mcdm method application in sugar factory

Comparative analysis of MCDM methods for pipe material selection
in sugar industry
L. Anojkumar a,⇑
, M. Ilangkumaran a
, V. Sasirekha b
a
Department of Mechatronics Engineering, K.S. Rangasamy College of Technology, Tiruchengode, 637215 Namakkal, Tamil Nadu, India
b
Department of Computer Applications, K.S. Rangasamy College of Engineering, Tiruchengode, 637215 Namakkal, Tamil Nadu, India
a r t i c l e i n f o
Keywords:
FAHP
TOPSIS
VIKOR
ELECTRE
PROMETHEE
Material selection
Corrosion
Wear
a b s t r a c t
The material plays an important role in an engineering design process. The suitable material selection for
a particular product is one of the vital tasks for the designers. In order to fulfil the product’s end require-
ments, designers need to analyze the performance of various materials and spot suitable materials with
precise functionalities. Due to the presence of large number of materials with diverse properties, the
material selection process is complicated and time consuming task. There is a necessity of systematic
and efficient approach towards material selection to choose best alternative material for a product.
The aim of this paper is to describe the application of four Multi Criteria Decision Making methods for
solving pipes material selection problem in sugar industry. FAHP-TOPSIS, FAHP-VIKOR, FAHP-ELECTRE,
FAHP-PROMTHEE are the four methods used to choose the best alternative among the various materials.
The ranking performance of various MCDM methods is also compared with each other and exploring the
effectiveness and flexibility of VIKOR method. Five stainless steel grades such as J4, JSLAUS, J204Cu,
409 M, 304 and seven evaluation criteria such as yield strength, ultimate tensile strength, percentage
of elongation, hardness, cost, corrosion rate and wear rate are focussed in this study to choose the suit-
able material.
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1. Introduction
In the design and development of any structural elements,
material selection is one of the most challenging issues and it is
also critical for the success and to meet the demands of cost reduc-
tion and better performance. Generally, experts are choosing a
material by adopting the trial and error methods with investment
of huge cost or build on collection of past data leading to lass of
time (Shanian & Savadogo, 2006). While selecting alternative
materials, a clear understanding of functional needs for each indi-
vidual component is required and various important criteria need
to be considered. An improper selection can negatively affect
productivity, profitability and reputation of an organization
(Karande & Chakraborty, 2012). The complex inter-relationships
between variety of materials and its selection criteria frequently
make the material selection process a difficult and time consuming
task. Hence, a systematic and efficient approach to material selec-
tion is necessary in order to select the best alternative for a prod-
uct. Thus the great efforts need to be extended to determine
criteria that influence material selection for a product to eliminate
unsuitable alternatives and select the apt material alternative
using simple and logical methods (Rao & Patel, 2010). The non
commensurable and conflicting nature of the evaluation criteria
of material selection can be solved using MCDM method. The
aim of this paper deals with the selection of opt material for the
pipes from the set of five material alternatives and seven evalua-
tion criteria for sugar industry application.
2. Literature review
This section aims to review the various perceptions of method-
ologies in material selection problem, application of MCDM in
material selection, literature review on sugar industry and identi-
fication of research gap.
2.1. Literature review based on material selection methodologies
In this section, the material selection methodologies are re-
viewed for replacing the existing material to select a right candi-
date material. The selection of material methodologies presented
in this article contains important selection attributes and its appli-
cations. Sapuan, Jacob, Mustapha, and Ismail (2002) proposed a
prototype knowledge based system (KBS) for material selection
in the engine components. Manshadi, Mahmudi, Abedian, and
Mahmudi (2007) have proposed Weighting Factor Method
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http://dx.doi.org/10.1016/j.eswa.2013.10.028
⇑ Corresponding author. Tel.: +91 9943570353.
E-mail address: anoj83@gmail.com (L. Anojkumar).
