Water Qual Expo Health (2011) 3:25–36DOI 10.1007/s12403-011-0041-z

Fuzzy Based Health Risk Assessment of Heavy MetalsIntroduced into the Marine Environment

Abdullah Mofarrah · Tahir Husain

Received: 20 October 2010 / Revised: 28 February 2011 / Accepted: 2 March 2011 / Published online: 23 March 2011© Springer Science+Business Media B.V. 2011

Abstract There are concerns among scientists about thesignificant amount of heavy metals introduced into the ma-rine environment by the petroleum industry during explo-ration and production phases. The toxicity of heavy metalssuch as arsenic (As), cadmium (Cd), chromium (Cr), andmercury (Hg) are of particular concern, because they maypose major human health risks through consumption of con-taminated food. This study conducts a conservative humanhealth risk assessment study for the selected heavy metalsdischarged into the marine environment through petroleumoperations. Probabilistic risk assessment technique, togetherwith fuzzy set theory, is used to incorporate uncertaintiesinto the risk assessment model. Random and fuzzy variableswere integrated to develop the membership functions to in-dividuals’ risk at different fractiles, and corresponding cu-mulative distribution functions (CDF) of risks were devel-oped. The α-cut concept was used to handle fuzzy arith-metic and Monte Carlo simulation (MCS) was used to carryout the statistical calculations. Using human ingestion path-way, the 90th percentile membership function of cumula-tive cancer risk due to various heavy metals was calculated,and the support of this fuzzy cancer risk is from 1.0E–08 to2.50E–05. Non-cancer risk was evaluated as well and foundto be within the acceptable limits.

Keywords Heavy metals · Produced water · Human healthrisk · Probabilistic risk assessment · Fuzzy set

A. Mofarrah (�) · T. HusainFaculty of Engineering and Applied Science, MemorialUniversity, St. John’s, NL, A1B 3X5, Canadae-mail: abdullah.mofarrah@gmail.com

T. Husaine-mail: thusain@engr.mun.ca

1 Introduction

Produced water (PW) is the largest discharge byproduct gen-erated in oil and gas operations. It contains formation wa-ter, injected water, small volumes of condensed water, andother chemicals added during the oil/water separation pro-cess (USEPA 1993). PW contains significant amounts oftoxic metals as well as industrial additives (OGP 2005). Ex-cessive levels of metals in the marine environment can affectmarine biota, and pose health risks to people through con-sumption of seafood (Andre et al. 1990; Frodello et al. 2000;Canli and Furness 1995; DFO 2001). In many countries fishis the principal source of protein, and fishermen through-out the world harvest numerous tons of sea fish every year(Miller and Tyler 1998). According to King and Riddle(2001) metal pollutants are currently considered to be someof the most toxic contaminants present worldwide. The re-lease of metal ions into the ocean through PW dischargesadversely affects water quality and poses a serious threatto aquatic life and human health. According to research byRobinson and Avenant-Oldewage (1997), two factors con-tribute to the damaging effect of metals: (i) inadequate bio-logical degradation, and (ii) the trend of metals to accumu-late and remain in the biota body. Some heavy metals, evenat very low concentrations, are potentially toxic to living or-ganisms (Ober et al. 1987). Heavy metals in PW can affectmarine life at every trophic level and pose health risks topeople through the consumption of seafood. In this study,human health risk was estimated based on the consumptionof contaminated fish because significant amounts of heavymetals can accumulate in their body tissue (Neff 2002).

Risk assessment studies generally involve identificationof the origin of pollutants, their movement within the en-vironment, and exposure pathways. The resulting humanhealth risk can be calculated by using data, models, and nec-essary assumptions related to the exposure. The goal of risk

26 A. Mofarrah, T. Husain

assessment is to estimate the severity and likelihood of harmto human health from exposure to a substance or activity thatcan cause harm to human health. There are several modelsavailable for health risk assessment (Cohrssen and Covello1989; USEPA 1989, 1991). The application of such methodsdepends on the nature and availability of data. Uncertain-ties in risk estimates may arise from different sources, suchas measurement or estimation of parameters, natural vari-ability in individual’s response, variability in environmentalconcentration of toxicants over time and space, and unverifi-able assumptions in dose-response models or extrapolationsof the results of these models (Kentel and Aral 2004).

