FUZZY TOPSIS APPROACH TO IMPROVE QUANTITATIVE
RISK ANALYSIS CONSIDERING DIFFERENT CRITERIA
AND THEIR MUTUAL EFFECTS
Mohammad-Hossein Sarbaghi
1
, Majid Shakhsi-Niaei
2
and Seyed Hossein Iranmanesh
2
1
Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran
2
Industrial Engineering Department, College of Engineering, University of Tehran, Tehran, Iran
Keyword: Project management, Risk analysis, PMBOK standard, Fuzzy, TOPSIS.
Abstract: In PMBOK, a widely used project management standard, different risks are ranked based on two criteria:
their probability and their impact on the project objectives. The multiplication of these two criteria is
considered as the index of ranking the risks. This index ignores other criteria and also works weak in some
special situations. In addition, it seems ambiguous when an expert is asked to determine the impact of risks
on the project objectives via only one variable. This paper proposes a fuzzy multi-criteria approach to
effectively analyze the impact of the risks on different important aspects of a project. The proposed
approach works in a fuzzy environment with linguistic variables. The concept of linguistic variable is very
useful in situations where decision problems are too complex or too ill-defined to be described properly
using conventional quantitative expressions. Finally, the proposed approach is performed in a case study
and the results have been compared with a deterministic TOPSIS method; which shows a significant
difference in rankings when the fuzziness has been incorporated in the risk analysis process.
1 INTRODUCTION
Projects have strategic, technical, economical and
national elements and reaching to their defined
targets will face with threats and opportunities that
affect critical objectives of project like schedule,
cost, and quality. The root of these threats and
opportunities can be found in the set of non-
deterministic conditions or uncertainties that occur
as a result of technical, managerial, commercial,
internal and external issues. Project risk is defined as
uncertain event or condition that will result positive
or negative impact on the project objectives, if
happens (Konstantinos, 2002).
Risk management is the systematic process of
identifying, analyzing, and responding to project
risks. It includes maximizing the probability and the
consequences of positive events and minimizing the
probability and the consequences of adverse events
towards project objectives.
Some guides, so called standards, exist for risk
management, including: New Zealand and
Australian standard AS/NZS4360, analysis and
management guide of APM named PRAM,
commercial risk management guide of England
called M_O_R, and the most popular of them,
presented by PMI institute called PMBOK standard
(PMI, 2004). This standard proposes tools for
qualitative and quantitative risk analysis.
In this paper, a fuzzy TOPSIS method is
proposed to improve the qualitative risk analysis.
The proposed approach is implemented in an oil and
petrochemical company.
The rest of the paper is organized as follows.
Section 2 briefly describes the risk management
based on PMBOK standard. Section 3 explains the
proposed approach for improving the risk analysis
process. Section 4 shows the case study results and
section 5 compares them with the results of a
deterministic version of TOPSIS method.
2 QUALITATIVE RISK
ANALYSIS
Regard to PMBOK (PMI, 2004) risks are prioritized
and ranked using two factors: Risk probability, P,
and impact on the project objectives, I. Then these
219
Sarbaghi M., Shakhsi-Niaei M. and Hossein Iranmanesh S..
FUZZY TOPSIS APPROACH TO IMPROVE QUANTITATIVE RISK ANALYSIS CONSIDERING DIFFERENT CRITERIA AND THEIR MUTUAL
EFFECTS.
DOI: 10.5220/0003539902190222
In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 219-222
ISBN: 978-989-8425-74-4
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
risks are ranked using risk score, R.S., index, where:
R.S. = P × I (1)
Then, a risk acceptance level will be determined
and risks are classified into three groups including:
high, moderate, and low important risks. Figure 1 is
an example of probability-impact (PI) matrix to
determine whether a risk is considered low,
moderate, or high.
Probability (P) Risk score=P*I
0.9 0.05 0.09 0.18 0.36 0.72
0.7 0.04 0.07 0.14 0.28 0.56
0.5 0.03
0.05 0.10 0.20 0.40
0.3 0.02 0.03
0.06 0.12 0.24
0.1 0.01 0.01 0.02 0.04
0.08
Impact (I) 0.05 0.10 0.20 0.40 0.80
High importance
Moderate importance
Low importance
Figure 1: Probability-impact (PI) matrix.
