CN103440525A - Urban lake and reservoir water bloom emergency treatment multiple-target multiple-layer decision-making method based on Vague value similarity measurement improved algorithm - Google Patents

Abstract

The invention discloses an urban lake and reservoir water bloom emergency treatment multiple-target multiple-layer decision-making method based on a Vague value similarity measurement improved algorithm and belongs to the technical field of environment engineering. The urban lake and reservoir water bloom emergency treatment multiple-target multiple-layer decision-making method includes the following steps that a decision-making hierarchical model is constructed, a decision-making matrix is obtained, a reference attribute-target Vague collective matrix is determined, a reference attribute weighted average Vague value is calculated and decision-making ordering is carried out on alternative schemes. After ordering is finished, the larger the relative close degree is, the more ideal the alternative schemes are. According to the urban lake and reservoir water bloom emergency treatment multiple-target multiple-layer decision-making method based on the Vague value similarity measurement improved algorithm, multiple-target multiple-level emergency treatment decision-making on lake and reservoir water bloom is achieved and the effect of treating the water bloom with high efficiency is finally achieved. The urban lake and reservoir water bloom emergency treatment multiple-target multiple-layer decision-making method has great significance in improvement of pertinency, scientificity and high-efficiency performance in treating the water bloom and plays an important role in protecting and improving the water environment of the urban lake and reservoir.

Description

Improve the multi-level decision-making technique of urban lake storehouse wawter bloom Emergency management multiple goal of algorithm based on Vague value similarity measure

Technical field

The present invention relates to a kind of wawter bloom Emergency management decision-making technique, belong to field of environment engineering technology, specifically, refer to a kind of multi-level decision-making technique of urban lake storehouse wawter bloom Emergency management multiple goal of improving algorithm based on Vague value similarity measure.

Background technology

Urban lake storehouse wawter bloom is a kind of typical case performance of body eutrophication, and its harmfulness not only is the freshwater resources that severe contamination is rare, even havoc ecologic environment and can directly threaten by food chain the mankind's health by the algae toxin of its generation.According to incompletely statistics, there is more serious Eutrophication Status in the urban lake storehouse of China more than sixty percent, the Water quality degradation.Repeatedly wawter bloom has been broken out in the storehouse, freshwater lake in a plurality of cities of China in the last few years, reservoir water source as potable water suffers severe contamination, daily life has been caused to very large social influence, therefore, strengthen urban lake storehouse wawter bloom and administer the vital task that has become China's guarantee economic development and social base construction.

Breaking out of wawter bloom is the coefficient results of many factors such as physics, chemistry and bioprocess by water body, but concern complexity between each key element, because it exists randomness, uncertainty and the feature such as non-linear, although have at present the multiple resolution for wawter bloom, to the selection shortage theoretical property guidance of resolution.The critical factor and the mechanism that due to wawter bloom, occur it be unclear that, and fail so far to draw the most effective wawter bloom Emergency management method.

Emergent decision-making is studied and is utilized at numerous areas, but the research aspect wawter bloom Emergency management decision-making research is few, and conventional emergent decision-making faces the problems such as data message scarcity, expert opinion subjectivity are strong, therefore, need to provide corresponding Emergency management decision-making technique for the multi-level characteristics of multiple goal of these conventional emergent existing problems of decision-making and urban lake storehouse wawter bloom treatment decision-making.

Multiobjectives decision (multi-objective decision making, MODM) refers to the decision-making of carrying out under mutual conflict, incommensurable a plurality of target conditions having.The sort method (technique for order preference by similarity to ideal solution, TOPSIS) that Hwang and Yoon proposition approach ideal solution solves decision-making problem of multi-objective.Due in the wawter bloom treatment decision-making of urban lake storehouse, there is resolution to the influence degree of environment and the multiple goal of financial cost, can adopt Multiobjective Decision Making Method to carry out decision-making to the resolution of urban lake storehouse wawter bloom.

The Vague collection is the expansion to fuzzy set, fuzzy set has expanded [0 to being subordinate to concept, 1] interval, the thought of Vague collection is considered to be subordinate to and the non-evidence that is subordinate to two aspects simultaneously, the boundary of its degree of membership is described by a tlv triple, this tlv triple has meaned the information of decision maker to a certain things support, opposition and abstention three aspects: simultaneously, makes it when processing uncertain information, than traditional fuzzy set, stronger expression ability be arranged.Therefore, for the treatment decision-making of urban lake storehouse wawter bloom, parameter, concept and event etc. that all decision maker can not explication, all can be processed into the Vague collection.

The father Cloud of information theory. the Ai Er Wood. Shannon proposes the concept of " information entropy ", has illustrated the relation of probability and information redundance with mathematical linguistics.Therefore, in the wawter bloom treatment decision-making process of urban lake storehouse, the expression of expert opinion adopts the Vague collection, and the exploit information entropy method of obtaining of weight can farthest be avoided the defects such as the subjectivity that exists in conventional decision-making is strong.

Yet, Vague collection and information entropy method are applied to, in the multiobjectives decision of urban lake storehouse wawter bloom Emergency management, still have following problem:

1. existing multiobjectives decision is only carried out decision-making on decision objective and two levels of alternatives, yet in the Emergency management decision-making of urban lake storehouse wawter bloom, except thering are multiobject characteristics, in the wawter bloom generative process of urban lake storehouse, a plurality of ATTRIBUTE INDEX such as various water quality, environment and social factor also be can not ignore the impact of urban lake storehouse wawter bloom Emergency management program decisions, therefore need the Multiscale modelling problem of research urban lake storehouse wawter bloom treatment decision-making.

