incorporating the lcia concept into fuzzy risk assessment as a tool for environmental impact...

ORIGINAL PAPER

Incorporating the LCIA concept into fuzzy risk assessmentas a tool for environmental impact assessment

Kevin Fong-Rey Liu • Chih-Yuan Ko •

Chihhao Fan • Cheng-Wu Chen

Published online: 23 August 2012

� Springer-Verlag 2012

Abstract Environmental impact assessment (EIA) is a

procedural tool for environmental management that iden-

tifies, predicts, evaluates and mitigates the environmental

impact of development proposals. In the process of EIA,

EIA reports, prepared by developers, are expected to

delineate the environmental impact, but in practice they

usually determine whether the amounts or concentrations

of pollutants comply with the relevant standards. Actually,

many analytical tools can improve the analysis of envi-

ronmental impact in EIA reports, such as life cycle

assessment (LCA) and environmental risk assessment

(ERA). Life cycle impact assessment (LCIA) is one of

steps in LCA that takes account of the causal relationships

between environmental hazards and damage. Incorporating

the concept of LCIA into an ERA as an integrated tool for

the preparation of EIA reports extends the focus of the

reports from the regulatory compliance of the environ-

mental impact, to determine the significance of the envi-

ronmental impact. Sometimes, when using integrated tools,

it is necessary to consider fuzzy situations, because of a

lack of sufficient information; therefore, so ERA should be

generalized to a fuzzy risk assessment (FRA). Therefore,

this paper proposes the integration of a LCIA and a FRA as

an assessment tool for the preparation of EIA reports,

whereby the LCIA clearly identifies the causal linkage for

hazard–pathway–receptor–damage and then better explain

the significance of the impact; furthermore, a FRA copes

with fuzzy and probabilistic situations in the assessment of

pollution severity and the estimation of exposure proba-

bility. Finally, the use of the proposed methodology is

demonstrated in a case study of the expansion plan for the

world’s largest plastics processing factory.

Keywords Fuzzy risk analysis � Life cycle impact

assessment � Fuzzy logic � Environmental impact

assessment

1 Introduction

Environmental risk assessment (ERA) is a widely used

analytical tool in environmental management. ERA is

founded on the concepts of hazard and risk. An environ-

mental hazard is an object, event or situation with the

potential to cause damage to physical surroundings,

resources, ecosystems, humans, etc. An environmental risk

refers to the severity of the damage and the likelihood that

the damage will actually occur. Five stages have been pro-

posed for a wide-ranging ERA (DEFRA 2011; RSC 2008) as

follows (see Fig. 1). Firstly, problem formulation, some-

times also known as hazard identification, typically involves

the identification of the causal linkage for hazard–pathway–

receptor-damage. Secondly, release assessment determines

the severity of a hazard, based on a consideration of its

K. F.-R. Liu (&) � C. Fan

Department of Safety, Health and Environmental Engineering,

Ming Chi University of Technology, New Taipei City 24301,

Taiwan, ROC

e-mail: [email protected]

C. Fan


C.-Y. Ko

SG Development Environmental Consultants Ltd.,

51591 Changhua, Taiwan, ROC


C.-W. Chen

Institute of Maritime Information and Technology, National

Kaohsiung Marine University, Kaohsiung 80543, Taiwan, ROC


123

Stoch Environ Res Risk Assess (2013) 27:849–866

DOI 10.1007/s00477-012-0621-x

magnitude, spatial extent and temporal duration. Thirdly,

exposure assessment has two components: the probability

that the hazard will occur and the probability or degree of the

receptors being exposed to the hazard. Fourthly, dose–

response assessment considers the probability or degree of

damage that results from exposure to standardized hazards

(hazards that have standard values). The final important step

is risk characterization, which simultaneously evaluates the

significance of a risk by considering the likelihood that the

hazard will occur and the severity of the hazard.

Fuzzy risk assessment (FRA) during an ERA deals with

situations where some assessments are performed using

fuzzy information. For example, an assessment of hazard

severity can be a subjective decision-making process which

is usually modeled by fuzzy logic (Zadeh 1996). The

evaluation of the probability of a receptor becoming

exposed to a hazard or the assessment of the probability of

damage resulting from exposure to a standardized hazard

can involve precise numbers or probability distributions.

However, these numbers and distributions may be assigned

through expertise or experience, if information is insuffi-

cient. Such cases are usually fuzzy and can be converted

into possibility distributions (Zadeh 1978).

Life cycle assessment (LCA) is another widespread ana-

lytical tool for environmental management. The term LCA is

generally reserved for the analytical procedure or method

that includes the compilation and evaluation of the inputs

and outputs and the potential impact of a product or process

throughout its life cycle (ISO 14040 2006). One important

step in LCA is the life cycle impact assessment (LCIA),

which considers the causal relationships between environ-

mental hazards and damage and devises a methodology to

assess the level of damage. Thus, incorporating the LCIA

concept into an ERA (or FRA) can help to identify the causal

linkage for hazard–pathway–receptor–damage, in problem

formulation. It can also aid a better understanding of the

environmental significance, during risk characterization.

Indeed, the combination of a LCIA and an ERA (or FRA) is a

beneficial tool for environmental management.

Environmental impact assessment (EIA) is a procedural

tool which involves the processes of identification, predic-

tion, evaluation and mitigation of the biophysical, social and

other relevant effects of development proposals, before

major decisions and commitments are made (Petts 1999).

Development proposals for which there is a concern of

adverse impact on the environment should prepare EIA

Hazard i

Spatial extent (Ei)Hazard severity (Si)

S=f1(M, E, D) Severitytransformation

(STi)

Frequency of hazard occurrence (Fi)

Magnitude (Mi)

Temporal duration (Di)

Direct or indirecteffect j

Standard value (SVi)

Standard severity (SSV-i)SSV=f1(ST, E, D)

Receptor k

Probability of receptor being exposed to effect (P1-j)

Probability of damage resulting from exposure to effect (P2-jkl)

Risk of damage l (Rjkl)R=f2(ST, F, P1, P2)

Damage l

Level of damage resulting from exposure to hazard

Dose-response assessment

Level of receptor being exposed to hazard

Exposure assessment

Risk characterization

Individual receptor

Hazard

Pathway

Receptor

Damage

Problemformulation

Release assessment

Magnitude

Spatial extent

Temporal duration

A group of receptors

Probability or frequency of hazard occurrence


Probability of receptors being exposed to hazard

Probability of damage resulting from exposure to hazard

Exposure assessment

Hazard

Pathway

Receptor

Damage

Problem formulation

Release assessment

Magnitude

Spatial extent

Temporal duration

Significance of risk


Probability or frequency of hazard occurrence

Probability or degree of a receptor being exposed to hazard

Exposure assessment

Dose-response assessment

Probability or degree of damageresulting from exposure to

a standardized hazard

Fig. 1 Framework for environmental risk assessment

850 Stoch Environ Res Risk Assess (2013) 27:849–866

123

reports. These reports should then be forwarded to compe-

tent authorities for review. EIA reports are expected to

evaluate environmental impact, but in practice they usually

only detail the amounts or concentrations of pollutants and

ensure that these comply with the relevant standards. Link-

ing a LCIA to an ERA (or FRA) as an assessment tool for the

preparation of EIA reports extends the focus of the report

from the regulatory compliance of the environmental

impact, to assess type and degree of damage that develop-

ment projects can cause. This is helpful to review commit-

tees or stakeholders, when determining the significance of

the environmental impacts. In summary, this study proposes

an integrated framework of a LCIA and a FRA, to take

account of fuzzy conditions in the framework and to use this

as a new analytical tool to help estimate significance in an

EIA. Finally, the expansion plan for the world’s largest

plastics processing factory is used as a case study in order to

demonstrate the use of the tool.