Expert Systems with Applications 41 (2014) 2964–2980
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(WFM) through combination of non-linear normalization with a
Modified Digital Logic (MDL) method and demonstrated the ability
of the methods with comparison of Digital Logic (DL) method. The
MDL method applied to select a best material for cryogenic storage
tank and spar for the wing structure. Sapuan (2001) has proposed
KBS in the domain of polymeric based composite material selection
process. Ljungberg (2007) has proposed model for selecting suit-
able material for development sustainable products. Ramalhete,
Senos, and Aguiar (2010) have develop the digital tool for material
selection problem. Findik and Turan (2012) attempted the
weighted property index (WPIM) method to select the best mate-
rial for lighter wagon design. Finally the results shows aluminum
alloy is the opt material for lighter wagons. Fayazbakhsh, Abedian,
Manshadi, and Khabbaz (2009) proposed the Z-transformation
method for selecting the suitable material for cryogenic storage
tank. Bovea and Gallardo (2006) have applied the life cycle impact
assessment method for evaluating and selecting the suitable mate-
rial for eco-design. Enab and Bondok (2013) have used the finite
element method for choosing the suitable material for designing
the tibia component of cemented artificial knee. Florez and
Castro-Lacouture (2013) proposed a mixed integer linear program-
ming model with combination of objective and subjective factors
and to select the appropriate building material. Ipek, Selvi, Findik,
Torkul, and Cedimoğlu (2013) attempted to solve the materials
selection problem in the manufacturing field using expert system
model.
2.2. Literature review on MCDM in material selection
One of the most important stages in material selection process
is ranking and choosing the right material for a particular applica-
tion. MCDM methodologies are rapidly growing in the material
selection problem. Mainly a large number of factors influencing
the selection process into a critical issue (Chatterjee, Athawale, &
Chakraborty, 2011). Holloway (1998) explained the importance
of material selection in engineering applications and also enlight-
ened the impact of environment due to improper selection of
material. Jahan, Ismail, Sapuan, and Mustapha (2010) and Jahan, Is-
mail, Mustapha, and Sapuan (2010) reported that, the material
selection using MCDM techniques are increasing gradually in engi-
neering applications. Shanian and Savadogo (2006) have proposed
Elimination and Choice Expressing the Reality (ELECTRE) model for
selecting suitable material for loaded thermal conductor. Karande
and Chakraborty (2012) applied the multi objective optimization
on the basis of ratio (MOORA) method for select the opt material
for flywheel, cryogenic storage tank, product used in high temper-
ature oxygen rich environment and sailing boat mast. Bahramina-
sab and Jahan (2011) are used comprehensive VIKOR method to
material selection for femoral component of knee replacement in
medical field. Rao (2008) applied the improved compromise rank-
ing method to select the apt material for engineering applications,
from which two examples are illustrated to explain the proposed
model. The first one is to select the apt material for metallic bipolar
plate and another one is to select optimum material for high tem-
perature environment with four alternatives and four criteria.
