doi:10.1006/jema.2001.0483, available online at http://www.idealibrary.com on
Identification of river water quality using the
Fuzzy Synthetic Evaluation approach
Ni-Bin Chang
*, H. W. Chen and S. K Ning
Department of Environmental Engineering National Cheng-Kung University Tainan, Taiwan, R.O.C.
Received 21 November 1999; accepted 8 June 2001Proper identification of water quality conditions in a river system based on limited observations is an essential task for meeting the goals of environmental management. Various classification methods have been used for estimating the changing status and usability of surface water in river basins. However, a discrepancy frequently arises from the lack of a clear distinction between each water utilisation mode, the uncertainty in the quality criteria employed and the vagueness or fuzziness embedded in the decision-making output values. Owing to inherent imprecision, difficulties always exist in some conventional methodologies when describing integrated water quality conditions with respect to various chemical constituents, biological aspects, nutrients, and aesthetic qualities. This paper presents a comparative study using three fuzzy synthetic evaluation techniques to assess water quality conditions in comparison to the outputs generated by conventional procedures such as the Water Quality Index (WQI). Based on a set of data collected at seven sampling stations, a case study for the Tseng-Wen River system in Taiwan was used to demonstrate their application potential. The findings clearly indicate that the techniques may successfully harmonise inherent discrepancies and interpret complex conditions. A further, newly developed fuzzy synthetic evaluation approach described in this paper might also be useful for verifying water quality conditions for the Total Maximum Daily Load (TMDL) program and be helpful for constructing an effective water quality management strategy.
2001 Academic Press
Keywords: water quality index, water quality management, fuzzy logic, fuzzy synthetic evaluation,
environmental monitoring, fuzzy clustering, fuzzy pattern recognition.
Introduction
Many countries have introduced a scheme for river water quality monitoring and assessment, exam-ining separate stretches of freshwater in terms of their chemical, biological and nutrient constituents and overall aesthetic condition (Horton, 1965; Sii, 1993; Heinonen and Herve, 1994; and Dojlido et al., 1994). General indices are used as comprehensive evaluation instruments to help assess conditions at the earliest stage to clarify monitoring priorities for regulatory agencies dealing with pollution control problems.
Numerous interpretations of water quality have been addressed in the literature. Horton (1965) made a pioneering attempt to study the general
ŁCorresponding author. Email: a1211@mail.acku.edu.tw
indices, selecting and weighting parameters. One well-known assessment methodology is the Water Quality Index (WQI), developed by the National Sanitation Foundation (NSF) using the Delphi technique as a tool in a formal assessment pro-cedure (Ott, 1978). WQI was originally designed to include nine constituents designed for making an integrated assessment of water quality conditions in order to meet utilisation goals. This was consid-ered a promising approach in the 1980s and 1990s. Considerable advances have since been made based on WQI using slightly modified concepts (Chou, 1990; Heinonen and Herve, 1994; Dojlido et al., 1994; Suvarna and Somashekar, 1997). However, discrepancies frequently arise from the lack of clear distinctions between each mode, the uncertainty in the quality criteria employed and the imprecision, vagueness, or fuzziness in the decision-making out-put values. Sometimes, it is difficult to judge water
quality condition on a seasonal basis due to uneven rainfall and run-off in a particular reach. Conflict-ing trends can appear in the analysis. The need for an advanced classification method, capable of accounting for fuzzy information has long been recognised.
Sii et al. (1993) first discussed the uncertainties involved in using fuzzy membership with values ranging from 0 to 1 to form an applicable fuzzy set instead of the 0 to 100 scale used in conventional rating curves in WQI. This has been widely discussed (see Genther and Glesner, 1997; Delgado
et al., 1998; and Ishibuchi et al., 1999). Lu et al. (1999) applied fuzzy synthetic evaluation
techniques for assessing the reservoir eutrofication phenomenon in Taiwan. This paper presents a comparative study of fuzzy synthetic evaluation approaches versus WQI. Emphasis is placed on two newly developed techniques ‘fuzzy information intensity’ and ‘defuzzification for fuzzy reasoning.’ A problem-oriented analysis describing the impact of water pollution due to uneven seasonal rainfall in the Tseng-Wen River system in southern Taiwan will be used to assess the technique’s potential application.