In this method, risks that have high probability
and high impact have higher priority. Some guides
propose other criteria besides the risk probability
and impact factor like: Capability of the company to
respond to the risk (McDermott et al, 1996),
uncertainty of estimation (Klein and Cork, 1998), or
efficiency and swiftness to respond to the risks
(Lambert et al, 2001). Using these criteria can
remarkably help the risk management process.
In this paper, different criteria can be used in a
fuzzy multi-criteria method. This procedure is
explained in section 3.
3 PROPOSED APPROACH FOR
IMPROVING RISK ANALYSIS
In this paper, we used a fuzzy TOPSIS method
proposed by Chen (2000) for ranking the risks which
improve the risk analysis in two aspects:
Using risk score cannot comply the aim and
outputs of risk analysis in reporting correct
priority of risks. For example, some risks with
high impact and low probability have low risk
score. So that project face with serious problem
if it happen even the probability is low. But,
more criteria can be used in the proposed
approach.
In PI matrix, if two risks have the same risk
score, will treated the same. But two risks with
equal risk score never have same importance.
Because probability scale and risk impact do not
have same importance. But, in the proposed
approach different weights can be considered in
order to make the criteria different.
This way, multi-criteria decision-making
methods in comparison with impact-probability
method (PI matrix) are more efficient, regarding
various criteria. One of these methods is fuzzy
TOPSIS which considers the evaluation in a fuzzy
area. In this approach, we consider four criteria and
risks are ranked base on their impact on project
objectives like: schedule, cost, quality, health,
safety, and environment (HSE), and synergy factor.
Because the most important criteria for risk ranking
with every probability scale is effect of them on
project objectives, also event probability is
considered while identifying of risks and are omitted
impossible risks (risks with zero probability) from
risks list, therefore using impact criteria for risk
ranking is sufficient. In addition, mentioned
objectives are not independent but influence each
other. Projects have some risks that make other
major risk(s) however themselves have low impact
on project objectives. There are other risks that
influence major or important risks. The meaning of
synergy is consideration of such risks.
4 CASE STUDY
The proposed approach has been implemented in an
oil and petrochemical company.
After identification of major and important
project risks, they are weighted according to fuzzy
TOPSIS procedure. Table 1 shows linguistic
variables used for implying the weight of each
criterion.
Table 1: Linguistic variables for the importance weight of
each criterion.
Linguistic value Fuzzy Number
Very low (VL) (
0; 0; 0.1
)
Low (L)
(0; 0.1,0.3)
Medium low (ML)
(0.1;0.3;0.5)
Medium (M)
(0.3;0.5;0.7)
Medium high (MH) (
0.5; 0.7; 0.9
)
High (H) (
0.7; 0.9; 1
)
Very high (VH) (
0.9; 1; 1
)
Table 2 and 3 show the identified risks and their
evaluations. Table 4 shows the rank of risks and
three groups made based on the rankings. This way,
the risks have been sorted based on their total score
achieved by fuzzy TOPSIS; then the first 30% of the
list have been reported as high-important risks,
second 30% as medium important, and the remained
ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics
220
as low important risks. Thus, the main attention will
be paid to the high-important risks.
The next groups of risk will be taken into
consideration if the required resources, i.e. money,
time, and etc., are still available.
Table 2: Risk descriptions.
Code description
R1
Uncompleted pilot and elaborative plan and disclosing their results in preparation
of stuffs
R2 Correction of ASBUILT plan due to repugnance and operational limitations
R3 Uncompleted pilot and elaborative plan and disclosing their results in execution
R4 Natural condition of ground
R5 Sea storming and not to transfer equipment and materials to destination
R6 Low visibility due to existing of dust so not to transfer air and sea transports
R7 Rain fall
R8 Severe wind blowing
R9 Uncovering of inventory
R10 Scrimpy place of inventory
R11 Scrimpy safety of inventory
R12 Not permission by control room of employer
R13
Not regarding to permit principle and out breaking problems that threaten oil’s
bulk safety
R14
Resistance of employee against uninstalling old equipment and replacement new
equipment
R15 Distance between hostage, office, and workshop
R16 Distance between workshop, operational place and road, accommodation
R17 Employee strike
R18 Learning of unskillful employee for repetitive works
R19 Employing of native worker
R20 Low quality of materials and stuffs
R21 Delay in delivering of concrete
R22 Mistake in selection of proper contractor
R23 Acceptation of high work burden more than capacity by contractor
R24 Hiring of expert contractor according to analyses
R25 Delay in accomplishment of project milestones
R26 Incorrect assessment of labor rate
R27 Not outfit workshop at the correct time
R28 Lack of the expert labor
R29 Weak assessment of labor and required expert
R30 Using night work shift
R31 Machines and equipment failure
R32 Changing executive specification due to not to be optimum
R33 Inaccuracy in financial statement accounting
5 COMPARING THE RESULTS
WITH A DETERMINISTIC
TOPSIS METHOD
In this section, we compare the results when a
deterministic version of TOPSIS is implemented. To
do so, we first defuzzified the evaluations presented
in table 3 via a defuzzification method, so called the
center of area, proposed by Zhao and Govind
(1991). In this defuzzification method, if the
triangular fuzzy number is
),,(
~
321
aaaA
; its
deterministic value is calculated from equation 2:
1
3
)12()13(
a
aaaa
A
(2)
Then, a deterministic TOPSIS method is
performed over this data which has been resulted in
the rankings presented in table 5.
