Application of two-stage fuzzyset theoryto river
qualityevaluation in Taiwan
Shiow-MeyLiou*, Shang-Lien Lo, Ching-Yao Hu
Graduate Institute of Environmental Engineering, National Taiwan University, 71, Choshan Road, Taipei 106, Taiwan Received 19 February2002; received in revised form 26 September 2002; accepted 30 September 2002
Abstract
An indicator model for evaluating trends in river qualityusing a two-stage fuzzyset theoryto condense efficiently monitoring data is proposed. This candidate data reduction method uses fuzzyset theoryin two analysis stages and constructs two different kinds of membership degree functions to produce an aggregate indicator of water quality. First,
membership functions of the standard River pollution index (RPI) indicators, DO, BOD5, SS, and NH3-N are
constructed as piecewise linear distributions on the interval [0,1], with the critical variables normalized in four degrees of membership (0, 0.33, 0.67 and 1). The extension of the convergence of the fuzzyc-means (FCM) methodologyis then used to construct a second membership set from the same normalized variables as used in the RPI estimations. Weighted sums of the similaritydegrees derived from the extensions of FCM are used to construct an alternate overall index, the River qualityindex (RQI). The RQI provides for more logical analysis of disparate surveillance data than the RPI, resulting in a more systematic, less ambiguous approach to data integration and interpretation. In addition, this proposed alternative provides a more sensitive indication of changes in qualitythan the RPI. Finally, a case studyof the Keeling River is presented to illustrate the application and advantages of the RQI.
r2003 Elsevier Science Ltd. All rights reserved.
Keywords: River pollutant index; River quality index; Fuzzy theory; Fuzzy c-means; Similarity degree; Sensitive analysis
1. Introduction
Creating and maintaining environmental indicators that are scientificallysound but easyfor the laypublic to grasp is essential when complex environmental quality trends need to be effectivelyused in developing and
communicating environmental public policy [1,2]. The
River pollution index (RPI), for example, is used by EPA of Taiwan to explore monitor trends for both planning and day-to-day management of surface water qualityfor the public. The RPI involves four para-meters: dissolved oxygen (DO), biochemical oxygen
demand (BOD5), suspended solids (SS), and ammonia
nitrogen (NH3-N), each of which is ultimatelyconverted
to a four-state qualitysub-index (1, 3, 6, and 10). The overall index is then divided into four pollution levels (non-polluted, lightlypolluted, moderatelypolluted, and grosslypolluted) byaveraging the four sub-indices (see Table 1). Aggregated classification indices were
devel-oped in the 1970s[3–5], and the adequacyand sensitivity
of this classification to subtle changes in water quality
has been the subject of considerable recent debate[6,7].
In the latest two decades, there has been much research
into indices[8–13]. One possible improved approach is
suggested bydevelopments in the area of fuzzytheory
[14], which was first developed byZadeh [15]. In the
previous two decades, the theoryof fuzzysets had
advanced in a varietydisciplines [16,17], including the
calculation of qualityindices from environmental
monitoring data[18–20]. Fuzzymethods are appealing
because theyare suited to modelling the continuum characteristic of the underlying complex environmental *Corresponding author. Tel.: 936052767; fax:
+886-23928821.
E-mail address:[email protected] (S.-M. Liou).
0043-1354/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 3 - 1 3 5 4 ( 0 2 ) 0 0 4 7 9 - 7
interactions that the qualitydata seek to measure. The fuzzyc-means (FCM) algorithm has proved to be effective in exploratorydetection of data structures, and has successfullybeen applied to a varietyof
clustering problems [21]. The convergence analysis of
the algorithm has attracted a considerable amount of attention since the publication of Bezdek’s convergence
theoryin 1978[22].
A linkage of the convergence of FCM is used potentiality. It is widely accepted that, according to the conventional FCM algorithm, similaritymeasure-ment could provide the answer to represent the degree to which a data set belongs to a particular group. However, in this studythe similaritydegrees of an object do not onlydirectlyinfer the objects to a specific qualitylevel, but also provide an intermediate measurement to convert degrees into an overall qualityindex. The main goal of the present work is that the constituents be transformed and aggregated and an overall index calculated with the area of fuzzytheory. It would be a powerful tool to cope with certain complicated situa-tions. The River qualityindex (RQI) is referred to in this paper to distinguish it from other overall indices.
