Design and pilot run of Fuzzy Synthetic Model (FSM) for risk evaluation in civil engineering.
Abdul-Rahman, Hamzah ; Wang, Chen ; Lee, Yee Lin 等
1. Introduction
In the past few years, several quantitative-based approaches have
been introduced for construction risk management such as Fault Tree
Analysis, Monte Carlo Analysis, and Sensitivity Analysis (Ahmed et al.
2007). These sophisticated methods could deal with massive numerical
data to deliver reliable statistical risk result. However, the
availability of high quality data especially during the early stage of
projects is a prerequisite for their effective applications (Sii, Wang
2003). Unfortunately, such data are limited, ambiguous or even not exist
due to the great uncertainty inherent in construction projects.
Therefore, the quantitative approaches could not suitably and
effectively handle the risks (Franceschini, Galleto 2001).
In the mid of 1960s, Professor Lofti Zadeh introduced fuzzy logic
to mathematically represent the uncertainty and vagueness inherited in
the real world (Zadeh 1965). Scholars have presented the use of fuzzy
logic in construction projects such as duration management (Zieliaski
2005; Chen, Hsueh 2007), cost estimation (Cheng et al. 2010; Idrus et
al. 2011), risk management (Zhang, Zou 2007; Lee, Lin 2010), safety
management (Dagdeviren, Yuksel 2008), supply chain management (Chen,
Huang 2006; Wei et al. 2007) and earned value management (Naeni et al.
2011). The extensive application of Fuzzy logic in the realm of
construction demonstrated its easiness to be developed, understood and
applied (Kasabov 1996). According to Dweiri and Kablan (2006), fuzzy
logic is an excellent tool that could greatly improve the chances of
achieving a better quality construction project. Eventually, it resulted
in superior project performance and subsequent project success in the
field of construction. Fuzzy logic is a tool to deal with
decision-making environments characterized by vagueness, impression, and
subjectivity (G., Bojadziev, M. Bojadziev 2007). The integration of
Fuzzy logic in project risk management could give rise to satisfactory
results by effectively addressing the uncertainties and subjectivities
associated with construction activities. Moreover, fuzzy logic provides
a more realistic way than traditional mathematical models to cope with
problems that are vague in nature (Heshmaty, Kandel 1985). Based on
Fuzzy Set Theory (FST), this study intends to develop a holistic risk
assessment model using to estimate the construction risks especially for
situations with incomplete data and vague environments. This paper
introduces the principles and algorithm of its risk assessment
framework. Further, a Pilot Run for the developed Fuzzy Synthetic Model
(FSM) is presented.
2. Fuzzy logic and FST in construction risk management
Fuzzy Set Theory (FST), or, Fuzzy Logic, resembles human ability in
inferring an approximate answer to a question based on a store of
knowledge that is vague, inexact, incomplete, or not totally reliable
(Zadeh 1978). In other words, Fuzzy logic simulates the way human brain
works to solve real-world problems (Yager 2002) such as in forecasting,
decision making, and management, which are characterized by uncertainty,
impression, and subjectivity (G. Bojadziev, M. Bojadziev 2007;
Negnevitsky 2004).
No construction project is risk free. Risk can be managed,
minimized, shared, transferred or accepted. It cannot be ignored (Latham
1994). Over years, scholars have proposed a variety of risk management
methodologies for real practise, yet most of them are similar in
process, following a systematic three-step approach: identify, assess,
and mitigate construction risks (Flanagan, Norman 1993; Berkeley et al.
1991; Lyons, Skitmore 2004). Out of the three steps, risk assessment
process is the most controversial issue (Baloi, Price 2003). Meantime,
there were a few research studies attempted to use FST to formalize
subjectivity issues in the construction risk analysis. One of the
earliest FST-based approaches was outlined by Nguyen (1985) to solve
decision-making problems during the selection of bid contracts. Kangari
and Riggs (1989) presented a composited fuzzy-knowledge-based system to
analyze risk but revealed the limitations of probability-based approach
in risk assessment process: difficult in the quantifying qualitative
data, where precise data is unavailable in real situation. This issue
activated the subsequent courses of exploration to investigate the fatal
weakness of the probability approach in construction project risk
evaluation.
Being pioneers in adopting Analytic Hierarchy Process (AHP) within
construction decision problem analysis, Mustafa and Al-Bahar (1991)
assessed risks through the appraising of probability and impact of risk
occurrence. AHP was developed by Saaty (1980, 1990) to cope with complex
decision-making problems. AHP was applied by Dey et al. (1994) and Riggs
et al. (1994) to combine objective and subjective data as an attempt to
analyze cost risk where risk was modelled as Probability-Impact (P-I).
Zhi (1995) proposed using AHP to evaluate risk in international
projects. Chun and Ahn (1992) on the other hand, integrated FST into
risk analysis model to quantify the imprecision inherent in the accident
progression event trees. Using FST, Paek et al. (1993) established a
risk algorithm for the assessment of bidding price of construction
projects. Wirba et al. (1996) applied FST to capture human reasoning in
the identification and evaluation of risks.
In the 2000s, since the outset of millennium, there have been
rigorous investigations to efficaciously model and evaluate the
construction project risk. Risk began to be dealt comprehensively using
multi-criteria decision-making (MCDM) techniques to facilitate the
complex decision-making process in risk assessment. Despite the
availability of many others techniques, both AHP and FST turned out as
the most favoured methodologies in handling ill-defined subjective
problems. They were perceived as the best ever approaches in
problem-solving that encompassing multiple criteria. For instance,
Hastak and Shaked (2000) proposed an AHP model to assess the risk of
overseas projects. Baccarini and Archer (2001) used both the probability
and impact risk parameters to rank project risks. Likewise, Jannadi and
Almishari (2003) attempted to analyze risks concerned with project
activities. Risk is modelled by probability and "exposure" to
all hazards of an activity. Ward and Chapman (2003), however, criticized
on the P-I risk model that it yielded unnecessary uncertainty by
oversimplifying the estimation of risk impact and probability.
Zhang (2007) expounded the deficiencies of the P-I grid.
Alternatively, "project vulnerability" is introduced to
enhance the recognition of risk consequences. In the same year, Cagno et
al. (2007) used the P-I risk model to quantify the cost risk by
determining the sources of risks, affected activities, and risk owners.
Besides, a three-dimensional risk model called
Significance-Probability-Impact was presented where
"significance" is defined as the degree to which a
practitioner assesses risk intuitively. Recently, Cioffi and Khamooshi
(2009) generated a probability-based model to estimate the overall risk
impact on contingency budget. Based on both AHP and decision tree, Dey
(2001) sought to effectively manage construction cost risk as early as
on the inception stage. In addition, Dikmen et al. (2007a) adopted AHP
to appraise uncertainties and opportunities of the overseas construction
projects. The overall project risk level was computed by multiplying the
relative impact and the relative likelihood of each risk. All the
individual risk impacts were summed up to obtain final score. In
contrast, Zayed et al. (2008) applied AHP to allocate weighs to risks
before calculating the risk level. Some researchers attempted to
integrate FST into risk assessment process. They focus mainly on the
improvement of the efficiency of the conventional risk assessment tools,
though rather new tools have been proposed by Huang et al. (2001) and
Cho et al. (2002). Using the risk hierarchical breakdown structure, Tah
and Carr (2000) proposed a fuzzy qualitative risk assessment model,
where experts' subjective judgments were captured within the model
to assess the risk impact. Noticing the drawback of FST in such an
application, Tah and Carr (2001) proposed a new combination rule in the
aggregation process of a predominant risk factor. Choi et al. (2004)
developed a FST model to analyze risks using objective probabilities,
subjective judgments, and linguistic variables. Similarly, Shang et al.
(2005) designed a Fuzzy-based mechanism for risk assessment for the
conceptual design stages of a construction project. Zheng and Ng (2005)
applied FST to assess the cost and budget in construction projects.