2. for different decision-making levels, need to provide rational form and describe the association between each level.

3. when the multi-level decision-making of multiple goal, for a plurality of targets, not only need to determine reference scheme corresponding to each target, and need to determine each target under reference scheme corresponding affect attribute.

4. how according to the significance level of each target under reference scheme, comprehensively provide all targets under reference scheme corresponding affect attribute, in order to calculate the distance of each alternatives and reference scheme, need to be studied comprehensive method.

5. existing Vague value Similarity Measures has only been considered interval two ends distance, the core distance of Vague value mostly, and do not consider unknown degree, therefore need comprehensive study to consider the Vague value Similarity Measures of interval two ends distance, core distance and the unknown degree of Vague value.

6. how according to the attribute that affects that affects attribute and reference scheme of alternatives, and the significance level that respectively affects attribute, the relative approach degree of each alternatives of COMPREHENSIVE CALCULATING and reference scheme, thus final alternatives decision-making sequence provided, need to specifically study.

Summary of the invention

The present invention is studied urban lake storehouse wawter bloom Emergency management decision-making technique, and purpose is for environmental administration provides effective decision references foundation, to determine selecting which kind of resolution in which kind of situation, finally reaches the effect of efficient improvement wawter bloom.The present invention has built the decision model multi-level based on multiple goal, usings decision objective as the selection foundation of alternatives, usings and affects the evaluation index of attribute as alternatives, utilizes Vague collection theory to obtain reference scheme.On to the improved basis of Vague value Similarity Measures, alternatives is estimated to sequence, and then carry out intelligent decision for urban lake storehouse wawter bloom Emergency management.Specific aim, science and high efficiency important in inhibiting that the present invention administers improving wawter bloom, to the protection of urban lake storehouse water environment with improve and can play an important role.

For ease of explanation, in the present invention, all unexplained alphabetical implications are explained by following hypothesis: suppose that a is the alternatives collection, a={a ₁, a ₂... a _u, c is object set, c={c ₁, c ₂... c _v, b affects property set, b={b ₁, b ₂... b _w, u wherein, v, w means respectively alternatives collection, object set and affects the element number of property set.

The urban lake storehouse multi-level decision-making technique of wawter bloom Emergency management multiple goal based on Vague value similarity measure improvement algorithm provided by the invention mainly comprises following five steps:

Step 1, structure decision-making hierarchical model;

The multiple goal of take is carried out the wawter bloom Emergency management decision-making of urban lake storehouse as criterion, and its core is the decision problem stratification, forms respectively destination layer, solution layer and attribute layer.In the wawter bloom Emergency management decision-making of urban lake storehouse, it is main that to take resolution be according to building the decision-making hierarchical model to decision objectives such as the influence degree of environment and financial cost, using decision objective as the selection foundation of alternatives, using and affect the evaluation index of attribute as alternatives.

Step 2, obtain decision matrix;

For solution layer and destination layer, by expert opinion, form each alternatives in solution layer to the scheme of each decision objective in destination layer-objective decision matrix.For solution layer and attribute layer, according to detecting with investigation result, can construct in the attribute layer and respectively affect attribute to the scheme of each alternatives in solution layer-attribute decision matrix.Degree of giving preferential treatment to the families of the armymen and martyrs between level (can be specially satisfaction and degree of impact etc.) can pass through linguistic variable (language collection) to be determined, according to studying a question, can select a suitable linguistic variable to mean decision maker's preference information.The present invention adopts Vague set representations scheme-objective decision matrix and scheme-attribute decision matrix, i.e. scheme-target Vague collection matrix and scheme-attribute Vague collection matrix.

Step 3, definite with reference to attribute-target Vague collection matrix;

Scheme-target Vague is integrated to matrix conversion as scheme-target Relative optimal subordinate degree matrix.In scheme-target Relative optimal subordinate degree matrix, target is divided into to benefit type and cost type two classes, the optimal case of definite each target and the poorest scheme are as the reference scheme respectively, and according to scheme-attribute Vague collection matrix, obtain optimum attributes Vague value and the poorest attribute Vague value of corresponding scheme, thereby acquisition optimum attributes-target Vague collection matrix and the poorest attribute-target Vague collection matrix are as reference attribute-target Vague collection matrix.

Step 4, the average Vague value of computing reference attribute weight;

Adopt the information entropy power computing method of Vague collection, for optimum attributes-target Vague collection matrix and the poorest attribute-target Vague collection matrix, calculate respectively the weight of each target under reference scheme.Again by the ideal solution of the multi-objective problem of TOPSIS method (positive-ideal solution, PIS) and negative ideal solution (negative-ideal solution, NIS) thought applies to reference in the obtaining of the average Vague value of attribute weight, mean PIS and the NIS based on the Vague collection with VPIS and VNIS, be optimum attributes weighted mean Vague value and the average Vague value of the poorest attribute weight, as the average Vague value of reference attribute weight.

Step 5, alternatives decision-making sequence;

The present invention is improved existing Vague value Similarity Measures, utilizes the Vague value Similarity Measures after improving, and calculates the distance of each alternatives to VPIS and VNIS.Calculate again the relative approach degree of each alternatives to the distance of VPIS and VNIS according to each alternatives.Relatively approach degree means that this scheme approaches ideal solution and, away from the degree of negative ideal solution, the quality according to relative approach degree size to alternatives is sorted, and the alternatives that approach degree is larger relatively is unreasonable to be thought.