The WQI approach
The NSF made one of the pioneering attempts to study general water quality indices (Inhaber, 1976). Ott (1978) classified these indices into four general categories: general, specific use, planning and statistical. The WQI approach consisted of nine parameters, including dissolved oxygen, fae-cal coliforms, pH, biochemifae-cal oxygen demand, nitrates, phosphates, temperature, turbidity, and total solids (Canter, 1985). Its output ranges from 0 to 100. A value of 100 represents perfect water quality condition, while zero indicates water that is not suitable for the intended use without fur-ther treatment (Harkins, 1974). If fur-there are n types of constituents, with each assigned an asso-ciated weight via a decision-making process (i.e. the Delphi method), the selected index can then be calculated using the following equation (Canter, 1985): WQID n X iD1 wiqi n X iD1 wi ð100 .1/
in which qi is the water quality parameter of concern and wi the weight associated with it.
Although this has been one of the most promising approaches, the need for developing a uniform method for measuring water pollution control pro-gram results has long been recognised by the scientific community (Brown et al., 1970). In partic-ular, The United States Environmental Protection Agency (EPA) is still working on improved methods for measuring changes in water quality because the public requires more decisive responses regarding water safety.
The fuzzy synthetic evaluation
principle
Fuzzy set theory has been developed and exten-sively applied since 1965 (Zadeh, 1965). It was designed to supplement the interpretation of lin-guistic or measured uncertainties for real-world random phenomena. These uncertainties could originate with non-statistical characteristics in nature that refer to the absence of sharp bound-aries in information. However, the main source of uncertainties involving in a large-scale complex decision-making process may be properly described via fuzzy membership functions.
Fuzzy clustering analysis (FCA) and fuzzy syn-thetic evaluation (FSE) are two frequently used techniques. Unlike WQI, which uses an aggregate evaluation of the overall parameters considered, FCA is applied to clustering the raw data into sev-eral categories using the selected operators without respect to any predetermined criteria in relation to each category. Most of the rules designed for FCA are based on the proper search for centroids or rep-resentative objects around which all observations will be clustered on a minimum basis (Selim, 1984; Trauwaert et al., 1991). FSE is designed to group raw data into several different categories accord-ing to predetermined quality criteria, which can be normally described using a set of functions that are designed to reflect the absence of sharp bound-aries between each pair of adjacent criteria. FSE is more relevant than FCA to the assessment of water quality. A well-designed FSE may be capa-ble of covering the uncertainties existing in the sampling and analysis process, comparing the sam-pling results to the applied quality standards for each parameter, and summarising all of the indi-vidual parameter values (Ott, 1978; Lu et al., 2000). These uncertainties are seldom addressed by WQI. FSE typically comprises an input sub-system, output sub-system and a classification mechanism (Figure 1). Each sub-system describes or contains
Input data (water quality indices)
λ λ Classification mechanism I II III IV Justification based on various fuzzy operators
Figure 1. Basic fuzzy synthetic evaluation approach configuration.
a variety of uncertainties with different scales. To be flexible in application, the input parameter value can be expressed as a crisp or fuzzy value depending on the situation. The earlier methods frequently addressed the input data using a crisp value, while later applications tended to emphasise fuzzy values. At present, symmetrical triangular fuzzy membership functions are commonly used in the description of uncertainties in input sub-systems. Obviously, the greater the imprecision, the larger the tolerance interval applied. More-over, the classification mechanism is central to the process that represents a specific fuzzy reasoning basis. This mechanism is formed as a set of pre-determined membership functions that imply the fuzziness in the boundary between each category designed for classification, and designed for both performing the reasoning functions and generat-ing the outputs for later justification. Assessgenerat-ing all of the outputs in the output sub-system generated from this mechanism and expressed by member-ship values would provide an integrated insight into the classification goals. However, the output sub-system may also require fuzzy implication con-siderations when trying to interpret the outcome. WQI never specifically addresses this. It is known that such uncertainties are important because they can be influential for policy decision-making.
The estimation procedure can be divided into three steps. (1) A set of membership functions is developed into a synthetic classification mecha-nism. (2) A fuzzy relationship matrix between the standards required and the observations expressed as membership functions or crisp values is gener-ated. (3) All of the values that represent water quality are then summarized based on a particular fuzzy operator. Other extended approaches may use a slightly different framework prior to ending up with a final justification. The following sec-tions will discuss four different FSE approaches:
(1) simple fuzzy classification, (2) fuzzy similarity, (3) fuzzy information intensity and (4) defuzzifica-tion. The results obtained via these methods are compared. Case studies demonstrate how these new approaches could be used to successfully inter-pret uncertainties and harmonise discrepancies in a real world problem.
