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Complexitydriven Risk Decision Framework for Cost Overrun
using FuzzyBayesian Network
Farman Afzal ( farmanafzal@gmail.com )
University of Engineering and Technology https://orcid.org/0000000186379741
Fahim Afzal
University of Sialkot
Danish Junaid
Bahria University
Imran Ahmed Shah
Shah Abdul Latif University
Shao Yunfei
UESTC: University of Electronic Science and Technology of China
Research Article
Keywords: Risk assessment, cost overrun, complexityrisk interdependency, fuzzy logic, Bayesian network, construction projects
Posted Date: November 17th, 2022
DOI: https://doi.org/10.21203/rs.3.rs2216201/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
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Abstract
This study adheres to nd important complexityrisk interdependent causes of cost overrun in infrastructure transport projects rather
considering an independent state of project risk. Aiming for addressing cost overrun problem to facilitate decisionmakers, a
hierarchical breakdown structure of complex elements and complexitydriven risk factors at different levels of severity is
conceptualized along with their interdependency network of key relationships. In this work, an integrated approach of fuzzy logic with
the Bayesian belief network is employed for costrisk assessment while assuming linguistic scales of likelihood and consequences
parameters. The simulated results of costrisk decision framework imply that poor design issues, increase in material prices and delay
in relocating facilities show higher complexityrisk dependency and increase the risk of cost overrun in complex projects. This study
contributes to the body of knowledge by providing a practical hybrid risk decision framework to identify and evaluate the key
complexityrisk interdependencies in underline relations to the cost overrun problem in construction.
1. Introduction
Complex and dynamic nature of construction projects encountered a series of cost overrun issues over the years (Lee 2008; Eybpoosh
et al. 2011; Cantarelli et al. 2012; Qazi et al. 2016; Sarmento and Renneboog 2017). This cost failure is because of the presence of
uncertainty (Sadeghi et al. 2010) and the dynamic nature of a project (Pehlivan and Öztemir 2018). By denition, larger infrastructure
projects are complex (Fang et al. 2012) and dynamic (Cheng et al. 2010), often encounter cost overrun problem (Love et al. 2014). Lee
(2008) has presented the causes of cost overrun in Korean mega capital projects. The results of his study have shown that 95 to
100% of transport construction projects have the likelihood of cost overrun over 50%. Like in the other regions, Asian international
Infrastructure Transport Projects (ITPs) have also been confronting huge pressure concerning baseline cost divergence due to its
chaotic market structure (Liu et al. 2016). Similarly, AlHazim et al. (2017) have documented that almost 76% of large ITPs in Asia
have cost underestimation problems. In addition, various other studies have also discussed the phenomenon of cost overrun in ITPs
and employed various risk assessment models to nd out the unique causes of cost overrun (Hastak and Shaked 2000; Dikmen et al.
2007; Doloi 2011; Eybpoosh et al. 2011; Cantarelli et al. 2012; Fang and Marle 2013; Love et al. 2014; Samantra et al. 2017; Olaniran
et al. 2017), but the issue remains static due to the unique dynamic nature of each construction project (Yuan et al. 2018; Tabei et al.
2019). This all happened because of the complex relationship between complexity and complexitydriven risk factors (Qazi et al.
2016). Therefore, baseline cost escalation adheres to the implementation of contingency plans for project progress in managing
complexity and complexitydriven risk within an uncertain environment (Khodakarami and Abdi 2014; Islam and Nepal 2016; Love et
al. 2016).
A growing number of studies have been found in the literature containing hybrid methods in measuring the causes of cost overrun
under high uncertainty (Sadeghi et al. 2010; Shaee 2015; Kabir et al. 2016; Islam et al. 2017; Yazdi and Kabir 2017). The use of fuzzy
hybrid methods, such as fuzzy analytical network processing (Shaee 2015), Fuzzy Bayesian Belief Networks (FuzzyBBNs) (Kabir et
al. 2016), fuzzy neural networks (Chan et al. 2009) and fuzzy Monte Carlo simulation (Sadeghi et al. 2010), appear to be superior over
multicriteria decision models (Hastak and Shaked 2000; Li et al. 2013; Valipour et al. 2015; Shariat et al. 2019) to evaluate the
interdependencies between the events under high uncertainty (Shaee 2015; Mehlawat and Gupta 2016; Islam et al. 2017). In order to
better evaluate the vulnerability exist in subjective risk information (Yildiz et al. 2014) and addressing the range of probabilities in the
form of membership functions rather in absolute crisp values (Islam and Nepal 2016; Kabir et al. 2016), an integrated approach of
Fuzzy Set Theory (FST) (Karimiazari et al. 2011; Islam et al. 2017) and Bayesian Network (BN) (Qazi et al. 2016; Islam et al. 2017;
Yazdi and Kabir 2017) is used. The approach appears to be effective in order to nd the causes of cost overrun with limited
information under high complexity (Fang et al. 2012; Fang and Marle 2012; Cheng and Lu 2015) and uncertainty (Chan et al. 2009;
Sadeghi et al. 2010; Cárdenas et al. 2013; Salling and Leleur 2015).
In the past, various risk assessment frameworks are formulated to assess the causes of cost overrun, but these frameworks did not
reect the complexityrisk interdependencies phenomenon in order to nd the causes particularly in risk assessment process (Dikmen
et al. 2007; Fang and Marle 2013; Qazi et al. 2016; Samantra et al. 2017). Limited studies are found in the literature that have
emphasized on the complex relationship between complexity drivers and risk factors (Marle and Vidal 2016; Qazi et al. 2016). Prior
research has addressed two schools of thought with regards to the risk as an element of complexity (Fang et al. 2012; Fang and
Marle 2013) or having the distinct characteristic of dening cost overrun (Hastak and Shaked 2000; Samantra et al. 2017). This study
focusses on the fact that in dynamic conditions where uncertainty is high, the presence of complexity usually instigates the impact of
risk in a project. Therefore, project complexity and complexitydriven risk factors cannot be evaluated separately in order to nd the
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causes of cost overrun. Subsequently, the main aim of this research is to nd the important hierarchical breakdown structure of
complexityrisk interdependent causes of cost overrun in ITPs and to propose a risk assessment framework considering complex
complexityrisk interdependencies that escalate the project cost. The proposed framework has employed ‘trapezoidal fuzzy
membership function’ to quantify the equivalent linguistic terminologies against rating for complexity elements and risk factors and a
Bayesian inference approach of Directed Acyclic Graph (DAG) to measure and nd important interdependencies within a structured
framework between complexity and complexitydriven risk factors for cost overrun.