Recently, the probabilistic risk assessment (PRA) methodhas become well accepted in analyzing uncertainties in riskestimate. PRA is the general term of risk assessment thatuses probability theory to model the likelihood of differ-ent risk levels in a population or to characterize the uncer-tainty in risk estimates (Maxwell and Kastenberg 1999). Themost widely used PRA approach to characterize uncertaintyin risk assessment studies is Monte Carlo (MC) simulation(USEPA 1996b). The final result of the PRA approach is aprobability distribution which reflects the combination of allinput distributions. However, if the input distributions pro-vide variability, then the output risks may provide some vari-ability. If the input distributions reflect uncertainty, then theoutput risk distribution may provide information about theuncertainty in the estimated risk (USEPA 2001). Moreover,in many cases, the risk assessment parameters contain sub-jective information related to risk and its occurrence, andeither expert judgment or subjective interpretation is usedto define these parameters. In such cases, the PRA analy-sis may not be sufficient to represent the true nature of theparameters’ uncertainty.

Fuzzy set theory, introduced by Zadeh (1965), is a tech-nique which has gained popularity to handle system uncer-tainties as well as subjective interpretations into the risk as-sessment models. A fuzzy number is a fuzzy set on the realline that satisfies the conditions of normality and convexity(Nasseri 2008). Use of fuzzy numbers in the models allowsthe incorporation of uncertainty on parameters, properties,and geometry (Zadeh 1965).

Recently, hybrid models have been gaining popularity inhuman risk assessment (Kentel and Aral 2004; Yong et al.1995; Jianbing et al. 2007), which allow crisp, random, orfuzzy variables in the system.

The human health risk assessment from PW dischargesis associated with several parameters that are naturally vari-able and difficult to characterize by available statistical ap-proaches (Chowdhury 2004). On the other hand, the fuzzyset theory is capable of describing such variability which canproduce results with moderate acceptability (Klir and Yuan1995; Dubois and Parade 1988; Zimmermann 2001).

Fig. 1 Construction of triangular membership function

The objective of this study is to develop a systematic hy-brid procedure combining the fuzzy set theory and the prob-abilistic technique to calculate human health risk throughconsumption of fish contaminated by PW. Based on theavailability in PW and level of toxicity, four heavy metals,arsenic (As), cadmium (Cd), chromium (Cr) and mercury(Hg), were chosen as the contaminants of concern of thisstudy.

1.1 Fuzzy Set Operations

Zadeh (1965) introduced fuzzy set concept to model impre-cise information. There are different types of fuzzy num-bers, among which triangular and trapezoidal fuzzy num-bers are mostly used ones to represent linguistic informa-tion (Lee 1996). A fuzzy number M is a convex normal-ized fuzzy set, which is characterized by a given interval ofreal numbers, each with a grade of membership between 0and 1 (Deng 1999). For simplicity, triangular fuzzy num-ber (TFN) was used in this study. The general form of TFNis shown in Fig. 1. The TFN is defined by three real num-bers, expressed as (l,m,n). The parameters l,m, and n,respectively, indicate the smallest possible value, the mostpromising value, and the largest possible value that describea fuzzy event. The mathematical definition of a triangularmembership function (MF) can be described as (Kaufmannand Gupta 1988):

μ(x/M̃

) =

⎧⎪⎪⎨

⎪⎪⎩

0, x < l,

(x − l)/(m − l), l ≤ x ≤ m,

(n − x)/(n − m), m ≤ x ≤ n,

0, x > n

The TFNs for this study were developed in such a way thatthe most likely value has a membership grade of unity, con-sidering the fact that the lower and upper bonds have a mem-bership value of zero in that fuzzy set. The arithmetic offuzzy set is little different than regular arithmetic. For ex-ample the fuzzy algebraic operations of two TFNs, namely

Fuzzy Based Health Risk Assessment of Heavy Metals Introduced into the Marine Environment 27

Fig. 2 Human health riskassessment framework

A(l1,m1, n1) and B(l2,m2, n2), are as follows (Kaufmannand Gupta 1988):

A + B = (l1 + l2,m1 + m2, n1 + n2)

A − B = (l1 − n2,m1 − m2, n1 − l2)

A · B = min(l1l2, l1n2, n1l2, n1n2),mostlikely(m1m2),

max(l1l2, l1n2, n1l2, n1n2);and if 0 /∈ (l2, n2), then

A/B = A · B−1

= min(l1/l2, l1/n2, n1/l2, n1/n2),

mostlikely(m1/m2),max(l1/l2, l1/n2, n1/l2, n1/n2)

To incorporate the fuzzy variable in the risk assessmentmodel, the TFN was cut horizontally at a finite number oflevels between 0 and 1 to conduct the α-cut analysis asshown in Fig. 1.