Comparing tables 4 and 5, a significant
difference has been resulted when the uncertainty
is incorporated in the risk analysis process.
Table 3: Evaluations of the identified risks.
Schedule Cost Quality H.S.E. Synergy
w
i
(0.1,0.3,0.5)
(0.077,0.233,0.
433)
(0.033,0.177,0.
277)
(0.077,0.233,0.
433)
(0,0.1,0.3)
R1 (3,5,7) (2.33,4.33,6.33) (0,1,3) (0,1,3) (3,5,7)
R2 (3,5,7) (1,3,5) (0,1,3) (0,1,3) (4.33,6.33,8.33)
R3 (4.33,6.33,8.33) (3,5,7) (1,3,5) (0,1,3) (5,7,9)
R4 (1,3,5) (1,3,5) (0,1,3) (1,3,5) (0.78,2.33,4.33)
R5 (2.33,4.33,6.33) (3,5,7) (0,1,3) (0,1,3) (0,1,3)
R6 (2.33,4.33,6.33) (2.33,4.33,6.33) (0,1,3) (1,3,5) (0,1,3)
R7 (4.33,6.33,8.33) (3,5,7) (1,3,5) (4.33,6.33,8.33) (0.78,2.33,4.33)
R8 (2.33,4.33,6.33) (1,3,5) (0,1,3) (2.33,4.33,6.33) (0.78,2.33,4.33)
R9 (0.78,2.33,4.33) (1,3,5) (1,3,5) (1,3,5) (0,1,3)
R10 (0,1,3) (1,3,5) (1,3,5) (0,1,3) (0,1,3)
R11 (1,3,5) (5,7,9) (0,1,3) (3,5,7) (0,1,3)
R12 (0.78,2.33,4.33) (0.78,2.33,4.33) (0,1,3) (0,1,3) (0,1,3)
R13 (2.33,4.33,6.33) (1,3,5) (0,1,3) (7,9,10) (4.33,6.33,8.33)
R14 (2.33,4.33,6.33) (1,3,5) (0,1,3) (0,1,3) (1,3,5)
R15 (2.33,4.33,6.33) (1,3,5) (0,1,3) (0.78,2.33,4.33) (0,1,3)
R16 (1,3,5) (2.33,4.33,6.33) (0,1,3) (0,1,3) (0,1,3)
R17 (5,7,9) (3,5,7) (0,1,3) (0,1,3) (2.33,4.33,6.33)
R18 (3,5,7) (1,3,5) (5,7,9) (3,5,7) (0.78,2.33,4.33)
R19 (5,7,9) (5,7,9) (0,1,3) (0,1,3) (1,3,5)
R20 (3,5,7) (1,3,5) (5,7,9) (0,1,3) (3,5,7)
R21 (1,3,5) (0,1,3) (0,1,3) (0,1,3) (3,5,7)
R22 (3,5,7) (1,3,5) (7,9,10) (0,1,3) (4.33,6.33,8.33)
R23 (7,9,10) (5,7,9) (3,5,7) (0,1,3) (3,5,7)
R24 (3,5,7) (1,3,5) (5,7,9) (0,1,3) (4.33,6.33,8.33)
R25 (7,9,10) (1,3,5) (1,3,5) (0,1,3) (5,7,9)
R26 (5,7,9) (0,1,3) (1,3,5) (0,1,3) (2.33,4.33,6.33)
R27 (5,7,9) (1,3,5) (0,1,3) (0.78,2.33,4.33) (1,3,5)
R28 (3,5,7) (1,3,5) (1,3,5) (0,1,3) (1,3,5)
R29 (3,5,7) (0,1,3) (3,5,7) (0,1,3) (2.33,4.33,6.33)
R30 (7,9,10) (1,3,5) (0,1,3) (1,3,5) (0,1,3)
R31 (5,7,9) (3,5,7) (0,1,3) (0,1,3) (0.78,2.33,4.33)
R32 (5,7,9) (3,5,7) (1,3,5) (0,1,3) (1,3,5)
R33 (0,1,3) (7,9,10) (0,1,3) (0,1,3) (0,1,3)
Table 4: Ranking and categorizing of the identified risks.