2 Literature review

2.1 Applying fuzzy methods to environmental risk

The relevant studies for the application of fuzzy methods to

environmental risks fall into three categories. The first uses

fuzzified multiple criteria decision making, such as a fuzzy

analytic hierarchy process, fuzzy synthetic evaluation, or a

fuzzy ranking method, to select the best drilling waste

discharge option (Sadiq et al. 2004), to determine the health

risk associated with disinfection by-products (Sadiq and

Rodriguezb 2004), to estimate the aggregated risk of vari-

ous environmental activities, pollution sources, or routes for

a given process (Sadiq and Husain 2005), to select drilling

fluid for offshore oil and gas operations (Tesfamariam and

Sadiq 2006), to rank contaminated sites (Zhang et al. 2009),

or to rank weighted alternatives in watershed ecological risk

management (Hao and Chen 2010) and to assess the water

quality–quantity-ecosystem (WQQE) for a River basin (Liu

et al. 2011). The second category of study views the eval-

uation of environmental risk as a process of subjective

judgment, so fuzzy rule-based methods are used to assess

the risk to human health from radioactive materials in water

(Shakhawat et al. 2006), the cancerous and non-cancerous

risks associated with disinfection by-products in drinking

water supplies (Sadiq et al. 2007), the risk of groundwater

contamination (Li et al. 2007) and the risk of the accidental

release of eco-toxic substances in hazardous plants (Darbra

et al. 2008). The third category fuzzifies probability meth-

ods to evaluate environmental risk. For example, Chen et al.

(2003) integrated fuzzy and stochastic modeling methods to

assess the environmental risk of contaminated groundwater

systems. Guyonnet et al. (2003) combined Monte Carlo

random sampling of probability distribution functions with

fuzzy calculus to estimate human exposure, via vegetable

consumption, to Cadmium in the surficial soils of an

industrial site in the north of France. Kentel and Aral (2004,

2005) proposed fuzzy Monte Carlo analysis to allow the use

of incomplete information with expert judgment in health

risk assessment. Karimi and Hullermeier (2007) employed

fuzzy set theory to complement probability theory, to

express the fuzzy likelihood of natural hazards. Li et al.

integrated fuzzy and stochastic approaches to assess the risk

of petroleum contamination (Li et al. 2003) and suscepti-

bility to asthma due to air pollution (Li et al. 2008). Fuzzy

process capability indices were proposed by Kaya and

Kahraman (2009), to determine the risk levels associated

with the air pollutants in Istanbul. Rehana and Mujumdar

(2009) developed an imprecise fuzzy waste load allocation

model that simultaneously addressed randomness and

imprecision, for water quality management in a river sys-

tem, subject to the uncertainty that had arisen due to partial

ignorance. Mofarrah and Husain (2011) incorporated a

technique for the probabilistic risk of contamination and

fuzzy set theory in a study to assess the risk to human health

risk from selected heavy metals that were being discharged

into a marine environment, because of petroleum opera-

tions. Qin (2011) proposed a fuzzy parameterized proba-

bilistic analysis method, which integrates environmental

transport modeling, fuzzy transformation, probabilistic risk

assessment and fuzzy risk quantification into a general risk

assessment framework, to assess risks associated with

problems of environmental pollution-control.

2.2 Combining LCA and risk assessment

The similarities and differences between a LCIA and a

HERA were thoroughly discussed by Udo de Haes et al.

(2006) and Bare (2006). In short, they noted that specific

HERA studies are usually restricted to one single substance

in a particular site, whereas specific LCIA studies deal with

hundreds of chemicals at a global level. Benetto et al.

(2007) proposed three methods for the combination of LCA

and ecological risk assessment in mineral waste reuse

scenarios: synthesis of the results of LCA and ERA into the

original categories in the LCA; substitution of the LCA

results with ERA results, within the categories of the LCA,

and a definition of the new impact categories that incor-

porate them. Most recent studies have focused on the

second method. For example, Khan et al. (2002) developed

a risk-based LCA framework for process plant design,

which substituted some original impact categories with

additional human health, ecological and security risks.

Sonnemann et al. (2003) and Bare (2006) replaced the

human toxicity impact category with a risk assessment that

considered the pollution dispersion model and population

Stoch Environ Res Risk Assess (2013) 27:849–866 851

123

density. Socolof and Geibig (2006) replaced the non-car-

cinogenic toxicity and ecological toxicity impact categories

in the LCA with the concept of a hazard quotient (HQ).

Nishioka et al. (2002) employed a LCA to assess the

environmental impact of residential insulation and used

pollution dispersion models and epidemiological statistics

to perform an ERA. Carpenter et al. (2007) used the LCA

software, PaLATE, to assess the risk caused by the use of

recycled materials in roadway construction and the

groundwater contaminant transport software, Hydrus2D, to

predict pollution concentrations, in order to improve

PaLATE.

3 Materials and methods

The integrated framework that combines the LCIA concept

with a FRA encompasses the following steps: (1) the use of

the LCIA concept to identify the causal linkage for hazard–

pathway–receptor–damage; (2) the use of fuzzy logic for

release assessment; (3) the use of severity transformation

(ST) to compare with standard values; (4) the estimation of

the frequency of hazard occurrence; (5) the estimation of

the probability that the receptors will be exposed to mid-

point effects; (6) the evaluation of the probability that a

receptor will be exposed to standardized hazards, (7) the

use of the vertex method to compute the risk of damage and

(8) the use of the distance method to defuzzify the risk.

3.1 Use of the LCIA concept to identify hazard–

pathway–receptor–damage

In practice, EIA reports usually detail the amounts or

concentrations of pollutants and ensure that these comply

with the relevant standards. Their scope should be extended

from regulatory compliance to the evaluation of the envi-

ronmental impact, and further to the interpretation of sig-

nificance. Environmental significance refers to whether the

midpoint and endpoint effects caused by pollutants are

important for stakeholders. Initially, the evaluation of sig-

nificance recognizes the possible midpoint effects and

damage (endpoint effects) caused by a hazard and deter-

mines their importance. Existing LCIA methods provide

this means to identify the cause-effect relationship between

hazards, pathways, receptors and damage. This study pro-

poses a three-step procedure to identify the cause–effect

relationship for hazard–pathway–receptor–damage, as

follows.

1. Identification of hazards. In accordance with the

characteristics of the factories studied, some hazards

(pollutants) are selected, as shown in part A of Fig. 2.

For example, the IPCC has identified six greenhouse

gases that cause climate change: carbon dioxide (CO2),

from fossil fuel combustion, forest clearing, cement

production, etc.; methane landfills (CH4), from the

production and distribution of natural gas and petro-

leum, fermentation from the digestive systems of

livestock, rice cultivation, fossil fuel combustion, etc.;

nitrous oxide (N2O), from fossil fuel combustion,

fertilizers, nylon production, manure, etc.; hydroflu-

orocarbons (HFCs), from refrigeration gases, alumi-

num smelting, semiconductor manufacturing, etc.;

perfluorocarbons (PFCs), from aluminum production,

the semiconductor industry, etc., and sulfur hexafluo-

ride (SF6), from electrical transmissions and distribu-

tion systems, circuit breakers, magnesium production,

etc.

