lacks the consideration of the interaction influence among indexes and the like, and realizes the reliable evaluation of the eutrophication state of the shallow lake.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of a hierarchical structure of a comprehensive evaluation model for water quality in shallow lakes.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
The embodiment provides a shallow lake eutrophication evaluation method based on a fuzzy hierarchical evaluation model, which comprises the following steps:
step one, determining an evaluation standard of a model:
selecting a plurality of water body pollution indexes as evaluation indexes of the eutrophication degree of the shallow lake, and quantifying the relationship between each evaluation index and the eutrophication degree of the shallow lake so as to determine the evaluation standard of the eutrophication model of the shallow lake;
step two, constructing a fuzzy level evaluation model:
according to the mathematical principle of an Analytic Hierarchy Process (AHP), constructing an ordered hierarchical structure divided into a target layer V, a criterion layer A and a scheme layer B;
step three, establishing a judgment matrix of each level:
respectively establishing a V-A layer judgment matrix and an A-B layer judgment matrixCalculating the maximum characteristic root lambda of each single-level judgment matrix by using a square root methodmaxAnd the corresponding normalized feature vector W, and carrying out consistency check; then, utilizing all the single-level sequencing results in the same level to carry out total level sequencing, and simultaneously, checking the consistency; finally, a single-ordering weight set W ' of the layer A relative to the layer V and a single-ordering weight set W ' of the layer B relative to the layer A are obtained through calculation, and then a total-ordering weight set W ' of the layer B is obtained;
step four, establishing a fuzzy relation matrix of the evaluation factors and the evaluation grades:
the classification limit is described by adopting membership in fuzzy mathematics and according to the monitoring value x of the evaluation factor iiStandard value d corresponding to evaluation gradeiLinear interpolation relationship therebetween to determine membership function rijThereby forming a fuzzy relation matrix of the evaluation factors and the evaluation grades
Figure BDA0003409560690000051
Step five, comprehensively evaluating result expression:
the weight set W and the fuzzy relation matrix corresponding to the weight set W
Figure BDA0003409560690000061
And (3) obtaining a fuzzy hierarchical evaluation model by adopting a weighted average method, obtaining the membership of the water quality of the shallow lake to each eutrophication level after completing fuzzy synthesis weighted linear transformation, and determining the eutrophication evaluation level of the evaluated object according to the maximum membership principle.
Further, the plurality of water body pollution indicators in the first step include a permanganate index (COD)Mn) Total phosphorus index (TP), total nitrogen index (TN) and chlorophyll a index (Chla), and the eutrophication degree of shallow lakes refers to poor nutrition, medium nutrition, rich nutrition, light rich nutrition, medium rich nutrition and heavy rich nutrition.
Further, in the second step, the target layer V refers to water quality evaluation factor weighting, and the criterion layer A refers to a factor monthly mean value A1And the maximum value of the sum factor2Scheme layer B refers to the permanganate index (COD)Mn) Value B1Total phosphorusIndex (TP) value B2Total nitrogen index (TN) value B3And chlorophyll a index (Chla) value B4。
Further, the method for establishing the V-a layer judgment matrix in step three is as follows:
the basis for establishing the V-A layer judgment matrix is as follows: considering the importance of the two factors of the layer A to the comprehensive evaluation of the water quality of the landscape water body, the monthly mean value A of the index is considered1Specific maximum value A2Obviously important, according to the content and meaning of the judgment matrix scale, if two factors are compared, one is obviously more important than the other, the scale is 5, and the V-A layer judgment matrix can be obtained:
Figure BDA0003409560690000062
further, the method for establishing the layer a-B judgment matrix in the third step is as follows:
determining the matrix element b of the layerst，
Each criterion A1、A2The sub-exponential formula beta is used for the monitoring values of all indexesij＝Cij/CsjStandardization of wherein CijIs aiMean (or maximum) of monitoring values of jth index under criterion, CsjIs the maximum allowable concentration value of the jth index,
for each of the criteria that are to be followed,
let betaki＝max{βij|j＝1,2,…,4}，
βli＝min{βij|j＝1,2,…,4}i＝1，2，
Calculating Deltai＝(βki-βli)/9，
Is provided with
Figure BDA0003409560690000063
For arbitrary betasAnd betatIn contrast, it determines the matrix element bstIs determined by:
Figure BDA0003409560690000071
the judgment matrix of 4X 4A-B layers can be obtained according to the formula.
Further, the single-rank weight set W' and the total-rank weight set W ″ in step three are calculated as follows:
W’＝(w1’，…，wj’，…，wn’)，
Figure BDA0003409560690000072
W”＝(w1”，w2”，w3”，w4”)，
Figure BDA0003409560690000073
in the formula: bijRepresenting a relative importance value; ciRepresenting the single rank weight of the A-layer relative to the V-layer; dijRepresenting the single rank weight of the B-layer relative to the a-layer.