Fuzzy synthetic evaluation
Simple fuzzy classification
Quality management involve addressing the dif-fering water uses to which water is put. Complex situations frequently arise from overlapping or obscure boundaries. The simple fuzzy classifica-tion method utilises the membership funcclassifica-tions to describe standards in relation to differing uses. The measurements of water quality constituents are converted directly into a series of crisp numbers used to search for the corresponding membership values for a final FSE. If the quality criteria are divided into five groups, as shown in Figure 2, the fuzziness defined indicates the possible over-lapping ranges. The tolerance levels, dIII or dIV in Figure 2, reflect this imprecision. The larger the tolerance level, the more difficulties generated
λ
I II III IV V
1
0
dIII dV
Figure 2. Definition of fuzzy membership functions for the simple fuzzy classification method.
by the process. Fuzzy membership functions, sub-jectively derived for classification purposes, are used to design the relationship matrix based on mapping the observations drawn from the mon-itoring system to the relevant water uses. Cal-culating the membership values corresponding to each water quality parameter helps generate the matrix. The output is organized into an evalua-tion matrix for use in the later decision analysis stages. The remaining procedure is to analyse this matrix using several classification methods to identify the degree of similarity between the monitoring situation and the relevant usage mode. To perform the final justification properly, various fuzzy reasoning methods, including the fuzzy oper-ator method, weighted average method, distance method and the additive operation method, are applicable.
Fuzzy operator
Fuzzy operator method (FOM) utilises the max-min operator (Zadeh, 1965) as a tool to perform the FSE. Each of the membership values lij, standing for the fuzzy relationship between i-th parameter and j-th usage mode, must be considered independently via a fuzzy operation. As indicated by equations (2) and (3), while the operator kj is used to search for the minimum value of qijbased on all of the related parameters, the operator kpis applied to finding the maximum value in the set of kj. However, the final justification using the fuzzy operator method could be dominated by the most influential parameter. In addition, the evaluation could end up with a subjective classification procedure.
kjDminflijg .2/
kpDmaxfkjg .3/
Additive operation
The additive operation method, which emphasises that every parameter might be equally influen-tial in the classification process, minimizes the inherent bias existing in the previous method. Equations (4) and (5) express the main idea of the additive operation method.
kjD m X iD1 lij jD1, 2, . . . , n .4/ kpDmaxfkjg jD1, 2, . . . , n .5/ Weighted average
The weighted average method, as expressed by equations (6)–(8), provides a set of weights to express the relative importance of each parameter in order to be more consistent with the correspond-ing usage mode. Thus, wi is the defined weight associated with each parameter of concern in equa-tion (6), which is subject to the requirements in equation (7). kjD m X iD1 wilij jD1, 2, . . . , n .6/ m X iD1 wiD1 .7/ kpDmaxfkjg jD1, 2, . . . , n .8/ Distance operator
Although the additive operation and weighted average methods may improve the estimation reliability, both cannot describe the fuzziness in the measurement error in the input data. The distance method, a similar technique that enhances relative distance evaluation between each usage mode and observed parameter value, has a unique application potential in FSE. Cal-culating these relative distances, as defined in equation (9), may enable us to realise the rela-tive impact of each parameter among the overall observations with respect to each water utilization mode. kjD v u u u u u u u u t m X iD1 .wiðlij/2 n X jD1 m X iD1 .wiðlij/2 jD1, 2, . . . , n .9/
Fuzzy similarity method
With fuzzy similarity method, the first step is to normalise all of the quality criteria so that each has an independent membership function. At this stage, the highest value is set at 1 and the lowest at 0, and the others are between 0 and 1. Figure 3 depicts a typical example of the way to build an integrated membership function system. All of the membership values
λ A xi λE 1 λD λC λB λA B C D E
Figure 3. Definition of fuzzy membership functions for the fuzzy similarity method.