2. Identification of pathways. Prior to determining sig-

nificance, a diagram of the causal relationships

between hazards and receptors that includes all of

the relevant pathways allows stakeholders to under-

stand the midpoint effects of a pollution emission, as

shown in part B of Fig. 2. A hazard may cause several

midpoint effects. For example, N2O can simulta-

neously induce climate change and stratospheric ozone

depletion. However, N2O, CO2, CH4, PFCs or SF6 can

also cause a rise in temperature and, may result in a

rise in sea level and flooding.

3. Identification of receptors and their potential for

damage. The type of damage (endpoint effects)

brought about by a midpoint effect depends upon the

receptors, as shown in parts C and D of Fig. 2. For

example, climate change could possibly lead to human

malnutrition, infectious diseases, heat stress and the

loss of biodiversity in ecosystems, resulting in a

decrease in the production of crops and wood.

3.2 Use of fuzzy logic for release assessment (S)

Release assessment estimates the severity of a particular

hazard (S); this is determined by its magnitude (M), spatial

extent (E) and temporal duration (D). The magnitude of a

hazard refers to the concentration of its pollution source,

usually denoted by ppm, mg/L or mg/m3. The geographical

scale of a hazard often extends considerably beyond the

boundaries of the source of the hazard. Failure to consider

the spatial extent of damage may result in the scope of the

risk assessment being too limited (DEFRA 2011). The

spatial extent is expressed as the radius of an area where

the concentrations of pollutants are either higher than the

standard values, or more than double the average concen-

trations in neighboring counties, if the former condition

does not exist. The temporal scale is also an important


123

aspect in release assessment, because damage may be so

prolonged that it can be assumed to be permanent and the

environment beyond recovery (DEFRA 2011). The tem-

poral factor is measured by the duration of emission of

pollution over 1 year.

The appraisal of the severity of a hazard can be a sub-

jective decision-making process. This type of appraisal is

eminently suited to the use of fuzzy logic (Zadeh 1996).

Fuzzy logic is a tool that computes with words, when

modeling qualitative human thought processes, in the

analysis of complex systems and decisions. In fuzzy logic,

qualitative perception-based reasoning is represented by

‘IF-THEN’ fuzzy rules. A rule set for evaluation is shown

in Table 1, where ‘magnitude’, ‘spatial extent’, ‘temporal

duration’ and ‘severity’ are linguistic variables (Zadeh

1975) and ‘very low’, ‘low’, ‘medium’, ‘moderate’, ‘high’

and ‘very high’ are their possible fuzzy values, which are

defined by triangular fuzzy sets, as shown in Fig. 3. A

triangular fuzzy set can be expressed as a 3-tuple (l, m, r),

where l, m, r are the locations of the left, middle and right

vertices of the triangle, respectively. For example, ‘low’

magnitude is expressed as (0, 0, 125), in Fig. 3.

To evaluate the severity of a hazard, 19 rule bases,

containing 513 fuzzy rules, were produced. These 19 rule

bases and their corresponding membership functions were

constructed based on expertise. The fuzzy logic systems are

implemented with the MATLAB Fuzzy Logic Toolbox.

Three factual statements (i.e., Fact 1: NOx magnitude is

48.09 ppm; Fact 2: NOx spatial extent is 2.8 km; Fact 3:

NOx temporal duration is 1 year) are fed into this inference

mechanism and subjected to fuzzy logic (Zadeh 1975). The

theory of fuzzy reasoning is detailed in Appendix 1, but it is

easily explained by a graphical representation as shown in

Figs. 4 and 5. The four major steps to reaching a conclusion

using fuzzy logic, in these figures, are described as follows.

Step 1: Computing compatibilities. Compatibility des-

ignates the similarity of an antecedent. It refers to a fact

having the same linguistic variable or the suitability of a

specific rule regarding several facts that corresponds to the

respective antecedents. For Rule 6, the compatibility of

Fact 1 with ‘NOx magnitude is low’ is C6-1 = 0.770

(Fig. 4a); for Fact 2 with ‘NOx spatial extent is medium’,

the compatibility C6-2 is 0.767 (Fig. 4b); for Fact 3 with

‘NOx temporal duration is high’, the compatibility C6-3 is

TSP

Nuclides

VOCs

CO

NOX

SOX

NH3

BOD

PO43-

PFCs

N2O

CO2

CH4

SF6

HFCs

Pesticide

Heavymetals

Noise

Vibration

A. Hazard(Pollutant)

Increased radiative forcing

Climate change (temperature rise)

FloodingSea level rise

Increased chlorine content of stratosphere

Stratosphericozone depletion

Increased UV-B radiation

Direct exposure

Photochemicalozone formation Increased tropospheric ozone

concentration

Smog episodes (urban)

Conversionreleasing protons

Exposure of leaves

Deposition on soil or water

Decreasing pH

Eutrophication of aquatic systems

Increased algal growth Sedimentation

of dead algae

Reduced light input

Oxygen depletion near bottom

Altered species composition

Human direct exposure or intake

Ecosystem direct exposure

ground-, fresh- or marine water

agricultural or natural soil

Fish or animal meat

Vegetation crop

Exuding Al3+

Reducing nutrient

Direct exposure

Loss of habitats

Ionising radiation

Human

Human

Human

Human

Human

Human

Human

Human

Human

Fish

Crops and woods

Wildlife

Wildlife

Ecosystem

Wildlife

Ecosystem

Ecosystem

Ecosystem

Wildlife

Wildlife

Wildlife

Crops and woods

Crops and woods

Crops and woods

Crops and woods

Fish

Fish

Ecosystem

egamaD.DyawhtaP.B(midpoint effect) (endpoint effect)

Disappearance of species

Loss of biodiversity

Loss of fish catch

Loss of productivity of crops and woods

Malnutrition

Infectious diseases

Heat stress

Immunosuppression

Cataract

Cardiovasculardisease

Respiratory diseases

Human toxicity

Cancer

Psychasthenia

Sleep disorders

ST, F P1 P2C. Receptor

Fig. 2 Overview of the causal relationships between hazards, pathways, effects and possible damage (modified from Udo de Haes et al. 1999)


123

1.000 (Fig. 4c). It should be noted that ‘product’ is chosen

as the t-norm operator, rather than using another more

widely used t-norm operator, ‘min’, because the t-norm

operator, ‘product’, makes the conclusion sensitive to

every input; whereas, only one input controls the conclu-

sion in the case of the t-norm operator, ‘min’. The overall

compatibility of Rule 6 C6 with the three facts is

0.770 9 0.767 9 1.000, so C6 = 0.591 (Fig. 4d). The

compatibilities of other rules are calculated in the same

way.

Step 2: Scaling conclusions. Once the compatibility for

each rule has been calculated, the degree to which the

antecedents have been satisfied for each rule is known. As

shown in Fig. 4d, a new conclusion for Rule 6 is then

inferred by scaling the triangular conclusion, whose height

is C6. The use of the implication operator ‘product’ results

in the scaling of each conclusion.

Step 3: Aggregating scaled conclusions. Inferred con-

clusions with the same linguistic variable must be aggre-

gated. As shown in Fig. 5, the triggered rules are Rules 3,

6, 12 and 15. Aggregation is the process by which the fuzzy

sets representing the scaled conclusions of triggered rules

are combined into a single fuzzy set. In Fig. 5, the final

conclusion is a combination of two triangles, and it is

aggregated as the union of all of the scaled conclusions.

Step 4: Defuzzifying the overall conclusion. In many

cases, the final output of an inference system is a single

number. Defuzzification is a method to justifiably convert a

fuzzy set into a precise value. This study utilized the

center-of-gravity method, which takes the centroid of the

area under the curve of the membership function of a fuzzy

set as the answer. Figure 5 shows that the score of severity

for NOx is 29.5 (S). An analysis of the sensitivity of

operators in fuzzy logic is detailed in Appendix 2.