In addition, Thomas et al. (2006) generated a fuzzy fault tree to
enhance risk assessments by considering the opinions of different
experts. A fuzzy decision-making model was designed by Wang and Elhag
(2007) for a bridge construction project. The model evaluates risks
based on the likelihood and consequences of occurrence. In consideration
of overseas projects, Dikmen et al. (2007b) adopted an influence
diagrams to create a fuzzy risk assessment approach to prioritize risk
based on cost excess of budget. Meanwhile, Zeng et al. (2007) used FST
to cope with uncertainty whereas AHP was applied to decompose and to
prioritize multiple risk sources. Risks were first described in
linguistic values and later transformed into fuzzy numbers. In the most
recent, Lee and Lin (2010) suggested the use of AHP in fuzzy risk
assessment in construction projects. Linguistic terms and Fuzzy numbers
were directly adopted, rather than the use of quantitative data in risk
assessment process. Likewise, Nieto-Morote and Ruz-Vila (2011) presented
a risk assessment framework based on the FST, which could effectively
capture the subjective judgements decompose large number of risks. The
most notable distinction was the adoption of a risk discrimination
algorithm to solve the inconsistencies in the computation process. Table
1 overviews the developed risk assessment techniques from 1980s till the
year of 2011.
3. Fuzzy Analytic Hierarchy Process (Fuzzy-AHP)
Fuzzy-AHP has been extensively adopted to solve qualitative MCDM
problems in the context of construction risk assessment. Together with
hierarchical structure analysis, FST could excellently handle the
ambiguity inherited in the conventional data evaluation process, which
encompasses identification, evaluation, and prioritization of the MCDM
problems (Chen 2001). One of the significant aspects of Fuzzy-AHP is its
ability in solving ill-defined and vague problems in construction
projects and reaching a reliable final decision (Zeng et al. 2007; Zhang
et al. 2002; An et al. 2005). Being proven to be more advanced and
efficacious in tackling complex MCDM problems, Fuzzy-AHP generally
follows a process, structured in a three-step approach, namely: a)
generation of risk hierarchy tree; b) pairwise comparison to establish
fuzzy comparison matrix; c) fuzzy prioritization of criteria.
3.1. Generation of risk hierarchy tree
Taxonomy of a typical hierarchy tree associated with construction
project risks is shown in Figure 1. The complex decision problems can be
formulated in the form of simple hierarchy tree. The overall goal is
placed at the highest level. The criteria affecting the goal are located
in the middle levels. The lowest level presents the decision options.
Before the hierarchy tree is structured, different risk factors have to
be exhaustively recognized. Usually, the construction practitioners have
intuitive methods of recognizing a risk source. This is in accordance
with the statement of Wang et al. (2004) that experts prefer to
intuitively identify risks using experience and knowledge gained from
previous contracts. There are, anyhow, some formal risk identification
tools such as Checklist, Influence Diagrams, Cause and Effect Diagram,
Failure Mode and Effect Analysis, and Fault Trees Analysis (Zavadskas et
al. 2010; Tah, Carr 2000).
Nevertheless, large construction projects tend to adopt formalized
risk identification tools, and vice versa. All the sources of
uncertainties identified are classified within the hierarchy tree
structure so that they can be thoroughly evaluated. Various risk
classification methods are shown in Table 2. The methods adopted to
classify construction risks depend largely on the nature of a project as
well as the management skills of experts. Once the decomposition of risk
problems into a hierarchy tree is completed, risk assessment process is
carried out to determine the relative importance, dominance or
preference of the decision criteria with regards to the goal of the
problems.
3.2. Pairwise comparison to establish Fuzzy comparison matrix
The importance weighs of criteria is determined in the pairwise
comparison manner. Anyhow, the difference between pairwise comparison
process in Fuzzy-AHP and normal AHP is in the use of Fuzzy comparison
scale, where Fuzzy numbers are integrated into the original comparison
scale to substitute the nine exact numbers in Fuzzy-AHP. Experts could
intuitively express their preferences as the Fuzzy numbers could
accurately describe the expert's verbal judgments in the process
Zadeh (1965). The Fuzzy comparison scale works excellent in capturing
the subjective experience and knowledge of experts through the
application of the Fuzzy numbers (Chang, Yeh 2002; Kahraman et al. 2004)
within Fuzzy-AHP. Using the advanced comparison scale, experts could
express their judgments using natural languages such as "equally
important" and "absolutely more important" which are
directly corresponding to Fuzzy scale of (1, 1, 1) and (17/2, 9, 19/2),
respectively. Reciprocal scale is adopted whenever the later criterion j
is more dominant than the former criterion i. As such, the expert no
longer face difficulty in giving fixed judgments, which is in the form
of exact numbers, but rather interval judgments, which is in the form of
Fuzzy numbers. There are various types of Fuzzy numbers proposed in
Fuzzy comparison scale, yet the triangular and trapezoidal shapes are
the most frequently used membership functions in construction risk
analysis practice due to their simplicity in application (An et al.
2005). They have been proven to be able to efficaciously formulate
problems where the data available is of subjective and vague (Kahraman
et al. 2004; Chang et al. 2007). In comparison, the triangular shape
membership functions are the most often used in representing the Fuzzy
numbers (Karsak, Tolga 2001) in the Fuzzy comparison scales. Likewise,
Pedrycz (1994) expressed that a triangular Fuzzy number (TFN) is the
easiest and simplest way to approach the convex functions. Moreover, if
the pairwise comparison process involves group-decision-making, the
experts' preferences on particular criterion have to be aggregated.
This is because experts with different background and experience would
have different preference on a particular criterion. Hence, it needs to
aggregate the individual preferences into the group preference to
average out the relative importance weightings of the criteria. The
aggregation process is carried out for every criterion, until all
criterions have their own group preferences. The groups preferences,
which are remain in Fuzzy numbers, are arranged in a systematic manner
to yield a Fuzzy comparison matrix. Pairwise comparison is used to
calculate the relative importance weighing of each risk criterion with
the incorporation of Fuzzy numbers to capture the subjective
expert's judgments in the process. The output is a Fuzzy comparison
matrix (Ding, Liang 2005; Xu, Chen 2007).
[FIGURE 1 OMITTED]
3.3. Fuzzy prioritization of criteria
Since Saaty (1980) had proposed the AHP, many researchers enrolled
in the extension of the eigenvector priority method to overcome its
inconsistency in producing results. As an attempt to produce reliable
final priority weighs, researchers adopted different types of Fuzzy
prioritization approaches, for instance, the earliest attempt in
prioritizing fuzzy weighs was accomplished by van Laarhoven and Pedrycz
(1983) in which triangular fuzzy numbers were compared according to
their membership functions. Likewise, Buckley (1985) used trapezoidal
fuzzy numbers to
integrate the fuzzy priorities of comparison ratios. A new approach
called Fuzzy Synthetic Analysis (FSA) for computation of a sequence of
weigh vectors (Chang 1996) suggested the application of extent analysis
method for the synthetic extent values of the Fuzzy pairwise
comparisons. The term "synthetic" expresses the process of
evaluation whereby several individual criterions of an evaluation are
synthesized and aggregated to a final form. Despite the diversity of
Fuzzy prioritization approaches, FSA is the most abundant used method in
the literatures indicating its popularity in prioritizing decision
variables. It has been perceived as the best prioritizing method due to
its simple and easy in application (Chan, Kumar 2007).
4. Methods and procedures in developing FSM
To appropriately conduct the qualitative technique in the
development of FSM, a developing team was established consisting of
construction engineers, IT professionals, risk managers, and
mathematicians. Owing to the nature of the developers where their
experiences, perceptions, and opinions are necessities to the
enhancement of the model, the qualitative approach was adopted in this
study. The qualitative technique enables on-the-spot directness to the
information in which rapid, immediate response could be obtained from
the elites, where it is not possible when the quantitative technique
such as questionnaire surveys are conducted. The developing team
consists of a range of experts of different specialties, whose detailed
information regarding their contribution towards the birth of FSM is
summarised in Table 3.
The use of probability theory to deal with the construction project
of one-time characteristic complicates the risk analysis process.
Conventional approaches are impractical in those real situations where
high quality data are absent yet they could not effectively deal with
the subjective human assessments, for instance, the fixed scale of 1-9
used in the pairwise comparison process is incapable to describe the
interval judgment of experts. The authors adopted the Fuzzy-AHP
technique as the decision-making framework for construction risk
analysis in the developed model since the Fuzzy-AHP allows a more
accurate description of the subjective data, where the fuzzy pairwise
comparisons are more rational in reflecting experts' uncertain
judgments than crisp one. Such a model could facilitate the
decision-making process, where the complex uncertainty inherited in
subjectivity is able to be captured and mitigated optimally. The project
performance is significantly affected by construction risks in concerns
of cost, time, and quality. The developed FSM is to holistically solve
multi-criteria complex problems in the real practice of construction.
