3. 4. 1 Modelling
According to Gaussian dispersion simulation, it is suggested that the pollution situation surrounding the Second Ring Road is serious, and the results of the compartment model indicate that it will take a long time for the air quality to restore to the original state. Due to a lack of experience in pollution treatment, there are many problems in control measures regarding air pollution.
In addition, people may have uncertainties to clearly understand the air pollution. Therefore, we establish an improved FAHP to propose and screen treatment schemes for atmospheric particulates. Zhao et al. (2011) according to the characteristics of urban traffic environment, a comprehensive evaluation index system for urban traffic environment is established. Then use the fuzzy analytic hierarchy process to determine the weights of the specific indicators in the evaluation model, and make a comprehensive evaluation of the development trend of the urban traffic environment. Taking Shanghai as an example for verification, the correctness of the model, the rationality of the evaluation index system and the feasibility of the evaluation method are analyzed. Chen et al. (2012) used the improved AHP method to determine the weighted average method of weights to evaluate the status of heavy metal pollution in typical vegetable fields in the suburbs of Nanjing. AHP (Analytic Hierarchy Proces s) and FAHP (Fuzzy Analytic Hierarchy Process) are used to choos between Barcode and RFID system for the company warehouse data collection system (Erkan et al., 2014). The flowing processes are shown in Fig 20.
Fig. 20.
The optimized comprehensive treatment steps of the Improved FAHP Methos.
3. 4. 1. 1 Proposal of Feasible Schemes
Four feasible schemes are proposed in this paper after we take Chengdu topographic, climatic features, geological structure, expert opinion, investigation conclusion and the aim of energy saving and emission reduction into account, as hown in Table 2
Table 2.
Presentation of four workable treatment schemes.
Treatment scheme 
M_{1}(A+M_{0}) 
M_{2}(B+M_{0}) 
M_{3}(C+M_{0}) 
M_{4}(D+M_{0}) 
Concrete measures 
A: increase of installations
to enclose the construction
site; setting up of dust
screen 
B: sealing up of exposed
loads of motor vehicles;
washing of wheels stuck
with heavy dirt 
C: artificial rainfall; coverage
of exposed windrow easy to
produce dust 
D: regular manual watering;
regular ground cleaning 
M_{0}: further promotion of traffic restrictions, prohibition of construction within a certain wind speed, employment
of green building materials, slower speed of traffic, better tree planting and grass growing around construction site and
finally intensity of local supervision 
This paper adopts the improved FAHP to select the appropriate treatment schemes for atmospheric particulates (Kang et al 2010) The establishment of Comprehensive Evaluation Index System of the improved FAHP is shown in Fig. 21.
Fig. 21.
Comprehensive evaluation in dex system of the Improved FAHP.
In the improved FAHP, through comparison between every two indexes, the fuzzy judgment matrix A=(a_{ij})_{n×n} is obtained:
 1) a_{ii} = 0.5, i=1, 2, ⋯ n;
 2) a_{ij} + a_{ji} = 1, i=1, 2, ⋯ n
The matrix usually adopts 0.10.9 to distribute the index weights, as shown in Table 3.
Table 3.
Scaling and its significance.
Scaling 
Definition 
Description 
0.5 
Of same importance 
Two factors making comparison with each other are of same importance 
0.6 
Of slightly more importance 
One factor is slightly more important than the other one 
0.7 
Of evidently more importance 
One factor is evidently more important than the other one 
0.8 
Of considerably more importance 
One factor is considerably more important than the other one 
0.9 
Of extremely more importance 
One factor is extremely more important than the other one 
0.1, 0.2, 0.3, 0.4 
Converse comparison 
If two factors satisfy a_{i} / a_{j} = r_{ij}, then through converse comparison we can get a_{j} / a_{i} = 1r_{ij}. 
3. 4. 1. 2 Establishment of Mathematical Model
The fuzzy complem entary judgment matrix is show as follows through comparison between every two indexes a_{1}, a_{2}, ⋯ a_{n}·
STEP 1 By calculating each sum of every row of statistics of judgment matrix using the formula ri=∑k=1naik,i=1,2,⋯,n, and then conducting the following mathematical substitution.
We can obtain the consistent matrix R=(r_{ij})_{n×n}·
STEP 2 Normalizing rank
If
Wi=∑j=1naij∑i=1n∑j=1naiji, j=1,2,⋯, n  (5)