Further, the consistency test method in the third step is as follows:
the maximum characteristic root of the matrix is judged,
Figure BDA0003409560690000074
the index of the consistency is that the consistency index,
Figure BDA0003409560690000075
in the formula: n represents the order of the decision matrix,
the proportion of the consistency is that,
Figure BDA0003409560690000076
in the formula, RI represents average random consistency index, and when CR is less than or equal to 0.1, the matrix is judged to meet the requirement of consistency test; otherwise, the matrix elements need to be compared two by two again until the consistency check is passed.
Further, the step four membership function rijIndicating the likelihood that the evaluation factor i can be rated as a jth evaluation level, r, based on the monitored value of the ith evaluation factorijAnd
Figure BDA0003409560690000077
the calculation formula of (a) is as follows:
Figure BDA0003409560690000078
Figure BDA0003409560690000079
Figure BDA0003409560690000081
further, the fuzzy hierarchical evaluation model establishing method in the fifth step is as follows:
Figure BDA0003409560690000082
Figure BDA0003409560690000083
represents the synthetic operation, i.e.:
Figure BDA0003409560690000084
Figure BDA0003409560690000085
the following results were obtained:
Figure BDA0003409560690000086
example one
A certain shallow lake in the sea is taken as a research object for explanation, and the specific steps are as follows:
the collected water quality monitoring data of the lake from 5 months to 9 months are shown in table 1.
TABLE 1 Water quality monitoring data (COD therein) of a shallow lake in Shanghai City for 5-9 monthsMnPermanganate index, TP total phosphorus index, TN total nitrogen index, Chla chlorophyll a index)
Figure BDA0003409560690000087
The weight set is obtained by using the fuzzy hierarchical evaluation model constructed by the invention, and the weight set is shown in a table 2.
TABLE 2 weight values of 4 evaluation factors from 5 months to 9 months in a shallow lake in Shanghai City
Figure BDA0003409560690000088
Figure BDA0003409560690000091
According to the predetermined evaluation criteria, see table 3, and the membership degree of the water quality of the shallow lake from 5 months to 9 months to 6 eutrophication levels is calculated according to the membership degree calculation formula, see table 4.
TABLE 3 evaluation reference standard for shallow lake water quality eutrophication model
Figure BDA0003409560690000092
TABLE 4 membership of water quality of a shallow lake in Shanghai city for 5-9 months to 6 eutrophication levels
Figure BDA0003409560690000093
According to the principle of maximum membership degree, the evaluation result of the shallow lake water quality sample can be obtained, and is shown in table 5.
Figure BDA0003409560690000094
Although the present invention has been described in detail with respect to the above embodiments, it will be understood by those skilled in the art that modifications or improvements based on the disclosure of the present invention may be made without departing from the spirit and scope of the invention, and these modifications and improvements are within the spirit and scope of the invention.

Claims (9)

1. A shallow lake eutrophication evaluation method based on a fuzzy hierarchical evaluation model is characterized by comprising the following steps:
step one, determining an evaluation standard of a model:
selecting a plurality of water body pollution indexes as evaluation indexes of the eutrophication degree of the shallow lake, and quantifying the relationship between each evaluation index and the eutrophication degree of the shallow lake so as to determine the evaluation standard of the eutrophication model of the shallow lake;
step two, constructing a fuzzy level evaluation model:
according to the mathematical principle of an Analytic Hierarchy Process (AHP), constructing an ordered hierarchical structure divided into a target layer V, a criterion layer A and a scheme layer B;
step three, establishing a judgment matrix of each level:
respectively establishing a V-A layer judgment matrix and an A-B layer judgment matrix, and calculating the maximum characteristic root lambda of each single-layer judgment matrix by using a square root methodmaxAnd the corresponding normalized feature vector W, and carrying out consistency check; then, utilizing all the single-level sequencing results in the same level to carry out total level sequencing, and simultaneously, checking the consistency; finally, calculating to obtain the single-row sequence of the layer A relative to the layer V and the layer B relative to the layer AA weight set W 'is obtained, and then a B-layer total ordering weight set W' is obtained;
step four, establishing a fuzzy relation matrix of the evaluation factors and the evaluation grades:
the classification limit is described by adopting membership in fuzzy mathematics and according to the monitoring value x of the evaluation factor iiStandard value d corresponding to evaluation gradeiLinear interpolation relationship therebetween to determine membership function rijThereby forming a fuzzy relation matrix of the evaluation factors and the evaluation grades
Figure FDA0003409560680000011
Step five, comprehensively evaluating result expression:
the weight set W and the fuzzy relation matrix corresponding to the weight set W
Figure FDA0003409560680000012
And (3) obtaining a fuzzy hierarchical evaluation model by adopting a weighted average method, obtaining the membership of the water quality of the shallow lake to each eutrophication level after completing fuzzy synthesis weighted linear transformation, and determining the eutrophication evaluation level of the evaluated object according to the maximum membership principle.
2. The method for evaluating the eutrophication of shallow lakes based on the fuzzy hierarchical evaluation model as claimed in claim 1, wherein the water pollution indicators in the first step include permanganate index (COD)Mn) Total phosphorus index (TP), total nitrogen index (TN) and chlorophyll a index (Chla), and the eutrophication degree of shallow lakes refers to poor nutrition, medium nutrition, rich nutrition, light rich nutrition, medium rich nutrition and heavy rich nutrition.