3.3 Use of ST to compare with standard values (ST)

All outputs of fuzzy logic are linearly transformed so that

their lower bounds (5.23) correspond to 0.0 and the outputs

of standard values (94.8) correspond to 100.0 as shown in

Fig. 6. For example, the standard value of NOx in the

manufacturing processes is 250 ppm, so fuzzy logic infers

a value of 94.8. The result of ST is (29.5 - 5.23)/(94.8 -

5.23) 9 100 = 27.1.

3.4 Estimation of the frequency of hazard occurrence

(F)

The frequency of a hazard occurrence is defined as the

number of occurrences per year, which can be a precise

number, a probability distribution or a possibility distri-

bution. If historical records are insufficient and a precise

frequency or a probability distribution over possible fre-

quencies is not available, the frequencies may be assigned

using expertise or experience. These values are usually

fuzzy and can be converted into possibility distributions

(Zadeh 1978). When the methodology is applied to an EIA,

the frequency is estimated as ‘1’ for a continuous release of

pollutants from a factory.

3.5 Evaluation of the probability of a receptor being

exposed to a midpoint effect (P1)

Further investigation is not required, if no actual or potential

pathway exists between a hazard and the receptor (DEFRA

2011). For example, heavy metal contamination of a soil

poses no risk to humans if there are no residents near the

site. The evaluation of the probability of a receptor being

Table 1 Fuzzy rules for the evaluation of severity

Rule

no.

IF part THEN part

Magnitude Spatial

extent

Temporal

duration

Severity

1 Low Low Low Very low

2 Low Low Medium Very low

3 Low Low High Low

4 Low Medium Low Low

5 Low Medium Medium Low

6 Low Medium High Low

7 Low High Low Low

8 Low High Medium Low

9 Low High High Slightly

low

10 Medium Low Low Very low

11 Medium Low Medium Slightly

low

12 Medium Low High Moderate

13 Medium Medium Low Slightly

low

14 Medium Medium Medium Moderate

15 Medium Medium High Moderate

16 Medium High Low Moderate

17 Medium High Medium Moderate

18 Medium High High High

19 High Low Low Moderate

20 High Low Medium High

21 High Low High High

22 High Medium Low Moderate

23 High Medium Medium High

24 High Medium High Slightly

high

25 High High Low High

26 High High Medium Slightly

high

27 High High High Very high


123

exposed to a midpoint effect (P1) can yield a precise number

or a probability distribution, if sufficient information is

available; otherwise, it can be assigned using expertise or

experience, which is usually fuzzy and expressed by a

possibility distribution. For example, NOx can increase

tropospheric ozone concentration and the probability of the

receptors being exposed to the effect is subjectively esti-

mated as ‘approximately 0.1’, which is represented as a

triangular fuzzy set of the 3-tuple (0.0, 0.1, 0.2).

3.6 Assessment of the probability of damage resulting

from exposure to a standardized hazard (P2)

The probability of damage (endpoint effect) resulting from

exposure to a standardized hazard (P2) is defined as the

percentage of humans, ecosystems, crops and woods,

wildlife or fish production that sustains damage when

pollution reaches standard values. Even when exposed to

the same midpoint effect, the likelihood of damage is

probabilistic and depends on the likely susceptibility of an

individual receptor to the effect. Assessing P2 is an extre-

mely complicated task, which is riddled with uncertainty,

because the relevant knowledge of toxicology, epidemiol-

ogy and ecology is still incomplete. Therefore, it will

become a precise number or a probability distribution, once

the related knowledge is available; otherwise, it can be

assigned subjectively using expertise or experience as a

fuzzy number. For example, NOx, SOx, VOCs or CO can

increase tropospheric ozone concentration and further

cause human respiratory diseases. Their standard values for

the outlet of an emission pipe are 250, 650, 100 and

2000 ppm, respectively. The probability of respiratory

diseases resulting from exposure to the pollution that has

reached standard values is subjectively assessed as

‘approximately 0.3’, which is expressed as a triangular

fuzzy set of the 3-tuple (0.2, 0.3, 0.4). The P2 value of

‘approximately 0.3’ denotes that about 30 % of human

exposure to increased tropospheric ozone concentration

caused by the standard values of the relevant pollutants

induces respiratory diseases.

3.7 Use of the vertex method to compute the risk

of damage (R)

The risk of damage (R) is a function of four variables, ST,

F, P1 and P2:

R ¼ fðST; F; P1; P2Þ ð1Þ

The vertex method was proposed by Dong and Shah

(1987) to compute functions of fuzzy variables and is

applied herein to compute R in Eq. (1). The vertex method

uses an a-cut and the interval analysis technique. Using a-

cut, each fuzzy variable characterized by a convex

membership function is converted into a group of

intervals with various a values. Intervals with the same avalue are processed by interval analysis, which results in an

interval function with the a value. At the a-cut level, the

interval function is denoted as follows:

Ra ¼ f STa;Fa; Pa1; P

a2

� �ð2Þ

where

Ra ¼ RaL;R

aR

� �; STa ¼ aa

1; ba1

� �; Fa ¼ aa

2; ba2

� �;

Pa1 ¼ aa

3; ba3

� �; Pa

2 ¼ aa4; b

a4

� � ð3Þ

The interval computation is equivalent to solving a

minimization problem for the lower bound and a

maximization problem for the upper bound as follows:

1

(x)

Low hgiHmuideM

ppm

(a) Magnitude

1

(x)

Low hgiHmuideM

km

(b) Spatial extent

1

(x)

Low hgiHmuideM

year

(c) Temporal duration

0 7 7.365321

0 10070605040302010

1

(x)

x

(d) Severity (NOx)

80 90

Verylow Moderate

VeryhighHigh

Slightlyhigh

SlightlylowLow

0 25020015010050

4

0 10.80.60.40.2

Fig. 3 Membership functions of fuzzy values for linguistic variables

a magnitude, b spatial extent, c temporal duration and d severity


123

RaL ¼ min f2 st; f; p1; p2ð Þ; Ra

R ¼ max f2 st; f; p1; p2ð Þ ð4Þ

such that st [ [a1a, b1

a], f [ [a2a, b2

a], p1 [ [a3a, b3

a],

p2 [ [a4a, b4

a].

In statistics, the notion of risk is often modeled as the

expected value of an undesirable outcome. Therefore, the

risk of damage is defined as:

R ¼ ST� F� P1 � P2 ð5Þ

That is, R is considered as the fuzzy expected value of the

percentage of humans, ecosystems, crops and woods,

wildlife or fish production that sustains damage. Equation

(5) becomes

RaL ¼ aa

1 � aa2 � aa

3 � aa4; Ra

R ¼ ba1 � ba

2 � ba3 � ba

4 ð6Þ

For example, the ST of NOx is 27.1; F is estimated as ‘1’

for a continuous release of NOx; P1 is subjectively estimated

as ‘approximately 0.1 (0.0, 0.1, 0.2)’ and P2 is

‘approximately 0.3 (0.2, 0.3, 0.4)’. This gives RL0? = 27.1 9

1 9 0.0 9 0.2 = 0.000, RR0? = 27.1 9 1 9 0.2 9 0.4 =

2.168, RL1 = RR

1 = 27.1 9 1 9 0.1 9 0.3 = 0.813 and so

on. As shown in Fig. 7, the result for R is not exact, but is very

Step 1: Computing compatibilities Step 2: Scaling conclusions

1Medium

Rule 6:

250

1 Low

(a)12548.09

C6-1= 0.770

7.3

(b)3.652.8

C6-2= 0.767

1High

C6-3= 1.000

(c)0.5 1

0010

1Low

(d)

C6 = 0.770X0.767X1= 0.591

33.3

Scaled conclusion

Fig. 4 Computing compatibilities and scaling conclusions in fuzzy logic. a magnitude (ppm), b spatial extent (km), c temporal duration (year)

and d severity

Step 3: Aggregating scaled conclusions

Rule 3: Rule 6:

Rule 12: Rule 15:

0010

1Low

sC3 = 0.179

33.3 0010

1Low

sC6 = 0.591

33.3

1

0010

Moderate

sC12 = 0.090

33.3 66.7 0010

1

sC15 = 0.295

Moderate

33.3 66.7

29.5

Step 4:Defuzzifyingthe overall conclusion

0 100

1

s

Severity

0.5910.295

ModerateLowCentroid

Fig. 5 Scaling and aggregating conclusions in fuzzy logic

Output of fuzzy logic Severity transformation

Lower bound=5.230

100Standard value = 94.8

Example value = 29.5

100

0

27.1

Fig. 6 Severity transformation


123

similar to a triangular fuzzy number and can be

approximately represented as a triangular fuzzy set (0,

0.813, 2.168), which gives the fuzzy expected value of the

percentage of humans that suffer respiratory diseases due to

increased tropospheric ozone concentration.

3.8 Use of the distance method to defuzzify risk

The last step is to defuzzify the risk, R, in order to ultimately

obtain a precise number. The center of gravity or distance

methods (Cheng 1998; Chu and Tsao 2002) are widely used

for defuzzification. The two isosceles triangles, A(50, 75,

100) and B(60, 75, 90) shown in Fig. 7 should result in dif-

ferent levels of risk, but they are not distinguishable by either

the center of gravity method or the distance method, because

they have the same centroid, AC(75.000, 0.333), and the

same distance of 75.001 from the centroid to the origin. In

addition, for the purpose of being conservative, the right

wing of the possibility distribution of a risk should be given

more emphasis than the left wing. Therefore, the left wing of

the possibility distribution of risk, R, is reduced to half; that

is, it is multiplied by a weight of 0.5. The weights for the right

and left wings of the possibility distribution of a risk can be

determined by a panel of experts. After scaling down, the left

wing of R becomes a new fuzzy number, R0, with a centroid,

R0C(1.098, 0.295), and the distance, dR0, from the centroid to

the origin, is 1.137, as shown in Fig. 7. The distance, dR0,

indicates the expected value of the percentage of humans that

suffer from respiratory diseases due to increased tropo-

spheric ozone concentration.

4 Case study

4.1 Case description

A plastics factory, established in 1958, covers about

178.9 ha in an industrial zone of Yunlin County, Taiwan. It

is the world’s largest plastics processing factory, generat-

ing plastic products, petrochemical raw materials, elec-

tronic materials, polyester fiber products, etc. In 2009, its

output reached 3.71 million tons and its turnover was up to

US$5.4 billion. In response to market demand, the com-

pany wished to increase the supply of raw materials to 5.03

million tons of products and proposed a US$28.63 billion

expansion plan.

An environmental impact statement (EIS) was submitted

for review, in December 2009. According to the EIS, the

major air pollutants were SOx, NOx, VOCs, CO, TSP and

noise and the primary water pollutants in the treated

wastewater were BOD and PO43-. The emission details are

listed in Table 2. Before the expansion, the emissions of

SOx, NOx, VOCs, CO and TSP were, respectively, 838.6,

886.4, 291.2, 3,047.9 and 272.5 tons/year, which resulted

in concentrations in the emission pipes of 54.35 ppm,

48.09 ppm, 46.48 ppm, 432.31 ppm and 29.59 mg/m3,

respectively. After the expansion, the emissions were pre-

dicted to be 942.5, 1073.2, 416.9, 3047.9 and 341.0 tons,

respectively, and the concentrations in emission pipes were

predicted to be 61.09 ppm, 58.23 ppm, 66.53 ppm,

432.31 ppm and 37.02 mg/m3, respectively. Noise was

forecasted to increase slightly from 65.95 to 66.15 dB,

after the expansion. The treated wastewater was discharged

into the sea at the rate of 187,638 CMD, before the

expansion, but it was forecast to reach 257,638 CMD, after

the expansion. The level of BOD and PO43- were all

maintained within the standards (30 and 4 mg/L). The

relevant magnitudes, spatial extents and temporal durations

are summarized in the third to fifth columns of Table 2.

4.2 Results

The inferred severities of all pollutants (S) are determined

by their magnitude, spatial extent and temporal duration,

using fuzzy logic. These are listed in the second to last

column of Table 2. Using ST, the comparisons of the

inferred severities of all pollutants with the standard values

are shown in the last column of Table 2. Before and after

the expansion, the STs for noise, BOD and PO43- are very

high (denoted by italic values in Table 2), because their

magnitudes are very close to the standard values; the

remainder of the STs are acceptable. After the expansion,

the magnitudes of all pollutions are larger and their spatial

extents are wider, making their STs higher; in particular,

VOCs increase by 29.3 % (from 52.9 to 68.4, denoted by

single-underline in Table 2) and TSP increases by 22.6 %

(from 46.1 to 56.5, denoted by double-underline in

Table 2).

The frequency (F) of occurrence of an environmental

pollutant is defined as the number of occurrences per year

and is ‘1’ for a continuous release. No damage occurs if no

(x)

Risk of damage

0

10075502.1680.813

1 R

(1.098, 0.295)

'RA

B

60 90

µ

Fig. 7 Result for R using the vertex method


123

receptor is exposed to effects. The probabilities of recep-

tors being exposed to midpoint effects (P1) and the prob-

abilities for all damage resulting from exposure to

standardized hazards (P2) are derived from the real situa-

tion, in Fig. 2, and then assigned by experts, in the form of

possibility distributions rather than probability distribu-

tions, due to the lack of sufficient information, as shown in

Table 3.

The damage (endpoint effects) caused by pollutants

through various midpoint effects is summarized in the first

two columns of Table 4. In this study, the risk of damage

(R) is defined as the product of ST, F, P1 and P2. The vertex

method is thereby used to compute R, when any of its

factors are fuzzy. The output is also a fuzzy number, which

is not exact, but is very similar to a triangle and can be

approximately represented as a triangular fuzzy set of the

3-tuple (l, m, r), as shown in Table 4. R is then defuzzified,

in order to obtain a final precise result. The distance

(d) from the centroid (x, y) of R0 (with a scaled left wing of

R) to the origin is employed as the defuzzification method

in this study and is interpreted as the percentage of humans,

ecosystems, crops and woods, wildlife or fish production

that sustains damage. The fuzzy risks of damage and their

defuzzifications are shown in Table 4.

Before and after the expansion, the loss of fish resulting

from BOD and PO43- is severe, because of the high STs, as

denoted by double-underlined values in Table 4. Never-

theless, the risks resulting from VOCs and TSP show the

greatest increases (29.1 and 22.4 %) after the expansion, as

denoted by the bold numbers in Table 4. However, the

greatest absolute increase in the risk of damage is in the

risk of respiratory diseases caused by TSP, which increases

from 14.675 to 17.980, an increase of 3.306; the second

highest absolute increase of 1.594 represents the loss of

productivity of crops and woods caused by VOCs; the third

highest absolute increase is 1.110 for the disappearance of

species caused by VOCs. These absolute increases are all

indicated by single-underlines in Table 4. It should be

noted that although they are the second and third ranked

absolute increases, they represent increases of as much as

29.1 %.