corresponding to all of the selected xi values form an evaluation matrix. Equations (10)–(18) are expressions which describe the similarity between two sets of membership values lA and lA0. In this situation, lA represents the values derived from the observations while lA0 stands for the values gained via t required standards defined in each usage mode. The output from this analysis leads to justification for classifying water quality as mode A rather than mode B. Regardless of which equation is applied, the final justification requires choosing a critical or cut-off value in the decision analysis. Hamming distance d.A, A0/D m X iD1 jlA.xi/ lA0.xi/j .10/ d.A, A0/D1 m m X iD1 jlA.xi/ lA0.xi/j .11/ Euclid distance e.A, A0/D " m X iD1 jlA.xi/ lA0.xi/j2 #1 2 .12/ e.A, A0/Dp1 me.A, A 0/ .13/ Minkowski distance M.A, A0/D " m X iD1 jlA.xi/ lA0.xi/jp #1 p .14/ M0.A, A0/D 1 p p mM.A, A 0/ .15/
Hamming proximityD1 d.A, A0/ .16/ Euclid proximityD1 e.A, A0/ .17/
Fuzzy proximityDN.A, A0/ D n X iD1 minlA.xi/, l0A.xi/ n X iD1 maxlA.xi/, l0A.xi/ .18/
Fuzzy information intensity
The fuzzy information intensity method empha-sises the inclusion of measurement error in the input data by assigning a tolerance level (i.e. the base of membership function) to each type of obser-vation. Accordingly, the larger the tolerance level, the greater the uncertainty involved in the sam-pling and analysis procedure. Figure 4 illustrates a comparative case study, in which the values of lA and lB could differ according to whether the input data are defined as crisp values or fuzzi-fied values associated with an assigned tolerance interval. Using the latter, applied in Figure 4(b), may reflect inherent uncertainties in response to possible measurement errors and may gener-ate different sets of values for the final decision analysis.
Figure 5(a) presents two usage modes (A and
B) in which Ai and Bi represent the compar-ative basis for differentiating membership values. The parameter f as indicated in Figure 5(b), repre-sents the possible measurement error or tolerance embedded in the input information. If Qq1, Qq2, and Qq3 are a set of monitoring data, described as the fuzzified inputs relating to a specific qual-ity parameter, the membership values associated with these three observations can be expressed in terms of relative fuzzy intensity, denoted by q1/Ai, q2/Ai, and q3/Ai. When determin-ing how close Qq1, Qq2, and Qq3 are to the required A mode level, the corresponding membership values, Qq1, Qq2, or Qq3, are equivalent to that marked by the corresponding hatched area in Figure 4(b), respectively. Figure 6 illuminates the fuzzy mem-bership function built for mode A based on a given quality parameter. Including information such as the relative fuzzy intensity in the FSE process may generate a new assessment matrix covering all five usage modes based on the same set of monitoring data, thereby creating an applicable classification mechanism.
λ 1 λB λA 0 A q B λ 1 λB λA 0 A q B fuzziness (a) (b) xi xi
Figure 4. Overlap between the fuzzy input data and the quality criteria.
λ 1 0 Ai ∆Ai λ 1 0 (a) (b) ∆Bi Bi xi xi Ai Bi f ∆q2 ∆q˜1 ˜ ∆q˜3 q˜3 q˜2 q˜1
Figure 5. Information intensity existing within a mode and between modes.
λ
1
0
∆q˜3/∆Ai ∆q˜1/∆Ai ∆q˜2/∆Ai
Figure 6. Fuzzy membership function for mode A based on a given water quality index.
Defuzzification
Defuzzification is a concept drawn from fuzzy con-trol theory (Ross, 1995), which emphasises the decomposition of complex membership functions into one crisp value in response to the inter-pretation and implementation of the output from the fuzzy classification or fuzzy reasoning process. The crisp value can approximately represent the deterministic characteristics of the fuzzy reasoning
process based on the assessment matrix, and help convert the uncertainty into an applicable action when solving real world problems. Among the defuzzification methods that have been commonly used in the field of fuzzy control, the gravity method is one of the most promising.