2 Methodology

To estimate the human health risk associated with the heavymetals in PW, the fuzzy based risk assessment approach pro-posed by Kentel and Aral (2004) was modified to develop asystematic procedure, which is composed of the followingphases: (1) prediction of exposure concentration for the fish,(2) computation of chronic daily intake by human through

ingestion of fish, and (3) characterization of the health risk.Figure 2 shows the fuzzy based hybrid health risk assess-ment concept.

2.1 Prediction of Exposure Concentration for the Fish

Once PW is discharged into the ocean, it is diluted and dis-persed. As a result, the pollutant concentration decreasesas the effluent travels away from the discharge point. Hy-drodynamic modeling plays an important role in predict-ing the rate of pollutant dispersion and dilution after dis-charge. There are various models available to estimate thedilution of PW in the ocean (Huang et al. 1998; Lee andCheung 1991; Mukhtasor 2001; Proni et al. 1996). Com-pared with the other studies, dilution results of Mukhtasor’s(2001) model are found to be more realistic (Chowdhury2004). To predict environmental concentration, Mukhtasor’s(2001) dilution model was used in this study as follows:

SQ

uz2= (0.13)

(z

lb

)(−0.31)

+ (0.46)e(−0.22)/(z/ lb) (1)

where S = dilution in centerline of the plume, Q = PWdischarge rate (m3/s), u = ambient water velocity at dis-charged location (m/s), z = water depth above the dischargepoint (m), lb = vertical distance at which effluent velocityreduced to ambient velocity (m) which is calculated as fol-lows:

lb = Qg(ρa − ρo)

u3ρa

(2)

28 A. Mofarrah, T. Husain

where g = acceleration due to gravity = 9.81 m/s2, ρa =sea water density (kg/m3), ρo = PW density (kg/m3). Thebulk dilution (Sb) was predicted as Sb = 2.01S for z/lb ≤0.1 and Sb = 1.74S for z/lb ≥ 10. For the transition stage,the Sb was calculated based on interpolation suggested byMukhtasor (2001). The dilution and dispersion of the out-fall plumes are governed by the ambient flow characteristics(Huang et al. 1996). Once the discharged plume achievesambient velocity, the far field dispersion occurs, and the re-gion between the far field and the discharge points is knownas the near field (Doneker and Jirka 1990; Huang et al. 1996;Mukhtasor 2001). The plume rises in the near field re-gion and surface impingement takes place in the regionknown as the control volume zone (Huang et al. 1996;Mukhtasor 2001). Generally, bulk dilution is used to calcu-late the pollutant’s concentration within the control volume;the physical concentration at this region can be determinedas (Huang et al. 1996):

Cw(x,y) = Co

Sb(x,y)

(3)

where Co = initial pollutant concentration, Cw = predictedenvironmental concentration, and x, y represent the spacecoordinates.

The area of the control volume zone is variable, and theinfluence of this zone is generally less than 100 m from thepoint of discharge (Mukhtasor 2001). Based on this infor-mation, this study assumed the control volume zone 100 mfrom the point of discharge, which provided a conservativecalculation for this assessment.

The PW discharge rate (Q) varies from platform to plat-form. To estimate the human health risk, this study consid-ered a constant Q of 0.212 m3/s suggested by Mukhtasor(2001). The variation of Q occurs over a long period of timeduring the production phase; thus PW discharge rate can beassumed as constant at its maximum level.

The ambient water velocity (u) in the ocean generallyvaries between 0.03 and 0.3 m/s (Brandsma and Smith1996; Smith et al. 1996). The USEPA (1995) estimated anambient water velocity of 0.05 m/s for the Louisiana bay. InEastern Canada this value varies between 0.033 and 0.253m/s with a most likely value of 0.096 m/s (Chowdhury2004). Huang et al. (1996) used average u of 0.202 m/swith standard deviation 0.107 m/s in their study. Based onthe collected information on u, a lognormal distribution withlog mean and standard deviation of 0.25 and 0.125, respec-tively, was estimated for this study.