4.3 Discussion

4.3.1 Comparisons with health risk assessment and a LCIA

In the context of an EIA, risk assessment usually charac-

terizes the nature and magnitude of health risks to humans

and ecological receptors from chemical contaminants and

other stressors, that may be present in the environment (US

EPA 2012). Recently, one study reported an assessment of

the health risk from air pollution for the same case study

(Hsiao 2009). It concluded that the average HQ of SO2,

NO2, CO and VOCs at the neighboring Tai-Si township,

from 2007 to 2008, were 1.52 9 10-2, 4.77 9 10-2,

1.35 9 10-2 and 4.76 9 10-2, respectively; the cancer

risk due to benzene (a carcinogenic VOC) is 3.80 9 10-5.

Compared with the results provided by Hsiao, this study’s

method not only assesses the risks of health effects (car-

diovascular disease, psychasthenia, sleep disorders, respi-

ratory diseases and human toxicity), but also assesses the

risks to the ecosystem (loss of biodiversity and disap-

pearance of species) and natural resources (loss of pro-

ductivity of crops, woods, and fish catch), owing to the

addition of a LCIA framework. On the other hand, another

study (Chiu 2011) used a LCIA method (Eco-indicator 99)

to improve the EIA report for the same case study and

found that the damage due to carcinogens, respiratory

organics, respiratory inorganics, climate change, ozone

layer, ecotoxicity and acidification/eutrophication was

1.03 9 10-1 (daly), 2.79 (daly), 3.26 9 10-3 (daly),

1.42 9 10-4 (daly), 1.83 9 10-2 (daly), 6.76 9 10-6

(paf m2 year) and 1.29 9 10-8 (pdf m2 year), respec-

tively. Compared with the results provided by Chiu, this

study’s method further considers the probabilities of the

occurrence of a hazard, of a receptor being exposed to a

hazard, and of damage resulting from exposure to a stan-

dardized hazard, because of the addition of a FRA.

4.3.2 Calculation of joint risks

Various pollutants may cause the same damage through

different midpoint effects. For example, NOx, VOCs and

CO can cause the formation of photochemical ozone and

further cause respiratory diseases. TSP can also directly

cause respiratory diseases. For example, the risks of

respiratory diseases from the four pollutants, after the

expansion, are 1.255 (3.2 km), 2.787 (8.6 km), 1.207

(1.8 km) and 17.980 (8.3 km), respectively, as shown with

a italic values in Table 4. Their joint risk, under the

assumption of independence, is 22.211 within 1.8 km;

21.267 between 1.8 and 3.2 km; 20.266 between 3.2 and

8.3 km; and 17.980 between 8.3 and 8.6 km, as shown in

Table 5. In Table 5, any risk higher than 10.0 is shown

with a italic values and the risks shown with a bold values

indicate values higher than 20.0. Loss of fish catch is as

much as 40.0 within 2.01 km, both before and after the

expansion, because the area is very close to the point of

discharge into the sea. Respiratory diseases also present a

risk of damage, after the expansion, because the joint risk

exceeds 20.0. Respiratory diseases show the greatest

absolute increase (3.750), which implies an increase in the

expected value for the percentage of humans that are the

subject of respiratory diseases.


123

4.3.3 Influence of fuzziness in risk assessment

Fuzziness in probabilities occurs because of a lack of a

complete knowledge of the variability in the exposure of

receptors (P1) and their responses (P2) and it can cause an

extra risk of damage. The wider the right and left wings of

the possibility distribution of a risk, the more the fuzziness

and greater the extra risk represent. Precise probabilities in

risk assessment result in lower risks, as shown in the last

column of Table 5. For example, the risk of respiratory

diseases within 1.8 km after the expansion is 22.211; but

this risk is reduced to 20.159, if no fuzziness exists in P1

and P2.

4.3.4 Reduction of the environmental impact

The combination of a LCIA and a FRA as an assessment

tool for the preparation of EIA reports provides more

information and assists review committees or stakeholders

in understanding the significance of the environmental

impact. Appropriate environmental management plans can

be proposed only after the significance of the environ-

mental impact has been ascertained. For example, if there

is goal to reduce the risk of respiratory diseases, after the

expansion, from 3.750 to below 2.000, by cutting down one

of the four associated pollutants (NOx, VOCs, CO and

TSP), this goal is impossible, even if the emission of NOx

or CO is completely removed. However, it is possible if the

risk of respiratory diseases resulting from VOCs can be

reduced from 2.787 (see Table 4) to 0.594, or the risk of

respiratory diseases resulting from TSP can be reduced

from 17.980 (see Table 4) to 16.135. Obviously, the latter

is easier and less expensive. Accordingly, the ST of TSP,

after the expansion, must be reduced from 56.5 (see

Table 2) to 50.7; its severity (S) must be reduced from 55.8

(see Table 2) to 50.6; its magnitude (M) must be reduced

Table 2 Emission details for the case study and the severity evaluation using fuzzy logic

Pollutant Emission Magnitude Spatial extent

(km)

Temporal duration

(year)

S ST (%)

Standard

SOx Outlet of emission pipes;

manufacturing process;

TSP for 10,000–20,000 N m3/min

650 (ppm) 11.3 1.00 94.8 100

NOx 250 (ppm) 7.3 1.00 94.8 100

VOCs 100 (ppm) 10.8 1.00 94.8 100

CO 2,000 (ppm) 4.5 1.00 94.8 100

TSP 73 (mg/m3) 12.2 1.00 94.8 100

Noise Category VI for factory plant 80 (dB) 1.5 1.00 94.8 100

BOD Discharge point 30.00 (mg/L) 2.35 1.00 94.8 100

PO43- 4.00 (mg/L) 2.35 1.00 94.8 100

Before the expansion

SOx 838.6 (ton/year) 54.35 (ppm) 2.8 1.00 22.2 18.9

NOx 886.4 (ton/year) 48.09 (ppm) 2.8 1.00 29.5 27.1

VOCs 291.2 (ton/year) 46.48 (ppm) 7.1 1.00 52.6 52.9

CO 3,047.9 (ton/year) 432.31 (ppm) 1.8 1.00 31.1 28.9

TSP 272.5 (ton/year) 29.59 (mg/m3) 7.3 1.00 46.5 46.1

Noise – 65.95 (dB) 1.406 1.00 79.3 82.7

BOD 187,638 CMD 30.00 (mg/L) 2.01 1.00 89.7 94.3

PO43- 4.00 (mg/L) 2.01 1.00 89.7 94.3

After the expansion

SOx 942.5 (ton/year) 61.09 (ppm) 3.0 1.00 22.9 19.7

NOx 1073.2 (ton/year) 58.23 (ppm) 3.2 1.00 32.2 30.1

VOCs 416.9 (ton/year) 66.53 (ppm) 8.6 1.00 66.5 68.4

CO 3,047.9 (ton/year) 432.31 (ppm) 1.8 1.00 31.1 28.9

TSP 341.0 (ton/year) 37.02 (mg/m3) 8.3 1.00 55.8 56.5

Noise – 66.15 (dB) 1.407 1.00 79.4 82.8

BOD 257,638 CMD 30.00 (mg/L) 2.23 1.00 93.0 98.0

PO43- 4.00 (mg/L) 2.23 1.00 93.0 98.0


123

from 37.02 mg/m3 (see Table 2) to 32.73 mg/m3; its spa-

tial extent (E) must be reduced from 8.3 km (see Table 2)

to 7.7 km. In summary, the emission of TSP must be

reduced from 341.0 ton/year (see Table 2) to 301.4 ton/

year, which can be accomplished by the installation of

more dust collectors.

