Fuzzy Model for Risk Evaluation in Construction Projects
AMAURY A. CABALLERO AND KANG K. YEN
Department of Electrical and Computer Engineering
Florida International University, Miami, Florida
USA
Abstract: - When dealing with activities that are uncertain and variable, associated risks are
often permanent and complex. Traditionally, many risk analysis models are based on
quantitative techniques, which require numerical data. In industrial projects, the
consequences of not taking the different risk factors into account are related to failure in the
form of unusual delays in project completion, with cost surpassing the budgeted cost and
sometimes even failing to meet quality standards and operational requirements. Thus,
effective analysis and management of industry-associated risks remain a big challenge to the
industry practitioners. The purpose of this work is to establish a simple method of evaluating
the risk and uncertain factors that are present in a construction project. The research uses as a
basis a questionnaire survey and in-depth interviews conducted in the State of Florida. From
this information, a risk management fuzzy logic model for the construction sub-contractors is
proposed.
Key Words: Construction, Risk management, Risk allocation, Project management, Fuzzy
logic models.
1 Introduction
Different parties in a construction project
face a variety of uncertain factors. These
factors can be compiled under the category
of risk. Making decisions on the basis of
assumptions, expectations, estimates and
forecasts of future events involves taking
risks. Risk and uncertainty characterize
situations where the actual outcome for a
particular event or activity is likely to
deviate from the estimate or forecast value
[1].
The process of taking a project from initial
investment appraisal to completion, then
into use, is complex, generally bespoke,
and entails time-consuming design and
production processes. It requires a
multitude of people with different skills
and expertise and the coordination of a
wide range of disparate, yet interrelated
activities. Such complexity, moreover, is
compounded
by
many
uncontrollable factors [2].
external,
In the context of project management, risk
management is defined as: "A formal
orderly process for systematically
identifying, analyzing, and responding to
risk events throughout the life of a project
to obtain the optimum or acceptable
degree of risk elimination or control" [3].
In practice, a risk management system
must be practical, realistic and must be
efficient on cost and schedule control. In
any industrial project, an effective risk
management system depends very much
on the characteristics and conditions of the
project and the attitude of the individuals
of the decision-making group.
The risk management, which embraces
risk analysis and risk response, is a matter
of increasing significance. The effect of
not delivering a project according to its
predetermined requirements can be
disastrous to all parties concerned. In
analyzing the causes of project failures, it
is clear that little or no attention has been
paid to the problems that can materialize
in most projects.
modeling. It is the process of
systematically
and
continuously
identifying, classifying, and assessing the
risks associated with a project. In this
research, the critical risks were identified
in three stages as follows:
2 Identification of Critical Risks
As shown in Figure 1, risk identification
process is the first step in risk management
Risk Identification
Risk Classification
Risk Analysis
Risk Attitude
Risk Evaluation
Fig. 1. Steps Adopted for Building a Risk Management Model



Identification of all possible risks,
which may be encountered by a
risk analyzer through detailed
literature and Internet search.
Identification of critical risks that
may apply to the particular case
under analysis. These risks are
identified from a list generated
through
a
questionnaire
to
practitioners in the field.
Verification of critical risks via
interviews with professionals.
There are two factors that are always
present when analyzing risk: the
probability or chance of occurrence of the
different possible events, and the
maximum potential loss, expressed as a
percent of the total cost lost due to each
event. These two factors will be used as
inputs in the fuzzy logic model.
3 Development of the Risk
Management Fuzzy Logic Model
The risk management model for any
application has to be developed based on a
systematic
methodology
of
risk
identification, risk classification, risk
allocation and risk response. This risk
management information, can be used by
the risk manager to accurately classify the
identified risk element, estimate their
chance of occurrence to decide whether to
avoid the risk completely, retain it and try
to reduce its impact by taking preventive
steps, or finally, transfer it to a party better
able to handle it. From the obtained
information, a mathematical model can be
developed. This model gives the manager
a quantified evaluation of the risk that can
be used as an element to compare different
projects.
Fuzzy logic appears like an attractive tool
for solving this task. As indicated by
Zadeh [4], it is very difficult for
conventional quantification to express
reasonably those situations that are
complex or hard to define. From this, the
notion of a linguistic variable is necessary.
A linguistic variable is a variable whose
values are words or sentences. Here these
expressions are used to compare two
uncertainty factors.
Let’s define the vector C, as the chance of
occurrence of the different possible events.