Jahan, Mustapha, Ismail, Sapuan, and Bahraminasab (2011) applied
VIKOR method for selecting the suitable material for rigid pin of
shaft. Chatterjee, Athawale, and Chakraborty (2009) proposed a
compromised ranking and outranking method for material selec-
tion problem. Here, ELECTRE I is used to obtain partial ranking
and ELECTRE II is used for computing the final ranking of alterna-
tives. Maniya and Bhatt (2010) have proposed the preference
selection index method to select the best material to avoid the
relative importance among criteria. Hambali, Sapuan, Ismail, and
Nukman (2009) discussed the importance of Analytical Hierarchy
Process (AHP) in material selection problem. Sapuan, Hambali,
Ismail, and Nukman (2010) proposed AHP for selecting the suitable
composite material for bumper beam. Mayyas and group (2011)
proposed an AHP method for the material selection of automobile
body panels. Cicek and Celik (2010) have proposed modified Fuzzy
Axiomatic Design Model Selection Interface Algorithm (FAD-MSI)
model and successfully applied to the various material selection
problems. Wang and Chang (1995) proposed a fuzzy multiple cri-
teria decision making approach for selecting the best suited tool
steel material for a specific manufacturing application, such as
die design, jig and fixture design. Shanian and Savadogo (2009)
have proposed TOPSIS, block TOPSIS and VIKOR for material selec-
tion problem in high safety requirements in structural elements of
aerospace and nuclear industries. Rao and Patel (2010) have pro-
posed a novel multiple attribute decision making (MADM) method
to helps the decision maker to deal with the problem of material
selection for an engineering design considering both qualitative
and quantitative attributes. Jahan, Ismail, Sapuan, et al. (2010)
and Jahan, Ismail, Mustapha, et al. (2010) applied the linear assign-
ment method for material selection and reported that, it is
relatively simple comparing to other MCDM methods. Chatterjee
and Chakraborty (2012) have proposed the extended PROMETHEE
II (EXPROM2), a complex proportional assessment of alternatives
with gray relations (COPRAS-G), ORESTE (Organization, Rangement
Et Synthese De DonnesRelationnelles) and operational competi-
tiveness rating analysis (OCRA) methods for gear material selection
problem. Chatterjee et al. (2011) proposed complex proportional
assessment (COPRAS) and evaluation of mixed data (EVAMIX)
methods to evaluate a suitable material for cryogenic storage tank.
Ilangkumaran, Avenash, Balakrishnan, Barath Kumar, and Boopathi
Raja (2013) have proposed FAHP integrated with preference rank-
ing organization method for enrichment evaluation (PROMETHEE)
to evaluate the optimum material for automobile bumper. The
impeller material selection problem is solved by using FAHP-TOP-
SIS method (Jajimoggala & Karri, 2013). Liu, Liu, and Wu (2013)
have presented an interval 2-tuble linguistic VIKOR (ITL-VIKOR)
method for solving the material selection problem under uncertain
and incomplete environment. Chakraborty and Chatterjeeb (2013)
have applied VIKOR, TOPSIS and PROMETHEE methods for material
selection problem and also found that among the three methods,
the VIKOR model produced ideal results. Maitya and Chakraborty
(2013) have proposed Fuzzy TOPSIS method to select the suitable
abrasive material for grinding wheel. Jahan and Edwards (2013)
used VIKOR method for material selection problem with interval
numbers and target based criteria. Mansor, Sapuan, Zainudin,
Nuraini, and Hambali (2013) have describe the application of Ana-
lytical Hierarchy Process (AHP) for evaluating the suitable natural
fiber polymer composite for the design of passenger vehicle center
lever brake component.
2.3. Literature review on sugar industry
Handful researchers have made an attempt to reduce the failure
rate in the sugar industrial equipment. The many failures were
interrupted the production process and create financial impact.
Due to this reason for increased machine ideal time, maintenance
time and reduce production quality in the sugar industry. The fol-
lowing literature are detailed the problems in the sugar industry.
Pravin, Rajesh, Singhal, and Goyal (2007) reported that, U$250 mil-
lion is lost due to corrosion failures in Indian sugar industries.