Eq.(5) is the formula calculating the judgment matrix weight vector.
Let G_{n} be the set of all judgment matrix. And we supposed A=(a_{ij})_{n×n} and B=(b_{ij})_{n×n} ∈ G_{n}, used norm AB=∑i=1n∑j=1naijbij to represent distance between A and B and denoted it by ρ(A, B)=AB.
STEP 3 The consistency check of the judgment matrix (Xu, 2002).
To estimate the reasonability of the weight, we need a further check of the consistency of the judgment matrix.
Definition: Matrix A=(a_{ij})_{n×n} and B=(b_{ij})_{n×n} are both the judgment matrix.
IA,B=1n2∑i=1n∑j=1naijbij  (6)

Denoting I(A, B) as the compatibility index of sum.
W=(w_{1}, w_{2}, ⋯, w_{n})^{T} is weight vector of the judgment matrix, of which ∑i=1nWi=1,wi≥0i=1,2,⋯,n.
Let wij=wiwi+wj∀i, j=1,2,⋯,n be Nmatrixn.
W* denotes characteristic matrix for the judgment matrix A.
α denotes the attitude of the decision maker. Judgment matrix is considered to be satisfyingly consistent when compatibility index I(A, W*) ≤ α. The less α is, the higher decision maker asks of the consistency of fuzzy matrix. In this paper, α = 0.1
Multiple comparing judgment matrix based on the same element set X is generally given by multiple experts on practical issue.
Ak=aijkm×n, k=1,2,⋯, m  (8)

We can obtain every weight set W_{k}.
Wk=W1k,W2k,⋯, Wnk,k=1,2,⋯, m  (9)

Then in order to check the consistency of the judgment matrix:
 1) Check the satisfying consistency of A_{k}
 2) Check the satisfying consistency of matrixes
IAk,Al≤a,k≠l,k,l=1,2,⋯, m  (11)

It can be proved that the judgment matrix A_{k}(k=1, 2, ⋯, m) is consistent and acceptable. That means if Eqs. (10) and (11) are satisfied, considering the mean value of m audiencce sets as the distributed weight vector for element set X is reasonable and reliable. Formual for weight vector
meets
Wi=1n∑k=1mwik, i=1,2,⋯, n  (13)