The procedure involves two essential steps. The first confirms the fuzziness in the input data by ensuring that the standards described in all usage modes are expressed by fuzzy membership functions. If not, a set of reasonable tolerance intervals with respect to all usage modes must be generated and a classification mechanism similar to the one depicted in Figure 2 must be built. The second is to calculate the centroid co-ordinates (xA,c,lA,c) based on the gravity method instead of reading the membership values directly, as shown in equation (19). In Figure 7(b), the classification mechanism requires generating all of the new membership values l0
A,cand l0B,cderived according to the x- co-ordinates (xA,c and xB,c), as indicated in equation (20), and an assessment matrix for performing fuzzy reasoning at the same time. Based on the methods mentioned in equations (10)–(17), the fuzzy reasoning process becomes
λ 1 λB λA 0 A q B λ 1 0 A B (a) (b) fuzziness xA,cxB,c xi A xi (xA,c, λA,c) (xB,c, λB,c) ' ' '
Figure 7. Method for identifying membership value using the defuzzification method.
applicable for final decision analysis.
xcD R l.xi/Ðxidxi R l.xi/dxi .19/ l0Dl.xc/ .20/
Overall, two revised FSE schemes were devel-oped in this study: (1) fuzzy information intensity, to describe the uncertainties embedded in the input data set before performing the fuzzy classification mechanism; (2) defuzzification, to supplement the output information illustration so that it is more applicable for decision analysis. Both approaches still require either the weighted average method or the distance method to perform the fuzzy reasoning in order to achieve the ultimate classification goal.
Case study
Background
The Tseng-Wen River Basin, located in southern Taiwan, is a narrow and steep watershed. The main stream in this system is 138 km in length and drains toward the Taiwan Strait. The Tseng-Wen Reservoir is a multipurpose reservoir designed for flood control, hydroelectric power generation, irrigation, water supply, recreation and flow aug-mentation. It is located in the upstream area of the system, as shown in Figure 8 (Chang et al., 1996a, b). The entire watershed area is 1176 km2, of which the Tseng-Wen Reservoir watershed occu-pies 481 km2. It was designed to store 708 million m3of water with a surface area of 17 km2. Average rainfall in this watershed area is close to 3000 mm per year, which is a little higher than the aver-age annual rainfall of 2600 mm for the entire river
basin. At present, the reservoir watershed is pre-dominantly forest and agricultural land. Chang
et al. (1996a, b) assessed the impact of non-point
source pollution on reservoir water quality in an uncertain environment with respect to a future land development program. Land use within a reservoir watershed that meets both economic and environmental goals via an inexact optimisation approach has been fully discussed by Chang et al. (1999). The average slope of the basin is about 1/57. The total population is approximately 160 000 and most of the residents live in the middle and lower reaches. The Hoe-Chueh and Tsai-Loao tributaries are located nearby and three smaller reservoirs surround the area. The Wu-San-Tou Reservoir, a separate impoundment connected to the Tseng-Wen Reservoir by a tunnel, performs short-term water storage for agricultural irrigation in the largest irrigation area in southern Taiwan, Chia-Yi and Tainan Countries. Because of insufficient stream flow, uneven rainfall, seasonal run-off and pollution from residential and pig farming effluent, the water supply for the coastal cities is facing a severe challenge. The Nan-Hwa Reservoir supplies both Kaohsiung and Tainan Cities. The water is pumped from a river weir located on the neigh-bouring Kao-Ping River system into an associated tunnel and stored in the reservoir temporarily for processing. The Jing-Men Reservoir is the smallest reservoir in the Tseng-Wen River Basin designed only for local irrigation.
Table 1 lists the official classification for water utilisation modes from A to E, with each desig-nated to meet several uses. Discontinuity between the several indices in D and E would result in additional difficulties in the integrated water qual-ity condition classification. The Tseng-Wen River system was classified into only two different usage modes, B and C, as shown in Figure 8. Three gauge stations and 20 stations for water quality
5 0 10 km N S E W Tseng-Wen River Basin Taipei City Kaohsiung City 1 Tseng-Wen 3 2 Tseng-Wen 1 3 Feng-Lee 4 Yu-Ching 5 Erh-His 6 Yu-Feng 7 Shan-Shang 8 Chis-Pa 9 Pa-Shih-Chou 10 Tseng-Wen-Hsi 11 Jen-Ai 12 Kuan-Yueh 13 Fan-Tsai-Tien 1 14 Fan-Tsai-Tien 2 15 Hou-Ying 16 Ma-San 17 His-Wei 18 An-Ting 19 Fsi-Kang 20 Hou-Hsing Tseng-Wen Reservoir Hydraulic Monitoring Station: 1: Yu-Tien 2: Tso-Chen 3: Ma-San Nan-Hua Reservoir Sampling location Mode of water utilization
Class B Class C
Tseng-Wen River Basin 1 4 3 RK 60.9 2 1 Wu-San-Tou Reservoir RK 35.5 5 2 6 7 8 9 RK 39.5 10 11 12 13 14 3 16 15 17 18 RK 26.2 19 20 RK 5.0 RK 45.6 RK 16.8
Figure 8. Geographical location and system environment of the Tseng-Wen River Basin.