The algorithm of the proposed model consists of six phases, which are
discussed as follows.
4.1. Establishment of risk assessment team
Owing to the large burdens during the project risk analysis, the
decision-making process was conducted by a group of risk assessment
experts. Due to their different background, experience, and knowledge,
each expert in the risk assessment team has different impacts on the
final decision. The experts with higher degree of knowledge and more
related experience on the targeted project have more substantial impact
in the risk assessment process so that their contribution factors are
given more weigh in the model. This is due to the reason that the final
result is more consistent as the risk analysis process is undertaken
comprehensively by different experts with various competencies. The
contributions factors are used to determine the weighing for different
evaluators. Basically, the relative weighing of the experts is
determined by their competence on the basis of their experience,
knowledge, and expertise related to the targeted project. The formulas
for contribution factors are presented in Section 5. The risk assessment
team is responsible to classify and to structure all potential risks
within a hierarchy tree in the next step.
4.2. Structure a hierarchy tree
Structuring of a hierarchy tree aims to decompose the goal into
adequate details in which all the criteria could be thoroughly assessed.
Generally, the top level of the hierarchy tree is the overall goal of
the decision problem. In the context of construction risk analysis, the
goal is defined as risk evaluation. The subsequent levels present the
general risk sources, then their specific risk factors, which are
evaluated. The lowest level is the alternative of decision options, with
regards to the goal, which are determined based on the kind of results
desired in the end of analysis. To determine the decision criteria, it
entails the understanding of the underlying factors impacting the goal.
Hence it is essential to investigate all potential sources of
uncertainty likely to affect a project. The recognized risks are
classified in a way that the risks with similar characteristics are
grouped together in the hierarchy. The construction uncertainty is
commonly modelled based on the integration of two risk parameters: a)
the probability of occurrence and b) severity of risk impact. The
hierarchy tree was constructed as shown in Figure 2. The complex
decision problems were structured within a simple hierarchical
structure, where the decision criteria were placed comprehensively into
five levels. The top level is defined as "Construction Project
Risks" to reflect the overall goal. It is followed by two risk
parameters that serve as the evaluation basis for risks. The third level
is where all major risk sources are located, with their respective risk
factors in the subsequent level. The lowest level presents the project
objectives including time, cost, and quality.
As illustrated in Figure 2, the general risks and their specific
sub-factors are located respectively in the third and the fourth level.
Eventually, the project objectives such as time, cost, and quality are
placed in the bottom level. It could mitigate the uncertainty depending
on the relative risk impact towards the project objective. Compromises
such as targeted budget, good scheduled time, and high project quality
are guaranteed when all the project objectives are accomplished.
[FIGURE 2 OMITTED]
4.3. Pairwise comparison using Fuzzy comparison scale
The risk assessment process is carried out once the hierarchy tree
is established. Most frequently there are multiple contradicting risk
sources existing in a project. This complicates the decision-making
process as the experts need to consider various criteria simultaneously.
Hence, it is a necessity to prioritize risks for further attention. To
do so, the experts need to firstly determine the relative weigh of each
criterion in the same hierarchy, via pairwise comparison process, so
that their relative priority weighs could be calculated. The greatest
advantage of pairwise comparison is that the experts are allowed to
focus on the comparison of just two objects, which makes the observation
as free as possible from extraneous influences. To systematically
capture the valuable subjective judgments of experts in the risk
analysis, Fuzzy comparison scale is proven to be accurate and intuitive
in reflecting the qualitative judgments where decision makers could
specify preferences in the form of natural language regarding the
importance of each criterion. The most common used Fuzzy numbers are
both the triangular and trapezoidal Fuzzy number (TFN). In this study,
the simplest form of TFN was applied for representing the linguistic
judgments, as TFN was sufficient to produce a reliable result. The fuzzy
scale of TFN is intuitively easy to use and to calculate so that it was
adopted to improve the pairwise comparison process.
4.4. Aggregation of individual TFNs into group TFN
Every individual in the risk assessment team has a TFN preference
for criterion in the hierarchy tree. The individual TFNs of particular
criterion should be aggregated into the group TFN preference. The
rationale of this step is to integrate all the individual TFN
preferences for particular criterion so that the Fuzzy comparison
matrices remain consistent. The aggregation process is completed once
the individual TFNs of every criterion in the hierarchy tree are
converted into group TFN. All group TFNs are arranged in a matrix
structure, which is called "Fuzzy comparison matrices".
Consequently, the relative priority weigh of each criterion was
calculated using the Fuzzy prioritization method in the next step.
4.5. Calculation of priority weighs at different hierarchy level
It is usually not possible to address all risks with a same degree
of attention, as resources available for risk management are limited.
Concentration on risks with higher priority is essential for efficient
risk management. This step aims to calculate the relative priority
weighs of decision criteria in the same level, with respect to their
upper criterions. Since the conventional eigenvector prioritization
method is being doubt of its consistency, the Fuzzy prioritization
method was used in this step to calculate the final priority weighs in
the proposed model.
4.6. Systemization of results
The relative priority weigh of each criterion attained through
previous steps was synthesized to obtain the final priority weigh. This
process was computed by synthesizing all relative priority weighs of
particular decision criteria from the bottom level to the top level. The
outcome is a normalized vector of the overall weighs of the
alternatives, which are then ranked in order. In response to the final
ranking of each criterion, the users can take risk mitigation actions.
Risk mitigation is a plan that reduces risk impact on the project
performance. Options available for mitigation include
"control", "avoidance", and "transfer". A
mitigation plan could be carried out to reduce or to eliminate the risks
with the selected higher priority weighs, with respect to the time, cost
and quality of a project.
5. Mechanism and appearance of the developed FSM
Eventually, a Fuzzy Synthetic Model, abbreviated as FSM, was
developed as shown in Figure 3. There are six steps within the model,
which are delineated in the following sections.
Step 1: Establishment of Risk Assessment Team. In this step, the
weighs were calculated to allocate difference contribution factors to
the experts. If there are m experts in the risk assessment team, the
[k.sup.th] expert [E.sub.k] is allocated a contribution factor [c.sub.k]
as defined in Eq. (1):
[c.sub.1] + [c.sub.2] + ... + [c.sub.m], where [c.sub.k] [0, 1].
(1)
[FIGURE 3 OMITTED]
Step 2: Structuring Risk Hierarchy Tree. The risk identification
process was conducted based on the nature of a project. This is to
anticipate potential risks on the stage of project development. The
intuitive method was applied. The risks identified were structured into
a simple hierarchy tree. The risks are grouped on the basis of their
characteristics and the level of decomposition is non-limited. It
depends on the variables to be measured in a project.
Step 3: Pairwise Comparison Using Fuzzy Comparison Scale. Pairwise
comparison was carried out to determine the relative importance weighs
of criteria. Every expert in the risk assessment team is required to
compare those risks in a pairwise manner, via fuzzy scale, to produce a
Fuzzy comparison matrix as shown in Eq. (2). TFN is used to convert the
corresponding linguistic judgment according to the Fuzzy comparison
scale:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)
where [??] represents a fuzzified reciprocal n-n judgment matrix
containing all pairwise comparison [[??].sub.ij] between elements i and
j for all i,j = {1,2, ..., n}; [??] and all [[??].sub.ij] are triangular
fuzzy numbers [[??].sub.ij] = ([l.sub.ij], [m.sub.ij], [u.sub.ij]) with
[l.sub.ij] the lower and [u.sub.ij] the upper limit and [m.sub.ij] is
the point where the membership function [mu](x) = 1.
Step 4: Aggregation of Individual TFNs into Group TFN. The pairwise
judgments of individual TFNs were aggregated into a group Fuzzy number
using the operational laws base on Zadeh (1965), which are defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)
where [??] represents a fuzzified reciprocal n-n judgment matrix
containing all pairwise comparison [[??].sub.ij] between elements i and
j for all i, j = {1, 2, ..., n}; [??] and all [[??].sub.ij] are
triangular fuzzy numbers [[??].sub.ij] = ([l.sub,ij], [m.sub,ij],
[u.sub,ij]) with [l.sub,ij] the lower and [u.sub,ij] the upper limit and
mij is the point where the membership function [mu](x) = 1.