2. Materials and methods
2.1. Membership function
A classical (crisp) set is normallydefined as a collection of elements that can be a finite and countable space of an object. Each single element can either belong to a set or not. Alternatively, for a fuzzy set one can define the number of elements byusing the characteristic function, in which 1 indicates membership and 0
non-membership. [15]. The theoryof fuzzymembership
function is a theoryof graded concepts [23] in which
membership in a set is represented as a continuous value rather than the familiar binomial zero or one. Measure-ments of environmental monitoring parameters encom-pass natural scales that mayrange from a few micrograms per litre to hundreds of grams per litre (when the units are a concentration), or mayrequire
comparison among measurements with different natural units. These differences in natural scale between the various qualityindicators makes data pre-processing veryimportant because this is a necessarystep in allowing an adequate comparison between the different indicators. Poor pre-processing methods can produce biases that mayoveremphasize the importance of one factor in the overall qualitymeasurement. Subindex was widelyused in water qualitymeasurement in earlier research because it recognizes that water qualitydoes not go instantaneouslyfrom ‘‘good’’ to ‘‘bad’’ as water
qualitychanges beyond the guideline value
[3,8,10,11,24]. In other words, the crucial characteristic (membership function) for fuzzyset theoryis the same as the virtue of subindex for qualityassessment. The transformation of a parameter estimate into environ-mental qualityis performed through the use of a value function relating the various levels of the parameter estimation to the appropriate levels of environmental
quality[10,24].
2.2. Fuzzy c-mean algorithm
The general FC algorithm partitions a data set of n objects or pattern vectors into c clusters or groups
ðcpnÞ: This partitioning is achieved byminimising an
objective function, Jm; using an iterative procedure. The
criterion function is as follows.
JmðU ; V ; X Þ ¼X c i¼1 Xn k¼1 mmikjj~xxk ~vvijj2A; 1pmpN; ð1Þ
where ~xxkARp represents an object data k with
p-dimension; X ¼ ~ðxx1; ~xx2; :::::~xxnÞARpn denotes a matrix
of object data; the degree of membership, mikA½0; 1;
measures the likelihood of observation ~xxk belonging to
cluster i; U ARcn is a matrix of similaritydegrees;
~vviARpis the prototype of the ith cluster (i=1yc);
V ARpc is a matrix of cluster centroids; jj~xxk ~vvjj2A
represents distance functions, and when the covariance matrix of all the observations in the data set is equivalent to the identitymatrix I, then the distance metric becomes equivalent to the Euclidean distance Table 1
The classification ranks defined bythe river pollution index (RPI)
Items/ranks Good Slightlypolluted Moderate polluted Gross polluted
DO (mg/L) Above 6.5 4.6–6.5 2.0–4.5 Under 2.0
BOD5(mg/L) Under 3.0 3.0–4.9 5.0–15 Above 15
SS (mg/L) Under 20 20–49 50–100 Above 100
NH3-N (mg/L) Under 0.5 0.5–0.99 1.0–3.0 Above 3.0
Index scores ðSiÞ 1 3 6 10
Sub-index Under 2 2.0–3.0 3.1–6.0 Above 6.0
Sub-index ¼1 4
P4 i¼1Si:
norm, and mA 1; N½ ; which is called the fuzziness index, regulates the degree of partition fuzziness. Minimization
of Jm under the following constrains yields an iterative
minimization pseudo-algorithm well known as the FCM
algorithm[25–28].
ðiÞ 0pmikp1 8i; k; ð2aÞ
ðiiÞ X c i¼1 mik¼ 1 8k; ð2bÞ ðiiiÞ 0pX n k¼1 mikon: ð2cÞ
The components ~vvi and the membership degrees mik
are updated according to the following expressions.