The invention has the advantages that:

1. tri-layer (being destination layer, solution layer and the attribute layer) model of storehouse, the lake wawter bloom treatment decision-making that the present invention proposes, the multiple goal characteristics of storehouse, lake wawter bloom treatment decision-making have not only been considered, more considered the impact of a plurality of ATTRIBUTE INDEX such as various water quality, environment and social factor on the wawter bloom Emergency management program decisions of storehouse, lake, reacted all sidedly the relation between decision objective, scheme and attribute, the model of decision-making is more conformed to actual conditions.

2. the present invention is directed to different decision-making levels, employing scheme-target Vague collection matrix carrys out associated between description scheme layer and destination layer, and scheme-attribute Vague collection matrix carrys out the associated of description scheme layer and attribute interlayer, solved problem associated between each level of reasonable description.

3. the present invention integrates matrix conversion as scheme-target Relative optimal subordinate degree matrix by scheme-target Vague, obtain reference scheme corresponding to each target, again by scheme-attribute Vague collection matrix, obtain with reference to attribute-target Vague collection matrix, thereby solved the problem of determining the reference attribute Vague collection that each target is corresponding.

4. the present invention adopts the weight of the information entropy of Vague collection as each target under the reference scheme, utilize the TOPSIS method, obtain with reference to the average Vague value of attribute weight, thereby solved the significance level according to each target, comprehensively provide reference attribute Vague value problem corresponding to all targets, and farthest avoid the defects such as the subjectivity that exists in conventional decision-making is strong.

5. the present invention passes through in existing Vague value similarity measure formula, the description of increase to the unknown degree of Vague value, and according to similarity measure definition criterion, the Vague value Similarity Measures of interval two ends distance, core distance and the unknown degree of the improved Vague of considering value has been proposed, Vague value similarity measure after making to improve is described more comprehensive, has improved the accuracy of measurement.

The present invention according to each alternatives affect attribute with reference to the average Vague value of attribute weight similarity, and adopt the information entropy of Vague collection to affect the weight of attribute as each, obtain distance and the relative approach degree of each alternatives and reference scheme weighted mean Vague value, thereby carry out alternatives decision-making sequence, realize the multi-level Emergency management decision-making of multiple goal of storehouse, lake wawter bloom, finally reached the effect of efficient improvement wawter bloom.

The accompanying drawing explanation

Fig. 1 the present invention is based on the process flow diagram that Vague value similarity measure improves the multi-level decision-making technique of storehouse, lake wawter bloom Emergency management multiple goal of algorithm;

Fig. 2 is the decision-making hierarchical model in embodiment 1;

Fig. 3 is the relative approach degree of each alternatives of the employing decision-making technique of the present invention in embodiment 1;

Fig. 4 is the relative approach degree of each alternatives of the existing decision-making technique of employing in embodiment 1.

Embodiment

Below in conjunction with drawings and Examples 1, the present invention is described in further detail.

The invention provides a kind of multi-level decision-making technique of storehouse, lake wawter bloom Emergency management multiple goal of improving algorithm based on Vague value similarity measure, flow process as shown in Figure 1, concrete steps are as follows:

Step 1, structure decision-making hierarchical model;

In the wawter bloom Emergency management decision-making of urban lake storehouse, mainly with resolution, influence degree and the financial cost of environment built to the decision-making hierarchical model.Administer situation for urban lake storehouse wawter bloom, choose such as a plurality of decision objectives such as " on the surrounding enviroment impacts " as destination layer; Choose such as a plurality of alternativess such as " lake endogenous nutritive salt biological prevention, microorganism algal control, diversion are washed away, artificial aeration " as solution layer; Choose such as a plurality of attributes that affect such as " total nitrogen, total phosphorus, pH values " as the attribute layer.For example, shown in Fig. 2.

Step 2, obtain decision matrix;

Degree of giving preferential treatment to the families of the armymen and martyrs between level (can be specially satisfaction and degree of impact etc.) and non-degree of giving preferential treatment to the families of the armymen and martyrs (can be specially not satisfaction and not degree of impact etc.) can pass through linguistic variable (language collection) to be determined, ten one-level language collection of the present invention's use Vague value representation are as shown in table 1.

Ten one-level linguistic variables of Vague value representation for table 1

Grade	Grade	Vague value span	Typical case Vague value	Representative value abstention situation
					Definitely good (AG)	absolutely good	[1,1]	[1,1]	0
Fine (VG)	very good	(0.9,1)	[0.9,0.95]	0.05
					Good (G)	good	(0.85,0.9]	[0.8,0.9]	0.1
Better (FG)	fairly good	(0.7,0.85]	[0.7,0.85]	0.15
					In good (MG)	medium good	(0.6,0.8]	[0.6,0.8]	0.2
Medium (M)	medium	[0.5,0.5]	[0.5,0.5]	0
					Middle poor (MP)	medium poor	(0.45,0.6]	[0.4,0.6]	0.2
Poor (FP)	fairy poor	(0.3,0.45]	[0.3,0.45]	0.15
					Poor (P)	poor	(0.15,0.3]	[0.2,0.3]	0.1
Very poor (VP)	very poor	(0,0.15]	[0.1,0.15]	0.05
					Absolute difference (AP)	absolutely poor	[0,0]	[0,0]	0