4.3.5 Difficulties encountered

Several difficulties were encountered in integrating the con-

cept of a LCIA and a FRA as an assessment tool for the

preparation of EIA reports. Further work is still required to

overcome these difficulties. Firstly, the probabilities of

midpoint effects (e.g. climate change) resulting from envi-

ronmental hazards (e.g. CO2 emission) must be considered.

This type of probability was neglected in this study, because

some are still the subject of debate in the scientific community.

Secondly, gathering sufficient epidemiological studies to

determine the probability of damage resulting from exposure

to standardized hazards proved difficult, so subjective judg-

ment was used to assign the associated probabilities. The third

difficulty arose because of the need to calculate the joint risk of

damage resulting from various midpoint effects and the

aggregation of risks required an assumption of independence.

If these difficulties could be overcome, this model would

prove very beneficial for an EIA.

Table 3 Probabilities of receptors being exposed to midpoint effects (P1) and the probabilities of damage resulting from exposure to stan-

dardized hazards (P2)

Receptor Effect P1 Damage P2

Human Climate change (0.6, 0.7, 0.8) Malnutrition (0.0, 0.1, 0.2)

Infectious diseases (0.2, 0.3, 0.4)

Heat stress (0.4, 0.5, 0.6)

Ozone depletion (0.3, 0.4, 0.5) Cancer (0.1, 0.2, 0.3)

Immunosuppression (0.1, 0.2, 0.3)

Cataract (0.3, 0.4, 0.5)

Ionising radiation (0.1, 0.2, 0.3) Cancer (0.1, 0.2, 0.3)

TSP (direct effect) (0.4, 0.5, 0.6) Cardiovascular disease (0.0, 0.1, 0.2)

Respiratory diseases (0.5, 0.7, 0.9)

Noise and vibration (direct effect) (0.1, 0.2, 0.3) Psychasthenia (0.3, 0.4, 0.5)

Sleep disorders (0.5, 0.6, 0.7)

Photochemical smog (0.1, 0.2, 0.3) Respiratory diseases (0.3, 0.4, 0.5)

Increased tropospheric ozone concentration (0.0, 0.1, 0.2) Respiratory diseases (0.2, 0.3, 0.4)

Acidification (0.1, 0.2, 0.3) Human toxicity (0.1, 0.2, 0.3)

Ecotoxicity (0.1, 0.2, 0.3) Human toxicity (0.5, 0.6, 0.7)

Cancer (0.0, 0.1, 0.2)

Ecosystem Climate change (0.7, 0.8, 0.9) Loss of biodiversity (0.0, 0.1, 0.2)

Ionising radiation (0.2, 0.3, 0.4) Loss of biodiversity (0.5, 0.6, 0.7)

Acidification (0.3, 0.4, 0.5) Loss of biodiversity (0.2, 0.3, 0.4)

Eutrophication (0.4, 0.5, 0.6) Loss of biodiversity (0.2, 0.3, 0.4)

Ecotoxicity (0.1, 0.2, 0.3) Loss of biodiversity (0.5, 0.6, 0.7)

Crops and woods Climate change (0.7, 0.8, 0.9) Loss of productivity of crops and woods (0.2, 0.3, 0.4)

Ozone depletion (0.4, 0.5, 0.6) Loss of productivity of crops and woods (0.3, 0.4, 0.5)

Increased tropospheric ozone concentration (0.2, 0.3, 0.4) Loss of productivity of crops and woods (0.2, 0.3, 0.4)

Acidification (0.2, 0.3, 0.4) Loss of productivity of crops and woods (0.4, 0.5, 0.6)

Wildlife Ozone depletion (0.2, 0.3, 0.4) Disappearance of species (0.0, 0.1, 0.2)

Increased tropospheric ozone concentration (0.2, 0.3, 0.4) Disappearance of species (0.1, 0.2, 0.3)

Acidification (0.1, 0.2, 0.3) Disappearance of species (0.1, 0.2, 0.3)

Eutrophication (0.1, 0.2, 0.3) Disappearance of species (0.3, 0.4, 0.5)

Fish production Ozone depletion (0.2, 0.3, 0.4) Loss of fish catch (0.1, 0.2, 0.3)

Acidification (0.0, 0.1, 0.2) Loss of fish catch (0.3, 0.4, 0.5)

Eutrophication (0.3, 0.4, 0.5) Loss of fish catch (0.5, 0.6, 0.7)


123

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5.4

37

0.2

89

5.4

45

2.7

36

6.1

56

10

.94

57

.03

20

.28

97

.03

81

.59

4

CO

Res

pir

ato

ryd

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ses

0.0

00

0.8

66

2.3

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1.1

70

0.2

95

1.2

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0.0

00

0.8

66

2.3

11

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70

0.2

95

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0.0

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%

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of

spec

ies

0.5

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66

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70

0.2

92

2.0

90

0.5

78

1.7

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66

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70

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92

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89

2.9

83

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99

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21

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69

0.2

89

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83

0.0

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TS

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lar

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94

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00

2.8

23

6.7

75

3.5

46

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89

3.5

58

0.6

49

22

.4%

Res

pir

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9.2

15

13

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31

9.3

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14

.67

20

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41

4.6

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11

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21

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23

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7.9

78

0.2

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6

No

ise

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7.6

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50

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97

.69

00

.01

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.1%

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7.3

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11

.16

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1.1

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00

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98

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94

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PO

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48


123

5 Conclusions

This study proposes the integration of a LCIA and a FRA

by using a LCIA to identify the causal linkage for hazard–

pathway–receptor–damage, using fuzzy logic for release

assessment, using ST for comparison with standard values,

estimating the frequency of hazard occurrence, estimating

the probability that the receptors will be exposed to mid-

point effects, evaluating the probability of receptors being

exposed to standardized hazards, using the vertex method

to compute risk of damage and using distance method to

defuzzify the risk. The tool can be used to assess EIA

reports, because a LCIA can clearly identify the causal

linkage for hazard–pathway–receptor–damage and then

better explain the significance of the impact; furthermore,

FRA copes with fuzzy and probabilistic situations in the

assessment of pollution severity and the estimation of the

probability of exposure.

The integrated tool was demonstrated with a practical

case study. The release assessment shows that the STs of

BOD and PO43- are very high before and after expansion,

due to their high concentrations. However, the greatest

relative increases in ST are VOCs (by 29.3 %) and TSP (by

22.6 %). The risk characterization shows that the high STs

for BOD and PO43- also lead to a severe reduction on the

fish catch of more than 20.0. Meanwhile, the risks resulting

from VOCs and TSP have the greatest relative increases

(29.1 and 22.4 %) after expansion. However, the greatest

absolute increase in risks is 3.306 for the respiratory dis-

eases caused by TSP. The joint risk of respiratory diseases

exceeds 20.0 and has the greatest absolute increase (3.750)

which implies an increase in the expected value of the

percentage of humans that are the subject of respiratory

diseases. Assuming that the risk of respiratory diseases

resulting from TSP can be reduced from 17.980 to 16.135,

which means that the concentration of TSP must be reduced

from 37.02 to 32.73 mg/m3 and that its emission must be

reduced from 341.0 to 301.4 tons, by installing more dust

collectors, the increase of 3.750 will be reduced to 2.000.