According to USEPA (1995), sea water density (ρa)

ranges between 1005 and 1027 kg/m3; the arithmetic meanof these two values (i.e., 1038 kg/m3) was used in this study.

According to Brandsma and Smith (1996), density of PW(ρo) is 988 kg/m3. Smith et al. (1996) suggested ρo value

of 1014 kg/m3. Chowdhury (2004) used various PW den-sity ranges from 988 to 1014 kg/m3. Based on the literatureinformation and data variability, this parameter was mod-eled as a fuzzy variable, and a TFN with the minimum, themost likely value and the maximum value of 988, 1005 and1014 kg/m3 respectively (i.e., TFN (988, 1005, 1014)) wasselected for the present study.

The water depth above the discharge point (z) is highlyvariable and it is the most dominant factor in predicting dilu-tion of pollutants. Mukhtasor (2001) used a variable depth ofdischarge ranging from 8 to 20 m. This depth varies between2.5 and 150 m, depending on the location and type of plat-form (Brandsma and Smith 1996; Meinhold et al. 1996). Thez value is between 1.3 and 5 m in Louisiana bay, while in theBass Strait, this depth is approximately 12 m (Brandsma andSmith 1996; Meinhold et al. 1996). Based on the literaturereview, z is represented as a TFN (5, 12, 25).

2.2 Estimation of Chronic Daily Intake

The chronic daily intake (CID) (mg/kg day) of heavy metalsvia the ingestion of fish was calculated as (USEPA 1991):

CDI = Cf × FIR × FR × EF × ED × CF

BW × AT(4)

where FIR = fish ingestion rate (g/day), FR = fractionof fish from contaminated sources, EF = exposure fre-quency (days/year), BW = human body weight (kg), ED =exposure duration (years), CF = conversion factor forfish tissue concentration and fish ingestion (10−6),AT =average time in days, and Cf = chemical concentration infish tissue (µg/kg). According to Chowdhury (2004), Cf

can be calculated as:

Cf = Wc

Fed × Wt

(5)

where Wc = total accumulated contaminants in a fish (µg),Fed = fraction of edible part of fish, Wt = weight of fish(kg). Wc can be calculated as follows (Chowdhury 2004):

Wc = (Cexp × BCF × Wt × FL) (6)

where FL = lipid content in a fish (µg/kg), BCF =bioconcentration factor, and Cexp = exposure concentration(µg/l) which is computed as (Chowdhury 2004):

Cexp = Cw × p × BAF (7)

where p = exposure probability of fish in the contaminatedwater (assumed 100%), BAF = bioavailable fraction, Cw =predicted environmental concentration. Combining (5), (6)and (7) results in (8):

Cf = Cw × p × BAF × BCF × FL

Fed

(8)

Fuzzy Based Health Risk Assessment of Heavy Metals Introduced into the Marine Environment 29

Table 1 Fuzzy convention for prediction of bulk dilution

Crisp values Random parameters Simulation Fuzzy parameter CDF multiple with α-cut Output

Constant Distributions MCS and generate CDF αlower CDF multiple α-cut low CDF of risk at α-cut low

Constant Distributions MCS and generate CDF αupper CDF multiple α-cut high CDF of risk at α-cut high

Finally, the cumulative cancer risk (CR) from As, Cd, Cr andHg was calculated by adding the chronic daily intake valuesmultiplied by the corresponding slope factors for these fourheavy metals as follows:

CR =n∑

i=1

CIDi × SFi (9)

where SFi = carcinogenic slope factor for the pollutanti (mg/kg day)−1, n = the number of pollutants. CDIi =chronic daily intake value for the pollutant i (mg/kg day),i = 1,2,3,4, representing As, Cd, Cr and Hg.