Scheme-target Vague collection matrix means with A, and according to the transformation rule of linguistic variable and Vague value, the Vague value representation of alternatives under decision objective is as follows:

$A_{u\×v}=[t_{\mathrm{ij}}^A,1-f_{\mathrm{ij}}^A],i=\mathrm{1,2},\·\·\·u;j=\mathrm{1,2},\·\·\·v.$

Wherein

mean alternatives a _ito decision objective c _jsatisfaction,

mean alternatives a _ito decision objective c _jnot satisfaction, and $0\≤t_{\mathrm{ij}}^A+f_{\mathrm{ij}}^A\≤1,$ For simplifying mark, can make $1-f_{\mathrm{ij}}^A=t_{\mathrm{ij}}^{A*}.$

In like manner, scheme-attribute Vague collection matrix means with B, affects the Vague value representation of attribute under alternatives as follows:

$B_{u\×w}=[t_{\mathrm{ij}}^B,1-f_{\mathrm{ij}}^B],i=\mathrm{1,2},\·\·\·u;j=\mathrm{1,2},\·\·\·w.$

Wherein mean to affect attribute b _jto alternatives a _idegree of impact,

mean to affect attribute b _jto alternatives a _inot degree of impact, and $0\≤t_{\mathrm{ij}}^B+f_{\mathrm{ij}}^B\≤1$ , will

be designated as .

Step 3, definite with reference to attribute-target Vague collection matrix;

Scheme-target Vague is integrated to matrix conversion as scheme-target Relative optimal subordinate degree matrix.Conversion method is as follows:

If x _ijexpression is the relatively optimal degree degree of i row element to the j column element in the decision matrix of Vague set representations, and its computing formula is

$x_{\mathrm{ij}}=t_{\mathrm{ij}}-f_{\mathrm{ij}}=t_{\mathrm{ij}}+t_{\mathrm{ij}}^{*}-1---\left(1\right)$

T wherein _ijmean the degree of giving preferential treatment to the families of the armymen and martyrs of i row element to the j column element, f _ijmean the non-degree of giving preferential treatment to the families of the armymen and martyrs of i row element to the j column element,

.Draw thus the decision matrix shown by the relatively optimal degree kilsyth basalt

[x _ij] _m×n,1≤i≤m,1≤j≤n

Wherein, m, n means respectively line number and the columns of decision matrix.The decision matrix that the relatively optimal degree kilsyth basalt shows combines support information and the opposition information in the Vague value.

Adopt above-mentioned conversion method, the relatively optimal degree degree of i row element to the j column element in numerical procedure-target Vague collection matrix A , obtain scheme-target Relative optimal subordinate degree matrix .

In scheme-target Relative optimal subordinate degree matrix, establish

as target c _jduring for the benefit type,

corresponding alternatives a _ifor optimal case, its corresponding attribute Vague value is target c _junder optimum attributes Vague value,

corresponding alternatives a _ifor the poorest scheme, its corresponding attribute Vague value is target c _junder the poorest attribute Vague value; In like manner, as target c _jduring for the cost type,

corresponding alternatives a _ifor optimal case, its corresponding attribute Vague value is target c _junder optimum attributes Vague value,

corresponding alternatives a _ifor the poorest scheme, its corresponding attribute Vague value is target c _junder the poorest attribute Vague value.If target c _junder n is arranged or

when identical, by n

or

degree of giving preferential treatment to the families of the armymen and martyrs in the attribute Vague value of a corresponding n alternatives and non-degree of giving preferential treatment to the families of the armymen and martyrs are averaged rear as target c _junder optimum or the poorest attribute Vague value.

So far, obtained optimum attributes-target Vague collection matrix

$C_{v\×w}^{*}=[t_{\mathrm{ij}}^{C*},1-f_{\mathrm{ij}}^{C*}],i=\mathrm{1,2},\·\·\·v;j=\mathrm{1,2},\·\·\·w.$

The poorest attribute-target Vague collection matrix

$C_{v\×w}^{-}=[t_{\mathrm{ij}}^{C-},1-f_{\mathrm{ij}}^{C-}],i=\mathrm{1,2},\·\·\·v;j=\mathrm{1,2},\·\·\·w.$

Wherein,

, mean respectively target c _ithe degree of giving preferential treatment to the families of the armymen and martyrs of lower optimum attributes Vague value and non-degree of giving preferential treatment to the families of the armymen and martyrs,

,

mean respectively target c _iunder degree of giving preferential treatment to the families of the armymen and martyrs and the non-degree of giving preferential treatment to the families of the armymen and martyrs of the poorest attribute Vague value.

Step 4, definite with reference to the average Vague value of attribute weight;

At first adopt the conversion method in step 3 that optimum attributes-target Vague collection matrix and the poorest attribute-target Vague are integrated to matrix conversion as optimum attributes-target Relative optimal subordinate degree matrix and the poorest attribute-target Relative optimal subordinate degree matrix, then to these two matrixes, adopt information entropy power computing method to draw the weight of each target under optimal case and the poorest scheme respectively.

The information entropy power computing method of the Vague collection that the present invention adopts is as follows:

If x _ijexpression is the relatively optimal degree degree of i row element to the j column element in the decision matrix of Vague set representations, and the decision matrix that Relative optimal subordinate degree matrix means is

[x _ij] _m×n,1≤i≤m,1≤j≤n

Wherein, m, n means respectively line number and the columns of decision matrix.