~vvi¼ Pn k¼1ðmikÞm~xxk Pn k¼1ðmikÞm ; 1pipc; ð3Þ mik¼ 1=½jj~xxk ~vvijj 21=m1 A Pc j¼1 1 jj~xxk ~vvjjj21=m1A " #; 1pipc if jjxk vijj2 A> 0; ð4aÞ mik¼ 1; 1pipc; if jjxk vijj2A¼ 0; ð4bÞ Xc i¼1 mik¼ 1: ð4cÞ
The FCM algorithm uses Picard iteration through the loop defined byEqs. (3) and (4) to obtain the
prototypes, which produce the minimal Jm for a
fixed group number c. An observation, ~xxk; is assigned
to the cluster i (i=1yc), when its degree of membership
of that particular cluster mik; is greater than its
membership values of all other clusters. Bezdek provides an excellent treatise on the familyof fuzzyk-means
methods[29].
2.3. The river quality index model
Based on the convergence theoryof the FCM, the similaritymeasure of two fuzzysets is revealed in Eq. (4), which explores the relationships between two observations (both vectors are of p-dimensions) related to the values of distance measures. Similaritymeasures are large when the two objects being compared share a considerable amount of commonality, and small when theydiffer significantlyfrom each other. Distance measures varyinverselyto similaritymeasures in
magnitude [29]. The extension of the above properties
is employed in quality assessment. The parameter m regulates the association fuzziness degree of similarity
measures and distance measures. Instead of seeking the optimal prototypes for a fixed group number c, cluster
nucleus ~vvi represents qualitymeasurements, which
reflects or even is defined as a specific qualitylevel orderlyarranged and assigned in advance. The proto-types are defined as the specific quality. Four nucleuses were defined, nil, moderate, severe, and extreme impacts
for the fish farm explored in Silvert[30]. Hence, Eq. (4)
is redefined as follows in qualityevaluating application (see Eq.(5). mik¼ 1=½jj~ffk ~eeijj 2=ðm1Þ A Pc j¼1 1 jj~ffk ~eejjj2=ðm1ÞA " #; ð5Þ
where ~ffk represents the data point transformed from
concentration to the memberships of qualityfor a given
use. The prototype, ~eei; is defined as a specific
quality-ordered level and is assigned in advance, and mikA½0; 1 is
the similaritydegree of data point ~ffk to ith specific
qualitylevel.
The RQI is used to address the monitoring data of the river environment based on this extended FCM methodology. Since the similarity measures measure the commonalityof the observation and assigned specific quality-ordered levels, an overall quality index
of an observation~xxk; can be obtained from the
accumulated summing up of its similaritydegrees to
all of the specific quality-ordered levels mik (for i=1 to
c). The greater the commonalityof an observation similar to the good qualitylevel, the higher is its overall score gained. It is obvious that onlyif the increased points are assigned does it not matter how large are the values of the weighting points. The weighting points of
qualitylevels qiA½0; 1 (for i ¼ 1 to c) are registered into
equal parts according to the number of specific quality-ordered levels for having a general formula, which could be applied in anynumber of qualitylevels. The points
are divided into qi=0, 0.5 and 1, c=3 for example,
which represents the similaritydegree weights of the object to three specific quality-ordered levels, respec-tively. By accumulating one set of weighted similarity
degrees, the RQI of observation ~xxk is derived (as
Eq. (6)).
RQIk¼ ðX
c
i¼1
mik qiÞ 100: ð6Þ
Ultimately, for the public’s recognition, the factor of 100 is employed. Hence, the value of the RQI is ranged from 0 to 100.
3. Results and discussion
Based on the two-stage fuzzyset, the RQI is established. To undertake this research, a program was
developed to implement the RQI. The flow chart of the
program is drawn inFig. 1.