The fuzzy based hybrid risk assessment model (Fig. 2)starts with the identification of different variables in a riskassessment model. For this modeling, experts can choosea parameter as fuzzy, random variable or constant. Basedon the available information for this study, (9) is simpli-fied as:

CR =n∑

i=1

(Cw × FRI × BCF

BW

)× (FL × ED)

⇑ ⇑fuzzy variables random variables

×(

FR × EF × P × BAF × CF × SFi

Fed × AT

)

⇑constants (10)

The combined non-carcinogenic risk is normally ex-pressed by a dimensionless term called hazard index (HI).This is simply the ratio of the chronic daily intake to the ref-erence dose. For this study, the HI is written in hybrid riskassessment form as follows:

HI =n∑

i=1

(Cw × FRI × BCF

BW

)× (FL × ED)

⇑ ⇑fuzzy variables random variables

×(

FR × EF × P × BAF × CFi

Fed × AT × RfDi

)

⇑constants (11)

where Rf Di = carcinogenic reference dose for the pollutanti (mg/kg day). For each fuzzy variable, five levels of α-cut,

0, 0.25, 0.50, 0.75 and 1.0, are used separately. Monte Carlosimulation (MCS) is applied to generate cumulative distribu-tion functions (CDFs) with random variables and constants.The CDFs are multiplied separately with upper and lower α-cut levels of each fuzzy variable to generate combined riskCDFs (i.e., one for lower and one for upper level of α-cut) asshown in Table 1. Finally, for each α-cut level, risks mem-bership functions (MFs) at different fractile of risk are de-veloped. The following sections describe the application ofthe fuzzy based risk assessment technique.

2.3 Estimation of Risk Assessment Parameters

The data for fish edible parts can be calculated as the sumof the moisture and lipid content in a fish. According tothe USEPA (1996), the fraction of edible parts of fish (Fed)

ranges between 64% and 87% with a mean value of 78%of whole fish, which is used for this study. The Storage andRetrieval database (STORET 2007) reported that mean lipidpercent (FL) in edible parts of fish varies between 0.8% and4.5%, and the whole body percent lipid ranges from 3.8% to6.3% for various groups of fish species. Conversely, the Na-tional Study of Chemical Residues (NSCRF 2007) databasereported that the lipid content in the edible part of a fishranges from 1.6% to 4.9%. This data shows a lognormaldistribution with mean and standard deviation of 1.125 and1.021, respectively, which is used for this study.

The available information suggests that the ingestion ofmarine fish by humans is almost 50% of their total fishconsumption (USEPA 1996a; Schultz et al. 1996; Dellen-barger et al. 1993). The total of marine fish ingested byhumans might not have been exposed to the PW plume,and thus the use of 50% contaminated fish ingestion (FR)will still provide a conservative prediction in risk estima-tion.

Bioconcentration factors (BCFs) are used to assess pol-lutant residues in aquatic organisms to the pollutant concen-tration in ambient waters. From the literature review, thefish BCF values for As found range from 4 to 114 l/kg(USEPA 1986; Clement Associates 1988). Fish BCF valuefor Cd ranging from 20 to 300 l/kg is reported in litera-ture (John et al. 1987; Taylor 1983; Atchison et al. 1977;Middaugh et al. 1975; USEPA 1986). Fish BCF for Cr hasbeen reported ranging from 1 to 16 l/kg (Clement Asso-ciates 1988; USEPA 1986). High accumulation of Hg in fish

30 A. Mofarrah, T. Husain

Table 2 Parameters used in the various models

Parameters Symbol/unit Type Distribution References

PW discharge rate Q (m3/s) 0.212 Mukhtasor (2001)

Acceleration due to gravity (g) m/s2 Constant 9.80 Mukhtasor (2001)

Ambient water velocity (u) m/s Lognormal μ = 0.25, σ = 0.125 Section 2.1

Water depth above the discharge point (z) m Fuzzy TFN (5, 12, 25) Section 2.1

Sea water density (ρa) Constant 1038 USEPA (1995)

PW density (ρo) kg/m3 Fuzzy TFN (988, 1005, 1014) Section 2.1

Averaging time AT (days) Constant 25, 550; for cancer risk estimation USEPA (1999)

10, 950; for cancer risk estimation

Exposure frequency EF (days/year) Constant 350 USEPA (1991)

Exposure duration ED (years) Lognormal μ = 5.32, σ = 3.09 Benekos et al. (2007)

Body weight BW (kg) Fuzzy TFN (55, 70, 85) Section 2.3

Fish ingestion rate FIR (g/day) Fuzzy TFN (40, 105, 170) Section 2.3

Bioconcentration factor BCF (l/kg) Fuzzy TFN of As (4, 54, 114) Section 2.3

TFN of Cd (20, 113, 300)

TFN of Cr (IV) (1, 10, 19)

TFN of Hg (3190, 4095, 5000)

Fraction of contaminated fish ingested FR (%) Constant 50 USEPA (1996a, 1996b, 1997)

