FUZZY TOPSIS APPROACH TO IMPROVE QUANTITATIVE

RISK ANALYSIS CONSIDERING DIFFERENT CRITERIA

AND THEIR MUTUAL EFFECTS

Mohammad-Hossein Sarbaghi

, Majid Shakhsi-Niaei

and Seyed Hossein Iranmanesh

Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran

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

 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

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:

)12()13(

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

(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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