Step 4: Aggregation of Individual TFNs into Group TFN. The pairwise
judgments of individual TFNs were aggregated into a group Fuzzy number
using the operational laws base on Zadeh (1965), which are defined as:
--Fuzzy addition:
[[bar.M].sub.1] [direct sum] [[bar.M].sub.2] = ([l.sub.1] +
[l.sub.2], [m.sub.1] + [m.sub.1]; [u.sub.1] + [u.sub.2]); (3)
--Fuzzy multiplication:
[[bar.M].sub.1] [dot encircle][[bar.M].sub.2] [approximately equal
to] ([l.sub.1] + [l.sub.2], [m.sub.1] + [m.sub.1]; [u.sub.1] +
[u.sub.2]); (4)
--The inverse of triangular fuzzy number
[??] = [l.sub.1], [m.sub.1], [u.sub.1]):
[M.sup.-1.sub.1] [approximately equal to] (1/[u.sub.1],
1/[m.sub.1], 1/[l.sub.1]; (5)
[FIGURE 4 OMITTED]
--The scalar multiplication of a triangular fuzzy number:
k x [[??].sub.1] = (k x [l.sub.1], k x [m.sub.10], k x [u.sub.1])
if k > 0; (6)
k x [[??].sub.1] = (k x [u.sub.1], k x [m.sub.10], k x [l.sub.1])
if k > 0. (7)
Step 5: Fuzzy Synthetic Analysis. Fuzzy synthetic analysis was
carried out to calculate the relative priority weighs of criteria.
According to Chang (1996), there are three procedures involved as
described below:
Procedure 1: Calculate the Fuzzy Synthetic Extent Values:
[S.sub.i] = [[summation].sup.m.sub.j=i] [M.sup.1.sub.gi] [cross
product][[[summation].sup.m.sub.j=i] [M.sup.1.sub.gi]]; (8)
Procedure 2: Calculate the Degree of Possibility:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (9)
where: V ([M.aub.1] [greater than or equal to] [M.sub.2]) = 1 if
[m.sub.1] [greater than or equal to] [m.sub.2]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (10)
V ([M.sub.1] [greater than or equal to] [M.sub.2]) = hgt ([M.sub.1]
[intersection] [M.sub.2]) [l.sub.1] - [u.sub.2]/[m.sub.2] - [u.sub.2]) -
([m.sub.1] - [l.sub.1]; (11)
Procedure 3: Calculate the Normalized Weigh Vectors:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (12)
Assuming that:
d'([A.sub.i]) = min V([S.sub.i] [greater than or equal to]
[S.sub.k]) (13)
for k = 1, 2, ..., n; k [not equal to] i. Then the weigh vector is
given by Eq. (14):
W' = [(d'([A.sub.1]), d'([A.sub.2]), ...,
d'([A.sub.n])).sup.T], (14)
where: [A.sub.1] (i = 1, 2, ..., n) are n elements.
Via normalization of W?, the normalized weigh vectors are as Eq.
(15):
W = [(d ([A.sub.1]), d ([A.sub.2]), ..., d ([A.sub.n])).aup.T],
(15)
where W is a non-fuzzy number.
Step 6: Synthesizing Final Weighs. Finally, the relative priority
weighs of the criteria were synthesized across the hierarchy tree to
produce final weighs with respect to project objectives. Consequently,
risk controlling process could take place to mitigate and monitor the
highest risky uncertainty.
6. Pilot Run and validation of FSM
The Pilot Run project for the developed FSM was conducted with a G7
contractor who managed to assess the potential risks in a ten-floor
high-rise building project at Kepong, Kuala Lumpur. The goal is to take
into account all the possible impact of risks towards the project
objectives. The Pilot Run project is presented here to validate the
implementation of the developed FSM.
6.1. Pilot Run: established risk assessment team
Four experts in the G7 contractor were selected to form a risk
assessment team. The profiles of these 4 experts are presented in Table
4. Prior to the risk analysis process, the contribution factor for the
first expert c1 was calculated based on his working experience related
to the risk assessment on this type of construction, so that his
weighing was determined by Eq. (16). Similarly, the contribution factors
for other experts were calculated as shown in Table 4:
[C.sub.1] for [E.sub.1] = 7/ 7 + 11 + 5 + 9 = 0.22. (16)
6.2. Pilot Run: structured hierarchy tree
The hierarchy tree was structured as shown in Figure 4. The top
level is the overall goal of the risk assessment problem defined as
"Construction Risks" followed by two risk parameters, namely:
risk likelihood and risk severity that located at the second level. The
third and fourth levels are where all the identified risks situated. The
lowest level presents the project objectives including time, cost, and
quality. In this Pilot Run project, the risk assessment team identified
five critical risk factors: Design, Nature, Financial & Economic,
Political & Environment, and Job site-related. Under these five main
factors, there are eighteen sub-factors as listed in Figure 4.
6.3. Pilot Run: pairwise comparison using fuzzy scale
In this step, pairwise comparison for every criterion was conducted
at all these 5 levels in the hierarchy structure. Triangular fuzzy
numbers (TFNs) in the pairwise comparison scale were used to determine
the priorities of different criteria. Table 5 demonstrates the pairwise
comparison results on determining the relative importance weighs for
criteria with respect to "Weather" at level 4.
6.4. Pilot Run: aggregation of individual TFNs into group TFN
In this step, the contribution factor of each expert was multiplied
with the corresponding individual TFNs.
All the individual TFNs were aggregated into the group TFN. The
aggregation score of each criterion was calculated using Eqs (3), (4),
and (6). For instance, the aggregation score of "Cost and
Time" under "Weather" was calculated as (3.18, 3.68,
4.18) as shown in Eq. (17). The aggregated scores for other criteria
were obtained in the same way. Once the aggregation process was
completed, the fuzzy comparison matrix of the criteria was produced as
shown in Table 6:
[S.sup.*.sub.cost & time] = (5/2,3,7/2)[cross product]0.22
[cross product] (9/2, 5,11/2) [cross product] 0.34 [cross product]
(5/2,3,7/2) [cross product] 0.16 [cross product] (5/2,3,7/2) [cross
product] 0.28 = (3.18,3.68,4.18). (17)
6.5. Pilot Run: calculated priority weighs using FSA
The priority weighs of the criteria were computed using FSA. From
Table 6, the value of fuzzy synthetic extent with respect to each
criterion was calculated using Eq. (8). The results are:
[S.sub.Time] = (1.47, 1.54, 1.62) [cross product] 1/17.03 + 1/15.04
+ 1/17.93 = (0.09, 0.10, 0.12);
[S.sub.Cost] = (4.44, 4.98, 5.53) [cross product] 1/17.03 + 1/15.04
+ 1/17.93 = (0.26, 0.32, 0.40);
[S.sub.Quality] = (7.88, 8.88, 9.98) [cross product] 1/17.03 +
1/15.04 + 1/17.93 = (0.46, 0.58, 0.72).
[FIGURE 5 OMITTED]
Using these vectors, Eqs (9) to (12) were used to obtain the degree
of possibility. The results are:
V ([S.sub.Time] [greater than or equal to] [S.sub.Cost]) = 0;
V ([S.sub.Time] [greater than or equal to] [S.sub.Quality]) = 0;
V ([S.sub.Cost] [greater than or equal to] [S.sub.Time]) = 1;
V ([S.sub.Cost] [greater than or equal to] [S.sub.Quality]) 1 ;
V ([S.sub.Quality] [greater than or equal to] [S.sub.Time]) = 1;
V ([S.sub.Quality] [greater than or equal to] [S.sub.Cost]) = 1.
Similarly, using Eq. (13), the results were calculated as:
V ([S.sub.Time] [greater than or equal to] [S.sub.Cost],
[S.sub.Quality]) =
[S.sub.Time] [greater than or equal to] [S.sub.Cost], and
[S.sub.Time] [greater than or equal to] [S.sub.Quality] = 0;
V ([S.sub.Cost] [greater than or equal to] [S.sub.Time],
[S.sub.Quality]) =
[S.sub.Cost] [greater than or equal to] [S.sub.Time], and
[S.sub.Cost] [greater than or equal to] [S.sub.Quality] = 1;
V ([S.sub.Quality] [greater than or equal to] [S.sub.Time],
[S.sub.Cost]) =
[S.sub. Quality] [greater than or equal to] [S.sub.Cost], and
[S.sub.Quality] [greater than or equal to] [S.sub.Cost] = 1.
