CN115409318B - Natural-based water purification scheme optimization method integrating fuzzy AHP and MDS - Google Patents
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Abstract
The invention discloses a natural water purification scheme optimization method based on fuzzy AHP and MDS, which relates to the technical field of water, wastewater and sewage treatment and comprises the following steps: constructing a criterion layer comprising environment, economy, ecology and management and technology and determining a plurality of evaluation indexes of an index layer according to the characteristics of a water purification scheme based on nature, and acquiring actual data of the evaluation indexes; constructing a hierarchical framework comprising a target, the criterion layer, the index layer and a water purification scheme according to a hierarchical analysis method, and normalizing qualitative and quantitative indexes in the criterion layer by adopting a fuzzy matter element theory; constructing a judgment matrix according to a analytic hierarchy process, carrying out hierarchical sequencing on the criterion layer and the index layer by utilizing the judgment matrix, and then carrying out consistency test so as to output the synthetic weight of each index; the water purification schemes based on nature are ordered by multidimensional scaling and the optimal scheme is selected.
Description
Technical Field
The invention relates to the technical field of water, wastewater and sewage treatment, in particular to a natural water purification scheme optimization method based on a fuzzy AHP (analytic hierarchy process) and MDS (multidimensional scaling process) integrated method.
Background
The presently preferred methods for water purification schemes are mainly the following: linear programming, dynamic programming, nonlinear programming, gray correlation analysis and analytic hierarchy process. However, these methods have disadvantages when the scheme is preferred.
Problems with the prior preferred method: the linear programming method, the dynamic programming method and the nonlinear programming method only consider the cost minimization and neglect other aspects, but the scheme with the minimum cost is not necessarily the optimal water purification scheme, because the factors of environment and ecology are important, the optimal water purification scheme is a scheme with the comprehensive optimal factors of cost, pollutant emission, ecological environment and the like; the gray correlation analysis ignores the weights of the judgment criteria and the indexes, and the two factors are important bases of scheme preference; the conventional analytic hierarchy process cannot fuse qualitative indexes when the schemes are preferred, cannot classify the schemes with similar advantages and disadvantages, and has insufficient flexibility.
The evaluation index of the existing water purification scheme is used for the problems existing when the water purification scheme is based on nature: the evaluation index of the existing water purification scheme cannot be used for a natural-based water purification scheme, which is one of the natural-based solutions proposed by the international union of natural protection (International Union of Conservation Nature), with the objective of coping with global water pollution challenges by utilizing the water purification function of some natural ecosystems. The evaluation indexes of the conventional water purification schemes (such as an activated sludge process and an A2/O process) generally only comprise cost (such as investment and operation cost) and pollutant purification efficiency, and the natural-based water purification scheme needs to consider various aspects such as hydrogeology, occupied area, space utilization and the like besides the evaluation indexes of the conventional water purification schemes.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a natural water purification scheme optimization method based on the integration of fuzzy AHP and MDS, which constructs a judgment matrix by combining FME on the basis of AHP through constructing a hierarchical framework based on the natural water purification scheme, sorts the schemes by MDS, selects the optimal natural water purification scheme, and further optimizes the schemes by combining correlation.
In order to achieve the above purpose, the present invention may be performed by the following technical scheme:
a natural-based water purification scheme optimization method integrating fuzzy AHP with MDS, comprising:
according to the characteristics of a water purification scheme based on nature, constructing a criterion layer comprising environment, economy, ecology and management and technology, and collecting real evaluation index data of the water purification scheme based on nature;
constructing a hierarchical framework comprising a target, a criterion layer, an index layer and a water purification scheme according to an AHP hierarchical analysis method, and normalizing qualitative and quantitative indexes in the criterion layer by adopting an FME fuzzy matter element theory;
constructing a judgment matrix, carrying out consistency test through the hierarchical ordering and the hierarchical total ordering of the index layers, and outputting the synthetic weight of each index;
and sequencing the natural water purification schemes by adopting relevance through an MDS multidimensional scale, identifying similar schemes in the quality evaluation, and selecting an optimal scheme.