Table 1. Water quality standards applicable to river systems in Taiwan
Class utility A B C D E standard index 1. Public water supply (primary level) 2. Swimming 1. Public water supply (secondary level) 2. Fishery (primary level) 1. Public water supply (third level) 2. Fishery (secondary level) 3. Industry water supply (primary level) 1. Irrigation 2. Industrial water supply (secondary level) Environmental protection pH 6Ð5–8Ð5 6Ð0–9Ð0 6Ð0–9Ð0 6Ð0–9Ð0 6Ð0–9Ð0 DO, mg/L >6Ð5 >5Ð5 >4Ð5 >2Ð0 >2Ð0 Coliform, <50 <5000 <10000 – – MPN/100ml <1 <2 <4 – – BOD5(20°C), <25 <25 <40 <100 – mg/L SS, mg/L
DO: Dissolved Oxygen; BOD5: Biochemical Oxygen Demand; SS: Suspended Solids.
monitoring were included in this study. While land use enhancement in the middle river reaches is a priority, increasing public concern for potable water quality has brought many similar develop-ment programs under intensive debate. Optimal management strategies in the downstream area
of the system were assessed by Chen and Chang (1998). The study focused on how the waste load in each drainage district can be effectively reduced when facing lower stream flowrate and receiving higher pollution impact from the highly populated regions in the dry season.
Analytical procedure
Figure 9 summarises the analytical procedure. The initial data set was taken from 20 mid- and down-stream monitoring stations in the Tseng-Wen River system, and analysed in November 1997. Data collected from seven stations were finally selected for this study, as listed in Table 2. Five of the seven measurements were used: DO, BOD5, NH3-N, pH, and SS,
WQI was applied to generating the basic outputs, with independent weights selected for each quality parameter. Normalisation of each parameter was required to maintain internal consistency. Final estimation of the weights was drawn from the base-line associated weight information commonly used in Taiwan. As shown in Table 3, the revised weights were normalised to one based on the five qual-ity parameters. Three FSE techniques – simple fuzzy classification, fuzzy information intensity and defuzzification – were applied sequentially for the quality classification. The membership func-tions are shown in Figure 10. Distance method was
employed as the classification mechanism. Five quality parameters and four usage modes consti-tuted the fuzzy relation matrix, with 20 elements in the decision analysis.
Results and discussions
Figure 11 indicates the pollution impact con-tributed by the middle stream area located between RK30 and RK40 on the river. Some of these loca-tions are classified as non-compliance regions. The water quality condition reaches class D in three out of the four seasons. With only a few stations able to meet the official requirements in summer, several data points fall into the boundary between
C and D, making justification ambiguous. Any
deci-sion maker responsible for handling public health and safety cannot ignore such discrepancies. The authority in charge of any possible task force would have to enforce particular pollution control and monitoring measures with regard to the critical time periods and areas.
Start
Confirm water quality classification criteria Select water body
Select water quality indices
Select one of the following evaluation methods according to the features of water body.