The critical risk factors such as ‘inappropriate project designing and poor engineering process’, ‘increase in the price of construction
material’ and ‘delay in transferring existing facilities’ show a high dependency on other complexity elements. The unique contribution
of the present work is to articulate an ecient hybrid approach of fuzzy logic and Bayesian inference for developing structured
priority of potential complexitydriven risks related causes of cost overrun and designing interdependency network for cost overrun in
ITPs.
The procedural steps of the following sections of the paper have been described below. Section 2 has illustrated the preliminaries of
Bayesian inference and FST. Section 3 has explained the procedural steps taken to dene complexity and risk network with empirical
evidence in ITPs. The study ndings and implications have been discussed in Section 4. Finally, conclusions, research limitations and
future directions have been delineated in Section 5.
2. The Construction Of Multistate Fuzzy Bayesian Network
Bayesian Belief Network (BBN) is a graphically designed method called DAG, where nodes denote prior probabilities of risk events and
arrows denote the conditional probabilities between the risk events (Liu 2010). The arrows signify the dependency between mutually
exclusive risk elements inside the risk network (Weber et al. 2012). Thus, the combined effect of prior and conditional probabilities
computes the probability of dependent risk event in a network. In addition, one of the benets of BBN is that it can update the
probabilities frequently in the system when new information for the input factors become available (Khodakarami and Abdi 2014;
Wang et al. 2016). BBN has the ability of backpropagation that helps in measuring the probability of events that may not be
observed directly (Islam et al. 2017).
With the FuzzyBBN hybrid approach, fuzzy logic initially characterizes and measures assessment criteria (i.e., likelihood and
consequences of risk) as per the subjective evaluation of Decision Makers (DMs) on a linguistic scale and then transforms them into
fuzzy membership functions (Kimiagari and Keivanpour 2018). Fuzzy arithmeticmean has been employed herein to compute
aggregate fuzzy membership results in absolute value (Mehlawat and Gupta 2016). For BN these absolute values are further
transformed in threepoint estimates according to the experts’ mental state.
2.1. Bayesian Inference
A general form of BN can be stated as
D = <(X, E), P >
, where
(X, E
) form shows a DAG with
n
number of nodes.
X
represents random
nodes and
E
represents directed edges of these nodes.
P
states the conditional probabilities of each node
and a set of joint probabilities. In BN parameters, the conditional probability of the child node
Xi
is expressed quantitatively under all
the combinations of values of its father node π(
X
i). However, the prior probability value of the root node is expressed in a different
probability state. Conditional probability inference of node
Xi
is independent of other nodes in the same DAG network except for its
father node
π(Xi).
Therefore, under the same inference of π(
X
i), other nodes, except
Xi
, are expressed in
A( Xi
)
, this is also stated in
Eq.1.
1
BN expresses the joint probability distribution of events using conditional probabilities between child and father nodes. The joint
probability distribution for BN inference is given as:
X = {
X
1,
X
2,…,
Xn
}
P
(
Xi

π
(
Xi
),
A
(
Xi
)) =
P
(
Xi

π
(
Xi
))
P
(
X
) =
P
(
X
1,
X
1, … ,
Xn
) =
n
∏
i
=1
P
(
Xi

π
(
Xi
))
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2
Normalized probability of each risk event can be expressed as follows:
3
The prior probabilities of the independent risk events can also be expressed as:
4
2.2. Fuzzy Logic
A wellrecognized decision tool for uncertainty measurement called fuzzy logic allows the vulnerability of the risk events based on
subjective evaluation. FST exclusively addresses an issue in the form of a full or nonmembership function. Construction risks are not
normally characterized due to the complex and uncertain nature of the problems (Lin and Jianping 2011). Conversely, FST adjusts
basic binary logic to catch vagueness and uncertainty in characterizing risk data (Zhang et al. 2017). Fuzziness is a transformation
process of an element in a set of nonmembership and membership state (Kabir et al. 2016). However, the basic limitation of the
fuzzy model is that it does not consider the complex interrelationship effects of risks within or beyond the group (Jin 2010;
Karimiazari et al. 2011). Consequently, fuzzy models can only treat the independent state of risk under high uncertainty in a system.
Thus, to overcome this limitation, other methods are applied in a combination of fuzzy logic to address the complexity and
uncertainty of interdependent risk events in a system (Islam et al. 2017). Because of the limitations of risk data availability and
vagueness in experts’ judgment, it is rather dicult to nd accuracy in risk calculation. Therefore, in this work, a fuzzy membership
function is developed to transform the linguistic evaluation of the likelihood and consequences of complexity and risk.
Generalized trapezoidal fuzzy membership function has been dened as a fuzzy function , which belongs to real
eld
R
, dened as a membership function . Therefore, the trapezoidal fuzzy membership function is
expressed as follows:
5
Similarly, a b c d and b y c is the cross over distribution interval in . Weight = 1] belongs to the maximum height of
, is dened as a regular trapezoid fuzzy membership function, expressed as
3. Methodology: Procedural Steps
This section follows the steps taken to collect the data for assessing the likelihood and consequences of complexity drivers and risk
factors in relation to the cost overrun. In this study, experts’ subjective judgment is recorded through personal interviews from
construction experts, who have been associated with metropolitan construction projects in underdeveloping countries. For the
recording of subjective judgments, ten experts as DMs from a different area of expertise with more than fteen years’ construction
experience have been nominated to participate in the decisionmaking process by the project authorities. Subjective evaluation of
complexity and risk related to cost overrun has been recorded in three rounds according to the requirement of the designed method. In
P
(
Xn
i
)
=
(
PXi
)
∑
n
i
=1
P
(
Xi
)
n
∑
i
=1
P
(
Xn
i
)
= 1,
i
= 1, 2, 3,…,
n
~
F
= (
a
,
b
,
c
,
d
;
ω
)
δ
~
A
(
Z
) :→ [0, 1] ,
z
∈
R δ
~
A
(
Z
)
δ
~
F
(
Z
) =
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
0,
y
< 0
ω
,
a
≤
y
<
b
ω
,
b
≤
y
≤
c
ω
,
c
<
y
≤
d
0,
y
> 0
y
−
a
b
−
a
d
−
y
d
−
a
≤ ≤ ≤ ≤ ≤ ~
F
[
ω
δ
~
F
(
Z
)~
F
~
F
= (
a
,
b
,
c
,
d
;1) .