As a further technical scheme of the invention, the construction of a hierarchical framework comprising a target, a criterion layer, an index layer and a water purification scheme according to an AHP hierarchical analysis method comprises the following specific steps of normalizing qualitative and quantitative indexes in the criterion layer by adopting an FME fuzzy matter element theory:
firstly, under the environmental, economic, ecological and management and technical criterion layers, selecting characteristic indexes of each criterion, and constructing a hierarchical framework comprising a target, a criterion layer, an index layer and a water purifying scheme; meanwhile, the fuzzy matter element is constructed by adopting FME as follows:
R＝(N,C,V)；
wherein R is a fuzzy primitive, N is an object name, C is a characteristic of the object, V is a characteristic value of the object, and V comprises a fuzzy and qualitative description.
For n-dimensional m fuzzy primitives, a composite fuzzy primitive is constructed as follows:
wherein R is mn Is a complex fuzzy element, N i Represents the ith item (i=1, 2,., m), C k Represents the characteristic of the kth (k=1, 2, n.), V ik The kth eigenvalue of the ith object is represented.
And then normalizing the index, and normalizing the cost index according to the following formula:
for the environmental index, the normalization formula is:
in U ik Is normalized index value V ik Is the actual value of the index, minV ik Is the minimum value of the index, maxV ik Is the maximum value of the index.
And (3) assigning a qualitative index to the index in the range of [0,1] according to the qualitative description.
The normalized complex ambiguity bin is:
as a further technical scheme of the invention, the specific steps of constructing a judgment matrix according to the AHP analytic hierarchy process, carrying out consistency test through the hierarchical ordering of index layers and the hierarchical total ordering, and outputting the synthetic weight of each index comprise the following steps:
firstly, constructing a judgment matrix according to an AHP analytic hierarchy process, and comparing any index with other indexes under the same criterion (a) ij ) In terms of equivalent importance, less importance, moderately important, moderately important+, highly important, highly important+, very important, very important+, extremely important, in [1,9 ]]Importance value is given in natural number range, compared index is made, assignment a is carried out in reverse comparison ji ＝1/a ij The n×n-dimensional matrix is constructed as:
multiplying matrix a by the weight of the vector w= (W1, W2, wn) yields aw=nw, i.e.:
calculating the maximum eigenvalue lambda according to the judgment matrix max And calculating the consistency index CI and the average random consistency index RI. The consistency index calculation formula is as follows:
the one-time ratio CR calculation formula of the hierarchical total sequence is as follows:
when CR is less than or equal to 0.1, the judgment matrix is acceptable, and when CR exceeds the limit value, the judgment matrix is corrected.
After the consistency test is completed, the weight vector of each criterion relative to the target is obtained as follows:
in the method, in the process of the invention,is the weight of the kth criterion Ck relative to the target.
Also, the weight vector for each index relative to the criteria is:
wherein, I s ，l s+1 ，...，l t (s.ltoreq.t.ltoreq.n) represents the kth criterion C k The following index, s and t are the kth criterion C k The sequence numbers of the first and last indexes are next.
Then, the synthetic weight W of each index with respect to the target is obtained as:
as a further technical scheme of the invention, the steps of sorting the natural water purification scheme based on the relevance degree through the MDS multidimensional scale, identifying similar schemes in the quality evaluation and selecting the optimal scheme comprise the following specific steps:
first, calculate the correlation K of the index in each scheme by the combination weight and normalized index value of each index j The calculation formula is as follows:
K j ＝W i ×U ji ；
in which W is i Representing the composite weight of the ith index.
The Euclidean distance is then calculated with correlation as:
constructing a matrix by using Euclidean distance values, performing MDS analysis, and taking the first two principal components as feature vectors:
x(1)＝(E 11 ,，E 12 ，...，E 1k ，...，E 1N )′；
x(2)＝(E 21 ,，E 22 ，...，E 2N ，...，E 2N )′；
wherein x (1) and x (2) represent two eigenvectors, E, of a Euclidean distance value matrix 1k The 1 st eigenvector value representing the kth scheme in the Euclidean distance value matrix, E 2k And the 2 nd characteristic vector value of the kth scheme in the Euclidean distance value matrix.