Schultz et al. (1996)

Bioavailable fraction BAF Constant BAF of As = 1 USEPA (1996a, 1996b)

BAF of Cd = 0.994

BAF of Cr = 0.993

BAF of Hg = 0.850

Fish edible parts Fed (%) Constant 78 USEPA (1996a, 1996b)

Lipid percent in fish FL (µg/kg) Lognormal μ = 1.125, σ = 1.021 Section 2.3

Carcinogenic slope factor SF (mg/kg day)−1 Constant Oral SF of As = 1.5E+00 IRIS data base

Oral RfD of Cd = 1.5E+01

Oral RfD of Cr(IV) = 4.2E−01

Reference dose RfD (mg/kg day) Constant Oral RfD of As = 3.0E−04 IRIS data base

Oral RfD of Cd = 1.0E−03

Oral RfD of Cr(IV) = 3.0E−03

Oral RfD of Hg = 3.0E−04

tissues ranging from 3190 to 5000 l/kg is reported in liter-ature (USEPA 2005b; Clement Associates 1988). Due to awide data variation in literature, this study considered BCFas fuzzy variable and generated fuzzy TFNs are shown inTable 2.

Human fish ingestion rate (FIR) is highly variable param-eter, which depends on the people’s behavior. According toUSEPA (1997, 2005a), the fish ingestion rate varies from70 to 170 g/day for adult populations. It depends on sev-eral factors, such as population habit, sufficient supply, fishprice, income, education level of the community, and con-sumer preferences. Considering all the factors, this studyassumed fish ingestion rate as a fuzzy variable, and TFN isgenerated as reported in Table 2.

According to the USEPA (1999), human body weight(BW) is a variable parameter, and the average body weight

for adults can be considered 70 kg. Considering the uncer-tainty, this parameter is considered as fuzzy variable and aTFN is generated as shown in Table 2.

The metal composition in PW varies depending on thewell characteristics and properties of the injection water(OGP 2005). For this study, the metal concentration datawas compiled from different sources (Table 3). Consider-ing the high variability in data, metals concentrations in PWare modeled as fuzzy variables. The TFNs of metals con-centrations in PW were generated assuming the min andmax values of the data set as the smallest possible value andthe largest possible value, respectively; the most promisingvalue of the TFN was selected by taking the arithmetic meanof the rest data (Table 3). For example, the TFN of arsenicis (1.5, 6.85, 10.80).

Fuzzy Based Health Risk Assessment of Heavy Metals Introduced into the Marine Environment 31

Table 3 Typical heavy metal concentration in produced water (µg/l)

Heavy metals Treated PW* Gulf of Mexico Java sea six platform TFNs of metal concentration (Co) (µg/l)

avg min avg max min avg max

As 10.80 nr nr nr 1.5 4.7 9 TFN (1.5 , 6.85, 10.80)

Cd 22.80 nr 27 98 nd 0.5 nd TFN (0.5, 24.9, 98)

Cr 128.0 nr 186 390 7.5 124 185 TFN (7.5, 155.8, 390)

Hg 0.58 0.06 nr 0.19 0.004 0.006 0.012 TFN (0.004, 0.067, 0.58)

Note: nr: data not reported; nd: data not detected. Data compiled from Wideman (1996)*, Smith et al. (1996), Stephenson (1992), Stephenson etal. (1994) and Neff (1997, 2002)

3 Interpretations of Fuzzy Risk

Using framework in Fig. 2 provides fuzzy human health risk.In order to decide whether the resulting fuzzy health riskis acceptable, it should be compared with a crisp guidelinevalue. The comparison of a crisp value with another crispvalue is straightforward, but the comparison of a fuzzy num-ber with a crisp value (assuming the guideline risk is a crispvalue) is not straightforward (Guyonnet et al. 1999). In orderto compare fuzzy risks with crisp guideline values, the pos-sibility and the necessity measures suggested by Dubois andParade (1988) were used this study. The possibility (ψ) thatthe proposition (PFHR ≤ G) is true can be defined (Duboisand Parade 1988) as:

ψ(PFHR ≤ G) = Sup minx

[μPFHR(x),μG(x)

](12)

where μPFHR(x) = membership function of predicted fuzzyhealth risk (PFHR) for any value of x,μG(x) = membershipfunction of guideline crisp value (G) for any value of x :μG(x) = 1 if x ≤ G and 0 if x > G, Sup = largest value offuzzy number, and min = minimization operator. Similarly,the necessity measure Π is defined as:

Π(PFHR ≤ G) = Inf maxx

[1 − μPFHR(x),μG(x)

](13)

where Inf = smallest value and max = maximization op-erator. Various distinguishing scenarios for possibility andnecessity measures can be found elsewhere (Dubois and Pa-rade 1988).