Page 5/23
the rst round, data is collected to develop a hierarchical breakdown structure of potential complexity drivers and risk factors for cost
overrun on a binary scale. In the second round, the linguistic scale is used to record the likelihood and occurrence of complexity and
risk events. In the last round, prior and conditional probabilities are recorded for developing Bayesian inference of complexityrisk
interdependencies along with the expected variation in project cost.
This research process contains the following steps in order to nd complexityrisk breakdown structure and development of Bayesian
inference for cost overrun.
Step 1: Identication of potential complexity and risk factors to form a hierarchical complexityrisk breakdown structure for cost
overrun.
Step 2: Selection of suitable linguistic scales to record experts’ subjective judgments for both likelihood and consequences of
complexityrisk events.
Step 3: Transformation of linguistic data into an appropriate trapezoidal fuzzy function in accordance with a recommended fuzzy
scale set by the DMs. In the fuzzy decision matrix process, a collective opinion of DMs is obtained using fuzzy aggregation rule and
fuzzy control.
Step 4: Development of BBN for complexityrisk interdependencies based on the fuzzy triangular distribution probability values of key
prior complexity and conditional risk factors.
Step 5: For the analysis and reevaluation process, project cost data against each complexitydriven risk criteria is collected across
different construction projects, for sensitivity measurement. Threepoint joint estimates of cost overrun (i.e., low, medium, and high)
are determined against three estimates (i.e., pessimistic, most likely, and optimistic) of important risks that directly impact on cost
overrun assuming complexityrisk interdependences.
The specic identity of experts involved in the decisionmaking process is not supposed to reveal due to the reason of anonymity.
During the interview session, experts have been requested to record their judgments on a prescribed format of the questions. After
getting an initial response on a binary scale, a structured framework of complexity drivers and risk factors is drawn for further work.
3.1. Identication of Complexity and Risk Breakdown Structure
After intensive literature review, different complexity elements and complexitydriven risk factors have been transformed into binary
states of ‘True (T)’ or ‘False (F)’ for selection during interview process (Qazi et al. 2016). Afterwards, based on the experts’ aggregate
opinion, a breakdown structure of complexityrisk elements is obtained for the prioritization process. Tables1 and 2 present a total
sixteen complexity elements and twenty risk factors from ve different risk sources, i.e., engineering design, construction
management, construction safetyrelated, natural hazards, and social and economic, as dened by Hastak and Shaked (2000),
Dikmen et al. (2007), Fang et al. (2012), Qazi et al. (2016) and Samantra et al. (2017).
Page 6/23
Table 1
List of Complexity Elements for Cost Chaos in Mega Construction Projects
Complexity dimensions ID Complexity drivers under specic dimensions Reference
Engineering design (
D1
)
CG1
Lacking clarity and misalignment of goals Zidane and Andersen, 2018
PS2
Ambiguity in dening project scope Eybpoosh et al., 2011; Ahmadi et al., 2017
QS3
Quality standard Kabir et al., 2016; Iqbal et al., 2015
CS4
Conicting standards Shehu et al., 2014; JatoEspino et al.,
2014
IP5
Inadequate control procedures Cho and Eppinger, 2005
Construction
management (
D2
)
TM6
Uncertainty in technical methods Arashpour et al., 2017; Samantra et al.,
2017
IT7
Innovative technology Eybpoosh et al., 2011
LS8
Lacking skill with the technology in use Wang, 2011; Dikmen et al., 2010
LE9
Lacking experience with project team involved Floyd et al., 2017
CF10
Cash ow during construction Eybpoosh et al., 2011
BF11
Recurring breakdowns of construction
facilities and plan OuYang and Chen, 2017; OuYang and
Chen, 2017
Economic and social (
D3
)
SP12
Number of stakeholders and their perspectives Zayed et al., 2008; Afzal et al., 2018
PC13
Political condition Kim et al., 2009
MC14
Market competition Dikmen et al., 2010
CB15
Corruption and bribery Fazekas and Tóth, 2018; Tahir et al., 2011
GC16
Geological conditions Barakchi et al., 2017; Samantra et al.,
2017
Page 7/23
Table 2
List of Risk Factors for Cost Chaos in Mega Construction Projects
Risk dimensions ID Risk factors under specic dimensions Reference
Engineering design (
D1
)
PD1
Inappropriate project designing and poor
engineering process Eybpoosh et al., 2011
DE2
Design drawing errors Dikmen et al., 2010; Eisenhardt and
Graebner, 2007
IW3
Inconsistency in work items JatoEspino et al., 2014
SI4
Poor construction site inspections Doloi et al., 2012
Construction
management (
D2
)
CP5
The poor construction planning process Terstegen et al., 2016; Cho and Eppinger,
2005
ES6
Insucient experience and skill in construction
works Dikmen et al., 2010
DF7
Delay in relocating existing facilities Lazzerini and Mkrtchyan, 2011; Budayan
et al., 2018
SM8
Unstable supply of construction materials
required Boateng et al., 2015
Construction safety
related (
D3
)
PI9
Inadequate protection of nearby infrastructure
and facilities Zhang et al., 2016
SP10
Inadequate safety procedures of worker Tahir et al., 2011; Shaee, 2015
PE11
Ineffective protection of the environment Eybpoosh et al., 2011; Camós et al., 2016
TC12
Mismanagement of trac control Satiennam et al., 2006
Natural hazards (
D4
)
HR13
Heavy rainfall during construction Wang et al., 2016
SC14
Super cyclonic storm Wang et al., 2016
EQ15
Earthquake Chang, 2014
WS16
Ground water seepage problem Samantra et al., 2017
Social and economic
(
D5
)
PI17
Political interference Boateng et al., 2015; Valipour et al., 2015
PM18
Increases in prices of critical construction
materials Senouci et al., 2016; Fazekas and Tóth,
2018
WS19
Increases in workers’ salaries Eybpoosh et al., 2011; Doloi et al., 2012
NR20
Protest of nearby residents Tsavdaroglou et al., 2018
[Insert Table1]
[Insert Table2]
3.2. Linguistic Scales and Fuzzy Membership Function
Under the condition of uncertainty in subjective risk information, getting exact data of likelihood of occurrence and consequences in
relations with the complexity and risk events, the study necessitates the support of group decision to record experts’ subjective
judgments on a linguistic scale (Kabir et al. 2016; Mehlawat and Gupta 2016). For the effectiveness of subjective judgments in the
assessment process, a linguistic scale has been designed to measure the semantic strength of an event, as suggested by Rezakhani
et al. (2014) and Samantra et al. (2017). In addition, by following Eq.5, fuzzy numbers have been developed to represent a set of
linguistic measurement values for each property of complexity and risk event (Fouladgar et al. 2012; Zhang et al. 2017).