For the dimension of unified each element, need make normalized to decision-making entry of a matrix element.The evaluation X of i row element to the j column element _ijbe defined as:

$X_{\mathrm{ij}}=\frac{x_{\mathrm{ij}}}{{\mathrm{\Σ}}_{i=1}^m{x}_{\mathrm{ij}}}\∀i,j---\left(2\right)$

The entropy E of i row element to the j column element _jfor:

$\begin{array}{cc}{E}_j=-k\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{X}_{\mathrm{ij}}\ln X_{\mathrm{ij}}& \∀j---\left(3\right)\end{array}$

Wherein k is constant, k=1/lnm, and this has guaranteed 0≤E _j≤ 1.

Errored message degree d _jbe defined as:

d _j＝1-E _j. （4）

The definition weights omega _jvalue be

$\begin{array}{cc}{\mathrm{\ω}}_j=\frac{d_j}{{\mathrm{\Σ}}_{j=1}^n{d}_j}& \∀j---\left(5\right)\end{array}$

The ideal solution (PIS) of multi-objective problem in the TOPSIS method and negative ideal solution (NIS) are applied to reference in the obtaining of the average Vague value of attribute weight, mean PIS and the NIS based on the Vague collection with VPIS and VNIS, be optimum attributes weighted mean Vague value and the average Vague value of the poorest attribute weight, use with

, i=1,2 ..., v means respectively the information entropy power of each target under the information entropy power of each target under optimal case and the poorest scheme,

$\mathrm{VPIS}=\underset{i=1}{\overset{v}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{*}\·[t_{\mathrm{ij}}^{C*},1-f_{\mathrm{ij}}^{C*}],j=\mathrm{1,2},\·\·\·,w---\left(6\right)$

$\mathrm{VNIS}=\underset{i=1}{\overset{v}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{-}\·[t_{\mathrm{ij}}^{C-},1-f_{\mathrm{ij}}^{C-}],j=\mathrm{1,2},\·\·\·,w---\left(7\right)$

Step 5, alternatives decision-making sequence;

The present invention, according to the characteristics of Vague value Similarity Measures, considers interval two ends distance, core distance and the unknown degree of Vague value, has proposed a kind of Vague value similarity measure new method.

It is a domain that U is established in definition 1, and V is the upper all Vague set that collection forms of domain U, and A ∈ V, if B ∈ V. M (A, B) meets following criterion, claims M (A, B) for the similarity between Vague collection A, B.

（1）0≤M(A,B)≤1；

(2) if A=B, M (A, B)=1;

（3）M(A,B)＝M(B,A).

The similarity measure M (x, y) of definition 2Vague value x and y is:

$M(x,y)=1-\frac{|t_x-t_y-(f_x-f_y\left)\right|}{16}-\frac{|t_x-t_y+f_x-f_y|}{4}-\frac{2-t_x-t_y-f_x-f_y}{16}-\frac{|t_x-t_y|+|f_x-f_y|}{8}---\left(8\right)$

Wherein, t _x, f _x, t _y, f _ythe degree of giving preferential treatment to the families of the armymen and martyrs and the non-degree of giving preferential treatment to the families of the armymen and martyrs that mean respectively Vague value x and y.

Below the similarity measure of proof definition 2 meets the criterion 1～3 in definition 1.

For criterion 1, ∵ t _x, t _y, f _x, f _y∈ [0,1], ∴

$M(x,y)=1-\frac{|t_x-t_y-(f_x-f_y\left)\right|}{16}-\frac{|t_x-t_y+f_x-f_y|}{4}-\frac{2-t_x-t_y-f_x-f_y}{16}-\frac{|t_x-t_y|+|f_x-f_y|}{8}$

$\≤1-\frac{0}{16}-\frac{0}{4}-\frac{0}{16}-\frac{0}{8}\≤1.$

∵ again $|t_x-t_y-(f_x-f_y)|\≤2,|t_x-t_y+f_x-f_y|\≤\mathrm{2,2}-t_x-t_y-f_x-f_y\≤2,|t_x-t_y|+|f_x-f_y|\≤2,$

∴ $M(x,y)=1-\frac{|t_x-t_y-(f_x-f_y\left)\right|}{16}-\frac{|t_x-t_y+f_x-f_y|}{4}-\frac{2-t_x-t_y-f_x-f_y}{16}-\frac{|t_x-t_y|+|f_x-f_y|}{8}$

$\≥1-\frac{2}{16}-\frac{2}{4}-\frac{2}{16}-\frac{2}{8}\≥0.$

∴0≤M(x,y)≤1.

Vague value x and y have meaning of equal value, and therefore, criterion 2 and criterion 3 can be demonstrate,proved by the definition of M (x, y).Card is finished.

Define the Vague value Similarity Measures after the improvement of 2 propositions according to the present invention, calculate the Vague value similarity that affects attribute Vague value and VPIS and VNIS of each alternatives, thereby calculate the distance of each alternatives and VPIS and VNIS:

$d_i^{*}=\underset{j=1}{\overset{w}{\mathrm{\Σ}}}{\mathrm{\ω}}_{j}M\left(\right[t_{\mathrm{ij}}^B,t_{\mathrm{ij}}^{B*}],\mathrm{VPIS})---\left(9\right)$

$d_i^{-}=\underset{j=1}{\overset{w}{\mathrm{\Σ}}}{\mathrm{\ω}}_{j}M\left(\right[t_{\mathrm{ij}}^B,t_{\mathrm{ij}}^{B*}],\mathrm{VNIS})---\left(10\right)$

ω wherein _jadopt the information entropy power computing method of the Vague collection in step 4 to calculate and obtain scheme-attribute Vague collection matrix B, i=1,2 ..., u.