The dissimilarity between correlations i and j is represented by delta ij The incremental ordering is represented as follows:
delta ij Is the independent variable and d ij As a dependent variable, the matching degree of MDS is checked by using a shepherd chart, if the chart showsThe distribution of points on the 1:1 line or close to the MDS indicates that the degree of matching of the MDS is good, otherwise, the degree of matching of the MDS is poor, and the correlation is required to be checked. Based on d ij And delta ij Relation of d ij Fitting values of (a)Binding d ij And->Calculating the pressure value +.>The formula is as follows:
in the method, in the process of the invention,representing the minimum value of the pressure value, +.>Indicating that the principal component of MDS is optimal.
Computing square root E for eigenvector values for each scheme k ：
Pair E k Sorting from big to small, namely, the water purifying scheme based on nature is good and bad order, E k The scheme with the highest value is the optimal scheme, and MDS analysis can identify which schemes are similar in the quality evaluation.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the invention, the hierarchical framework based on the natural water purification scheme is constructed by collecting the real evaluation index data based on the natural water purification scheme, the judgment matrix is constructed by combining with FME on the basis of AHP, the judgment matrix is corrected by means of hierarchical sequencing of index layers and hierarchical total sequencing, and consistency check is carried out, the judgment matrix is corrected by means of MDS, the similar scheme in the good and bad evaluation is identified, the optimal natural water purification scheme is selected, and convenience is provided for a decision maker to flexibly select a final scheme when the similar optimal scheme exists.
2. In the method, weak links of different schemes can be identified through correlation comparison of indexes in different schemes, and suggestions are provided for optimizing different water purification schemes based on nature.
3. The invention mainly designs a complete water purifying scheme optimization method with wide applicability and objective and accurate evaluation result based on nature. The method can technically cover the evaluation of each judgment criterion and index of the natural water purification scheme, selects the optimal natural water purification scheme, identifies the schemes with similar advantages and disadvantages, and provides convenience for decision makers to flexibly select the final scheme. In addition, suggestions are provided for further optimization of different natural-based water purification schemes.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following description will briefly explain the drawings needed in the embodiments, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic illustration of the steps of a preferred method of a natural-based water purification scheme in accordance with an embodiment of the present invention;
FIG. 2 is a hierarchical framework diagram of a preferred method of water purification scheme based on nature in accordance with an embodiment of the present invention;
FIG. 3 is a block diagram of a method for integrating fuzzy AHP and MDS according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a decision matrix constructed based on an integrated fuzzy AHP and MDS method according to an embodiment of the present invention;
FIG. 5 is a flow chart of a consistency check in accordance with an embodiment of the present invention;
figure 6 is a shepherd diagram of validating MDS in accordance with an embodiment of the present invention;
fig. 7 is a graph of preferred results of an MDS method according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
Examples:
it should be noted that the terms "first," "second," and the like in the description and the claims of the present invention and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed or inherent to such process, method, article, or apparatus.
It is to be understood that the terms "center," "longitudinal," "transverse," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counter-clockwise," "axial," "radial," "circumferential," and the like are directional or positional relationships as indicated based on the drawings, merely to facilitate describing the invention and to simplify the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore should not be construed as limiting the invention.
In the description of the present invention, the meaning of "plurality" means at least two, for example, two, three, etc., unless specifically defined otherwise. Furthermore, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In the present invention, unless expressly stated or limited otherwise, a first feature "up" or "down" a second feature may be the first and second features in direct contact, or the first and second features in indirect contact via an intervening medium. Moreover, a first feature being "above," "over" and "on" a second feature may be a first feature being directly above or obliquely above the second feature, or simply indicating that the first feature is level higher than the second feature. The first feature being "under", "below" and "beneath" the second feature may be the first feature being directly under or obliquely below the second feature, or simply indicating that the first feature is less level than the second feature.
Referring to fig. 1 and 2, in an embodiment of the present invention, a preferred method of integrating fuzzy AHP with MDS based natural water purification scheme comprises:
s1: according to the characteristics of a water purification scheme based on nature, constructing a criterion layer comprising environment, economy, ecology and management and technology, and collecting real evaluation index data of the water purification scheme based on nature, wherein the specific steps comprise:
according to the characteristics of a water purification system based on nature, economy, environment, ecology and management are selected as criteria.