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Although many studies have followed different types of fuzzy membership functions for solving linguisticbased problems (Chang
2014; Russo and Camanho 2015), generalized fuzzy trapezoidal membership function has been selected for subjective assessments
due to the possible optimized constraints of other fuzzy functions (Prascevic and Prascevic 2017). In this research, the likelihood and
consequences for both complexity and risk events have been quantied by using linguistic scales of seven attributes (Samantra et al.
2017) and ve attributes (Amiri and Golozari 2011), respectively, with corresponding fuzzy membership function (Prascevic and
Prascevic 2017), as labelled in Tables3 and 4, and in Fig.1 as well.
Table 3
Fuzzy Linguistic Scale for Assessing Likelihood of Risk or Complexity
Linguistic scale Description Crisp
values Fuzzy membership function
)
Fuzzy
numbers
Very rare (VR) It can be assumed that the possibility of
occurrence is negligible 1LVL = (VRL, VRM, VRN, VRU)(0, .1, .1, .2;
1)
Rare (R) Unlikely but possible to occur an event in
operation 2LR = (RL, RM, RN, RU)(.1, .2,.2, .3;
1)
Occasional (O) Likely to occur event in operation 3 LO = (OL, OM, ON, OU)(.2, .3, .3, .4;
1)
Probable (P) Likely to occur event several times in operation 4 LP = (PL, PM, PN, PU)(.3, .4, .5, .5;
1)
Frequent (F) Likely to occur frequently 5 LF = (FL, FM, FN, FU)(.5, .6, .6 .7;
1)
Very frequent
(VF) Much frequent to occur 6 LVF = (VFL, VFM, VFN, VFU)(.6, .7, .7, .8;
1)
Absolutely
certain (AC) Expected to occur with absolute certainty 7 LAC = (ACL, ACM, ACN, ACU)(.8,.9, .9, 1;
1 )
Table 4
Fuzzy Linguistic Scale for Assessing Occurrence of Risk or Complexity
Linguistic
scale Description Crisp
values Fuzzy membership function
)
Fuzzy
numbers
Very low
(VL) It can be assumed that the magnitude if impact is
negligible. 1OVL = (VLL, VLM, VLN, VLU)(0, .1, .1, .2;
1)
Low (L) Possible to manage impact of event in operation 2 OL = (LL, LM, LN, LU)(.1, .2,.2, .3;
1)
Moderate
(M) Likely to encounter an impact of risk in operation 3 OM = (ML, MM, MN, MU)(.2, .3, .3, .4;
1)
High (H) Signicant impact of event in operation 4 OH = (HL, HM, HN, HU)(.3, .4, .5, .5;
1)
Very high
(VH) Absolute certain impact of an event in operation 5 OVL = (VHL, VHM, VLN, VHU)(.5, .6, .6 .7;
1)
[Insert Table3]
[Insert Table4]
[Insert Fig.1]
(
δ
~
F
(
Z
)
~
F
~
F
~
F
~
F
~
F
~
F
~
F
(
δ
~
F
(
Z
)
~
F
~
F
~
F
~
F
~
F
Page 9/23
3.3. Fuzzy Decision Matrix Process
1. During the decisionmaking process, using linguistic information of Tables3 and 4, a fuzzy decision matrix, for an
individual expert
h
(1, 2, 3,….,
g
) regarding the likelihood (L) and consequences (C) of complexityrisk elements is constructed
separately as articulated in Eq.6. Decision matrix addresses the states of
n
complexity inuencing factors (
C1
,
C2,…
,
Cn
) and
k
risk
factors (
R1
,
R2,…
,
Rk
) under
m
number of dimensions (
D1
,
D2,…
,
Dm
) by a group of
g
number of experts
Hg
. In complexity decision
matrix , (
i = 1, 2,…, m
and
j = 1, 2,…, n
) is specied separately like comparing the states of L and C for each criterion
Cm
against a group of
DMg
. Similarly, in the risk matrix , (
i = 1, 2,…, m
and
j = 1, 2,…, n
) is specied separately for
both states L and C for each criterion
Cm
against a group of
DMg
. Decision matrices for likelihood and
consequence of complexityrisk criteria against individual DM have been expressed herein in Eq.6, as recommended by Islam
and Nepal (2016), Kabir et al. (2016) and Khodakarami and Abdi (2014).
6
1. Involving multiple experts create the decisionmaking process more complex and uncertain (Islam and Nepal 2016; Kabir et al.
2016). As the DMs belong to different designations, experience and qualication, therefore, their opinion holds different weight
credibility in the decision process. The expert’s credibility factor is measured using as discussed by Kabir et al. (2016) and
based on an expert’s experience , qualication , and designation , particularly at risk
management in the construction domain. In this paper, the formulation is modied using a normalization factor
. Table5 describes the general prole of the experts and their weight criteria involved in the decision
making process. The normalization weight vector is computed such that the total credible weight of an expert is considered as 1
and remaining weights of DMs are . Therefore, for
K
number of experts, the credibility factor ( ) is derived as:
Table 5
General Prole of Experts and their Weight Criteria
Respondents Designation Experience Qualication DM’s weights Nweights
01 Principal Engineer 26 PostGraduate 0.8 0.127
02 Senior Engineer 18 Graduation 0.5 0.079
03 Principal Engineer 18 Graduation 0.4 0.063
04 Senior Engineer 20 PostGraduate 0.5 0.079
05 Principal Engineer 23 Ph.D. 0.6 0.095
06 Principal Engineer 20 PostGraduate 0.5 0.079
07 Senior Engineer 24 Graduation 0.5 0.079
08 Senior Engineer 24 Graduation 0.7 0.111
09 Principal Engineer 28 PostGraduate 0.8 0.127
10 Chief Engineer 30 PostGraduate 1 0.159
DMh
C
−
RL
/
C
DMh
CL
/
C
~
Fij
DMh
RL
/
C
~
Fij
DMr
C
−
RL
/
C
DM
1
DM
2⋯
DMg
DMr
C
−
RL
/
C
=
C
1×1
C
2×1
⋮
Cm
×1
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎣
˜
F
1×1
˜
F
1×2 ⋯
˜
F
1×
g
˜
F
2×1
˜
F
2×2 ⋯
˜
F
2×
g
⋮ ⋯ ⋱ ⋮
˜
Fm
×1
˜
Fm
×2 ⋯
˜
Fm
×
g
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦
Wh
Eh
∈ [0,1]
Qh
∈ [0,1]
Dh
∈ [0,1]
MAX
H
h
=1(
DhQhEh
)
β
Wk
≤ 1
Wk
Wh
=(
DkQkEk
)
β
MAXK
k
=1(
DkQkEk
)
β
Page 10/23
7
Where
β
is a weight vector used to assign the weight of individual DM; therefore, the higher
β
value shows the dominance of
DMg
in
assessment with higher and .