Given by Eqs (14) and (15), the weigh vector is [W.sub.w'] =
[(0, 1, 1).sup.T]. Finally, via normalization of [W.sub.w'], the
normalized weigh vector from Table 6 was calculated by using Eq. (16) as
Ww = (0, 0.5, 0.5)T, where [W.sub.w] are non-fuzzy numbers. This step
was repeated for each criterion at each level in the hierarchy tree to
derive their normalized weigh vectors. The matrices of pairwise
comparisons and their respective normalized weigh vector at level 4,
level 3, level 2, and level 1 are presented in Tables 7, 8, 9, and 10,
respectively.
[FIGURE 6 OMITTED]
6.6. Pilot Run: synthesized final results
Finally, the combination of priority weighs for each criterion at
all levels were computed to determine overall priority weighs for the
risks with respect to time, cost, and quality. The synthesized results
are given in Table 11. The graphic results as shown in Figs 5 and 6
indicate that the project has higher risk in cost than in time and
quality. Mitigation plan could then be executed to monitor and to
control those risks with a high ranking to ensure their accordance with
project objectives.
6.7. Validation of FSM
A validation process of the developed FSM was carried out to
determine whether this model was of application value for risk
evaluation in construction practices, which was conducted online by
randomly selected 9 practitioners in the construction sector worldwide.
Each parameter was given a 10-scale evaluation. The validation results
as shown in Table 12 indicate that the developed FSM could
systematically help practitioners to evaluate construction risks. The
values of flexibility, accessibility, completeness, reliability, user
friendly level, assistance in decision-making, and adaptability for
complexity are acceptable.
7. Benefits and limitations
The advantage of a Fuzzy-AHP model is that it could efficiently
quantify the valuable subjective data to cope with multiple
contradicting risk problems. Taking project objectives such as time,
cost, and quality into consideration are very important in the risk
assessment process. As to guarantee project success, it entails
effective risk management of a project. Compared with those existing
methods, the FSM developed in this study has the following benefits: a)
it accelerates the decision-making process. Construction practitioners
could conduct a complicated risk assessment process effectively using
the developed model which is simple and systematic in evaluation and
computation; b) it gives more convincing result with the consideration
of project objectives within the framework, hence it aids in an optimal
allocation of project resources to mitigate possible risks detrimental
to the success of a project in terms of time, cost, and quality; c) it
is able to capture the vagueness of human thinking style and to ensure
the consistency in multi-criteria decision-making process; and d) it
could be used in measuring risks across different stages of a project
life cycle, from the inception till the completion of a project.
Nevertheless, the developed FSM has a shortcoming that the computational
fuzzy calculations in this model are rather time-consuming, which needs
to be optimized in future study.
8. Conclusions and recommendations
Aiming to remove complex and unreliable process arising in
subjective judgments during construction risk assessments, the developed
FSM provides an appropriate approach to tackle the fuzziness involved in
the decision-making process. The pilot run revealed that the FSM could
accelerate the decision-making process and could provide optimal
allocation of project resources to mitigate possible risks detrimental
to the success of a project in terms of time, cost, and quality. Further
efforts are recommended in developing a decision support tool to conduct
the tedious fuzzy calculations to facilitate the overall risk assessment
process. Besides, since the computational fuzzy calculations in the
developed model is rather time-consuming, the simplification and the
optimization of the fuzzy calculation process should be paid attention
to in future research works.
doi: 10.3846/13923730.2012.743926
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Hamzah Abdul-Rahman (1), Chen Wang (2), Yee Lin Lee (3)
Faculty of Built Environment, University of Malaya, 50603 Kuala
Lumpur, Malaysia
E-mails: (1) arhamzah@um.edu.com; (2) derekisleon@gmail.com
(corresponding author); (3) cipmgroup@gmail.com
Received 01 Jul. 2011; accepted 07 Jul. 2011
Hamzah ABDUL-RAHMAN. Professor Dr Dip. Bldg (UiTM), BSc (Hons)
Central Missouri State University, MSc University of Florida, PhD
University of Manchester Institute of Science and Technology, FRICS,
MCIOB, MIVMM, is currently the Deputy Vice Chancellor (Research &
Innovation), University of Malaya and a full professor in the Faculty of
Built Environment, University of Malaya. He has served as the Deputy
Vice Chancellor for Development and Estate Management in charge of
development policies and construction projects from 1996 to 2003, and
the Deputy Vice Chancellor (Academic & International) from 2009-2010
in University of Malaya. He holds a PhD degree from the University of
Manchester Institute of Science and Technology (UMIST, UK), M.Sc. from
University of Florida and BSc (Hons) from Central Missouri State
University, Dip. Bldg (UiTM). His research interests include the
construction innovation & sustainability, project & facility
management, building energy efficiency, industrialized building system
(IBS), and renewable energy application in buildings, supported by his
vast publications. He is also a fellow member of the Chartered Institute
of Surveyors, United Kingdom (International).
Chen WANG. Dr, senior Lecturer of Construction Innovation and
Project Management in the Faculty of Built Environment, University of
Malaya. He was a senior engineer of China State Construction Engineering
Corporation (CSCEC). His research interests include Mathematics Modeling
for Civil Engineering, Fuzzy-QFD, the sustainability in construction
management, international BOT projects, energy conservation, and
building integrated solar application, supported by his vast
publications. He is also a perpetual member of The Chinese Research
Institute of Construction Management (CRIOCM), Hong Kong
(International).
Yee Lin LEE. Research fellow in the Center of Construction Facility
Management, Faculty of Built Environment, University of Malaya. Her
expertise is in Fuzzy Logic Computing, Fuzzy Quality Function
Deployment, and Building Physics.
