FUZZY COMPREHENSIVE ASSESSMENT, FUZZY CLUSTERINGANALYSIS AND ITS APPLICATION FOR URBAN TRAFFIC

ENVIRONMENT QUALITY EVALUATION

YANG TAO*Nanjing Institute of City Transportation Planning, No.15 Gao Jia Jiu Guan, Nanjing, Jiangsu, 210029,

People's Republic of China

and

YANG XINMIAOTransportation College, Southeast University, No.2 Si Pai Lou, Nanjing, Jiangsu, 210018, People's Republic of China

(Received 17 April 1997)

AbstractÐThis paper considers tra�c environment quality assessment methods in the context of their appli-cation as part of the Anshan City's Comprehensive Transportation Planning Project. In particular, it involvesapplying multistage fuzzy comprehensive assessment and fuzzy clustering analysis. The study proceeds byinitially setting up an assessment system and then moves on to establishing and determining assessment cri-teria, formulae for the subordination function, allocating weights and modeling and program design. Finally,the theoretical framework is explored in a case study context. # 1998 Elsevier Science Ltd. All rights reserved

Keywords: urban environmental quality, fuzzy cluster analysis, comprehensive assessment, China.

1. INTRODUCTION

While economic progress is improving the material standards of living in many developing coun-tries, many nations are encountering mounting environmental challenges. This is particularly so ina large number of urban areas. Motorised transport is one of the main contributors to the envir-onmental problems that they are now having to confront. This is resulting in increased problemsof atmospheric pollution and of high tra�c noise levels. How to give an objective and scienti®cassessment of urban environment quality when confronted by tra�c growth is an importantquestion for many of their policy makers.

China has just begun to do work in this ®eld although most of it is limited to analyzing theexisting state of environment qualitatively as tra�c levels increase. This work is particularlyassociated with one study, that of the Anshan City's Comprehensive Transportation PlanningProject. The paper is primarily theoretical but has an empirical content. The latter involvesapplying multistage fuzzy comprehensive assessment and fuzzy clustering analysis with calculatinga series of quantitative results of Anshan city from 1988 to 1993.

2. ELEMENTS ANALYSIS AND ASSESSMENT INDEX SYSTEM

The environment pollution associated with motorised transport has two primary aspects, auto-mobile tail gas and noise. As showing in numerous studies, seventy to eighty percent of air pollu-tion in Europe and America countries is from automobile tail gas (Organisation for EconomicCooperation and Development, 1988). This includes a range of local pollutants such as particles,lead and benzine, as well as global warming gases and gases that contribute to acid rain problems.

Transpn Res.-D, Vol. 3, No. 1, pp. 51±57, 1998# 1998 Elsevier Science Ltd

Pergamon All rights reserved. Printed in Great Britain

PII: S1361-9209(97)00021-7

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51

*Author for correspondence.

Vehicle noise is the major source of noise nuisance in urban area and is compounded in older citiesthat were not desired for this type of tra�c.

Quantifying and comparing the various elements that make up the environmental intrusionassociated with tra�c is problematic. China has a number of ways of summarising these problemsin composite measures. The Air Environment Quality Standard of China (GB3095-82) and theUrban Area Environment Noise Standard of China (GB3096-82) form two groups of assessmentsubsystems. These comprise eight assessment indexes that are selected for use in urban tra�cenvironment quality evaluation. The components of air pollution are CO, SO2, NOx, TSP, dust.There are noise factors Leq, L10 and L90 (Fig. 1).

3. THE MULTISTAGE FUZZY COMPREHENSIVE ASSESSMENT METHOD

The assessment sub-systems are amenable to application in a number of di�erent frameworks.However, given their nature, ordinal styles of analysis appear to be the most tractable. This work,therefore, makes use of the multistage fuzzy comprehensive assessment method to assessmenturban environment qualities when there are mounting levels of tra�c (Yager, 1977, 1982; Yeh,1975). The multistage framework helps in applying the analysis to real situations.

The approach adopted here embraces an assessment system (Fig. 1), determining assessmentcriteria, the formulae of subordination function, allocating weights, etc.