3. 4. 2 Solution of Model
3. 4. 2. 1 Confirmation of Weight Matrix
As for the four evaluation criteria mentioned, suppose there are two experts of this field made comparison between every two indexes on every factor according to scoring method in Table 3, we can obtain weight judgment matrix A_{1} as follows:
Table 4.
Judgment matrix  scored by expert 1.
A_{1} 
Economic index 
Effectiveness index 
Technical index 
Feasibility index 
Economic index 
0.5 
0.4 
0.6 
0.4 
Effectiveness index 
0.6 
0.5 
0.7 
0.6 
Technical index 
0.4 
0.3 
0.5 
0.2 
Feasibility index 
0.6 
0.4 
0.8 
0.5 
Table 5.
Judgment matrix  scored by expert 2.
A_{2} 
Economic index 
Effectiveness index 
Technical index 
Feasibility index 
Economic index 
0.5 
0.4 
0.7 
0.6 
Effectiveness index 
0.6 
0.5 
0.6 
0.7 
Technical index 
0.3 
0.4 
0.5 
0.4 
Feasibility index 
0.4 
0.3 
0.6 
0.5 
Table 6.
The judgment matrices RX1 originating from economic index X1  scored by expert 1.
R_{X1} 
Scheme 1 
Scheme 2 
Scheme 3 
Scheme 4 
Scheme 1 
0.5 
0.6 
0.6 
0.3 
Scheme 2 
0.4 
0.5 
0.6 
0.2 
Scheme 3 
0.4 
0.4 
0.5 
0.3 
Scheme 4 
0.7 
0.8 
0.7 
0.5 
Table 7.
The judgment matrices RX2 resulting from effectiveness index X2  scored by expert 1.
R_{X2} 
Scheme 1 
Scheme 2 
Scheme 3 
Scheme 4 
Scheme 1 
0.5 
0.6 
0.7 
0.4 
Scheme 2 
0.4 
0.5 
0.6 
0.2 
Scheme 3 
0.3 
0.4 
0.5 
0.1 
Scheme 4 
0.6 
0.8 
0.9 
0.5 
According to the Eq. (3), its weight vector is as follows:
W1=0.2444 0.2722 0.2167 0.2667
According to the Eq. (5), the calculation of characteristic matrix W_{1}^{*} is as follows:
w1*=0.50000.52690.46990.52170.47310.50000.44320.49480.53010.55680.50000.55170.47830.50520.44830.5000
According to the Eqs. (10) and (11), the compatibility index of A_{1} and W_{1}^{*} is: I(A_{1}, W_{1}^{*}) = 0.0884 < 1, thus the weight W_{1} is distributed reasonably.
A_{2} denotes the judgment matrix given by expert 2, as is shown in Table 5.
In a similar way, the weight vector can be calculated as:
W2=0.2611 0.2722 0.2278 0.2389
The calculation of the characteristic matrix W_{2}^{*} is as follows:
A2=0.50000.51040.46590.47780.48960.50000.45560.46740.53410.54440.50000.51190.52220.53260.48810.5000
Compatibility index of A_{2} AND W_{2}^{*} is: I(A_{2}, W_{2}^{*}) = 0.0805 < 1, thus the weight W_{2} is distributed reasonanly.
Meanwhile, the satisfying compatibility of matrix A_{1} and A_{2} is checked according to the Eqs. (10) and (11). That is: I(A_{1}, A_{2}) = 0.0875 < 1, thus the judgment matrices are identified to be consistent.
Synthesizing opinions of the two experts, weight vector W can be computed according to the Eq. (13):
W=120.2444+0.26110.2722+0.27220.2167+0.22780.2667+0.2389=0.2528 0.2722 0.2233 0.2528
3. 4. 2. 2 Establishment of Judgement Matrix
Establishing judgment matrix on the four schemes and adopting the scoring method given by experts in Table 3, we can obtain fuzzy matrix by comparison between every two indexes. To make it clear, this paper only shows one judgment matrix scored by one expert.
With the four judgment matrices shown above, the sort vector can be obtained for the four schemes according to Eq. (7).
Table 8.
The judgment matrices RX3 resulting from technical index X3  scored by expert 1.
R_{X3} 
Scheme 1 
Scheme 2 
Scheme 3 
Scheme 4 
Scheme 1 
0.5 
0.4 
0.5 
0.3 
Scheme 2 
0.6 
0.5 
0.6 
0.3 
Scheme 3 
0.5 
0.4 
0.5 
0.3 
Scheme 4 
0.7 
0.7 
0.7 
0.5 
Table 9.
The judgment matrices RX4 resulting from technical index X4  scored by expert 1.
R_{X4} 
Scheme 1 
Scheme 2 
Scheme 3 
Scheme 4 
Scheme 1 
0.5 
0.5 
0.6 
0.7 
Scheme 2 
0.5 
0.5 
0.6 
0.7 
Scheme 3 
0.4 
0.4 
0.5 
0.8 
Scheme 4 
0.3 
0.3 
0.2 
0.5 
Table 10.
Evaluation matrix composed of ordering vector.
Judgment Matrix R 
Scheme 1 
Scheme 2 
Scheme 3 
Scheme 4 
Scheme 1 
0.2500 
0.2333 
0.2278 
0.2889 
Scheme 2 
0.2611 
0.2333 
0.2111 
0.2944 
Scheme 3 
0.2333 
0.2500 
0.2333 
0.2833 
Scheme 4 
0.2667 
0.2667 
0.2556 
0.2111 
X1=0.2500 0.2333 0.2278 0.2889X2=0.2611 0.2333 0.2111 0.2944X3=0.2333 0.2500 0.2333 0.2833X4=0.2667 0.2667 0.2556 0.2111
The judgment matrix can be obtained according to the four sort vectors, as shown in Table 10.
3. 4. 2. 3 Result of Sorting on Schemes
B=W×R=0.25280.27220.23330.2528T×0.25000.26110.23330.26670.23330.23330.25000.26670.22780.21110.23330.25560.28890.29440.28330.2111=0.2536 0.2455 0.2315 0.2695
According to maximum membership degree, the optimized rank of the alternative four schemes is: scheme 4>scheme 2>scheme 3. And the final scheme involves eight methods: regular manual watering, regular ground cleaning, further promotion of traffic restrictions, prohibition of construction within a certain wind speed, employment of green building materials, slower speed of vehicles, better tree planting and grass growing around construction site, and intensity of local supervision.