This vector can be represented through:
C = [C1, C2, … , CN ],
(1)
where CN is the chance of occurrence of
event (type of risk) number N, which will
vary in general from one project to
another.
The vector M will represent the Maximum
Potential Loss, expressed as a percent of
the total cost lost due to each event.
Where,
M = [M1, M2, ……., MN ],
(2)
which is defined in a similar way to the
previously defined C.
These two vectors have been found in
different surveys as the most important
factors affecting the risk. Both vectors can
be taken as fuzzy inputs in a fuzzy model,
where the risk vector R will be the output.
This risk vector will be represented
through:
R = [R1, R2, ………RN],
(3)
where RN is the risk incurred due to the
event N.
There are two ways of assessing the risk
depending on the type of combination
process [5]. In the first one, each expert
system or fuzzy policy is executed as a
stand-alone component. The result of the
policy is used by the risk assessment
manager to derive a final value on a scale
between zero and one hundred. The other
approach (used in this work) combines
expert intelligence inside the model. The
result of this aggregation, a final outcome
fuzzy set, is then defuzzified using the
center of gravity technique to produce a
risk assessment measure.
As indicated in [6] and [7], fuzzy measure
F(X), is a set function defined on the
power set R(X) of X, and satisfies the
following properties:
a) F(0) = 0 and F(X) = 1; (boundary
conditions)
b) if A,B  R(X) and A  B then
F(A)  F(B); (monotonicity)
c) if Fk  R(X) for 1  k   and a
sequence {Rk} is monotone, then
lim k F(Rk) = F(lim k Rk); (sense of
inclusion).
A -fuzzy measure F is a fuzzy measure
with the following characteristic:
 A,B  R(X), A  B =,
then for  = 0,
F (AB) = F(A) + F(B)
(4)
Implying that A and B have additive
effect. This means that the evaluation of
the set {A,B} equals the sum of
evaluations for sets {A} and {B}. In other
words, it is possible to add the results for
each fuzzy output for obtaining a fuzzy
general output, assuming that each of them
is independent from the other. This result
can be extended for obtaining an average
value of the different fuzzy sets outputs.
The universe of discourse of the Chance of
Occurrence has been defined between 0
and 6. The center of gravity of each
membership function has been located as
follows: very low (VL)—1; low (L)—2;
medium (M)—3; high (H)—4; very high
(VH)—5. The Maximum Potential Loss
membership functions have been evenly
distributed between 0 and 50%. The output
Risk is represented as fuzzy functions
varying from 0 to 100%, where 0 is no risk
at all and 100% is the certainty of
occurrence of a non-desired situation. For
applying fuzzy logic to each event, the
rule set can be selected for each particular
case. The rules structure is of the type “if
X and Y, then Z”. This rule set may be
changed in dependence of the real
conditions under which the project is
developed.
A fully weighted average normalizes the
sum with the sum of credibility weights
and has the form of a minimum-variance
average:
q
 ω k Fk (x)
W(x) 
k 1
q
(6)
 ωk
k 1
4 Illustrative Example
Construction is a highly risk-prone
industry with not a very good track in
dealing with risks. A questionnaire was
distributed to construction subcontractors
involved in different specialty trades such
as concrete, earthwork, HVAC, piping,
etc.in the state of Florida, USA.
In this questionnaire different parameters
related to the risk involved in the activity
were considered. These parameters were:
Acts of God, Construction Related, Design
related, financial, Physical, and SocioPolitical. For each parameter a response
was solicited, related to the chance of
occurrence and the maximal potential loss.
The response was given for each
parameter as: Very low (VL), Low (L),
Medium (M), High (H), or Very High
(VH).
The responses for each parameter, from
the
different
subcontractors,
were
averaged to obtain a final value for each
parameter. As indicated by Kostko [8],
“for combining q experts or fuzzy systems
Fk: Rn
Rp
(5)
The q systems can be viewed as q experts
or knowledge sources. Then the combined
output F(x) answers a question: What do
we conclude from the answers of q experts
when we ask them question x?” The
proposed way is to use a weighted
average.
where Fk(x) is the expert evaluation of a
concrete situation and k  [0, 1] are the
experts’ credibility weights.
In the composition, the assigned number
to each response was the same used for the
center of gravity of the correspondent
membership function. The Risk is
presented on a scale from 0 to 100%. In
this application, only the factors with high
incidence in this particular place have
been taken into account. The results are
given by the used fuzzy logic software [9].