The technical features of the assessment factor set can be expressed as

U � U1�air pollution�;U2�noise pollution�g� �1�

U1 � u11�CO�; u12�SO2�; u13�NOx�; u14�dust�; u15�TSP�� �2�

U2 � u21�Leq�; u22�L10�; u23�L90�� �3�

According to the Chinese national environment standard and international experience, each indexis ordinal but can be related to physical indices. The environmental quality of an area is classi®edinto ®ve levels, namely: excellent, good, ordinary, poor, bad. In the absence of extensive objectivemeasurements on the ground, the assessment criterion used deployed mainly relies on expertopinion analysis with the indices for any area being determined by experts drawn from a numberof relevant ®elds including environment engineering and tra�c engineering. Hence, we have;

V � V1�excellent�;V2�good�;V3�ordinary�;V4�poor�;V5�bad�� �4�

The excellent level is taken to indicate the advanced environment quality found in many westernareas. It constitutes the ®rst class environment quality standard in China. The good level indicatesmore advanced levels in China, but is lower than the ®rst class. The third level is intermediatequality. The situation when moving below the third class standard is considered as poor or bad inChina. These expert judgements are designed to re¯ect the quantitative criteria established for

Fig. 1. Urban tra�c environment assessment system.

52 Yang Tao and Yang Xinmiao

each level of environmental quality. The objective boundaries for each level being those shownin Table 1.

The value of subordination of each factor relative to the ®ve assessment levels can be describedquantitatively by a set of formulae of subordination functions as following:

�e�x� �1 0 � x � D1

D2ÿxD2ÿD1

D1 < x < D2

0 0 � D2

8<: �5�

�g�x� �0 x � D1 or x � D3

xÿD1

D2ÿD1D1 < x < D2

1 x � D2D3ÿxD3ÿD2

D2 < x < D3

8>><>>: �6�

�o�x� �0 0 � x � D2 or x � D4

xÿD2

D3ÿD2D2 < x < D3

1 x � D3D4ÿxD4ÿD3

D3 � x � D4

8>><>>: �7�

�p�x� �0 0 � x � D3 or x � D5

xÿD3

D4ÿD3D3 < x < D4

1 x � D4D5ÿxD5ÿD4

D4 � x � D5

8>><>>: �8�

�b�x� �0 0 � x � D4

xÿD4

D5ÿD4D4 < x < D5

1 x � D5

8<: �9�

Environmental intrusion is a multifacited phenomenon but each aspect has its own level ofimportance in the social welfare function. Weighting the various e�ects is not easy. The weightingof assessment factors deployed here was determined at two levels. These weights were determinedby taking advice from experts in environment engineering and tra�c engineering. At the same timea form of benchmark analysis was performed as a second stage by considering the situationexisting in similar cities. Hence, we have;

A � A1�0:4�;A

2�0:6�

n o�10�

A1� A

11�0:3�;A

12�0:15�;A

13�0:1�;A

14�0:3�;A

15�0:15�

n o�11�

A2� A

21�0:25�;A

22�0:35�;A

23�0:40�

n o�12�

Table 1. The assessment criterion of tra�c environment quality

Criterion levels CO SO2 NOx Dust TSP Leq L10 L90

D1 (Excellent) 3.00 0.02 0.05 5.00 0.15 50 55 45D2 (Good) 3.50 0.10 0.07 8.00 0.20 55 60 50D3 (Ordinary) 4.00 0.15 0.10 15.00 0.30 60 65 55D4 (Poor) 4.50 0.20 0.13 20.00 0.40 65 70 60D5 (Bad) 5.00 0.25 0.15 40.00 0.50 70 75 65

Note: The unit measurement for CO, SO2, NOx and TSP is mgmÿ3, the unit of dust is t kmÿ2, the noise unit is dB(A).

Fuzzy comprehensive assessment 53

The ®rst stage assessment matrices of single factor, R1, R

2is:

R1�

r111 r112 r113 r114 r115r121 r122 r123 r124 r125

. . . . . .r151 r152 r153 r154 r155

26643775

R2

r211 r212 r213 r214 r215r221 r222 r223 r224 r225r231 r232 r233 r234 r235

24 35rkij � �j�x� k � 1; 2; i; j � 1; 2 ::: 5;

�1; �2; �3; �4; �5f g � �e; �g; �c; �p; �b

� The ®rst stage fuzzy comprehensive assessment indices, B

1,B

2are:

B1� A

1� R

1� �B

11B12B13B14B15� �13�

B2� A

2� R

2� �B

21B22B23B24B25� �14�

Two fuzzy algorithms are used, namely M�_;^� and M� � ;��. Thus, the second stage assessmentmatrices of the single factor R� and fuzzy comprehensive assessment B� can be determined.