[Insert Table5]
1. The fuzzy numbers in the decision matrix are multiplied by the weight score of the respective individual expert (
wh
).
Afterwards, fuzzy multiplication rule as shown in Eq.8 has been applied to get weighted elements of the matrix.
8
Here,
L
,
M
,
N
and
U
mean the lowest, low moderate, moderate and highest possible number of fuzzy trapezoidal function, respectively,
and the symbol ⊗ indicates fuzzy multiplication rule. All the matrices of individual DMs are transformed into one single matrix
following the fuzzy arithmetic average (Islam and Nepal 2016) by using Eq.9.
Elements of group matrix =
9
1. The elements of the group matrix are defuzzied using the following Eq.10. The defuzzication method–Center of Area (Hefei
2017; Yazdi and Kabir 2017)–is used to calculate the absolute values of likelihood and consequences.
10
1. Finally, fuzzy ifthen rules between the likelihood and consequence presented in Table6 are applied to nding the probability level
of risk for Bayesian inference (Cárdenas et al. 2014; Kabir et al. 2016; Yazdi and Kabir 2017).
Table 6
Fuzzy Control Rules between Likelihood and
Consequence
Level of severity Consequences
VL L M H VH
Likelihood VR VR VR VR R R
R VR R R R O
O VR R O O P
P VR O O P F
F VR O P P VF
VF R O P F AC
AC R P F VF AC
[Insert Table6]
Dh
,
QhEh
DMr
C
−
RL
/
C
(
DMh
C
−
RL
/
C
)
w
=
wi
⊗
(
¯
Fh
ij
)
L
,
wi
⊗
(
¯
Fh
ij
)
M
wi
⊗
(
¯
Fh
ij
)
N
wi
⊗
(
¯
Fh
ij
)
U
¯
FG
ij
=
k
=1
∑
h
=
g
¯
Fh
ij
⊗
wh
=
(
k
∑
h
=1
¯
Fh
ij
⊗
wh
)
L
,
(
k
∑
h
=1
¯
Fh
ij
⊗
wh
)
M
(
k
∑
h
=1
¯
Fh
ij
⊗
wh
)
N
(
k
∑
h
=1
¯
Fh
ij
⊗
wh
)
U
1
k
1
k
1
k
1
k
1
k
Center
of
Area
(
COA
) =
wi
=
( )
a
+
b
+
c
+
d
4
Page 11/23
Furthermore, Bayesian inference is developed to nd out the entire posterior probabilities of the complexity event and all intermediate
risk nodes of cost overrun.
3.4. Development of DAG Bayesian Belief Network
It is obvious that decision outcomes are dependent on the riskbearing attitude of the domain experts. Though the linguistic
probability scores of each identied complexityrisk factors may tend to alter when experts’ mental attitude is considered (Islam and
Nepal 2016; Kabir et al. 2016). Therefore, considering experts’ different riskbearing attitudes, i.e., pessimistic (P), most likely (ML) and
optimistic (O), the integration of fuzzy scores into Bayesian inference has become an effective approach in order to analyze
complexityrisk interdependencies (Islam et al. 2017; Yazdi and Kabir 2017). Tables7 and 8 show the computation of linguistic
probability scores of each identied complexityrisk factors with experts’ different riskbearing attitudes.
Table 7
Prior Probabilities Scores of Complexity Elements along with Fuzzy
Values
ID Likelihood Occurrence Probability
C.S L.V C.S L.V L.V P ML O C.S
CG1
0.59 F 0.19 VL VR 0 0 0.1 0.02
PS2
0.56 F 0.21 L O 0.3 0.4 0.5 0.40
QS3
0.49 P 0.31 H P 0.5 0.6 0.7 0.60
CS4
0.47 P 0.25 L O 0.3 0.4 0.5 0.40
IP5
0.65 F 0.19 VL VR 0 0 0.1 0.02
TM6
0.57 F 0.19 VL VR 0 0 0.1 0.02
IT7
0.45 P 0.33 H P 0.5 0.6 0.7 0.60
LS8
0.39 O 0.22 L R 0.1 0.2 0.3 0.20
LE9
0.50 P 0.25 L O 0.3 0.4 0.5 0.40
CF10
0.59 F 0.26 M P 0.5 0.6 0.7 0.60
BF11
0.42 P 0.24 L O 0.3 0.4 0.5 0.40
SP12
0.54 F 0.24 L O 0.3 0.4 0.5 0.40
PC13
0.69 VF 0.28 M P 0.5 0.6 0.7 0.60
MC14
0.56 F 0.28 M P 0.5 0.6 0.7 0.60
CB15
0.73 VF 0.18 L O 0.3 0.4 0.5 0.40
GC16
0.37 R 0.29 M R 0.1 0.2 0.3 0.20
Page 12/23
Table 8
Prior Probabilities Scores of Risk Factors along with Fuzzy Values
ID Likelihood Occurrence Probability
C.S L.V C.S L.V L.V P ML O C.S
PD1
0.55 F 0.11 VL VR 0 0 0.1 0.02
DE2
0.59 F 0.21 L O 0.3 0.4 0.5 0.40
IW3
0.55 F 0.23 L O 0.3 0.4 0.5 0.40
SI4
0.44 P 0.25 M O 0.3 0.4 0.5 0.40
CP5
0.77 VF 0.16 VL R 0.1 0.2 0.3 0.20
ES6
0.63 F 0.19 VL VR 0 0 0.1 0.02
DF7
0.52 F 0.24 M P 0.5 0.6 0.7 0.60
SM8
0.55 O 0.29 M O 0.3 0.4 0.5 0.40
PI9
0.52 O 0.26 M O 0.3 0.4 0.5 0.40
SP10
0.55 P 0.33 H P 0.5 0.6 0.7 0.60
PE11
0.49 O 0.26 M O 0.3 0.4 0.5 0.40
TC12
0.53 P 0.25 M O 0.3 0.4 0.5 0.40
HR13
0.27 R 0.26 M R 0.1 0.2 0.3 0.20
SC14
0.23 R 0.36 H R 0.1 0.2 0.3 0.20
EQ15
0.30 R 0.27 M R 0.1 0.2 0.3 0.20
WS16
0.39 O 0.41 H O 0.3 0.4 0.5 0.40
PI17
0.68 VF 0.18 L O 0.3 0.4 0.5 0.40
PM18
0.74 VF 0.15 L O 0.3 0.4 0.5 0.40
WS19
0.58 F 0.21 L O 0.3 0.4 0.5 0.40
NR20
0.47 P 0.38 H P 0.5 0.6 0.7 0.60
In order to design a DAGbased Bayesian inference, the judgments of DMs are rst transformed into fuzzy numbers, which provide a
probability of risk occurrence. These probabilities are the input variables of BBN for representing the causal relationships among the
complexityrisk elements of cost overrun.