4 Results and Discussion

For each fuzzy variable, the TFN was cut horizontally ata finite number of levels between 0 and 1 to conduct theα-cut analysis. At each α-cut level, the model was run todetermine the minimum and maximum (i.e., one for lowerand one for upper level of alpha-cut) possible values of theoutput. This information was then directly used to constructa joint cumulative distribution function (CDF) with random

variables and constant parameters as shown in Table 1. TheMCS with 10,000 iterations were used in this case. Finally,the corresponding fuzzy membership functions (MFs) of theoutput were generated at different α-cut levels.

Using (1) the CDFs of bulk dilution (Sb) were gener-ated at 0.25, 0.50, 0.75 and 1.0 α-cut levels as shown inFig. 3. Drawing a horizontal line cutting through the CDFs,the FMF of Sb for 90th fractile was generated (Fig. 3). Forexample, the values of i, j, k in Fig. 3 represented the 90thfractile values of FMF of Sb. Here, i and k represented theSb at 0.25 α-cut and j represented the most likely value ofSb (i.e., α-cut = 1). Applying (3), environmental concentra-tion (Cw) of metals was estimated using this 90th fractileFMF of bulk dilution at 0.25 α-cut. The TFNs of Cw areshown in Fig. 4.

The CDFs of cumulative cancer risk (i.e., one for lowerand one for upper limit of α-cut) and corresponding FMFswere generated at 0, 0.25, 0.50, 0.75 and 1.0 α-cut levels asshown in Fig. 5. For each α-cut level, FMFs were generatedat 30th, 60th and 90th fractiles of risk shown in Fig. 6. Ascan be seen from Fig. 6, the support of the risk membershipfunction provides the possible ranges of the risk for the in-dividuals at the corresponding fractile (0 α-cut levels). Therisk value corresponding to a membership value of 1.0 is themost likely risk to be occurred for the associated fractile.

Health regulations and water quality guidelines use 90thpercentile risk for decision making purpose (USEPA 1991).Hence, risk FMFs at 90th fractile was considered for furtherinterpretations.

The predicted cumulative cancer risk at 90th fractile isof 1.10E–07 to 2.5E–05 at 0.25 α-cut (Fig. 6a); 1.7E–06 to1.65E–05 at 0.50 α-cut (Fig. 6b); and 4.0E–06 to 1.25E–05at 0.75 α-cut levels (Fig. 6c). Due to lack of toxicity data,cumulative cancer risk was estimated only for arsenic, cad-mium and chromium. To compare the estimated total can-cer risk with the standard acceptable risk, the possibility(ψ) and necessity measures (Π) criteria described in Sect. 3were used. Different regions in the world use a 1 in 1 million(10−6) cancer risk as the most acceptable risk level (USEPA1991). However, cancer risk ranging from 1 in 10,000 (or

32 A. Mofarrah, T. Husain

Fig. 3 CDF and correspondingmembership function for bulkdilution

Fig. 4 TFNs of environmentalconcentrations

Fig. 5 CDFs of cumulativecancer risk for different α-cutlevels

Fuzzy Based Health Risk Assessment of Heavy Metals Introduced into the Marine Environment 33

Fig. 6 The membership function (MF) of risk to individuals at 30th,60th and 90th fractiles, (a) for α-cut 0, 0.25, and 1.0 level, (b) for α-cut0, 0.5, and 1.0 level, (c) for α-cut 0, 0.75, and 1.0 level