1. Simple fuzzy classification method 2. Fuzzy information intensity method 3. Defuzzification method
Assign the fuzziness of each water quality
index
Fuzzify the water quality classification criteria
Obtain fuzzy relationship matrix
Perform synthetic evaluation by using selected fuzzy operators
Justify the result of water quality classification according to fuzzy membership value
End
Table 2. The outcomes of sampling and analysis in the Tseng-Wen River Basin
Sampling Seasons pH DO BOD5 COD SS NH3-N Cl
location (mg/L) (mg/L) (mg/L) (mg/L) (mg/L) (mg/L) Feng-Lee Winter 7Ð9 5Ð2 10Ð3 39Ð0 49 5Ð6 23Ð0 Bridge Spring 8Ð0 6Ð9 3Ð4 15Ð4 245 0Ð4 6Ð0 Summer 8Ð2 8Ð3 4Ð0 19Ð8 64 0Ð4 24Ð0 Autumn 7Ð6 7Ð8 0Ð5 15Ð8 13 1Ð1 23Ð0 Erh-His Winter 8Ð6 10Ð9 6Ð4 36Ð0 76 0Ð4 60Ð0 Bridge Spring 8Ð0 7Ð0 3Ð6 19Ð3 420 0Ð5 11Ð0 Summer 6Ð6 7Ð6 5Ð0 58Ð0 286 0Ð4 18Ð0 Autumn 8Ð1 12Ð5 6Ð0 69Ð2 29 0Ð5 38Ð0 Pa-Shih- Winter 8Ð4 12Ð0 6Ð6 25Ð7 63 0Ð3 81Ð0
Chou Bridge Spring 4Ð3 5Ð9 9Ð5 230Ð0 19650 3Ð0 28Ð0
Summer 6Ð4 6Ð3 6Ð8 75Ð0 2535 0Ð7 30Ð0 Autumn 8Ð3 19Ð3 12Ð8 43Ð6 33 0Ð4 80Ð0 Tseng-Wen Winter 8Ð5 0 21Ð1 89Ð8 56 23Ð8 189Ð0 Bridge Spring 7Ð6 4Ð8 3Ð4 107Ð0 5571 1Ð5 20Ð0 Summer 7Ð0 6Ð0 3Ð5 34Ð0 282 0Ð8 37Ð0 Autumn 7Ð5 0 31Ð5 78Ð4 40 40Ð5 240Ð0 Ma-San Winter 7Ð3 7Ð3 9Ð5 39Ð0 45 2Ð7 122Ð0 Bridge Spring 7Ð1 3Ð8 6Ð2 80Ð0 1505 0Ð5 20Ð0 Summer 6Ð6 6Ð8 3Ð0 17Ð0 50 1Ð3 40Ð0 Autumn 7Ð4 10Ð8 34Ð1 92Ð0 82 8Ð1 115Ð0 His-Kang Winter 7Ð9 7Ð9 3Ð9 – 62 1Ð0 3500Ð0 Bridge Spring 7Ð0 4Ð7 6Ð0 – 38 2Ð3 19Ð0 Summer 6Ð6 7Ð6 8Ð2 – 48 4Ð8 30Ð0 Autumn 7Ð6 7Ð1 5Ð3 – 123 1Ð7 1130Ð0 Hou-Hsing Winter 7Ð9 8Ð0 3Ð6 – 64 0 1105Ð0 Bridge Spring 6Ð8 3Ð6 2Ð6 – 43 2Ð1 1110Ð0 Summer 5Ð7 10Ð0 7Ð3 – 2 34Ð0 1220Ð0 Autumn 7Ð9 7Ð8 1Ð0 – 35 0Ð8 1000Ð0
Table 3. The weights used in WQI method and the revised weights used in this case study
Water quality parameter Weight Revised weight
DO 0Ð22 0Ð28 BOD5 0Ð18 0Ð23 SS 0Ð09 0Ð12 TP 0Ð06 – NH3-N 0Ð13 0Ð17 Conductivity 0Ð04 – pH 0Ð16 0Ð21 E. coli 0Ð12 –
To avoid possible misinterpretation of the results, three FSE techniques were used to analyse the same data set. Table 4 presents the overall pic-ture of the final outputs representing an integrated and/or comparative insight into river basin man-agement. The plus or minus signs beside the clas-sifications in Table 4 indicate an increasing trend towards an improved or worse mode, respectively. Only clearly identifiable problem symptoms ver-ify non-compliance and initiate immediate water pollution control action.
The results generated by the third and fourth methods demonstrate an identical trend in com-parison to those obtained using simple fuzzy clas-sification and WQI. Comparing the outputs in the last two vertical columns of Table 4 reveals that the predictions from both methods not only exhibit external consistency but also imply that the improvement potential is equivalent. A detailed comparison of the predictions across all four meth-ods with regard to season and location suggests that WQI may be pessimistic. Such an observation is important, particularly in critical seasons and locations. Comparative analysis based on the out-puts in spring associated with the station located in RK35.5 clearly indicates that WQI presents the worst water quality situation (i.e. class D) while FSE suggests a relatively optimistic condition (i.e. class C). Similar situations occur in other cases. This infers that outputs from both simple fuzzy classification and FSE exhibit a mild optimistic trend when compared with WQI. It is conceiv-able that revision of input subsystem in the third method and output subsystem in the fourth method
100 SS mg/L 40 25 D C B A 1 0 λSS 6.5 DO mg/L 4.5 2 D C B A 1 0 λDO 4 BOD5 mg/L 2 1 D C B A 1 0 λBOD5 6.5 pH mg/L 6 5.5 B C D 1 0 λpH 2.4 NH3-N mg/L 0.6 0.3 D C B A 1 0 λNH3-N 5.5 6 A B C D 7 8 8.5 9 9.5 0.1
Figure 10. Membership functions defined for water quality classification.