[Insert Table7]
[Insert Table8]
The conditional probabilities of complexityrisk interdependencies have been recorded through the abovementioned decisionmaking
process along with the triangular distribution of cost data, i.e., low, medium and high. During the decision process, experts have been
asked to rst dene complexityrisk interdependencies and then record conditional probability values directly into the network
following the prior probability values of complexity elements.
[Insert Fig.2]
Page 13/23
The DAG in Fig.2 presents interrelationships within complexity elements and risk factors, where complexity is considered as a parent
node and risk as a child node, respectively. Consequently, risk factors, such as inappropriate project designing and poor engineering
process (PD1), delay in relocating existing facilities (DF7) and increases in prices of critical construction materials (PM18), show high
dependency in a network that directly impacts on the cost behaviour.
Bayesian inference in Fig.3 shows normalized joint probability with complexityrisk interdependencies for cost overrun function
calculated by using Equations 2 and 3 on threepoint estimations. Utility node shows to address the cost overrun causes that can be
controlled because of this complex relationship. Finally, three main risk factors, PD1, PM18 and DF7, are found to be important that
reect the direct impact on cost overrun depending on other posterior complexity elements and risk factors in a network.
[Insert Fig.3]
[Insert Table9]
Table 9
Cost Variation against the Probability States of Key Risk Sources (amount in million dollar)
PD1 Pessimistic
PM18 Pessimistic Most likely Optimistic
DF7 Pessimistic Most
likely Optimistic Pessimistic Most
likely Optimistic Pessimistic Most
likely Optimistic
Low 1.7 3 3 2.5 2.5 3 4 7.5 13.5
Medium 3.5 4.5 5 4.5 5.5 6 6.5 7.5 22
High 7.1 8 8 7.2 8 8 8 15 28
PD1 Pessimistic
PM18 Pessimistic Most likely Optimistic
DF7 Pessimistic Most
likely Optimistic Pessimistic Most
likely Optimistic Pessimistic Most
likely Optimistic
Low 7 8 8 8.5 11 14 14 20 20
Medium 14.5 14.5 10 15 16 21 18 22 25
High 21 21 22 23 23 25 25 28 30
PD1 Pessimistic
PM18 Pessimistic Most likely Optimistic
DF7 Pessimistic Most
likely Optimistic Pessimistic Most
likely Optimistic Pessimistic Most
likely Optimistic
Low 30 32 35 41 42 45 47 50 54.4
Medium 35 35 35 45 60 60 60 65 71.5
High 40 40 42 50 62 65 61 63 78.6
Threepoint joint estimates of cost overrun (i.e., low, medium, and high) are determined against three estimates (i.e., pessimistic, most
likely, and optimistic) of important risks that directly impact on cost overrun assuming complexityrisk interdependences. Table9
illustrates the variation of cost in dollars against important risk factors that have been found through Bayesian inference. Additional
cost required to manage risk within the complexityrisk network in ITPs has found between 1.7million (in case of pessimistic
approach of risk probability) to 78.6million dollar (in case of optimistic approach of risk probability).
3.5. Simulation Modelling for CostRisk Reevaluation
Risk analysis and reevaluation
Page 14/23
Right after taking the risk circulation conduct into view, the probability of risk is reconsidered and displayed as a numerical risk
frequency (Afzal et al. 2020), for a thorough description of the methodology used for simulation modelling. The outcomes of Monte
Carlo simulation are useful to estimate the costrisk for the project, grounded on historic cost data and to calculate the entire costs. In
order to reevaluate the FuzzyBBN results, real cost data or each important risk factor is collected from different construction projects
and there simulated values are used for further analysis. The overall cost of the project is calculated by the merge of base and risk
costs of all several components. The supplementary cost vital for allay of the risk is estimated through a contingency model, for the
timely completion of the project (Afzal et al. 2021).
The importance of the highlighted analysis is to know the risk factors of cost overrun that propagate a project into chaos and
calculate the necessary amount of the additional cost needed to handle cotchaos. In the next phase, specialists were requested to
measure the total cost of risk for each identied risk in a network. It is clear that risk scores differ based on the experience of the
specialist. In addition to this, the cost of a project is based on the risk level.
Furthermore, the present study aimed to evaluate the run over of cost while keeping the risk score into consideration that shows that
how much risk is taken by a specialist like pessimistic, most likely, and optimistic. By applying a threepoint calculation approach,
cost variation has been designated for virtual decisionmaking (Afzal et al. 2020). Through revaluation process of model, it is
validated that the maximum project cost ow is coming from the factors of inappropriate project designing and poor engineering
process, delay in relocating existing facilities have caused improper cost management and increases in prices of critical construction
materials.
Table10 summarises costbenet contingency values created by each risk factor's simulated scoring and the corresponding cost to
ameliorate each risk. The contingency index determines the budgetary allocation needed to reduce the project's risk impact despite of
concluding prior to its accomplishment.