1 × 10−4) to 1 in 1,000,000 (or 1 × 10−6) could be con-sidered as an acceptable regulatory limit for human healthrisk assessment (Graham 1993; Kelly 1991; Lohner 1997;Travis et al. 1987; USEPA 1991). In order to compare thepredicted fuzzy cancer risks, three different crisp values,such as 10−4,10−5, and 10−6, were considered as guide-line values. At highest guideline risk level (10−4), the possi-bility of predicted 90th fractile cancer risks was found wellacceptable for different scenarios of α-cut levels (Fig. 7),in this case both the possibility (ψ) and necessity measures(Π) are 1.0. If we compare the predicted cancer risk with10−5 guideline value, the possibility (ψ) measure was found1.0 and the necessity measures (Π) were found to be 0.58,0.70 and 0.90 corresponding to 0.25, 0.5 and 0.75 α-cut level(Fig. 7). On the other hand, 90th fractile predicted cancerrisk exceeded the guideline limit of 10−6 for all levels of α-cut (i.e., 0.25, 0.5 and 0.75). In this case the necessity mea-sure is zero with β of 0.45 only for 0.25 α-cut level as shownin Fig. 7. To provide a clear picture of the predicted cancerrisks, 90th percentile β and Π were also estimated as shownin Fig. 7, which is shown fairly below the risk level of 10−4.However, some level of human cancer risk is expected forthe population, if we consider 10−6 and 10−5 as guidelinerisk levels.

The sum of non-cancer risks associated by all pollutantsis called hazard index (HI). An HI less than 1 indicates thatthe predicted risk unlikely to pose potential human healthrisks. On the other hand, an HI greater than 1 indicates po-tential adverse health effects (USEPA 1989, 1995). For thisstudy, HI was estimated for As, Cd, Cr and Hg. The CDFsand corresponding 90th fractile FMFs of HI were generatedat 0, 0.25, 0.5, 0.75 and 1.0 α-cut levels (Fig. 8). The 90thfractile FMFs of HI were found in the range of 0.028 to0.332 at 0, 0.25 and 1.0 α-cut levels (Fig. 8a); 0.041 to 0.186at 0, 0.50 and 1.0 α-cut levels (Fig. 8b); and 0.058 to 0.118at 0, 0.75 and 1.0 α-cut levels as shown in Fig. 8c.

At the acceptable non-cancer risk level (i.e., 1.0), the pos-sibility of predicted 90th fractile HIs were found well ac-ceptable for different scenarios of α-cut levels, in this caseboth the possibility (ψ) and necessity measures (Π) werefound to be 1.0.

The 90th fractile FMFs of HI were mapped with a lin-guistic scale as follows: very low (VL), low (L), slightlylow (SL), medium (M), slightly medium (SM), slightly high(SH), high (H) and very high (VH), ranging between 0.01and values greater than 1.0 to provide the qualitative infor-mation of the HIs (Fig. 9). The predicted HIs were foundto be between very low and slightly low. From this study,it is clear that the non-cancer hazard from metals intro-duced into the marine environment through PW dischargedis within acceptable ranges. However, some level of cancerrisks, compared to the 1.0E–05 and 1.0E–06 guideline limit,is expected from this study. The developed risk membership

34 A. Mofarrah, T. Husain

Fig. 7 Interpretations of predicted 90th fractile cancer risk

Fig. 8 Fuzzy membershipfunctions of HI

Fig. 9 Linguistic scales of HI

function provided meaningful information for the analyst.The support of the risk membership function provides in-formation about the range of resulting uncertainty. For ex-ample, uncertainty associated with risk that has small sup-

port is respectively smaller than a larger support. The α-cutplays an important role in the risk estimation, as well as forrisk management. The lower α-cut covers a wider range ofuncertainty than the higher α-cut. For decision making pur-

Fuzzy Based Health Risk Assessment of Heavy Metals Introduced into the Marine Environment 35

pose, the selection of α-cut is critical and detailed assess-ment is needed.

5 Conclusions

This study conducted a human health risk assessment ofheavy metals introduced in marine environment through PWdischarge. The fish ingestion pathway was used to estimatethe cancer and non-cancer risk. A hybrid approach com-bining probability and fuzzy possibility theory was used inthis study. The predicted human health risks from heavymetals in PW are likely to be within regulatory acceptableranges. However, long-term effects from toxic metals can-not be ignored. The predicted fuzzy risk is compared withcrisp guideline values with the help of possibility and thenecessity measures. For simplicity, this study used triangu-lar fuzzy number; however, membership functions for fuzzyvariables do not need to be triangular. If other membershipfunctions are used as input variables, the computational pro-cedures of this methodology would not alter but the shapeof the resulting fuzzy risk would change.

Acknowledgement Financial support provided by the Natural Sci-ence and Engineering Research Council of Canada (NSERC) is highlyappreciated.

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