3.1. Membership functions for quality estimation
The four parameters: DO, BOD5, SS, and NH3-N are
employed in the study since these are the key parameters
suggested byearlier research [3,7,10,13,27]. Let X ¼
fxd; xb; xs; xng is a four-dimension sampling space of
river water, where d denotes DO (mg/L), b denotes
BOD5(mg/L), s represents SS (mg/L), and n indicates
ammonia nitrogen (mg/L). Segmented linear member-ship functions of the critical variables are constructed. Four crucial breakpoints: 0, 0.33, 0.67 and 1 are registered based on the four specific standard RPI levels. The average concentrations of each parameter in each pollution level of RPI index are determined in
accor-dance with the degree of water quality(seeTable 2). The
piecewise linear membership functions of the variables
are established as follows.
fdðxdÞ ¼ 1 for xd> 6:5; 2=3 þ ð1=3Þ xd 5:5 6:5 5:5 for 5:5pxdp6:5; 1=3 þ ð1=3Þ xd 3:25 5:5 3:25 for 3:25pxdp5:5 ð1=3Þ xd 2 3:25 2 for 2:0pxdp3:25; 0 for xdo2; ; 8 > > > > > > > > > > > < > > > > > > > > > > > : ð7Þ fbðxbÞ ¼ 1 for xbo3:0; 2=3 þ ð1=3Þ 3:95 xb 3:95 3:0 for 3:0pxbp3:95; 1=3 þ ð1=3Þ 10 xb 10 3:95 for 3:95pxbp10:0; ð1=3Þ 15 xb 15 10 for 10:0pxbp15:0; 0 for xb> 15:0; 8 > > > > > > > > > > > < > > > > > > > > > > > : ð8Þ fsðxsÞ ¼ 1 for xso20:0; 2=3 þ ð1=3Þ 34:5 xs 34:5 20:0 for 20:0pxsp34:5; 1=3 þ ð1=3Þ 75 xs 75 34:5 for 34:5pxsp75; ð1=3Þ 100 xs 100 75 for 75pxsp100; 0 for xs> 100; 8 > > > > > > > > > > > < > > > > > > > > > > > : ð9Þ fnðxnÞ ¼ 1 for xno0:5; 2=3 þ ð1=3Þ 0:7 xn 0:7 0:5 for 0:5pxnp0:7; 1=3 þ ð1=3Þ 2 xn 2 0:7 for 0:7pxnp2; ð1=3Þ 3 xn 3 2 for 2pxnp3; 0 for xn> 3; 8 > > > > > > > > > > > < > > > > > > > > > > > : ð10Þ
where fdðxdÞ; fbðxbÞ; fsðxsÞ; and fnðxnÞ represent the
membership functions of parameter DO, BOD5, SS,
and NH3-N, respectively. The rating curves of the four
criteria variables resulting from membership functions
as described above are shown inFig. 2. Nives[10]states
that selection of the rated value of qualityis an arbitrary one but the base of the surveyand the application of this method to the evaluation of surface water qualitycan be modified according to their territorial circumstances elsewhere.
Criteria parameters selecting
Membership functions constructing
Standard quality levels setting
Euclidean Distances computing Similarity degrees constructing
A case study Relative sensitivity analysis
of present indicator
RQI RQI properties analysing
Fig. 1. Schematic procedure of the proposed model for river qualityevaluation.