0 70 100 River location (RK) A W Q I 90 80 70 60 50 40 30 20 10 10 20 30 40 50 60 B C D Winter (January) Spring (March) Summer (July) Autumn (November)
Figure 11. Comparative outputs of water quality classifi-cation based on WQI.
may result in the same degree of impact on the classification outcome.
Overall, the observations gained in this study reopen arguments that WQI might generate pressure on the decision-maker because failure to maintain essential water quality cannot be properly justified. However, simple fuzzy classi-fication may not have the capability to inter-pret possible overlapping phenomena and higher classification capability may not be achievable without proper consideration of the inherent uncertainties embedded in the input and out-put data sets. These findings confirm applica-tion potential for the two newly developed FSE methods.
Table 4. Comparison of water quality conditions in Tseng-Wen River system
River Location Official NCKU Simple fuzzy Fuzzy Defuzzification
location requirement WQI classification information method
(RK) method intensity
method
Winter 60Ð9 Feng-Lee Bridge B D D C C
(January) 45Ð6 Erh-His Bridge B C C C C
39Ð5 Pa-Shih-Chou Bridge B C B B B
35Ð5 Tseng-Wen Bridge C D D D D
26Ð2 Ma-San Bridge C C C C C
16Ð8 His-Kang Bridge C C C C C
5Ð0 Hou-Hsing Bridge C B A A A
Spring 60Ð9 Feng-Lee Bridge B C B B B
(March) 45Ð6 Erh-His Bridge B C B B B
39Ð5 Pa-Shih-Chou Bridge B D D D D
35Ð5 Tseng-Wen Bridge C D C CC CC
26Ð2 Ma-San Bridge C D D D DC
16Ð8 His-Kang Bridge C C C C C
5Ð0 Hou-Hsing Bridge C C C C C
Summer 60Ð9 Feng-Lee Bridge B C B B B
(July) 45Ð6 Erh-His Bridge B C C C C
39Ð5 Pa-Shih-Chou Bridge B C C C C
35Ð5 Tseng-Wen Bridge C C CC CC CC
26Ð2 Ma-San Bridge C C B B B
16Ð8 His-Kang Bridge C C DC C C
5Ð0 Hou-Hsing Bridge C C C D D
Autumn 60Ð9 Feng-Lee Bridge B A A A A
(Nov.) 45Ð6 Erh-His Bridge B C BC B B
39Ð5 Pa-Shih-Chou Bridge B D C D D 35Ð5 Tseng-Wen Bridge C D D D D 26Ð2 Ma-San Bridge C D D D D 16Ð8 His-Kang Bridge C C D D D 5Ð0 Hou-Hsing Bridge C B A A A
Conclusion
Fuzzy set theory has revitalised the need for uncer-tainty analysis in many situations. Although many excellent WQI method applications exist, the fuzzy implications within the input data, the overlapping ranges of relevance between modes and the ambi-guity embedded in the output values systemati-cally weaken decision-making. Failure to address these issues will hinder progress. This analysis is designed to bridge the gap between environmental monitoring, water quality classification and man-agement by comparing the prediction capability of several deterministic and fuzzy classification meth-ods. It not only introduces the latest development of fuzzy classification methodology but also tries to promote fuzzy classification. Two revised FSE techniques were developed, applied and assessed. A case study was used to explore and compare them with the conventional deterministic classifi-cation method, WQI. Without proper consideration
of the fuzziness embedded in the input and out-put data, the classification capability could become pessimistic due to the inherent uncertainties. How-ever, more accurate information may be obtained by using fuzzy information intensity and defuzzi-fication. These newly developed techniques are therefore highly appropriate for monitoring water pollution at local, regional and national levels, including the Total Maximum Daily Load (TMDL) program, so that effective water quality manage-ment strategies can be conducted in the long run (Ning et al., 2000).
Acknowledgements
This manuscript benefited greatly from editorial assis-tance. Three anonymous reviewers also gave us invalu-able suggestions. We are grateful for financial help from the National Science Council (NSC87-2211-E-006-012) in Taiwan, Republic of China.
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