Uncertainty should be considered not only for the RA

part of the integration, but also for the LCIA. Uncertainty

in the LCA may be due to data, choices and relationships

(Finnveden et al. 2009). Data can show variability, be

badly-specified, erroneous, incomplete or imprecise and

Table 5 Joint risks of damage due to various pollutants before and after the expansion

Damage Before the expansion After the expansion

Extent

(km)

Joint risk

(fuzzy)

Extent

(km)

Joint risk

(fuzzy)

Increase

(fuzzy)

Joint risk

(crisp)

Cardiovascular disease 7.3 2.908 8.3 3.558 0.649 2.837

Psychasthenia 1.406 7.680 1.407 7.690 0.010 6.630

Sleep disorders 1.406 11.173 1.407 11.188 0.015 9.941

Respiratory diseases 1.8 18.461 1.8 22.211 3.750 20.159

2.8 17.469 3.2 21.267 19.429

7.1 16.520 8.3 20.266 18.660

7.3 14.675 8.6 17.980 16.940

Human toxicity 2.8 2.388 3.0 2.572 0.185 2.062

3.2 1.549 1.236

Loss of biodiversity 2.8 5.109 3.0 5.491 0.382 4.751

3.2 2.910 2.425

(In the sea) 2.01 17.328 2.23 17.971 0.643 15.073

Disappearance of species 1.8 8.585 1.8 9.870 1.285 8.291

2.8 6.635 3.0 7.948 6.654

7.1 3.801 3.2 6.982 5.866

8.6 4.911 4.114

(In the sea) 2.01 16.747 2.23 17.370 0.622 15.073

Loss of productivity of crops and woods 1.8 15.122 1.8 17.093 1.971 15.337

2.8 12.519 3.0 14.554 13.072

7.1 5.445 3.2 11.667 10.409

8.6 7.038 6.163

Loss of fish catch 2.01 43.232 2.23 44.666 1.434 41.996

(In the sea) 2.8 1.021 3.0 1.060 0.837


123

(d)(c)

(a) (b)

(h)(g)

(e) (f)

Fig. 8 Sensitivity analysis of the fuzzy logic system with different

operators. a Our selection (E&M vs. S), b our selection (D&M vs. S),

c And operator: min, d Implication operator: min, e Defuzzification:

Bisector, f Defuzzification: Mom, lom, som, g Membership function:

trapezoid, h Membership function: Gaussian


123

choices may be inconsistent in system boundaries, allocation

principles, and time horizon; relationships may be wrongly

assumed to have a linear dependence between outcomes and

inputs. The types of uncertainty in LCA can be approxi-

mately categorized as variable and fuzzy. Variability results

from spatial or temporal differences, or stochastic nature and

fuzziness occurs because of linguistic ambiguity or impre-

cise measurement. For example, Ardente et al. (2004) used

fuzzy methods to deal with inexact and incomplete input

data and again to evaluate the quality of life cycle inventory.

The authors are working on the fuzziness of a LCIA; how-

ever, because of limitations of space, this important topic

will be the subject of a future paper.

Acknowledgments The authors would like to thank the National

Science Council of the Republic of China (Taiwan) for financially

supporting this research under Contract NSC 99-2221-E-131-010-

MY2. The author also appreciates the editorial assistance provided by

Dr. Michael McGarrigle.

Appendix 1: Fuzzy Logic

Fuzzy logic (Zadeh 1996) has the ability to compute with

words, to model qualitative human thought processes in the

analysis of complex systems and decisions. Fuzzy logic

represents qualitative perception-based reasoning by ‘IF-

THEN’ fuzzy rules. An example of fuzzy logic, in which a

new fuzzy value is derived on the basis of a fuzzy rule (i.e.,

the ith rule in a fuzzy-rule base) with three antecedents and

three fuzzy facts, is represented as follows:

If X1 is Fi1 AND X2 is Fi2 AND X3 is Fi3 THEN Y is Gi

X1 is F01 AND X2 is F02 AND X3 is F02 AND X3 is F03Y is G01

ð7Þ

where Xj and Y are linguistic variables, Fij and F0j are fuzzy

sets of Uj and Gij and G0j are fuzzy sets of V. In the

framework of the compositional rule of inference (Zadeh

1975), G0j is computed by

G0i ¼ F01 ^ F02 ^ F03� �

� Fi1 ^ Fi2 ^ Fi3ð Þ ! Gið Þ ð8Þ

where ^ denotes a t-norm operator, � is a composition

operator and ? indicates an implication operator.

The selection of operators is important for the calcula-

tion of G0. If ‘sup-min’ is chosen as the composition

operator (Zadeh 1975), the membership function of G0 is

computed by:

lG0iðvÞ ¼ max

u1;u2;u3min lF01^F02^F03

u1; u2; u3ð Þ; lFi1^Fi2^Fi3!G

h

u1; u2; u3; vð Þi

ð9Þ

Furthermore, if ‘min’ is the t-norm operator (i.e.,

a ^ b = min (a, b)) and the Mamdani’s implication

operator (i.e., a ? b = min(a, b)), Eq. 9 becomes the

well-known ‘Mamdani’s fuzzy reasoning’, which can be

expressed as

lG0iðvÞ ¼ max

u1;u2;u3min lF0

1ðu1Þ; lF0

2ðu2Þ; lF0

3ðu3Þ; lFi1

ðu1Þ;h

lFi2ðu2Þ; lFi3

ðu3Þ; lGðvÞi

ð10Þ

Equation 10 can be further depicted in another form:

lG0iðvÞ ¼ min max

u1lF0

1^Fi1ðu1Þ;max

u2lF0

2^Fi2ðu2Þ;

�

maxu3

lF03^Fi3ðu3Þ; lGðvÞ

� ð11Þ

where F0j ^ Fij denotes the intersection of fuzzy sets F0j and

Fij; maxuj

lF0j^FijðujÞ is the highest degree of membership of

the intersection and can be interpreted as the compatibility

Cij between F0j and Fij; min maxu1

lF01^Fi1

�ðu1Þ;max

u2lF0

2^Fi2

ðu2Þ;maxu3

lF03^Fi3ðu3Þ� can be viewed as the overall

compatibility Ci between the facts and the rule; and Ci is

used to truncate Gi to obtain G0i. Moreover, if F0j is a precise

value (i.e., say uj), Eq. (11) becomes:

lG0iðvÞ ¼ min lFi1

u1ð Þ; lFi2u2ð Þ; lFi3

u3ð Þ; lGðvÞ� �

ð12Þ

where min lFi1u1ð Þ; lFi2

u2ð Þ; lFi3u3ð Þ

� �can be viewed as the

overall compatibility Ci between the facts and the rule; Ci

is used to truncate Gi to obtain G0i.

Appendix 2: Analysis of the sensitivity of operators

in fuzzy logic

The sensitivity analysis of this study’ fuzzy logic system

with different operators is expressed by three-dimensional

surfaces, which represent the dependency of the output

(severity) on any two of the three inputs (magnitude, spatial

extent and temporal duration), as shown in Fig. 8. When

any horizontal plane exists it implies that both of the inputs

are not sensitive to the output; in other words, any change in

the inputs within the plane does not alter the output. The

selection of operators (‘product’ for the ‘and operator’ and

the ‘implication operator’; ‘centroid’ for the ‘defuzzifica-

tion operator’) is acceptable in the sensitivity analysis, as

shown in Fig. 8a, b. Even if either the ‘and operator’ or the

‘implication operator’ uses ‘min’, the sensitivity analysis is

still acceptable, as shown in Fig. 8c, d. However, it is

unacceptable, due to the existence of horizontal planes, if

the ‘defuzzification operator’ uses other settings (‘bisector’,

‘mom’, ‘lom’, or ‘som’), or if the membership functions are

changed from ‘triangular’ into ‘trapezoidal’ or ‘Gaussian’.


123

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