Table 2
The key-points defined in the membership functions Membership degree (fxÞ 0 1/3 2/3 1 DO (mg/L) Above 6.5 5.5 3.25 Under 2.0 BOD5 (mg/L) Under 3.0 3.95 10 Above 15 SS (mg/L) Under 20 34.5 75 Above 100 NH3-N (mg/L) Under 0.5 0.7 2 Above 3.0
3.2. Optimal fuzziness index, m, and suitable number of specific quality level, c
The properties of the similaritydegrees based on the convergence theoryof the FCM are studied. Groups of synthetic data sets are used in which each of the
observations ~ffk (for k=1 to n) consists of four
homogeneous values (four-dimensional measurement space). In total, 101 subsets of observations ranging
from the terminal values ~ff0¼ 0; 0; 0; 0ð Þ to ~ff101¼
1; 1; 1; 1
ð Þ are used to compute the similaritydegrees
and the RQI. The usable parameters in Eq. (5) are set as follows: The Euclidean norm is chosen for distance function being well known and commonlyused. The fuzziness index, m, is set with 7/5, 5/3, 2, and 3. By varying specific quality-ordered levels, c, from 2 to 5, four sets of similaritydegree functions can be derived for each fuzziness index. In total, 16 index curves (4 values of m for m 4 possibilities for the qualitylevels) are
generated. Table 3explicates the notations used in the
synthetic data study. The subsets of ~ee0¼ (0, 0, 0, 0) and
~ee1¼ ð1; 1; 1; 1Þ; for example, represent the specific
quality-ordered level of perfectly ‘‘bad’’ and perfectly ‘‘good’’ quality. In other words, these represent the absolute poorest measurements and absolute best measurements that are possible. Using the definition of
mjk in Eq. (5), it is possible to calculate the similarity
degrees, m0kand m1k; between object ~xxkto the two levels
from interval 0; 1½ : This can be represented as follows
(see Eq. (11)). m0k¼ 1=jj~ffk ~ee0jj 2=ðm1Þ ð1=jj~ffk ~ee0jj2=ðm1ÞÞ þ ð1=jj~ffk ~ee1jj2=ðm1ÞÞ ; m1k¼ 1=jj~ffk ~ee1jj 2=ðm1Þ ð1=jj~ffk ~ee0jj2=ðm1ÞÞ þ ð1=jj~ffk ~ee1jj2=ðm1ÞÞ : ð11Þ
An overall index of object ~xxk is computed by
RQIk=½ðm0kÞ 0 þ ðm1kÞ 1 100 referring to
Eq. (6). Hence, the subsets of ~ee0=(0, 0, 0, 0),
~ee1=4=(0.25, 0.25, 0.25, 0.25), ~ee2=4=(0.5, 0.5, 0.5, 0.5),
~ee3=4=(0.75, 0.75, 0.75, 0.75), and ~ee1=(1, 1, 1, 1), for
example, sort the RQI based on five specific quality levels. 0 2.95 3.95 10 20 20 15.05 0 0.2 0.4 0.6 0.8 1 0 5 10 15 (b) 0 19.5 34.5 75 100.5120 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 120 Concentration (mg/L) (c) 0 0.45 0.7 2 3.05 0 0.2 0.4 0.6 0.8 1 0 2 4 (d) 6.558 5.55 3.25 2.04 0 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 Concentration (mg/L) degree of membership degree of membership (a) 5 Concentration (mg/L) Concentration (mg/L) degree of membership degree of membership
Fig. 2. The rating curves of the employed parameters: (a) DO (mg/L), (b) BOD5(mg/L), (c) SS (mg/L), (d) NH3-N (mg/L).
Table 3
The notations used in the synthetic data study
Notation Definition
~ee0=n1; ~ee1=n1; y; ~een2=n1and ~een1=n1 n specific quality-ordered levels
m0=n1; m1=n1; y; mn2=n1and mn1=n1 The similarityamong the synthetic data and their identified qualitylevels q0=n1; q1=n1; y; qn2=n1qn1=n1 The weighting points coincident with quality-ordered levels
The curves of RQI for the 101 synthetic data sets
based on two specific qualitylevels with five varying
fuzzyindex m are shown inFig. 3. Essentially, the RQI
rises with the increasing value of the defaulted data set, ~
ffk so the qualityof the observation could be explored.
In the case of c ¼ 2; m=3, the summarized RQI yields the average of the distance of a data set to a cluster nucleus so that the linear relationship between the subset
of synthetic data ~ffkand RQIkperfectlyexists. The slight
‘‘S’’ curves displaywhen either m=2 or m=5. Occa-sionally, such curves are preferred in quality assessment since theyare bonded to the membership functions not being perfect linearityin use. The RQI tend to be crisp when m=11/10 of which the values are either 100 or 0. Furthermore, the values of RQI are almost onlylocated on 50 while m=11, which represents the largest fuzzy
existing. Fadili [31]points out that when m-1; either
mik-1 or mik-0; the clusters tend to be crisp and while
m-N; we have mik-1=c: Hence, the range of 2pmp5
seems to be a good compromise for optimising the performance in qualityassessment. When m=1, the objective function is the classical within-group sum of
squared error (WGSSE), and the mik‘s can onlytake the
value 0 or 1. Furthermore, when m=1 the partition is hard, and for m>1, the partition is fuzzy. Increasing m
causes the partition to become fuzzier[27,28,31].