B� � A �R� � �A1;A

2� � A

1� R

1A

2� R

2

� �� �b1; b2; b3; b4; b5� �15�

Finally, the fuzzy comprehensive assessment result can be made.

W � B� � CT �16�

CT is the standard matrix designed to adjust the assessment results to range between 50 and 100.This allows more direct judgments to be made. To undertake this, a practical software was devel-oped to conduct the urban tra�c environment quality analysis applying multistage fuzzy com-prehensive method.

4. CASE STUDY

The basic analysis is applied to a case study of a major Chinese industrial urban area makinguse of the information made available in the Urban Comprehensive Transportation Planning ofAnshan City (1994±2010) in 1994. Anshan is the largest steel city located in northeast China.

The analysis was concerned with road transport a�ects on the environment. Fourteen mainroads were selected as the samples to be used in the environment quality assessment. Figure 2provides a road network map of Anshan city. Information was gathered for three noise indexesand ®ve air pollution indexes of these roads covering the period 1988 to 1993. This informationwas based on the environment survey data of the city. The methodology involved applying thedual stage comprehensive fuzzy assessment method to obtain annual index values for each road(Table 2).

Considering the historical analysis shown by the table, the environmental quality along thefourteen main roads has tended to fall over the period covered. Over the system, ®ve roads were ofpoor or bad environmental quality in 1988, but this rose to seven roads by 1993. A spatial analysisshows that the worst roads in 1993 were Jian Guo Road, Qian Jin Road, Tian Dong Er DaoRoad, Wu Yi Road, Min Shen Road, Ren Min Road, and Huan Gang Road. These are that arelocated in a dense residential area, business center, cultural or government area. This suggests thatthe implications of the environmental degradation may be under-stated by the analysis.

54 Yang Tao and Yang Xinmiao

5. FUZZY CLUSTERING METHOD

In addition to the above, Anshan's urban tra�c environment quality can be assessed using afuzzy clustering analysis method. The factors and the data used in the case study were same before.

Fuzzy clustering analysis embraces three main steps as follows:Step 1. Normalizing the sample data. Set

Xik � X0ik ÿ X0k

�k�17�

There,

X0k �

1

n

X1i�k

Xk �18�

�k ���������������������������������1

n

Xni�1�X0k ÿ X

0k�2

s�19�

X0k is the original value of k environment index of i road.Step 2. Calculating the similar matrix using included angle cosine method.

rij � 1

m

Xmk�1

exp�ÿ 3

4��Xi ÿ Xij�2

�2k� �20�

Table 2. The value of environment quality associated with major roads in Anshan City

Road name 1988 1989 1990 1991 1992 1993

Jian Guo Road 57.71 (14) 57.75 (14) 56.83 (14) 53.33 (14) 53.02 (14) 53.22 (14)Sheng Li Road 62.86 (8) 59.85 (6) 60.13 (7) 62.32 (7) 62.22 (6) 63.57 (4)Zhong Hua Road 65.43 (5) 63.57 (2) 63.45 (2) 65.64 (2) 61.51 (4) 64.31 (2)Yuan Lin Road 63.00 (7) 59.85 (7) 59.55 (10) 61.71 (8) 62.00 (7) 62.27 (7)Shuang Shan Road 66.55 (1) 65.39 (1) 61.66 (4) 63.85 (3) 65.94 (2) 63.23 (6)Qian Jin Road 59.20 (10) 58.07 (11) 57.62 (13) 57.71 (12) 55.56 (11) 54.09 (12)Tian Dong Er Dao Road 60.04 (9) 58.50 (10) 58.48 (11) 58.57 (11) 55.56 (12) 54.09 (13)Wu Yi Road 65.53 (4) 61.20 (4) 62.66 (3) 62.74 (5) 58.64 (8) 54.47 (10)Jian Shen Road 65.93 (2) 59.85 (8) 61.27 (5) 63.27 (4) 63.05 (5) 63.95 (3)Jian Fang Road 63.61 (6) 59.85 (9) 60.41 (6) 62.60 (6) 67.76 (1) 64.41 (1)Min Shen Road 58.76 (13) 58.07 (12) 59.82 (9) 59.82 (10) 56.22 (9) 56.44 (8)Ren min Road 59.15 (11) 58.07 (13) 60.02 (8) 60.10 (9) 56.08 (10) 55.81 (9)Xing Sheng Road 65.57 (3) 60.33 (5) 63.85 (1) 66.04 (1) 65.77 (3) 63.36 (5)Huan Gang Road 58.77 (12) 63.03 (3) 58.22 (12) 54.72 (13) 54.27 (13) 54.42 (11)

Note: The number in brackets indicates the position of that road among 14 main roads.