Table 1. Overview of risk assessment approaches from 1980s to 2000s
Period of Risk Assessment Approach/
Time Author Methodology
1980s Chapman and Cooper (1983) PERT, decision trees &
probability distributions
Cooper et al. (1985) Risk breakdown structure &
variation distribution
Nguyen (1985) FST
Franke (1987) Probability theory
Kangari and Riggs (1989) FST
The 1990s Yeo (1990) Probability, Range estimates
method & PERT
Mustafa and Al-Bahar (1991) AHP
Diekmann (1992) Probability
Chun and Ahn (1992) FST & event trees
Paek et al. (1993) FST
Dey et al. (1994) AHP
Riggs et al. (1994) AHP
Zhi (1995) AHP
Williams (1995) Probability
Wirba et al. (1996) FST
Tavares et al. (1998) Stochastic model
Mulholland and Christian Probability & PERT
(1999)
The 2000s Hastak and Shaked (2000) AHP and Probability
Tah and Carr (2000) FST
Dey (2001) AHP & decision trees
Tah and Carr (2001) FST
Baccarini and Archer (2001) Probability
Cho et al. (2002) FST
Ward and Chapman (2003) 6-steps minimalist approach
Baloi and Price (2003) FST
Jannadi and Almishari Probability
(2003)
Choi et al. (2004) FST
Shang et al. (2005) FST
Dikmen et al. (2007a) AHP
Cagno et al. (2007) Probability
Zhang (2007) Probability
Wang and Elhag (2007) FST
Zeng et al. (2007) FST & AHP
Zheng and Ng (2005) FST
Zhang and Zou (2007) FST & AHP
Dikmen et al. (2007b) FST & AHP
Han et al. (2008) Probability
Zayed et al. (2008) AHP
Cioffi and Khamooshi (2009) Probability theory
Lee and Lin (2010) FST
Nieto-Morote and Ruz-Vila FST & AHP
(2011)
Assess Risk against
Project Objective
Period of
Time Author Yes No
1980s Chapman and Cooper (1983) Time
Cooper et al. (1985) Cost
Nguyen (1985) Cost
Franke (1987) Cost
Kangari and Riggs (1989) [check]
The 1990s Yeo (1990) Cost
Mustafa and Al-Bahar (1991) [check]
Diekmann (1992) [check]
Chun and Ahn (1992) [check]
Paek et al. (1993) Cost
Dey et al. (1994) Cost
Riggs et al. (1994) Cost & time
Zhi (1995) [check]
Williams (1995) Quality
Wirba et al. (1996) [check]
Tavares et al. (1998) Cost & time
Mulholland and Christian Time
(1999)
The 2000s Hastak and Shaked (2000) [check]
Tah and Carr (2000) [check]
Dey (2001) Cost
Tah and Carr (2001) [check]
Baccarini and Archer (2001) Cost, time &
quality
Cho et al. (2002) [check]
Ward and Chapman (2003) [check]
Baloi and Price (2003) Cost
Jannadi and Almishari Time
(2003)
Choi et al. (2004) [check]
Shang et al. (2005) [check]
Dikmen et al. (2007a) [check]
Cagno et al. (2007) Time
Zhang (2007) [check]
Wang and Elhag (2007) [check]
Zeng et al. (2007) [check]
Zheng and Ng (2005) Cost & time
Zhang and Zou (2007) [check]
Dikmen et al. (2007b) Cost
Han et al. (2008) Cost
Zayed et al. (2008) [check]
Cioffi and Khamooshi (2009) Cost
Lee and Lin (2010) [check]
Nieto-Morote and Ruz-Vila [check]
(2011)
Table 2. Previous introduced risk classification methods
Risk
Classification Grouping risk
No. Author method based on:
1 Cooper and Nature and Primary and
Chapman magnitude secondary risk
(1987)
2 Wirba et al. Risk- Minor and major
(1996) breakdown structure risks
3 Tah and Carr Risk- External and
(2000) breakdown structure Internal factor
4 Dikmen et al. Influence Project risk &
(2007a) Diagram Country risk
5 Zayed et al. Hierarchy Macro and micro
(2008) structure level
6 Nieto-Morote Hierarchy Responsibility of the
and Ruz-Vila structure Construction
(2011) practitioners
Table 3. Developers' profiles and roles in the development of FSM
Developer Age Gender Location Specialty/Area
A 52 Male Kuala Project
Lumpur Monitoring
B 37 Male Kuala Fuzzy Model
Lumpur Development
C 33 Male Selangor Construction Risk
D 36 Female Kuala Construction IT
Lumpur Application
E 49 Male Selangor Construction
Monitoring
F 45 Male Selangor Mathematician
G 31 Female Kuala Risk Management
Lumpur
H 46 Male Kuala Construction Risk
Lumpur Modelling
I 51 Female Kuala Mathematician
Lumpur
Developer Roles in Developing the FSM
A Preliminary step: Considering the limitation of
Selection of Risk conventional AHP models in yielding
Analysis Approach reliable results owing to their
inability to effectively quantify
subjective data, Developer A aroused
the idea of integrating fuzzy tools
into the AHP to further enhance the
efficiency and practicability of the
model. Accordingly, the team decided
to synthesized FST, which was proven
as an excellent tool to capture
uncertain and subjective qualitative
data in decision-making process,
within the developed model.
B Preliminary step: Developer B adopted FST in the
Appearance of Model developed model although the concept
was unfamiliar in the context of
construction industry. Moreover,
Developer B mapped how to present the
model holistically. Important
elements such as mathematical
formulae have been added into the
model to enable an explicit picture
of the whole structure. The model so
that could be presented in a simple
but comprehensive way.
C Preliminary step: Developer C captured and incorporated
Selection of Risk the subjective data of construction
Analysis Approach processes into the risk analysis
techniques to increase the
consistency for risk management. The
real construction rarely adopt formal
risk analysis tools. The only
technique applied in the medium and
small firms is informal technique
such as rule of thumb.
D Step 2 & 6: Developer D provided the risk
Selection of Risk parameters used during the evaluation
Parameters of risks. Both the risk likelihood
and risk severity have been
considered in evaluating the risk
impact to avoid misleading solutions.
For example, a risk with high
likelihood of occurrence is not
necessarily with high level of
severity when it occurred.
E Step 1: Range of Developer E produced risk hierarchy
Expertise trees in different perspectives.
Besides, Developer E identified the
differences in risk management skills
according to the positions of
construction practitioners.
F Step 2: Risk Developer F multiplied the risk
Identification parameters in the analysis to
calculate the final risk impact of a
particular risk.
G Step 2: Risk Developer G identified the risks
Identification based on the type and nature of
projects. Besides, Developer G
figured out the risk identification
methods used in the model
development.
H Step 2: Project Developer H measured risk impacts
Objectives with regards to project objectives
such as time, cost, and quality
during the risk analysis process.
Step 3: AHP's Developer H applied Pairwise
Comparison Method Comparison process within the
developed model, where the risks were
compared to determine which one was
more dominance than the others in a
project.
I Step 4 & 5: Developer I embedded the mathematical
Mathematical formulas into the developed FSM.
Formulae