Page 15/23
Table 10
Simulated Results of CostRisk Comparative Analysis
Di Risk Factors
IDs Pessimistic
(P) Most likely (M) Optimistic
(O) Reevaluated simulation results
Risk
α= 0
Cost
α = 0
Risk α =
0.5 Cost
α =
0.5
Risk
α =
1
Cost
α = 1
Simulated
risk Simulated
cost Risk
SD Cost
SD
D1 PD10.05 6.75 0.08 9.10 0.08 11.45 0.07 9.74 0.01 11.50
DE20.04 5.55 0.06 6.90 0.07 8.42 0.06 6.72 0.01 8.51
IW30.04 5.64 0.07 7.40 0.07 8.55 0.06 7.45 0.00 8.62
SI40.03 2.10 0.06 2.55 0.06 3.12 0.05 2.61 0.01 3.14
D2 CP50.03 2.82 0.06 3.52 0.05 4.36 0.05 3.41 0.00 4.37
ES60.04 5.52 0.05 6.22 0.08 7.71 0.06 6.42 0.01 7.76
DF70.05 6.52 0.07 8.25 0.08 10.23 0.07 8.72 0.01 10.25
SM80.03 4.96 0.06 6.62 0.06 8.39 0.06 6.26 0.01 8.41
D3 PI90.01 0.36 0.03 0.55 0.05 0.68 0.02 0.38 0.01 0.72
SP10 0.02 0.17 0.04 0.26 0.04 0.27 0.03 0.44 0.00 0.29
PE11 0.01 0.09 0.03 0.15 0.04 0.12 0.02 0.20 0.00 0.14
TC12 0.02 0.22 0.03 0.35 0.05 0.36 0.02 0.40 0.01 0.37
D4 HR13 0.04 1.89 0.05 2.54 0.04 3.18 0.04 2.41 0.00 3.22
SC14 0.02 0.09 0.03 0.18 0.04 0.11 0.01 0.20 0.00 0.14
EQ15 0.04 0.17 0.04 0.24 0.06 0.33 0.02 0.31 0.01 0.36
WS16 0.03 0.58 0.05 0.66 0.02 0.74 0.03 0.71 0.00 0.76
D5 PI17 0.04 3.83 0.07 4.53 0.06 5.65 0.04 4.66 0.01 5.64
PM18 0.05 7.58 0.08 10.12 0.09 12.05 0.08 9.95 0.01 12.11
WS19 0.02 1.82 0.03 2.55 0.08 3.08 0.05 2.48 0.00 3.14
NR20 0.03 0.12 0.04 0.19 0.02 0.14 0.01 0.15 0.00 0.16
[Insert Table10]
4. Study Findings And Discussions
Probabilistic causal inferences about cost overruns in relation with complexityrisk interdependencies are acquired from a
combination of assumptions, experiments and data. While addressing the prevalent and complex cost problem, FuzzyBBN is applied
to explicate, determine and predict probabilities within a structured framework of complexityrisk interdependencies. FuzzyBBN
approach presented herein in a model for assessing dependency between complexityrisk related causes of cost overrun under
uncertainty (Islam and Nepal 2016).
An empirical study of metropolitan ITPs in Pakistan is presented herein on the important issue of cost overrun and its potential
control measures have been acquired through a decision process. In consideration of past literature and experts’ opinion, the study
Page 16/23
has assessed complexityrisk interdependencies by considering sixteen potential complexity elements and twenty risk factors from
different indigenous and exogenous sources, such as technical, managerial and environmental (Valipour et al. 2016; Zhang et al.
2016; Liu et al. 2016; Samantra et al. 2017). In this work, important dependencies are identied and subsequent risk management
plan is also suggested for mitigating or controlling the risks leading to project cost overrun.
The ndings of Bayesian inference show that three important interdependent risks, namely ‘inappropriate project design and poor
engineering process’, ‘increase in the price of construction material’ and ‘delay in relocating existing pipelines and facilities’, directly
effect on project cost and found very signicant in the context of ITPs in Pakistan. The maximum variation in project cost reected by
complexityrisk interdependencies is around 78.6million dollars and the maximum risk appears in ‘delay in relocating existing
pipelines and facilities’ with a joint probability value is 41.11%.
The key ndings of this research have suggested that risk cannot be considered independently to nd the causes of cost overrun in
constructions. Risk is derived through the existence of complexity in any project. Consequently, if the complexity level is low in a
project then the probability of risk occurrence is low. Similarly, if system complexity is high then the probability of risk occurrence is
high. Some risk events show high joint network dependency and some with low dependency. Such hidden complexityrisk
interdependencies are important in risk assessment of megaprojects where complexity and uncertainty are always high that usually
instigate the cost escalation. These ndings are consistent with the studies of Qazi et al. (2016), Love et al. (2014) and Fang et al.
(2012), who advocate that the risk is derived through system complexity.
An additional contribution of this research is viewed as to suggest a necessary risk control plan for timely managing construction
project risks to avoid cost escalation. This plan consists of the guidelines for effectively monitoring and controlling critical causes of
cost overrun in relation to complexityrisk interdependencies associated with the ITPs (as shown in Table11).
Table 11
Required Action Plan for Different Dimensions to Avoid Cost Escalation
Dimensions Required actions
Engineering
design (D1) Immediate action required to eliminate the design risk problem and keeping it as low as practically acceptable
by the stakeholders. Risk committee starts to review weekly action plan results.
Construction
management
(
D2
)
Decision team reviewed and categorized the action plan needed to eliminate the management related risks.
Construction
safetyrelated
(
D3
)
Immediate plan of action is required from the construction action team to implement and monitor standard
safety procedures in construction.
Natural
hazards (
D4
)The action plan is already determined by the risk committee and incorporated effectively for minimizing risk as
low as reasonability acceptable.
Social and
economic (
D5
)Sensitive risk factors are placed on the watch list and decided to review them frequently by the risk committee.
A further possible plan of action can be taken by tracking the risk rating scores and its sensitivity.
[Insert Table11]
From a risk mitigating and controlling point of view, the present research has explored that ‘policy decisions regarding investment
preferences from the local government’ have been found a major hurdle in determining the project cost over a project life cycle. This
increases the urgency of having competent managers who could deal effectively with public authorities. Secondly, ‘political
instability’, ‘poor economic situation’ and ‘law and order problems’ also instigate the issues related to construction designing, planning
and material prices. Before to initiate such megaprojects, standard technical and construction management related expertise are
required domestically to avoid the potential risk of cost overrun. Similarly, appropriate planning of cash ows over a project life is
mandatory for timely completion of a project rather facing cost overrun problem later that may drift a project into failure.