Economic guidelines for water purification schemes typically include investment, operating, and treatment costs. The natural-based water purification system can maintain the activities of microorganisms using soil or plants, remove pollutants in sewage, and has no treatment cost of chemical agents or culture activated sludge, etc., thus, the occupation cost is classified as another economic factor in addition to investment and operation.
Environmental guidelines consider the water quality index BOD of a typical water purification system 5 Besides the COD, suspended Substances (SS), total nitrogen, total phosphorus and fecal coliform, the hydrogeological factors such as the stability pond and the constructed wetland are required to be positioned outside the flood alluvial plain and at low gradient are considered, and all natural-based water purification systems need to consider the influence of flood and landslide.
Ecological and management guidelines consider maintenance and occupied space availability factors, and a natural water purification system can provide a green open space for local communities and provide habitats for wild animals in addition to purifying sewage, so that occupied space availability is an important ecological index.
Technical guidelines are used to evaluate the operation and additional requirements of a project, and the operation of some natural-based water purification systems is affected by seasonal factors, such as slow infiltration and surface flooding land treatment systems, and thus seasonal effects are used as a technical indicator.
In addition, there are additional requirements for different natural-based water purification schemes, stabilization ponds and constructed wetlands require that the site soil be impermeable or that penetration be minimized after site selection, surface flooding treatment systems rely on perennial herbs, and other natural-based water purification schemes may choose more plant species.
As shown in table 1, table 1 lists the indexes under each evaluation criterion.
Table 1 indexes under various evaluation criteria based on natural water purification scheme and functions thereof
In the embodiment, the index value of each adopted water purification scheme based on nature is real data, and the actual data of each scheme operation is obtained from the literature, so that the accuracy and the authenticity of the realization result can be ensured.
S2: according to AHP analytic hierarchy process, constructing a hierarchy frame comprising a target, a criterion layer, an index layer and a water purifying scheme, adopting FME fuzzy matter element theory to normalize qualitative and quantitative indexes in the criterion layer, specifically comprising the following steps:
a hierarchical framework is constructed that includes targets, criteria layers, index layers, and water purification schemes, with the goal of maximizing benefit. Not only is the best economic benefit achieved, but also the best trade-offs of cost, environmental acceptability, and ecology friendliness are achieved, the criterion layer and the target layer have been detailed in S1, and the water purification scheme includes a rapid filtration treatment system, a slow filtration land treatment system, a surface flooding land treatment system, an artificial wetland and a stabilization pond treatment system. Because the indexes constructed in the embodiment have qualitative and quantitative indexes, wherein the quantitative indexes comprise percentage indexes and synthetic indexes, different types of indexes have larger influence on the weight of the construction analytic hierarchy process, and the indexes are normalized to avoid adverse influence.
For the cost index, the normalization formula is:
for the environmental index, the normalization formula is:
in U ik Is normalized index value V ik Is the actual value of the index, minV ik Is the minimum value of the index, maxV ik Is the maximum value of the index.
And (3) assigning a qualitative index to the index in the range of [0,1] according to the qualitative description.
As shown in fig. 3, a method framework diagram for integrating fuzzy AHP and MDS is shown, which is described in detail in the following steps: establishing an analytic hierarchy process framework, comparing indexes in pairs, weighting the guidelines and the indexes, checking consistency, calculating correlation degree, calculating a Euclidean distance matrix, establishing a relationship between Euclidean distance and non-similarity, calculating a pressure value, analyzing MDS and selecting an optimal natural-based water purifying scheme.
S3: constructing a judgment matrix according to an AHP analytic hierarchy process, carrying out consistency test through hierarchical sequencing and hierarchical total sequencing of index layers, and outputting the synthetic weight of each index;
as shown in FIG. 4, which is a schematic diagram of the steps of constructing a judgment matrix, the steps include comparing any index with other indexes under the same criteria, and determining the importance of the judgment matrix according to the same importance, less importance, moderately importance+, height importance, height importance+, very importance, very importance+, and paramount importance, in [1,9]To assign importance value a within natural number range of (2) ij Comparing indexes, and assigning value a in reverse comparison ji ＝1/a ij And constructing a final judgment matrix after all the assignment.