Wesley, Goyal, and Mishra (2012) has absorbed, AISI 444 has the
better corrosion performance compared to AISI 1010 and similar
to AISI 304 grade steel. Rajesh Kumar (2011) has suggested sulpha-
nilamide, sulphapyridine and sulphathiazole as the anticorrosive
medium to reduce the corrosion of the process equipment in sugar
industries. Prado, Uquilla, Aguilar, Aguilar, and Casanova (2010)
evaluated the effect of sugar cane juice on carbon steel roll and
L. Anojkumar et al. / Expert Systems with Applications 41 (2014) 2964–2980 2965

studied the effect of austenitic stainless steel welded carbon steel
roll. The main wear mechanism silica is ploughing and cutting
the sugar cane roller shell (Casanova & Aguilar, 2008). Zumelzu
et al. (2003) made an attempt to find out the characteristics and
corrosion behavior of high-Cr White Iron. Buchanan, Shipway,
and McCartney (2010) conducted two abrasion–corrosion tests
such as Fe–Cr–C shielded metal arc welding (SMAW) hard facings
used in the sugar industry and an arc sprayed Fe–Cr-based coating
and concluded the abrasion–corrosion of SMAW high Fe–Cr–C
coatings performance is lower compared to electric arc sprayed
Fe–Cr based coating in slurry of sand and sugarcane juice. Panig-
rahi, Srikanth, and Singh (2007) examined the pitting corrosion
in evaporator vessel using mild steel. Montakarntiwong, Chusilp,
Tangchirapat, and Jaturapitakkul (2013) have investigated the
thermal power plant concretes strength and heat conduction.
Mariajaya prakash and Senthilvelan (2013) have applied Failure
Mode Effective Analysis (FMEA) and Taguchi method for finding
the failures of fuel feeding system. Hanamane, Attar, and Mudhol-
kar (2013) developed the embedded fuzzy logic module for cogen-
eration system to improve the steam generation performance and
saving fuel of boiler.
2.4. Research gap
The aforementioned literature sections proven that the impor-
tance of MCDM methods in the material selection process. The
suitable material for different application is evaluated and selected
using various MCDM methods. Whereas, the application of MCDM
for evaluating the suitable material for sugar industry equipment is
also one among them. The existing research in sugar industry have
proposed and used the various anti corrosive medium and coating
material on the critical equipment of sugar industry. But the fre-
quency of failures are not eradicated completely. In sugar industry
most of the pipe lines are corroded due to acidic nature of sugar-
cane juice. Keeping in view of the evidence the decision making
drives to increase the difficulty in selection of the appropriate
material. This paper focused on the development and application
of Hybrid MCDM techniques for selection of suitable material for
pipes.
3. Methods
3.1. FAHP method
AHP is a method proposed by Saaty (1980). In AHP, the decision
problem is structured hierarchically at different levels with each
level consisting of a finite number of elements (Khajeeh, 2010).
Laarhoven and Pedrycz (1983) applied fuzzy logic principles in
AHP and proposed them as FAHP. In the literature, FAHP has been
widely applied in many complicated decision making problems.
Chou and Liang (2001) have applied FAHP for shipping company
performance evaluation. Chang, Cheng, and Wang (2003) used
the FAHP method to determine the weights of criteria for perfor-
mance evaluation of airports. Hwang and Ko (2003) presented
the decision model for the best restaurant site selection using
AHP and FAHP. Similarly, Lin, Liang, and Lee (2006) applied FAHP
approach for suitable site selection for airport. Hsieh, Lu, and Tzeng
(2004) proposed fuzzy MCDM model for choosing the optimum
design model for public office building. Hwang and Hwang
(2006) proposed FAHP method for food service strategy evaluation
process. Ayag and Ozdemir (2006) evaluated machine tool alterna-
tives by applying an intelligent approach based on FAHP. Huang,
Chu, and Chiang (2008) presented a FAHP method for selecting
government sponsored development projects. Khoram, Shariat,
Azar, Moharamnejad, and Mahjub (2007) used FAHP to prioritize
the methods related to reuse of treated wastewater. Shyjith, Ilang-
kumaran, and Kumanan (2008) and Ilangkumaran and Kumanan
(2009) have proposed AHP for the optimum maintenance strategy
selection in textile industry. Khorasani and Bafruei (2011)
developed FAHP for the selection of potential suppliers in the
pharmaceutical industry. The procedural steps involved in FAHP
method are listed below:
Step 1: A complex decision making problem is structured using a
hierarchy. The FAHP initially breaks down a complex
MCDM problem into a hierarchy of inter-related decision
elements (criteria). With the FAHP, the criteria are
arranged in a hierarchical structure similar to a family
tree. A hierarchy has at least three levels: overall goal of
the problem at the top, multi criteria that define criteria
in the middle and decision criteria at the bottom.