The curves of RQI for the 101 synthetic data sets,
based on five specific qualitylevels with five varying
fuzzyindex m, are shown inFig. 4. Inversion takes place
when the subset of synthetic data ~ffk is closed to the
assigned standard qualitylevels, especiallywhen m=3, 5, and 21, where the RQI declines with increasing qualityor rises with decreasing quality. This incompa-tible phenomenon occurs because the methodology changes to crisp theoryfrom fuzzytheorywhen data points are coincident with anyspecific qualitylevel. That
is, when the observation ~ffkis located coincident with ~eei;
then ðjj~ffk ~eeijj2Þ1=ðm1Þ=0, and the values of the miks
onlygo to 0 or 1. Manynumbers of specific quality-ordered levels bring about the conflict repeatedlyand lead to the contrary. Moreover, for numbers of specific quality-ordered levels, the optimal range of fuzziness index, m, would be limited. The m=2 seems to be acceptable onlyfor optimising performance of quality assessment. Previously, there has been no theoretical basis for an optimal choice for the value of m in the C clustering algorithm; conventionally, m ¼ 2 is selected [31,32]. The properties of mikfor the convergence theory of FCM algorithm applying on quality assessment are explored. The redundant specific quality-ordered levels are unnecessarysince theyweaken the validitymeasure of RQI.
3.3. Sensitivity analysis
The sensitivityanalysis of the RQI is inspected in this study. From the above discussion, fuzziness index m=2 and two standard qualitylevels, perfect ‘‘bad’’ and perfect ‘‘good’’, are employed in the river quality assessment for optimising performance. The values of the RQI and the conventional RPI are converse for an observation since the RPI describes river pollution index, but the RQI denotes river qualityindex. A saturated polluted measurement would produce 0 for RQI and 10 for RPI; on the contrary, an absolute excellent measurement would come out 100 for RQI and 1 for RPI. Thus, for easycomparison between the two indices, the RPIt has been designed. The RPIt ranges from 0 to 9 according to the river qualityfrom bad to good, which is obtained bysubtracting 10 from the value of RPI. Hence, both of the RQI and RPIt are quality indices for river bodies.
In order to get the specific transferred vector, the
vector of the observation is set with ~xxk=(xd, xb, xs,
xn)=(4.37, 6.98, 54.81, 1.35), where ~ffk==(fd, fb, fs, fn) 0 10 20 30 40 50 60 70 80 90 100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RQIx f x c=2, m=11/10 c=2, m=2 c=2, m=3 c=2, m=5 c=2, m=11
Fig. 3. The curves of RQI for the 101 synthetic data sets based on two specific quality-ordered levels ðc ¼ 2Þ with five varying fuzzyindex (m). 0 10 20 30 40 50 60 70 80 90 100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RQIx f x c=5, m=6/5 c=5, m=2 c=5, m=3 c=5, m=5 c=5, m=21
Fig. 4. The curves of RQI for the 101 synthetic data sets based on five specific quality-ordered levels ðc ¼ 5Þ with five varying fuzzyindex (m).