3. The shallow lake eutrophication evaluation method based on the fuzzy hierarchical evaluation model as claimed in claim 1, wherein in the second step, the target layer V refers to the weighting of water quality evaluation factors, and the criterion layer A refers to the monthly mean value A of the factors1And the maximum value of the sum factor2Scheme layer B refers to the permanganate index (COD)Mn) Value B1Total phosphorus index (TP) value B2Total nitrogen index (TN) value B3And chlorophyll a index (Chla) value B4。
4. The shallow lake eutrophication evaluation method based on the fuzzy hierarchical evaluation model as claimed in claim 1, wherein the establishment method of the V-A layer judgment matrix in the third step is as follows:
the basis for establishing the V-A layer judgment matrix is as follows: considering the importance of the two factors of the layer A to the comprehensive evaluation of the water quality of the landscape water body, the monthly mean value A of the index is considered1Specific maximum value A2Obviously important, according to the content and meaning of the judgment matrix scale, if two factors are compared, one is obviously more important than the other, the scale is 5, and the V-A layer judgment matrix can be obtained:
Figure FDA0003409560680000021
5. the shallow lake eutrophication evaluation method based on the fuzzy hierarchical evaluation model as claimed in claim 1, wherein the method for establishing the judgment matrix of the layer A-B in the third step is as follows:
determining the matrix element b of the layerst，
Each criterion A1、A2The sub-exponential formula beta is used for the monitoring values of all indexesij＝Cij/CsjStandardization of wherein CijIs aiMean (or maximum) of monitoring values of jth index under criterion, CsjIs the maximum allowable concentration value of the jth index,
for each of the criteria that are to be followed,
let betaki＝max{βij|j＝1,2,…,4}，
βli＝min{βij|j＝1,2,…,4}i＝1，2，
Calculating Deltai＝(βki-βli)/9，
Is provided with
Figure FDA0003409560680000022
For arbitrary betasAnd betatIn contrast, it determines the matrix element bstIs determined by:
Figure FDA0003409560680000023
the judgment matrix of 4X 4A-B layers can be obtained according to the formula.
6. The shallow lake eutrophication evaluation method based on the fuzzy hierarchical evaluation model as claimed in claim 1, wherein the calculation method of the single-ranking weight set W' and the total-ranking weight set W "in the third step is as follows:
W’＝(w1’，…，wj’，…，wn’)，
Figure FDA0003409560680000031
W”＝(w1”，w2”，w3”，w4”)，
Figure FDA0003409560680000032
in the formula: bijRepresenting a relative importance value; ciRepresenting the single rank weight of the A-layer relative to the V-layer; dijRepresenting the single rank weight of the B-layer relative to the a-layer.
7. The shallow lake eutrophication evaluation method based on the fuzzy hierarchical evaluation model as claimed in claim 1, wherein the consistency test method in the third step is as follows:
the maximum characteristic root of the matrix is judged,
Figure FDA0003409560680000033
the index of the consistency is that the consistency index,
Figure FDA0003409560680000034
in the formula: n represents the order of the decision matrix,
the proportion of the consistency is that,
Figure FDA0003409560680000035
in the formula, RI represents average random consistency index, and when CR is less than or equal to 0.1, the matrix is judged to meet the requirement of consistency test; otherwise, the matrix elements need to be compared two by two again until the consistency check is passed.
8. The shallow lake eutrophication evaluation method based on the fuzzy hierarchical evaluation model as claimed in claim 1, wherein the membership function r in the fourth stepijIndicating the likelihood that the evaluation factor i can be rated as a jth evaluation level, r, based on the monitored value of the ith evaluation factorijAnd
Figure FDA0003409560680000036
the calculation formula of (a) is as follows:
Figure FDA0003409560680000037
Figure FDA0003409560680000038
Figure FDA0003409560680000039
9. the shallow lake eutrophication evaluation method based on the fuzzy hierarchical evaluation model as claimed in claim 1, wherein the fuzzy hierarchical evaluation model establishment method in the fifth step is as follows:
Figure FDA0003409560680000041
Figure FDA0003409560680000042
represents the synthetic operation, i.e.:
Figure FDA0003409560680000043
Figure FDA0003409560680000044
the following results were obtained:
Figure FDA0003409560680000045
CN202111524448.XA 2021-12-14 2021-12-14 Shallow lake eutrophication evaluation method based on fuzzy hierarchical evaluation model Pending CN114331053A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117390466A (en) * 2023-12-13 2024-01-12 江西省水利科学院(江西省大坝安全管理中心、江西省水资源管理中心) Lake steady state discrimination method based on similarity measurement

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117390466A (en) * 2023-12-13 2024-01-12 江西省水利科学院(江西省大坝安全管理中心、江西省水资源管理中心) Lake steady state discrimination method based on similarity measurement
CN117390466B (en) * 2023-12-13 2024-02-06 江西省水利科学院(江西省大坝安全管理中心、江西省水资源管理中心) Lake steady state discrimination method based on similarity measurement

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