The unique contribution of the present work is to articulate an ecient hybrid approach of fuzzy logic and Bayesian inference for
developing structured priority of potential complexitydriven risks related causes of cost overrun and designing interdependency
network for cost overrun in ITPs. The fuzzy concept has been empowered herewith to assist in converting the linguistic data of
probability into fuzzy scores that have been further employed in Bayesian inference. In addition, the application of FST and BBN have
Page 17/23
successfully tackled the system complexity and uncertainty as well as vagueness arising in the expert’s perception during the
subjective judgment decision process. It has been observed that the computation of interdependencies has supported to perceive the
degree of severity that requires being controlled for effective cost management in construction. The risk factors with high
interdependencies should be immediately controlled. Simulated results of costrisk data of different projects also validate the ndings
generated through FuzzyBBN modeling.
Theoretically, this study contributes in a way by providing a practical approach to evaluate the complexity and risks in construction
using ve simple steps: (1) Developing a structured hierarchical breakdown structure of potential complexity and risk factors in
complex infrastructure projects (see Tables1 and 2); (2) To transform a linguistic scale into a fuzzy trapezoidal function for
accessing uncertainty or vulnerability in subjective risk data during the decisionmaking process; (3) To calculate the probabilities of
each identied complexityrisk factors using fuzzy decisionmaking process; (4) To develop a unique complexityrisk interdependency
network to nd cost overrun causes and measure tentative variation in project cost considering complex interdependencies within a
system using Bayesian inference with threepoint estimates; (5)Suggesting a required action plan against important risk dimensions
for cost overrun (see Table10). Even more, this methodology may be used by experts from other engineering industries by replacing
and considering the complex relationship between complexity elements and risk factors and following the same steps presented here.
For a practical point of view, this study is subjected to introduce a decisionmaking framework that permits construction experts and
other engineering related project managers in a way: (1) to provide an approximation of the most frequent and critical complexity
driven risks in large construction projects particularly in unstable economies; (2) to quantify uncertainty exists in risk information and
designing interdependency network of complexityrisk oriented causes of cost overrun. The chosen risk assessment process may
provide multiple benets to managers in larger picture: (1) to implement proposed approach for nding the causes of cost overrun in
dynamic construction projects; (2) to foresee the consideration of the required technical capabilities in construction; (3) effective cost
allocation in the project plan while considering the critical associated risks; (4) the suggested action plans and early detection of risk
could improve the project delivery process within predetermined project cost while addressing expensive weaknesses in construction.
As likely, the critical risk factors such as ‘inappropriate project designing and poor engineering process’, ‘increase in the price of
construction material’ and ‘delay in transferring existing facilities’ show a high dependency on other complexity elements. Therefore,
in consideration of this, project managers should emphasize on the abovementioned risks during cost estimation while assuming a
risk dependency on complexity. In summary, the abovementioned suggestions for project and engineering managers can be
potentially achieved by considering the complexityrisk interdependency network under high uncertainty of cost found in this research.
5. Conclusions
Cost overruns that are experienced in large infrastructure projects usually have an adverse impact on an economy and its taxpayers,
particularly in underdeveloping economies. To improve decisionmaking, implementation of effective risk mitigation strategies and
reduce the likelihood of cost overrun being experienced, the undertaken study has been able to redress this prevalent cost problem
under high uncertainty. In this work, a practical risk assessment framework is developed as a reliable tool; since it has established risk
as a source of complexity network. In the present paper, FuzzyBBN approach is embedded for designing complexityrisk
interdependency network of cost overrun. Subsequently, this study has used experts’ tolerance level like optimistic, most likely and
pessimistic as input values for parents (complexity) and child (risk) nodes in BayesianDAG network. More precisely, the uncertainty in
the linguistic evaluation and experts’ mental state are overcome through fuzzy logic, and complexity in a structured framework of
cost overrun measured by using Bayesian inference.
While exploring the procedure of complexity and risk network identication, the study has articulated a hierarchical structure of
complexity and risk factors in relation to ITPs. The hierarchy has been constructed with sixteen complexity elements and twenty
potential risk factors classied into ve distinct risk dimensions. Further, for the DAG network, the probability values of important
complexity and risk factors obtained using the fuzzy decisionmaking process. Similarly, three important risk factors, namely
‘inappropriate design and poor engineering’, ‘increase in the price of construction material’ and ‘delay in transferring existing facilities’,
are found in a an interdependency network with their joint probabilities that have directly linked with project cost overrun and show
high severity level in a network.
The key ndings of this study have suggested that the independent nature of project risk cannot be assumed in ITPs rather it shows
high dependency on project complexity. Therefore, risk should always be considered in relation to project complexity, particularly in
Page 18/23
complex and dynamic nature of projects. In this decisionmaking process, subsequent risk control plan of actions have also been
suggested for mitigating the risks leading to project cost overrun issues.
Since the presented cost risk assessment approach and ndings described herein are explicitly a problemoriented, a proposed
framework may be adapted to evade cost overrun issues in other engineering management related domain. To employ the said risk
assessment framework in context to the specic problem, a clear understanding and knowledge of probable complexity and risks are
required. While assuming the limitations, this integrated fuzzybased risk assessment framework does not consider the sensitivity of
other types of fuzzy membership functions, because a scale for this study has been adopted from past literature. Further study can
be extended to check the sensitivity and applications of different fuzzy membership scales, such as continues function in regard to
the aforementioned risk assessment framework. This study follows simple DAG in Bayesian inference for the complexityrisk network
while assuming threepoint estimates. For better cost estimation in complex interdependencies, future research can be extended using
a credal network or dynamic Bayesian belief network which can be run in support of continues function. In addition, a similar
approach can also be applied in measuring the causes of schedule delays in the dynamic nature of projects. Finally, this article also
contributes to the body of knowledge by providing new generation framework for cost risk assessment under high uncertainty and
complexity in the construction industry.
Declarations
Data Availability
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Project complexity and risk probabilities
Project complexityrisk conditional probabilities
Project cost data against risk probabilities
Acknowledgement
The authors would like to acknowledge the nancial support provided by the National Natural Science Foundation of China under
grant No. 71572028 and 71872027.
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Figures
Figure 1
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Fuzzy trapezoidal membership function plots for likelihood and magnitude
Figure 2
Directed acyclic graph for complexityrisk interdependencies
Figure 3
Posterior and joint probabilities of important complexityrisk interdependencies