=(0.5, 0.5, 0.5, 0.5). Each of the four criteria parameters is varied over its possible transition interval, respec-tively, while the values of the others are kept fixed at the
initiation. To explain the relative analysis, Table 4
summarizes the salient features of the changes of suspended solids (SS). Based on the initial vector, the concentrations of SS are changed graduallyfrom 54.81 to 19.61 mg/L, and from 54.81 to 101.01 mg/L while the other criteria are fixed. The similaritydegree between the
object and the perfect ‘‘bad’’ qualitylevel m0 declines
with the lower concentration of SS, while the similarity degree between the object and the perfect ‘‘good’’
qualitylevel m1 increases. Both the RPIt and RQI
decline with the lower concentration of SS. The relative changes of RPIt are from +14% to -11% and RQI from +20% to -20% under the conditions of SS relatively changing from –50% to +50%. The relative changes of
RPIt and RQI are almost the same for BOD and NH3
-N. The relative changes of RPIt are from –11% to +14% and those of RQI are from –20% to +20% for DO under the concentration based on 4.3716 mg/L varying from –50% to +50%. The relative sensitivity of the conventional index (RPIt) and the proposed index
(RQI) are explicated in Fig. 5. The result shows that
three and four staircase steps appear in the conventional index, which is not continuous relating to the change of variable. The relative changes of RQI for the four criteria variables match with their membership functions separately. Furthermore, the overall relative change rate of RQI is greater than that of RPIt.
In summary, the variations of the four criteria parameters are more sensitivelyrepresented with RQI than RPIt. The RQI could sharplydistinguish the change of qualitywith the variation of parameters, which is crucial in evaluating quality.
3.4. A case study
The river qualityindices of RPIt and RQI are applied for three selected points along the Keelung River, the second largest river in Taipei. A map of the area is
shown in Fig. 6. The regular monitoring stations of
Nuanjiang Bridge, Jiangbei Bridge, and Baiyi Bridge are located upriver, middle-stream, and downstream, re-spectively. The historical data from 1991 to 2000 are collected from Environmental Protection Administra-tion of Taiwan. Monthlyaverages are used. There are a total of 120 data records.
A moving average is commonlyused to lead the changing tendencyof data marked. A 12-month moving average is employed in the case of water quality. The monthlytime series and 12-month moving average of
RPIt and RQI from 1991 to 2000 are drawn inFig. 7.
The index of RQI shows a remarkable difference among the upriver, middle-stream, and downstream locations. In Nuanjiang Bridge, the RQI score is above 80 for the
Ta ble 4 Rela tive sen sitivityanaly sis of the RQI and the RPI t for the refe rred samplin gs (m 0 =sim ilaritybe tween sample and absolut e ‘‘bad’’ quality , m1 =similaritybetw een sample and co mplete ‘‘good ’’ quality) C oncentra tion (mg/L) Transfe rred valu e Sim ilaritydegre e RQI RPIt DO BO D5 NH 3 -N SS Relat ivity chan ge rat e of SS (%) DO BOD 5 NH 3 -N SS m0 m1 RQI Rela tivity chan ge rate (%) RPI t Relat ivity chan ge rat e (%) (xd )( xb ) (xn) (xs )( fd )( fb )( fn )( fs ) 4.37 6.98 1.35 19.61 50 0.5 0.5 0.5 1.0 0.30 0.70 69.8 20 5.25 14 4.37 6.98 1.35 24.01 40 0.5 0.5 0.5 0.9 0.33 0.67 67.33 20 4.75 14 4.37 6.98 1.35 28.41 30 0.5 0.5 0.5 0.8 0.36 0.64 63.85 19 4.75 8 4.37 6.98 1.35 32.81 20 0.5 0.5 0.5 0.7 0.40 0.60 59.68 10 4.75 8 4.37 6.98 1.35 42.71 10 0.5 0.5 0.5 0.6 0.45 0.55 54.73 4 4.75 8 4.37 6.98 1.35 54.81 0 0.5 0.5 0.5 0.5 0.50 0.50 49.80 0 4 0 4.37 6.98 1.35 66.91 10 0.5 0.5 0.5 0.4 0.55 0.45 44.88 44 0 4.37 6.98 1.35 76.81 20 0.5 0.5 0.5 0.3 0.59 0.41 40.64 10 4 0 4.37 6.98 1.35 84.51 30 0.5 0.5 0.5 0.2 0.64 0.36 36.34 190 4 0 4.37 6.98 1.35 92.21 40 0.5 0.5 0.5 0.1 0.67 0.33 32.75 20 4 0 4.37 6.98 1.35 101.0 1 5 0 0.5 0.5 0.5 0.0 0.70 0.30 29.88 20 3 11
past 10 years. There is a decrease in quality from Nuanjiang Bridge to Jiangbei Bridge with a score of 80– 40 in the last decade reflecting the effect of the metropolitan area surrounding Keelung City. After the river flows into Taipei City, the river is in a seriously polluted state. The score decreases to around 20 in Baiyi Bridge for the past 10 years. The discharge of municipal
wastewater is considered to be the primarysource of pollution.