The relative approach degree of each alternatives:

${\mathrm{\σ}}_i=\frac{d_i^{-}}{d_i^{*}+d_i^{-}},i=\mathrm{1,2},\·\·\·,u---\left(11\right)$

σ _ilarger, mean that this alternatives more approaches ideal solution and more away from negative ideal solution, according to relative approach degree principle, can be according to σ _isize is sorted to the scheme quality, relatively approach degree σ _ilarger alternatives is unreasonable to be thought, otherwise alternatives is more undesirable.

Embodiment 1:

The present invention is directed to certain urban lake storehouse wawter bloom Emergency management decision problem, use the inventive method to carry out simulating, verifying, for the wawter bloom Emergency management decision-making of storehouse, lake provides the reference of science.

Step 1, structure decision-making hierarchical model;

According to this urban lake Al Kut point and research purpose, choose 12 kinds of wawter bloom resolutions such as " Inner nutrition salt methods " as alternatives, choose 4 of " on surrounding enviroment impacts ", " fund or labour drop into " etc. as decision objective, choose 14 kinds of attributes such as " blue alga biomass " as affecting attribute.As shown in Figure 2.

Step 2, obtain decision matrix;

By the mode of survey collect the expert to each alternatives the evaluation of estimate for decision objective, form the decision matrix (table 2, table 3) based on the language collection, in table, each monogram is expressed as grade, concrete implication is provided by first row in table 1.

Table 2 scheme-objective decision matrix

Table 3 scheme-attribute decision matrix

Carry out the conversion of language collection and Vague collection according to table 1, form corresponding Vague collection matrix (table 4, table 5).

Table 4 scheme-target Vague collection matrix

Table 5 scheme-attribute Vague collection matrix

Step 3, definite with reference to attribute-target Vague collection matrix;

According to formula (1), scheme-target Vague collection matrix is converted into to scheme-target Relative optimal subordinate degree matrix, as shown in table 6.

Table 6 scheme-target Relative optimal subordinate degree matrix

According to definite method of reference attribute-target Vague collection matrix, can draw optimum (poor) attribute-target Vague collection matrix (table 7, table 8).

Table 7 optimum attributes-target Vague collection matrix

The poorest attribute of table 8-target Vague collection matrix

Step 4, definite with reference to the average Vague value of attribute weight;

On the basis of reference attribute-target Vague collection matrix, can obtain the weight of target according to the computing method of Vague collection information entropy power, as shown in table 9.

Table 9 target information entropy weight

According to formula (6) and formula (7), can calculate VPIS and VNIS, as shown in table 10.

Table 10VPIS and VNIS

Step 5, alternatives decision-making sequence;

Calculate the similarity measure of each alternatives and VPIS and VNIS according to formula (8), calculate the distance of each alternatives to VPIS and VNIS according to formula (9) and formula (10), calculate the relative approach degree of each alternatives according to formula (11), in Table 11.

Each alternatives of table 11 is to distance and the relative approach degree of VPIS and VNIS

Relatively the relative approach degree of each alternatives is known, and under the prerequisite of considering the targets such as environment, cost, urban lake storehouse wawter bloom Emergency management scheme by from ideal scheme to the order of ideal scheme least, carrying out ranking results is:

A ₁₂＞A ₈＞A ₆＞A ₁₀＞A ₃＞A ₁₁＞A ₇＞A ₉＞A ₅＞A ₂＞A ₄＞A ₁

As shown in Figure 3, the ranking alternatives result conforms to expert opinion suggestion and result of practical application, shows that method provided by the invention has feasibility when solving this type of decision problem.

In addition, for the advantage of the decision-making technique that the present invention proposes is described more intuitively, separately provide the Vague diversity method result of decision in " the fuzzy matter element decision-making based on entropy power " that adopts Zhou Xiaoguang, to compare with the inventive method result.

As shown in Figure 4, the relative approach degree of each alternatives is in Table 12 for the result of decision of the Vague diversity method in " the fuzzy matter element decision-making based on entropy power " of employing Zhou Xiaoguang.

The relative approach degree of each alternatives of table 12

Alternatives decision-making ranking results from two kinds of methods, in the result of decision of the inventive method, the relative approach degree of resolution that the 12nd kind of scheme is artificial swamp is much larger than other schemes, illustrate that this scheme is relatively ideal, next is the 8th kind and the 6th kind of scheme, be artificial aeration and coagulating sedimentation, and the 1st kind of scheme Inner nutrition salt method is relatively least desirable, because the otherness of each scheme is larger, illustrate that this result of decision can play effective directive function to the wawter bloom Emergency management decision-making of urban lake storehouse; And in the result of decision of existing Vague diversity method, the relative approach degree of scheme is comparatively similar, there is no significantly to be better than the scheme of other schemes, only can find out the 1st kind of scheme and the 3rd kind of scheme, be Inner nutrition salt method and allelopathy algal control, this two schemes is relatively least desirable, because the otherness of each scheme is less, substantially can't play effective directive function to the wawter bloom Emergency management decision-making of storehouse, lake.