Total score Risk code Rank Group
0.5821 R18 1 High
0.5773 R7 2 High
0.5741 R23 3 High
0.5681 R20 4 High
0.5678 R24 5 High
0.5673 R22 6 High
0.5647 R3 7 High
0.5636 R13 8 High
0.5616 R32 9 High
0.5579 R25 10 High
0.5527 R8 11 Medium
0.5513 R29 12 Medium
0.5501 R17 13 Medium
0.5497 R28 14 Medium
0.549 R1 15 Medium
0.547 R11 16 Medium
0.5468 R19 17 Medium
0.5445 R27 18 Medium
0.5407 R26 19 Medium
0.5398 R31 20 Medium
0.5391 R2 21 Low
0.5375 R6 22 Low
0.5337 R4 23 Low
0.5332 R30 24 Low
0.5294 R9 25 Low
0.5292 R14 26 Low
0.5197 R5 27 Low
0.517 R15 28 Low
0.511 R21 29 Low
0.5098 R16 30 Low
0.4958 R33 31 Low
0.4844 R10 32 Low
0.4723 R12 33 Low
This way, the imprecision and vagueness of
evaluation measures has been considered.
FUZZY TOPSIS APPROACH TO IMPROVE QUANTITATIVE RISK ANALYSIS CONSIDERING DIFFERENT
CRITERIA AND THEIR MUTUAL EFFECTS
221
Table 5: Ranking and categorizing of the defuzzified risks.
Risk Score Rank Group
R7 0.793411 1 High
R18 0.737109 2 High
R13 0.626871 3 High
R11 0.578093 4 High
R8 0.569478 5 High
R23 0.545335 6 High
R6 0.52581 7 High
R9 0.525534 8 High
R3 0.513905 9 High
R27 0.511073 10 High
R4 0.508355 11 Medium
R22 0.496536 12 Medium
R32 0.495823 13 Medium
R24 0.492293 14 Medium
R30 0.490427 15 Medium
R20 0.487981 16 Medium
R25 0.464822 17 Medium
R19 0.457698 18 Medium
R15 0.452615 19 Medium
R17 0.446199 20 Medium
R28 0.437949 21 Low
R1 0.435378 22 Low
R31 0.427771 23 Low
R2 0.397198 24 Low
R5 0.39505 25 Low
R16 0.37233 26 Low
R14 0.369256 27 Low
R33 0.359939 28 Low
R29 0.334796 29 Low
R10 0.315488 30 Low
R26 0.300249 31 Low
R12 0.269112 32 Low
R21 0.224253 33 Low
6 CONCLUSIONS
In this paper, a new approach is proposed for
improving risk analysis process. This approach use
fuzzy TOPSIS method for ranking and prioritizing
different risks of a typical project. The proposed
approach has been implemented in a case study and
used to categorize the identified risks. Finally, a
comparison is provided when a deterministic version
of TOPSIS is implemented over the case study data.
The proposed approach, compared with the
conventional PI matrix, improves the risk analysis
process in the following aspects:
Using risk score cannot comply the aim and
outputs of risk analysis in reporting correct
priority of risks. For example, some risks with
high impact and low probability have low risk
score. So that project face with serious problem
if it happen even the probability is low. But,
more criteria can be used in the proposed
approach.
In PI matrix, if two risks have the same risk
score, will treated the same. But two risks with
equal risk score never have same importance.
Because probability scale and risk impact do
not have same importance. But, in the proposed
approach different weights can be considered
in order to make the criteria different.
Using fuzzy and linguistic values help the users
in describing the values in a more flexible
language and to deal with the imprecision and
vagueness of evaluation measures
Definition of synergy factor in TOPSIS model
and focusing on dependent risk(s) results in
better risk response planning.
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