The qualityof Nuanjiang Bridge is excellent since it is located at the source of the Keelung River, which has unspoiled and picturesque upper reaches with a number of waterfalls. The qualityof the middle-stream of Keelung River, Jiangbei Bridge, is slightlylower and -30% -20% -10% 0% 10% 20% 30% -0.5 -0.3 -0.1 0.1 0.3 0.5
Relatively change rate of DO concentration
-30% -20% -10% 0% 10% 20% 30% -0.5 -0.3 -0.1 0.1 0.3 0.5
Relativity change rate of BOD5
-30% -20% -10% 0% 10% 20% 30% -0.5 -0.3 -0.1 0.1 0.3 0.5
Relativity change rate of SS concentration
Relativity change rate of RQI and RPIt Relativity change rate of RQI and RPIt Relativity change rate of RQI and RPIt Relativity change rate of RQI and RPIt -30% -20% -10% 0% 10% 20% 30% -0.5 -0.3 -0.1 0.1 0.3 0.5
Relativity change rate of NH3-N concentration
has fluctuated in the latest decade but seems graduallyto have stabilized in the last 3 years. The grossly polluted downstream has seen some gradual improvement from 1998, presumablydue to two important remediation events. One of them is the opening of Bali sewage-treatment works in 1998. The other relates to a 1990s project that straightened two bends in the river near Tachi, which resulted in the conversion of riverbank areas into parkland from the original agri-culture areas.
4. Conclusion
In this research, a new and effective gradation model, the two fuzzyset theory, for diagnosing river qualityhas been developed and illustrated with the case studyof the Keelung River in Taiwan. A simple numerical scale relating to degree of qualitywould seem a feasible approach to assess variations in water qualityand to
conveyfindings in a comprehensive manner to others[3].
Firstly, environmental monitoring parameters measure-ments are processed with membership functions relating the various levels of parameter estimates to the appropriate levels of environmental quality. Secondly, the similaritydegrees, deriving from the extended convergence theoryof the FCM, are weighted, accumu-lated, and eventuallyconverted into the qualityindex. Fuzzytheoryprovides a method that permits an investigator to determine how much a particular set of monitoring measures represent elements of good quality as well as elements of bad quality. Fonck, Hammah, and Curran point out that similaritymeasures between sets are widelyused for querying in fuzzyknowledge bases
[29,33]. The model proposed in this research is a new creative idea in environmental evaluation index. It provides a less subjective, more sensitive, and more efficient model for evaluating qualityand changes in quality.
From the above discussion, the following conclusions can be drawn.
1. This paper has successfullypresented a strategyfor the assessment of qualityusing a similaritydegrees method based on the extended convergence of the FCM algorithm.
2. From the study, it is unnecessary to provide redundant specific quality-ordered levels in proceed-ing consecutive tendencyanalysis with the extended FCM evaluating model. Moreover, the range of
2pmp5 seems to be a good compromise for
optimising the performance of consecutive tendency analysis for two standard quality levels, perfect ‘‘bad’’ and perfect ‘‘good’’ being employed.
3. It is obvious that the value of the proposed overall river qualityindex, RQI, has a linear relationship with the change of the observation compared to the conventional index, RPI. Hence, the index of RQI shows remarkable difference among the upriver, middle-stream, and downstream for the case study of the Keelung River.
4. The model proposed in this research is a creative new idea in environmental evaluation. The choice of parameters (fuzziness index m and specific quality-ordered levels c) enhances the freedom of decision-makers. The flexibilityof the extended FCM model can engage different evaluating scenarios in quality assessment.
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