Claims (6)

1. improve the multi-level decision-making technique of urban lake storehouse wawter bloom Emergency management multiple goal of algorithm based on Vague value similarity measure, it is characterized in that:

Step 1, structure decision-making hierarchical model;

Described decision-making hierarchical model comprises destination layer, solution layer and attribute layer;

Step 2, obtain decision matrix;

For solution layer and destination layer, by expert opinion, form each alternatives in solution layer to the scheme of each decision objective in destination layer-objective decision matrix; For solution layer and attribute layer, according to detecting with investigation result, construct in the attribute layer and respectively affect attribute to the scheme of each alternatives in solution layer-attribute decision matrix; Degree of giving preferential treatment to the families of the armymen and martyrs between level is determined by linguistic variable, adopts Vague set representations scheme-objective decision matrix and scheme-attribute decision matrix, i.e. scheme-target Vague collection matrix and scheme-attribute Vague collection matrix;

Step 3, definite with reference to attribute-target Vague collection matrix;

Scheme-target Vague is integrated to matrix conversion as scheme-target Relative optimal subordinate degree matrix; In scheme-target Relative optimal subordinate degree matrix, target is divided into to benefit type and cost type two classes, the optimal case of definite each target and the poorest scheme are as the reference scheme respectively, and according to scheme-attribute Vague collection matrix, obtain optimum attributes Vague value and the poorest attribute Vague value of corresponding scheme, thereby acquisition optimum attributes-target Vague collection matrix and the poorest attribute-target Vague collection matrix are as reference attribute-target Vague collection matrix;

Step 4, the average Vague value of computing reference attribute weight;

Adopt the information entropy power computing method of Vague collection, for optimum attributes-target Vague collection matrix and the poorest attribute-target Vague collection matrix, calculate respectively the weight of each target under reference scheme; According to the TOPSIS method, with VPIS and VNIS, mean respectively ideal solution and the negative ideal solution based on the Vague collection again, obtain optimum attributes weighted mean Vague value and the average Vague value of the poorest attribute weight, as the average Vague value of reference attribute weight;

Step 5, alternatives decision-making sequence;

Calculate the distance of each alternatives to VPIS and VNIS; Calculate again the relative approach degree of each alternatives to the distance of VPIS and VNIS according to each alternatives; Quality according to relative approach degree size to alternatives is sorted, and obtains the alternatives of relative approach degree maximum as final decision scheme.

2. the multi-level decision-making technique of urban lake storehouse wawter bloom Emergency management multiple goal of improving algorithm based on Vague value similarity measure according to claim 1, it is characterized in that: scheme in step 2-target Vague collection matrix means with A, according to the transformation rule of linguistic variable and Vague value, the Vague value representation of alternatives under decision objective is as follows:

$A_{u\×v}=[t_{\mathrm{ij}}^A,1-f_{\mathrm{ij}}^A],i=\mathrm{1,2},\·\·\·u;j=\mathrm{1,2},\·\·\·v.$

Wherein

mean alternatives a _ito decision objective c _jsatisfaction, mean alternatives a _ito decision objective c _jnot satisfaction, and $0\≤t_{\mathrm{ij}}^A+f_{\mathrm{ij}}^A\≤1$ , order $1-f_{\mathrm{ij}}^A=t_{\mathrm{ij}}^{A*}$ ；

In like manner, scheme-attribute Vague collection matrix means with B, affects the Vague value representation of attribute under alternatives as follows:

$B_{u\×w}=[t_{\mathrm{ij}}^B,1-f_{\mathrm{ij}}^B],i=\mathrm{1,2},\·\·\·u;j=\mathrm{1,2},\·\·\·w.$

Wherein

mean to affect attribute b _jto alternatives a _idegree of impact,

mean to affect attribute b _jto alternatives a _inot degree of impact, and

, will be designated as

.

3. a kind of multi-level decision-making technique of urban lake storehouse wawter bloom Emergency management multiple goal of improving algorithm based on Vague value similarity measure according to claim 1, it is characterized in that: described scheme-target Vague is integrated to matrix conversion as scheme-target Relative optimal subordinate degree matrix, conversion method is as follows:

If x _ijexpression is the relatively optimal degree degree of i row element to the j column element in the decision matrix of Vague set representations, and its computing formula is

$x_{\mathrm{ij}}=t_{\mathrm{ij}}-f_{\mathrm{ij}}=t_{\mathrm{ij}}+t_{\mathrm{ij}}^{*}-1---\left(1\right)$

T wherein _ijmean the degree of giving preferential treatment to the families of the armymen and martyrs of i row element to the j column element, f _ijmean the non-degree of giving preferential treatment to the families of the armymen and martyrs of i row element to the j column element,

, draw thus the decision matrix shown by the relatively optimal degree kilsyth basalt:

[x _ij] _m×n,1≤i≤m,1≤j≤n

Wherein, m, n means respectively line number and the columns of decision matrix.