Table 4. Experts and their respective contribution factors in
the model Pilot Run
Working
Expert experience Contribution
([E.sub.k]) Title (Year) Factor ([C.sub.k])
[E.sub.1] Project 7 0.22
manager
[E.sub.2] Project 11 0.34
coordinator
[E.sub.3] Contractor 5 0.16
manager
[E.sub.4] Engineer in 9 0.28
Chief
Total 32 1.00
Table 5. Evaluation of sub-criteria with respect to "Weather"
(Level 4)
Time
Scale Converted TFN
Time [E.sub.1] 0.22
[E.sub.2] 0.34
[E.sub.3] 0.16
[E.sub.4] 0.28
Aggregation (1.00, 1.00, 1.00)
Cost [E.sub.1] 0.22 (5/2, 3, 7/2)
[E.sub.2] 0.34 (9/2, 5, 11/2)
[E.sub.3] 0.16 (5/2, 3, 7/2)
[E.sub.4] 0.28 (5/2, 3, 7/2)
Aggregation (3.18, 3.68, 4.18)
Quality [E.sub.1] 0.22 (9/2, 5, 11/2)
[E.sub.2] 0.34 (5/2, 3, 7/2)
[E.sub.3] 0.16 (9/2, 5, 11/2)
[E.sub.4] 0.28 (9/2, 5, 11/2)
Aggregation (3.82,4.32,4.82)
Cost
Scale Converted TFN
Time [E.sub.1] (2/7, 1/3, 2/5)
[E.sub.2] (2/11, 1/5, 2/9)
[E.sub.3] (2/7, 1/3, 2/5)
[E.sub.4] (2/7, 1/3, 2/5)
Aggregation (0.25,0.29,0.34)
Cost [E.sub.1]
[E.sub.2]
[E.sub.3]
[E.sub.4]
Aggregation (1.00, 1.00, 1.00)
Quality [E.sub.1] (5/2, 3, 7/2)
[E.sub.2] (5/2, 3, 7/2)
[E.sub.3] (5/2, 3, 7/2)
[E.sub.4] (9/2, 5, 11/2)
Aggregation (3.06,3.56,4.06)
Quality
Scale Converted TFN
Time [E.sub.1] (2/11, 1/5, 2/9)
[E.sub.2] (2/7, 1/3, 2/5)
[E.sub.3] (2/11, 1/5, 2/9)
[E.sub.4] (2/11, 1/5, 2/9)
Aggregation (0.22,0.25,0.28)
Cost [E.sub.1] (2/7, 1/3, 2/5)
[E.sub.2] (2/7, 1/3, 2/5)
[E.sub.3] (2/7, 1/3, 2/5)
[E.sub.4] (2/11, 1/5, 2/9)
Aggregation (0.26,0.30,0.35)
Quality [E.sub.1]
[E.sub.2]
[E.sub.3]
[E.sub.4]
Aggregation (1.00, 1.00, 1.00)
Table 6. Fuzzy comparison matrix with respect to "Weather"
(Level 4)
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.25,0.29,0.34) (0.22,0.25,0.28)
Cost (3.18, 3.68, 4.18) (1.00, 1.00, 1.00) (0.26,0.30,0.35)
Quality (3.82,4.32,4.82) (3.06,3.56,4.06) (1.00, 1.00, 1.00)
Table 7. (Level 4) Matrices of pairwise comparisons and
respective normalized weigh vectors
Vague/incomplete Design Scope: WVDS = (0.34, 0.66, 0)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.25,0.29,0.34) (0.22,0.25,0.28)
Cost (3.18, 3.68, 4.18) (1.00,1.00, 1.00) (0.26,0.30,0.35)
Quality (3.82,4.32,4.82) (3.06,3.56,4.06) (1.00, 1.00, 1.00)
Landslide: WL =(0.13, 0.48, 0.39)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.25,0.29,0.34) (0.22,0.25,0.28)
Cost (3.18, 3.68, 4.18) (1.00,1.00, 1.00) (0.26,0.30,0.35)
Quality (3.20,3.45,4.12) (3.06,3.28,4.18) (1.00, 1.00, 1.00)
Inflation: WI =(0, 0.40, 0.60)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.25,0.31,0.34) (0.36,0.41,0.43)
Cost (3.18, 3.68, 4.18) (1.00,1.00, 1.00) (0.28, 0.30,0.38)
Quality (3.82,4.32,4.82) (3.06,3.56,4.06) (1.00, 1.00, 1.00)
Changes in Local Law: WCLL =(0, 1, 0)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.27,0.31,0.34) (0.19,0.21,0.25)
Cost (3.20,3.45,4.12) (1.00, 1.00, 1.00) (0.17,0.18, 0.24)
Quality (3.51,4.32,4.94) (3.06,3.56,4.06) (1.00, 1.00, 1.00)
Improper Estimate: WIE =(0.03, 0.81, 0.06)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.26,0.30,0.35) (0.09,0.15,0.18)
Cost (4.06,4.56,5.06) (1.00, 1.00, 1.00) (0.20,0.25,0.30)
Quality (5.82,6.32,6.82) (4.13, 4.56,5.06) (1.00, 1.00, 1.00)
Errors and Omissions: WEO= (0.20, 0.62, 0.18)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.07,0.12,0.18) (0.09,0.15,0.18)
Cost (4.06,4.56,5.06) (1.00,1.00, 1.00) (0.12,0.17,0.21)
Quality (5.82,6.32,6.82) (4.13, 4.56,5.06) (1.00, 1.00, 1.00)
Wind Damage: WWD= (0, 1, 0)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.31,0.39,0.44) (0.32,0.39,0.48)
Cost (3.94, 4.11, 4.68) (1.00, 1.00, 1.00) (0.30, 0.33,0.36)
Quality (3.82,4.32,4.82) (4.09,4.56,5.06) (1.00, 1.00, 1.00)
Availability of Funds from Client: WAFC =(0.05, 0.58, 0.37)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.26,0.30,0.35) (0.09,0.15,0.18)
Cost (4.06,4.56,5.06) (1.00,1.00, 1.00) (0.20,0.25,0.30)
Quality (5.82,6.32,6.82) (4.13, 4.56,5.06) (1.00, 1.00, 1.00)
Changes in Government Policy: WCGP =(1, 0, 0)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.06,0.10,0.17) (0.06,0.15,0.18)
Cost (5.82,6.32,6.82) (1.00,1.00, 1.00) (0.11,0.16,0.20)
Quality (6.45,7.16,7.83) (5.15,5.36,6.24) (1.00, 1.00, 1.00)
Changes in Laws and Regulations: WCLR= (0.46, 0.54, 0)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.31,0.39,0.44) (0.32,0.39,0.48)
Cost (3.18, 3.68, 4.18) (1.00,1.00, 1.00) (0.28, 0.30,0.38)
Quality (3.51,4.32,4.94) (3.20,3.45,4.12) (1.00, 1.00, 1.00)
Requirement Permits & Approval: WRPA =(0.03, 0.73, 0.24)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.25,0.29,0.34) (0.22,0.25,0.28)
Cost (3.18, 3.68, 4.18) (1.00,1.00, 1.00) (0.26,0.30,0.35)
Quality (3.51,4.32,4.94) (3.20,3.45,4.12) (1.00, 1.00, 1.00)
Labor Dispute and Strike: WLDS =(0, 0.40, 0.60)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.31,0.39,0.44) (0.32,0.39,0.48)
Cost (3.18, 3.68, 4.18) (1.00,1.00, 1.00) (0.30, 0.33,0.36)
Quality (4.13, 4.56,5.06) (4.35,4.56,5.06) (1.00, 1.00, 1.00)
Damage to Equipment: WDE= (0, 1, 0)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.25,0.29,0.34) (0.22,0.25,0.28)
Cost (5.54, 5.64, 6.18) (1.00,1.00, 1.00) (0.26,0.30,0.35)
Quality (4.82,5.32,5.82) (6.06,6.56,7.06) (1.00, 1.00, 1.00)
Labor Injuries: WLI= (0.46, 0.54, 0)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.04,0.09,0.15) (0.08,0.11,0.13)
Cost (7.44,7.56,8.06) (1.00,1.00, 1.00) (0.20,0.25,0.30)
Quality (8.23,8.32,9.94) (7.20,7.45,8.12) (1.00, 1.00, 1.00)
Pollutions and Safety Rules: WPSR =(0, 0.97, 0.03)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.06,0.10,0.17) (0.06,0.15,0.18)
Cost (4.06,4.56,5.06) (1.00,1.00, 1.00) (0.11,0.16,0.20)
Quality (5.82,6.32,6.82) (4.13, 4.56,5.06) (1.00, 1.00, 1.00)
Defective Work: WDW= (0.05, 0.95, 0)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.04,0.09,0.15) (0.10,0.11,0.17)
Cost (7.44,7.56,8.06) (1.00,1.00, 1.00) (0.20,0.25,0.30)
Quality (8.12,8.32,8.94) (7.46,7.85,8.02) (1.00, 1.00, 1.00)
Labor Productivity: WLP =(0, 0, 1)T
Time Cost Quality
Time (1.00, 1.00, 1.00) (0.25,0.29,0.34) (0.22,0.25,0.28)
Cost (3.18, 3.68, 4.18) (1.00,1.00, 1.00) (0.26,0.30,0.35)
Quality (3.51,4.32,4.94) (3.20,3.45,4.12) (1.00, 1.00, 1.00)
Table 8. (Level 3) Matrices of pairwise comparisons and
respective normalized weigh vectors
Design: [W.sub.D] = [(0.67, 0.33).sup.T]
Vague/incomplete Errors and
Design scope omissions
Vague/ (1.00, 1.00, 1.00) (5.06,5.54,6.13)
incomplete
Design
scope (5.06,5.54,6.13) (1.00, 1.00, 1.00)
Political and Environmental: [W.sub.PE] = [(0.43, 0.37, 0.20).sup.T]
Change in laws Requirement for Pollutions and
and regulations permits and their safety rules
approval
Change in 1.00, 1.00, 1.00 0.13,0.16,0.22 0.25,0.27,0.35
laws and
regulations