Fig. 2. Road network map of Anshan City.

Fuzzy comprehensive assessment 55

Step 3. Madding the equal matrix through fuzzy clustering.

R�2� � R � R � �r�2�ij � �21�

r�2�ij � min 1;

Xmk�1

rik � rjk

( )�22�

R�4� � R�2� � R�2� �23�

Re � R2l � R2�lÿ1� � t�R� �24�

Thus, a clustering size � (04�41) will be determined as the clustering criterion according toclustering requirement. According to the clustering criterion and the equal matrix Re={rij}, theclustering results can be determined.

Considering this fuzzy clustering analysis method, a computer software had been developed,and Anshan's tra�c environment quality clustering of fourteen roads (using 1993 data) had beenworked out. The clustering results are shown in Tables 3±5. Considering the results in Table 5 x,fourteen roads can be classi®ed into three categories:

5.1. Category I. Roads 3, 4, 6, 9 and 13This category includes Zhong Hua Road, Yuan Ling Road, Shuang Shan Road, Jian Sheng

Road, and Xing Shen Road. These roads have relative good environment quality because of theirlocation that is distant from industrial area and because of their low tra�c volume.

Table 3. The environment quality similar matrix of Anshan's fourteen roads

Road 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 1.00 0.37 0.50 0.56 0.58 0.86 0.85 0.85 0.85 0.53 0.38 0.78 0.58 0.982 0.37 1.00 0.11 0.82 0.50 0.44 0.51 0.34 0.24 0.98 0.04 0.18 0.88 0.183 0.50 0.11 1.00 0.67 0.92 0.61 0.45 0.44 0.98 0.12 0.40 0.22 0.80 0.404 0.56 0.82 0.67 1.00 0.91 0.88 0.64 0.51 0.75 0.80 0.26 0.27 0.98 0.385 0.58 0.50 0.92 0.91 1.00 0.70 0.60 0.52 0.96 0.47 0.36 0.26 0.97 0.426 0.86 0.44 0.61 0.68 0.70 1.00 0.98 0.97 0.64 0.44 0.88 0.87 0.71 0.807 0.85 0.51 0.45 0.64 0.60 0.98 1.00 0.98 0.50 0.50 0.88 0.91 0.64 0.798 0.85 0.34 0.44 0.51 0.52 0.97 0.98 1.00 0.46 0.34 0.95 0.96 0.53 0.829 0.53 0.24 0.98 0.75 0.96 0.64 0.50 0.46 1.00 0.21 0.39 0.23 0.87 0.4110 0.36 0.98 0.12 0.80 0.47 0.44 0.50 0.34 0.21 1.00 0.04 0.19 0.66 0.1911 0.78 0.04 0.40 0.28 0.36 0.88 0.38 0.95 0.39 0.04 1.00 0.97 0.32 0.8112 0.77 0.18 0.22 0.27 0.26 0.87 0.91 0.96 0.23 0.19 0.97 1.00 0.27 0.7913 0.58 0.68 0.80 0.98 0.97 0.71 0.64 0.53 0.87 0.66 0.32 0.27 1.00 0.4114 0.98 0.19 0.40 0.38 0.42 0.80 0.79 0.82 0.41 0.19 0.81 0.79 0.41 1.00