Figure 2 shows the surface representation
for the risk as per the selected ranges of
the input variables and the established
fuzzy rules. The figure gives a general
idea of the risk variation as a function of
the Chance of Occurrence and the
Maximal Potential Loss.
The obtained values for each risk category
provide management knowledge on the
risk and uncertainty inherent in a project
and lead to better decision outcomes. It
could be desirable to represent the average
risk as some number expressed in percent.
The task here is to combine the results for
each
risk
parameter
after
the
defuzzification process, in other words,
reducing the amount of available
information in the model to a single scalar.
This calculation will give a number that
could help in getting an idea of the
average risk, but the particularities of the
process being modeled will be hidden
(part of the information will be lost), as
expressed by Cox [5]: “this single point in
the fuzzy hyperspace carries only two
dimensions of information: the expected
domain value (the horizontal displacement
in the fuzzy set), and the value’s degree of
membership in the output fuzzy set (the
vertical displacement in the fuzzy set).
Repeated combinations of fuzzy models at
this level tend to increase the overall
information entropy associated with the
entire system.” The result is a loss of
information that increases as the results of
many independent fuzzy models are
averaged.
The simplest way of getting the average is
assuming statistical independence among
all the events, as per equation (4), and
giving them the same weight, the obtained
risk average for the presented situation can
be calculated from
N
Rav = 1/N[  Ri
(7)
i=1
where N is the number of events (type of
risk).
Figure 2. Risk Surface Representation (X: Occurrence; Y: Loss; Z: risk)

5 Conclusions
1. In this study, the critical risks were
identified in three stages as follows:
Identification of all possible risks,
which may be encountered in a
construction project by a subcontractor
through
detailed
literature and Internet search.


Identification of critical risks in the
Florida construction industry.
These risks were identified from
the list generated in the first step
through the questionnaire.
Verification of critical risks in the
Florida construction industry via
interviews with professionals
2. The concept of risk management is
relatively new to the Florida construction
industry.
The
responses
to
the
questionnaire reveal that most subcontractors are not carrying out formal risk
management. In fact, some responses were
received stating that they were not aware
of a discipline called risk management. It
appears that Florida sub-contractors are
still not aware of the great benefits that
risk management provides or can provide
to the construction industry. It is found
that the Florida construction industry
prefers to eliminate and transfer risks
instead of finding a systematic procedure
to deal with them through such techniques
as risk retention or risk reduction.
3. The fuzzy logic model gives the subcontractor a quantified evaluation of the
risk that can be used as an element to
compare different projects. There exist
several advantages when implementing
decision-making models based on fuzzy
logic:



Experts related to the problem area
can present their evaluation of the
different parameters with concepts
such as “worse”, “better”, etc.,
without having to numerically
quantify their opinions from the
beginning of the evaluation
process.
The calculus using fuzzy logic is
simple
and
close
to
the
representation of knowledge.
There is a wide array of software
available for solving problems
utilizing fuzzy logic.
References
[1] Raftery, J. Risk Analysis in Project
Management, E & FN Spon, London SE1
8HN, UK. 1994.
[2] Flanagan, R., and Norman G. Risk
Management and Construction. Blackwell
Scientific Publications, Oxford, London,
1993.
[3] Al-Bahar, J.F. Risk Management in
Construction Projects: A Systematic
Analytical Approach for Contractors,
Ph.D. Dissertation, Department of Civil
Engineering, The University of California
at Berkeley, CA, 1988.
[4] Zadeh, L.A, The concept of a linguistic
Variable and its Application to
Approximate Reasoning, Part 1, 2, and
3, Information Sciences, Vol. 8, No. 2,
Vol. 8, No. 3, and Vol. 9, No.1, 1975.
[5] Cox E. D. Fuzzy Logic for Business
and Industry. Charles River Media Inc.
Publishers, 1995.
[6] Lee, K. M. and Leekwang, H.,
Identification of -fuzzy Measure by
Genetic Algorithms, Fuzzy Sets and
Systems, Vol. 75, pp. 301-309, 1995.
[7] Shih-Tong Lu, Ting-Ya Hsieh, and
Hsin-Lung Liu. Fuzzy Multicriteria
Analysis Approach to Assessment the Risk
and Uncertainty of construction Projects.
Proceedings of the 9th Bellman Continuum
International Workshop on Uncertain
Systems and Soft Computing. pp 124-132,
Beijing, China. July 24-27, 2002.
[8] Kostko B. Fuzzy Engineering. Prentice
Hall Publishers, 1997.
[9] Togai Infralogic, Inc. TIL Shell 3.0 BE