In this embodiment, the environmental criteria are taken as an example, and BOD is contained in the criteria 5 Removal rate, COD removal rate, suspended matter removal rate, total nitrogen removal rate, total phosphorus removal rate, fecal coliform removal rate, and hydrogeological risk index. BOD handle 5 The removal rate is sequentially compared with the self and COD removal rate, suspended matter removal rate, total nitrogen removal rate, total phosphorus removal rate, fecal coliform removal rate and hydrogeological risk, and the obtained values are obtained:
wherein w is 1 、w 2 、w 3 、w 4 、w 5 And w 6 According to the importance of [1,9 ]]A natural number is given to the inside of the container,representing BOD 5 The importance of removal rate to itself and other indicators (i=1, 2..6). In contrast, any other index and BOD 5 The importance of the removal rate is +.>I.e. a i1 ＝1/a 1i . And then, finally, obtaining a matrix with the indexes being assigned as elements in a pairwise comparison manner under the environmental criteria, constructing a matrix with the indexes being assigned as elements in a pairwise comparison manner under other criteria, and combining the matrixes constructed by the criteria to form a matrix A, wherein the matrix A is:
in this embodiment, the index layers are hierarchically ordered according to a criterion, and the importance of each index under the criterion is weightedThe characteristic vector is represented by the index pairwise comparison matrix under the criterion. Importance of the same criteria is weighted by W C The representation is the eigenvectors of the matrix for each criterion pair comparison. The composite weight of each index relative to the target is:
wherein, I s ，l s+1 ，...，l t (s.ltoreq.t.ltoreq.n) represents the kth criterion C k The following index, s and t are the kth criterion C k The sequence numbers of the first and last indexes are next.
A multiplied by the weight w= (W) of each criterion 1 、W 2 ，...，W N ) ' obtainingThe judgment matrix AW is:
the specific steps for performing the consistency check in this embodiment are shown in fig. 5, and include: calculating the maximum eigenvalue lambda of the judgment matrix max Calculating a consistency index CI, and calculating an average disposable ratio CR by combining the CI and the selected average random consistency index RI.
If CR is less than or equal to 0.1, the consistency check is passed, and if CR is more than 0.1, the consistency check is not passed, and the criterion and the index are re-weighted.
The consistency index calculation formula is as follows:
according to the size of the dimension c of the matrix, the average random uniformity index RI is found according to table 2.
TABLE 2 average random uniformity index RI
The one-time ratio CR calculation formula of the hierarchical total sequence is as follows:
s4: and sequencing the natural water purification schemes by adopting relevance through an MDS multidimensional scale, identifying similar schemes in the quality evaluation, and selecting an optimal scheme.
Calculating the correlation degree K of each index according to the combination weight of each index relative to the target and the normalized index value j ：
K j ＝W i ×U ji ；
In the middle of，W i The composite weight representing the ith index, U ji Is the normalized index value.
Calculation of Euclidean distance d with correlation ij The method comprises the following steps:
constructing a matrix by using Euclidean distance values, performing MDS analysis, and taking the first two principal components as feature vectors:
x(1)＝(E 11 ,，E 12 ，...，E 1k ，...，E 1N )′；
x(2)＝(E 21 ,，E 22 ，...，E 2N ，...，E 2N )′；
wherein x (1) and x (2) represent two eigenvectors, E, of a Euclidean distance value matrix 1k The 1 st eigenvector value representing the kth scheme in the Euclidean distance value matrix, E 2k And the 2 nd characteristic vector value of the kth scheme in the Euclidean distance value matrix.
The dissimilarity between correlations i and j is represented by delta ij The incremental ordering is represented as follows:
delta ij Is the independent variable and d ij As a dependent variable, the matching degree of MDS is checked by using a sheplate graph (as shown in FIG. 6), if the points in the graph are distributed on a 1:1 line or are close to the point that the matching degree of MDS is good, otherwise, the matching degree of MDS is bad, and the correlation is checked. Based on d ij And delta ij Relation of d ij Fitting values of (a)Binding d ij And->Calculating the pressure value +.>The formula is as follows:
in the method, in the process of the invention,representing the minimum value of the pressure value, +.>Indicating that the principal component of MDS is optimal.
Computing square root E for eigenvector values for each scheme k ：
Pair E k Sorting from big to small, namely, the water purifying scheme based on nature is good and bad order, E k The highest-valued scheme is the optimal scheme, while the MDS analysis can identify which schemes are similar in the merit evaluation (fig. 7).