Requirement 3.24, 3.78, 4.26 1.00, 1.00, 1.00 0.26,0.33,0.37
for permits
and their
approval
Pollutions 3.89,4.22,4.78 3.22,3.75,4.18 1.00, 1.00, 1.00
and safety
rules
Nature: [W.sub.N] = [(0.63, 0.15, 0.22).sup.T]
Weather Landslide Wind damage
Weather (1.00, 1.00, 1.00) (0.45,0.39,0.34) (0.22,0.25,0.28)
Landslide (4.18, 4.68, 5.18) (1.00, 1.00, 1.00) (0.26,0.30,0.35)
Wind (3.82,4.32,4.82) (3.06,3.56,4.06) (1.00, 1.00, 1.00)
damage
Financial and Economic: [W.sub.FE] = [(0.19, 0.04, 0.15, 0.05,
0.57).sup.T]
Inflation Availability of Changes in local
funds from client law
Inflation 1.00,1.00,1.00 0.16,0.21,0.25 0.18,0.20,0.27
Availability 5.03,5.25,6.26 1.00,1.00,1.00 0.26,0.31,0.32
of funds
from client
Changes in 5.15,5.36,6.24 6.32,6.46,6.88 1.00,1.00,1.00
local law
Changes in 6.45,7.16,7.83 6.22,6.46,6.84 5.17,5.56,6.67
govt. policy
Improper 6.64,7.25,7.46 6.45,7.16,7.83 5.82,6.32,6.82
estimate
Changes in Improper estimate
govt. policy
Inflation 0.17,0.21,0.28 0.22,0.27,0.33
Availability 0.10,0.15,0.22 0.13,0.15,0.18
of funds
from client
Changes in 0.19,0.22,0.23 0.21,0.33,0.35
local law
Changes in 1.00,1.00,1.00 0.19,0.26,0.30
govt. policy
Improper 5.15,5.36,6.24 1.00,1.00,1.00
estimate
Job Site-related: [W.sub.JS] = [(0.20, 0.08, 0.11, 0.07, 0.64).sup.T]
Labour dispute Defective work Damage to
and strike equipment
Labour 1.00,1.00,1.00 0.16,0.21,0.25 0.18,0.20,0.27
dispute and
strike
Defective 5.03,5.25,6.26 1.00,1.00,1.00 0.26,0.31,0.32
work
Damage to 5.15,5.36,6.24 6.32,6.46,6.88 1.00,1.00,1.00
equipment
Labour 6.45,7.16,7.83 6.22,6.46,6.84 5.17,5.56,6.67
productivity
Labour 6.64,7.25,7.46 6.45,7.16,7.83 5.82,6.32,6.82
injuries
Labour Labour injuries
productivity
Labour 0.17,0.21,0.28 0.22,0.27,0.33
dispute and
strike
Defective 0.10,0.15,0.22 0.13,0.15,0.18
work
Damage to 0.19,0.22,0.23 0.21,0.33,0.35
equipment
Labour 1.00,1.00,1.00 0.19,0.26,0.30
productivity
Labour 5.15,5.36,6.24 1.00,1.00,1.00
injuries
Table 9. (Level 2) Matrices of pairwise comparisons and respective
normalized weigh vectors
Risk Likelihood: [W.sub.RL] = [(0.42,0.29,0.10,0.07,0.12).sup.T]
Design Nature
Design (1.00,1.00,1.00) (0.35,0.41,0.44)
Nature (5.15,5.36,6.24) (1.00,1.00,1.00)
Financial and economic (5.17,5.56,6.67) (5.03,5.25,6.26)
Political & environmental (5.22,5.12,5.82) (6.22,6.46,6.84)
Job site-related (5.12,5.33,6.77) (6.45,7.16,7.83)
Risk Severity: [W.sub.RS] = [(0.21, 0.19, 0.10, 0.05, 0.45).sup.T]
Design Nature
Design (1.00,1.00,1.00) (0.16,0.21,0.25)
Nature (5.03,5.25,6.26) (1.00,1.00,1.00)
Financial and economic (5.11,5.24,6.26) (6.32,6.46,6.88)
Political & environmental (6.45,7.16,7.83) (6.22,6.46,6.84)
Job site-related (6.64,7.25,7.46) (6.66,7.34,7.78)
Financial and Political and
economic environmental
Design (0.37,0.40,0.46) (0.31,0.38,0.44)
Nature (0.26,0.31,0.32) (0.30,0.33,0.40)
Financial and economic (1.00,1.00,1.00) (0.29,0.33,0.38)
Political & environmental (5.15,5.36,6.24) (1.00,1.00,1.00)
Job site-related (5.82,6.32,6.82) (5.11,5.24,6.26)
Risk Severity: [W.sub.RS] = [(0.21, 0.19, 0.10, 0.05, 0.45).sup.T]
Financial and Political and
economic environmental
Design (0.04,0.10,0.14) (0.17,0.21,0.28)
Nature (0.06,0.12,0.16) (0.10,0.15,0.22)
Financial and economic (1.00,1.00,1.00) (0.17,0.22,0.22)
Political & environmental (5.17,5.56,6.67) (1.00,1.00,1.00)
Job site-related (5.22,5.12,5.82) (5.15,5.36,6.24)
Job site-related
Design (0.30,0.37,0.42)
Nature (0.33,0.35,0.38)
Financial and economic (0.31,0.33,0.38)
Political & environmental (0.29,0.36,0.38)
Job site-related (1.00,1.00,1.00)
Risk Severity: [W.sub.RS] = [(0.21, 0.19, 0.10, 0.05, 0.45).sup.T]
Job site-related
Design (0.22,0.27,0.33)
Nature (0.13,0.15,0.18)
Financial and economic (0.21,0.26,0.29)
Political & environmental (0.19,0.26,0.30)
Job site-related (1.00,1.00,1.00)
Table 10. (Level 1) Matrices of pairwise comparisons and
respective normalized weigh vectors
Construction Risks: [W.sub.N] = [(0.57, 0.43).sup.T]
Risk likelihood Risk severity
Risk likelihood (1.00, 1.00, 1.00) (0.16,0.29,0.31)
Risk severity (4.18, 4.68, 5.18) (1.00,1.00, 1.00)
Table 11. Combination of priority weighs
Sub-criteria: Design
Vague/
incompleteDesign Errors and Alternative
scope omissions priority weigh
Weigh 0.67 0.33
Time 0.34 0.20 0.30
Cost 0.66 0.62 0.64
Quality 0 0.18 0.06
Sub-criteria: Nature
Weather Landslide Wind
damage
Weigh 0.63 0.15 0.22
Time 0 0.13 0
Cost 0.50 0.48 1
Quality 0.50 0.39 0
Alternative
priority weigh
Weigh
Time 0.10
Cost 0.53
Quality 0.37
Sub-criteria: Financial and Economic
Inflation Available of fund Changes in
from client local law
Weigh 0.19 0.04 0.15
Time 0 0.05 0
Cost 0.40 0.58 1
Quality 0.60 0.37 0
Changes in Improper Alternative
govt. policy estimate priority weigh
Weigh 0.05 0.57
Time 1 0.03 0.07
Cost 0 0.81 0.71
Quality 0 0.16 0.22
Sub-criteria: Political and Environmental
Changes in Requirement for Pollutions and
laws and permits and safety rules
regulations their approval
Weigh 0.43 0.37 0.20
Time 0.46 0.03 0
Cost 0.54 0.73 0.97
Alternative Alternative
priority priority
weigh weigh
Weigh
Time 0.21 0.21
Cost 0.69 0.69
Sub-criteria: Design
Vague/ Errors and Alternative
incompleteDesign omissions priority
scope weigh
Quality 0 0.24 0.03 0.10
Sub-criteria: Job Site-related
Labour dispute Defective Damage to
and strike work equipment
Weigh 0.20 0.08 0.11
Time 0 0.05 0
Cost 0.40 0.95 1
Quality 0.60 0 0
Labour Labour Alternative
productivity injuries priority
weigh
Weigh 0.07 0.64
Time 0 0.46 0.30
Cost 0 0.54 0.51
Quality 1 0 0.19
Sub-criteria: Risk Likelihood
Design Nature Financial
and
economic
Weigh 0.42 0.29 0.10
Time 0.30 0.10 0.07
Cost 0.64 0.53 0.71
Quality 0.06 0.37 0.22
Political Job site- Alternative
and related priority
environmental weigh
Weigh 0.07 0.12
Time 0.21 0.30 0.21
Cost 0.69 0.51 0.61
Quality 0.10 0.19 0.18
Sub-criteria: Risk Severity
Design Nature Financial
and
economic
Weigh 0.21 0.19 0.10
Time 0.30 0.10 0.07
Cost 0.64 0.53 0.71
Quality 0.06 0.37 0.22
Political Job site- Alternative
and related priority
environmental weigh
Weigh 0.05 0.45
Time 0.21 0.30 0.23
Cost 0.69 0.51 0.58
Quality 0.10 0.19 0.19
Main criteria: Construction risks
Risk Risk Alternative
likelihood severity priority
weigh
Weigh 0.57 0.43
Time 0.21 0.23 0.22
Cost 0.61 0.58 0.60
Quality 0.18 0.19 0.18
Table 12. Validation results of FSM
Evaluator Flexibility Accessibility Completeness Reliability
A 7 8 8 9
B 9 8 7 8
C 8 7 8 10
D 8 7 9 8
E 7 8 9 10
F 7 7 9 9
G 9 9 8 9
H 8 7 7 8
I 8 8 9 10
MEAN 7.9 7.7 8.2 9.0
User Assistance in Adaptability
Evaluator Friendly Decision-making for complexity
A 9 10 10
B 9 9 9
C 10 9 10
D 9 8 9
E 10 10 10
F 10 9 10
G 9 9 10
H 9 10 9
I 9 9 10
MEAN 9.3 9.2 9.7