Table 4. The environment quality equal matrix of Anshan's fourteen roads

Road 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 1.00 0.71 0.71 0.71 0.71 0.86 0.86 0.86 0.71 0.71 0.86 0.86 0.71 0.982 0.71 1.00 0.82 0.82 0.82 0.71 0.71 0.71 0.82 0.98 0.71 0.71 0.82 0.713 0.71 0.82 1.00 0.97 0.97 0.71 0.71 0.71 0.98 0.82 0.71 0.71 0.97 0.714 0.71 0.82 0.97 1.00 0.97 0.71 0.71 0.71 0.97 0.82 0.71 0.71 0.98 0.715 0.71 0.82 0.97 0.97 1.00 0.71 0.71 0.71 0.97 0.82 0.71 0.71 0.97 0.716 0.86 0.71 0.71 0.71 0.71 1.00 0.98 0.98 0.71 0.71 0.96 0.96 0.71 0.867 0.86 0.71 0.71 0.71 0.71 0.98 1.00 0.98 0.71 0.71 0.96 0.96 0.71 0.868 0.86 0.71 0.71 0.71 0.71 0.98 0.98 1.00 0.71 0.71 0.96 0.96 0.71 0.869 0.71 0.82 0.98 0.97 0.97 0.71 0.71 0.71 1.00 0.82 0.71 0.71 0.97 0.7110 0.71 0.98 0.82 0.82 0.82 0.71 0.71 0.71 0.82 1.00 0.71 0.71 0.82 0.7111 0.86 0.71 0.71 0.71 0.71 0.96 0.96 0.96 0.71 0.71 1.00 0.97 0.71 0.8612 0.86 0.71 0.71 0.71 0.71 0.96 0.96 0.96 0.71 0.71 0.97 1.00 0.71 0.8613 0.71 0.82 0.97 0.98 0.97 0.71 0.71 0.71 0.97 0.82 0.71 0.71 1.00 0.7114 0.98 0.71 0.71 0.71 0.71 0.86 0.86 0.86 0.71 0.71 0.86 0.86 0.71 1.00

56 Yang Tao and Yang Xinmiao

5.2. Category II. Roads 2 and 10

This category includes Sheng Li Road and Jian Fang Road. These two roads are near toindustrial areas and have higher tra�c volumes and as a consequence su�ers more from air andnoise pollution than do Category 1 roads.

5.3. Category III. Roads 1, 6, 7, 8, 11, 12 and 14This category includes Jian Guo Road, Jian Jin Road, Tian Dong Er Dao Road, Wu Yi Road,

Min Shen Road,Ren Min Road, and Huan Gang Road. These roads are the worst roads in termsof tra�c induced pollution.

6. CONCLUSIONS

As countries' economies grow so public concern is turning to matters of environmental protec-tion. Growing income levels and the accompanying rise in consumption can impose major envir-onmental costs on society. The problems are being compounded in most countries by the rapidurbanisation that is a feature of post agricultural societies. One of the important new challenges,therefore, confronting urban transportation planners and urban environment project analysts indeveloping countries is the need to be able to incorporate environmental appraisal in their decisionmaking and advice. In this paper, the question is explored using multistage fuzzy comprehensiveassessment methods and fuzzy clustering analysis methods The index system, standard, and weightfactors of tra�c environment quality are proposed. The formulate of subordination function andthe models of the assessment system are presented. Finally, through an application example atAnshan City, it is shown that the works done in this thesis are signi®cant.

REFERENCES

Organisation for Economic Cooperation and Development (1988) Transport and the Environment. OECD, Paris.Yager, R. R. (1977) Multiple objective decision-making using fuzzy sets. Int. J. Man-Mach. Stud. 9, 375±382.Yager, R. R. (1982) Multicriteria decisions with soft information I and II. Fuzzy Mathematics 2, 3.Yeh, R. T. (1975) Fuzzy relations, fuzzy graphs and their applications to clustering analysis. In Fuzzy Sets and Their

Applications to Cognitive and Decision Processes, ed. L. A. Zadeh, pp. 125±149. Academic Press, New York.

Table 5. The environment quality clustering matrix of Anshan's fourteen roads

Road 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 1 0 0 0 0 1 1 1 0 0 1 1 0 12 0 1 0 0 0 0 0 0 0 1 0 0 0 03 0 0 1 1 1 0 0 0 1 0 0 0 1 04 0 0 1 1 1 0 0 0 1 0 0 0 1 05 0 0 1 1 1 0 0 0 1 0 0 0 1 06 1 0 0 0 0 1 1 1 0 0 1 1 0 17 1 0 0 0 0 1 1 1 0 0 1 1 0 18 1 0 0 0 0 1 1 1 0 0 1 1 0 19 0 0 1 1 1 0 0 0 1 0 0 0 1 010 0 1 0 0 0 0 0 0 0 1 0 0 0 011 1 0 0 0 0 1 1 1 0 0 1 1 0 112 1 0 0 0 0 1 1 1 1 0 1 1 0 113 0 0 1 1 1 0 0 0 1 0 0 0 1 014 1 0 0 0 0 1 1 1 0 0 1 1 0 1

Fuzzy comprehensive assessment 57