The MDS method preferred results show that P4 and P5 are similar, P1, P2 and P3 are similar, and P4 and P5 are superior to P1, P2 and P3.
For investment, running cost, occupied area cost and BOD 5 The removal rate, COD removal rate, suspended matter removal rate, total nitrogen removal rate, total phosphorus removal rate, fecal coliform removal rate, hydrogeological risk maintenance, occupied space availability, seasonal influence and additional requirements, and the index correlation degree of each scheme is respectively as follows: p1-fast filtration treatment system (0.3,0.9,0.81,0.96,1.00,1.00,1.00,0.38,0.33,0.3,0.9,0.5,0.9,0.9), P2-slow filtration land treatment system (0.26,0.7,0.13,1.00,0.99,0.72,0.78,1.00,0.93,0.5,0.7,0.9,0.5,0.7), a P3-surface flood land treatment system (0.16,0.7,0.19,0.96,0.89,0.89,0.96,0.73,1.00,0.5,0.9,0.7,0.5,0.5), a P4-constructed wetland (0.88,0.9,0.88,0.81,0.9,0.84,1.00,0.53,0.72,0.9,0.7,0.5,0.9,0.5), and a P5-stabilization pond treatment system (1.00,0.9,1.00,0.94,0.85,0.74,0.99,0.65,0.52,0.7,0.9,0.5,0.7,0.7). Through index correlation comparison of the schemes, the correlation of P1 is lower in investment, total phosphorus removal rate, fecal coliform removal rate and hydrogeological risk maintenance, and optimization is needed; the correlation degree of P2 is low in investment and occupied cost, and optimization is needed; p3 has lower correlation degree in investment and occupied cost and needs to be optimized.
It should be noted that, the present invention focuses on acquiring data, and focuses on calculating correlation based on the index synthesis weight and the normalized index value calculated by AHP and MDS method, and then sorting the pattern by MDS based on the correlation.
For the present invention, the key is not a series of processing of the data, but the method of the present invention enables the original data to be used for the preference of the scheme.
The beneficial effects of the invention include:
1. when preferred for natural-based water purification schemes, the method takes into account not only costs, but also environmental and ecological factors.
2. The method can not only optimize the scheme, but also identify the scheme with similar advantages and disadvantages, and provides convenience for a decision maker to flexibly select the optimal scheme when a plurality of winning schemes appear.
3. Through the correlation comparison of indexes in the schemes, weak links of different schemes can be identified, and suggestions are provided for optimizing different natural-based water purification schemes.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, and are not intended to limit the scope of the present invention. All equivalent changes or modifications made in accordance with the essence of the present invention are intended to be included within the scope of the present invention.
Claims (3)
1. A natural-based water purification scheme optimization method integrating a fuzzy analytic hierarchy process with a multidimensional scaling process, comprising the steps of:
constructing a criterion layer comprising environment, economy, ecology and management and technology and determining a plurality of evaluation indexes of an index layer according to the characteristics of a water purification scheme based on nature, and acquiring actual data of the evaluation indexes;
constructing a hierarchical framework comprising a target, the criterion layer, the index layer and a water purification scheme according to a hierarchical analysis method, and normalizing qualitative and quantitative indexes in the criterion layer by adopting a fuzzy matter element theory;
normalizing the index, and normalizing the cost index according to the following formula:
for the environmental index, the normalization formula is:
in U ik Is normalized index value V ik Is the actual value of the index, minV ik Is the minimum value of the index, maxV ik Is the maximum value of the index;
assigning a value to the qualitative index within the range of [0,1] according to the qualitative description;
the normalized complex ambiguity bin is:
C 1 … C n
constructing a judgment matrix according to a analytic hierarchy process, carrying out hierarchical sequencing on the criterion layer and the index layer by utilizing the judgment matrix, and then carrying out consistency test so as to output the synthetic weight of each index;
the specific steps of weighting the criterion layer and the index layer are as follows:
constructing a judgment matrix according to an analytic hierarchy process, comparing any index under the same criterion with other indexes, and determining the judgment matrix according to the equal importance, the less importance, the moderate importance+, the high importance, the high importance+, the very importance, the very importance+, the very importance and the very importance in [1,9 ]]To assign importance value a within natural number range of (2) ij Comparing indexes, and assigning value a in reverse comparison ji ＝1/a ij The n×n-dimensional matrix is constructed as:
matrix a multiplied by the weight of the vector w= (W 1 ，W 2 ，...，W n ) Aw=nw is obtained, i.e.:
calculating the maximum eigenvalue lambda according to the judgment matrix max Then, calculating a consistency index CI and an average random consistency index RI;
the consistency index calculation formula is as follows:
the one-time ratio CR calculation formula of the hierarchical total sequence is as follows:
when CR is less than or equal to 0.1, the judgment matrix is acceptable, and when CR exceeds the limit value, the judgment matrix is corrected;
after the consistency test is completed, the weight vector of each criterion relative to the target is obtained as follows:
in the method, in the process of the invention,is the kth criterion C k Weights relative to the target;
also, the weight vector for each index relative to the criteria is:
wherein, I s ，l s+1 ，...，l t (s.ltoreq.t.ltoreq.n) represents the kth criterion C k The following index, s and t are the kth criterion C k Sequence numbers of the first and last indexes;
then, the synthetic weight W of each index with respect to the target is obtained as:
sequencing water purification schemes based on nature through a multidimensional scaling method, and selecting an optimal scheme;
first, calculate the correlation K of the index in each scheme by the combination weight and normalized index value of each index j The calculation formula is as follows:
K j ＝W i ×U ji ；
in which W is i A composite weight representing the i-th index;
the Euclidean distance is then calculated with correlation as:
constructing a matrix by using Euclidean distance values, performing MDS analysis, and taking the first two principal components as feature vectors:
x(1)＝(E 11 ,，E 12 ，...，E 1k ，...，E 1N )′；
x(2)＝(E 21 ,，E 22 ，...，E 2N ，...，E 2N )′；
wherein x (1) and x (2) represent two eigenvectors, E, of a Euclidean distance value matrix 1k The 1 st eigenvector value representing the kth scheme in the Euclidean distance value matrix, E 2k A2 nd feature vector value representing a kth scheme in the Euclidean distance value matrix;
the dissimilarity between correlations i and j is represented by delta ij The incremental ordering is represented as follows:
delta ij Is an independent variableAnd d ij As a dependent variable, checking the coordination degree of MDS by using a sheplate graph, if points in the graph are distributed on or close to a 1:1 line, indicating that the coordination degree of MDS is better, otherwise, the coordination degree of MDS is not good, and checking the correlation degree; based on d ij And delta ij Relation of d ij Fitting values of (a)Binding d ij And->Calculating the pressure value +.>The formula is as follows:
in the method, in the process of the invention,representing the minimum value of the pressure value, +.>When it is indicated that the principal component of MDS is optimal;
computing square root E for eigenvector values for each scheme k ：
Pair E k Sorting from big to small, namely, the water purifying scheme based on nature is good and bad order, E k Scheme with maximum valueFor optimal solutions, MDS analysis can identify which solutions are similar in quality assessment.
2. The method of claim 1, wherein the natural-based water purification scheme is: a water purification regimen utilizing soil or plants to maintain the activity of microorganisms and which are sufficient to remove contaminants from sewage.
3. The method according to claim 1, wherein the specific steps of constructing a hierarchical framework according to a hierarchical analysis method and normalizing qualitative and quantitative indicators in the criterion layer by fuzzy primitive theory are as follows:
under the environmental, economic, ecological and management and technical criterion layers, selecting characteristic indexes of each criterion, and constructing a hierarchical framework comprising a target, a criterion layer, an index layer and a water purifying scheme;
meanwhile, the fuzzy matter element is constructed by adopting FME as follows:
R＝(N,C,V)；
wherein R is a fuzzy matter element, N is a matter name, C is a characteristic of the matter, V is a characteristic value of the matter, and V comprises a fuzzy and qualitative description;
for n-dimensional m fuzzy primitives, a composite fuzzy primitive is constructed as follows:
C 1 … C n
wherein R is mn Is a complex fuzzy element, N i Represents the ith item (i=1, 2,., m), C k The characteristics of the kth object (k=1, 2, n.), V ik The kth eigenvalue of the ith object is represented.
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