4. a kind of multi-level decision-making technique of urban lake storehouse wawter bloom Emergency management multiple goal of improving algorithm based on Vague value similarity measure according to claim 1, it is characterized in that: described reference scheme is as follows:

In scheme-target Relative optimal subordinate degree matrix, establish

, as target c _jduring for the benefit type, corresponding alternatives a _ifor optimal case, its corresponding attribute Vague value is target c _junder optimum attributes Vague value,

corresponding alternatives a _ifor the poorest scheme, its corresponding attribute Vague value is target c _junder the poorest attribute Vague value; As target c _jduring for the cost type,

corresponding alternatives a _ifor optimal case, its corresponding attribute Vague value is target c _junder optimum attributes Vague value, corresponding alternatives a _ifor the poorest scheme, its corresponding attribute Vague value is target c _junder the poorest attribute Vague value; If target c _junder n is arranged

or

when identical, by n

or

degree of giving preferential treatment to the families of the armymen and martyrs in the attribute Vague value of a corresponding n alternatives and non-degree of giving preferential treatment to the families of the armymen and martyrs are averaged rear as target c _junder optimum or the poorest attribute Vague value; So far, obtained optimum attributes-target Vague collection matrix:

$C_{v\×w}^{*}=[t_{\mathrm{ij}}^{C*},1-f_{\mathrm{ij}}^{C*}],i=\mathrm{1,2},\·\·\·v;j=\mathrm{1,2},\·\·\·w.$

The poorest attribute-target Vague collection matrix:

$C_{v\×w}^{-}=[t_{\mathrm{ij}}^{C-},1-f_{\mathrm{ij}}^{C-}],i=\mathrm{1,2},\·\·\·v;j=\mathrm{1,2},\·\·\·w.$

Wherein,

mean respectively target c _ithe degree of giving preferential treatment to the families of the armymen and martyrs of lower optimum attributes Vague value and non-degree of giving preferential treatment to the families of the armymen and martyrs, mean respectively target c _iunder degree of giving preferential treatment to the families of the armymen and martyrs and the non-degree of giving preferential treatment to the families of the armymen and martyrs of the poorest attribute Vague value.

5. a kind of multi-level decision-making technique of urban lake storehouse wawter bloom Emergency management multiple goal of improving algorithm based on Vague value similarity measure according to claim 1, is characterized in that, the information entropy power computing method of described Vague collection is as follows:

Use x _ijexpression is the relatively optimal degree degree of i row element to the j column element in the decision matrix of Vague set representations, and the decision matrix that Relative optimal subordinate degree matrix means is:

[x _ij] _m×n,1≤i≤m,1≤j≤n

Wherein, m, n means respectively line number and the columns of decision matrix;

For the dimension of unified each element, need make normalized to decision-making entry of a matrix element, the evaluation X of i row element to the j column element _ijbe defined as:

$X_{\mathrm{ij}}=\frac{x_{\mathrm{ij}}}{{\mathrm{\Σ}}_{i=1}^m{x}_{\mathrm{ij}}}\∀i,j---\left(2\right)$

The entropy E of i row element to the j column element _jfor:

$\begin{array}{cc}{E}_j=-k\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{X}_{\mathrm{ij}}\ln X_{\mathrm{ij}}& \∀j---\left(3\right)\end{array}$

Wherein k is constant, k=1/lnm, and this has guaranteed 0≤E _j≤ 1;

Errored message degree d _jbe defined as:

d _j＝1-E _j. （4）

The definition weights omega _jvalue be

$\begin{array}{cc}{\mathrm{\ω}}_j=\frac{d_j}{{\mathrm{\Σ}}_{j=1}^n{d}_j}& \∀j---\left(5\right)\end{array}$

With

with

the information entropy power that means respectively each target under the information entropy power of each target under optimal case and the poorest scheme,

$\mathrm{VPIS}=\underset{i=1}{\overset{v}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{*}\·[t_{\mathrm{ij}}^{C*},1-f_{\mathrm{ij}}^{C*}],j=\mathrm{1,2},\·\·\·,w---\left(6\right)$

$\mathrm{VNIS}=\underset{i=1}{\overset{v}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{-}\·[t_{\mathrm{ij}}^{C-},1-f_{\mathrm{ij}}^{C-}],j=\mathrm{1,2},\·\·\·,w---\left(7\right).$

6. a kind of multi-level decision-making technique of urban lake storehouse wawter bloom Emergency management multiple goal of improving algorithm based on Vague value similarity measure according to claim 1, it is characterized in that: the similarity measure M (x, y) of definition Vague value x and y is:

$M(x,y)=1-\frac{|t_x-t_y-(f_x-f_y\left)\right|}{16}-\frac{|t_x-t_y+f_x-f_y|}{4}-\frac{2-t_x-t_y-f_x-f_y}{16}-\frac{|t_x-t_y|+|f_x-f_y|}{8}---\left(8\right)$

Wherein, t _x, f _x, t _y, f _ythe degree of giving preferential treatment to the families of the armymen and martyrs and the non-degree of giving preferential treatment to the families of the armymen and martyrs that mean respectively Vague value x and y;

Each alternatives is respectively to the distance of VPIS and VNIS:

$d_i^{*}=\underset{j=1}{\overset{w}{\mathrm{\Σ}}}{\mathrm{\ω}}_{j}M\left(\right[t_{\mathrm{ij}}^B,t_{\mathrm{ij}}^{B*}],\mathrm{VPIS})---\left(9\right)$

$d_i^{-}=\underset{j=1}{\overset{w}{\mathrm{\Σ}}}{\mathrm{\ω}}_{j}M\left(\right[t_{\mathrm{ij}}^B,t_{\mathrm{ij}}^{B*}],\mathrm{VNIS})---\left(10\right)$

ω wherein _jadopt the information entropy power computing method of the Vague collection in step 4 to calculate and obtain scheme-attribute Vague collection matrix B, i=1,2 ..., u;

The relative approach degree of each alternatives:

${\mathrm{\σ}}_i=\frac{d_i^{-}}{d_i^{*}+d_i^{-}},i=\mathrm{1,2},\·\·\·,u---\left(11\right).$

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