Step 2: The crisp pair-wise comparison matrix A is fuzzified using
the triangular fuzzy number M = (l, m, u), the l and u rep-
resent lower and upper bound range respectively that
might exist in the preferences expressed by the decision
maker. The membership function of the triangular fuzzy
numbers M1, M3, M5, M7, and M9 are used to represent
the assessment from equally preferred (M1), moderately
preferred (M3), strongly preferred (M5), very strongly pre-
ferred (M7), and extremely preferred (M9). This project
employs a TFN to express the membership functions of
the aforementioned expression values on five scales which
are used for FAHP listed in Table 1.
Let c ¼ fcjjj ¼ 1; 2; . . . ; ng be a set of criteria. The result of
the pair-wise comparison on ‘‘n’’ criteria can be summa-
rized in an (n n) evaluation matrix A in which every
element aijði; j ¼ 1; 2; . . . ; nÞ is the quotient of weights of
the criteria, as shown:
A ¼
a11 a12 a1n
a21 a22 a2n
.
.
. .
.
. ..
. .
.
.
an1 an2 ann
2
6
6
6
6
4
3
7
7
7
7
5
; aii ¼ 1; aji ¼ 1=aij; aij–0:
ð1Þ
Step 3: The mathematical process is commenced to normalize and
find the relative weights of each matrix. The relative
weights are given by the right Eigen vector (W) corre-
sponding to the largest Eigen value ðkmaxÞ, as
Table 1
Membership function of fuzzy numbers.
Linguistic scale for importance Fuzzy number TFN (L, M, U) Reciprocal of TFN (1/U, 1/M, 1/L)
Just equal (1, 1, 1) (1, 1, 1)
Equal importance M1 (1, 1, 3) (0.33, 1, 1)
Weak importance of one over another M3 (1, 3, 5) (0.2, 0.33, 1)
Essential or strong importance M5 (3, 5, 7) (0.14, 0.2, 0.33)
Very strong importance M7 (5, 7, 9) (0.11, 0.14, 0.2)
Extremely preferred M9 (7, 9, 9) (0.11, 0.11, 0.14)
Intermediate value between two adjacent judgments M2, M4, M6, M8
2966 L. Anojkumar et al. / Expert Systems with Applications 41 (2014) 2964–2980

Aw ¼ kmaxw ð2Þ
It should be noted that the quality of output of FAHP is
strictly related to the consistence of the pair-wise compari-
son judgments. The consistency is defined by the relation be-
tween the entries of A:aij ajk = aik. The consistency index
(CI) is
CI ¼¼ ðkmax nÞ=ðn 1Þ ð3Þ
Step 4: The pair-wise comparison is normalized and priority
vector is computed to weigh the elements of the matrix.
The values in this vector sum to 1. The consistency of the
subjective input in the pair-wise comparison matrix can
be determined by calculating a consistency ratio (CR). In
general, a CR having a value less than 0.1 is good Saaty
(1980). The CR for each square matrix is obtained from
dividing CI values by Random Consistency Index (RCI)
values.
CR ¼ CI=RCI ð4Þ
The RCI which is obtained from a large number of simulations
runs and varies depending upon the order of matrix. Table 2 lists
the values of the RCI for matrices of order 1–10 obtained by
approximating random indices using a sample size of 500. The
acceptable CR range varies according to the size of matrix that is
0.05 for a 3 by 3 matrix, 0.08 for a 4 by 4 matrix and 0.1 for all lar-
ger matrices having n P 5. If the value of CR is equal to, or less than
that value, it implies that the evaluation within the matrix is
acceptable or indicates a good level of consistency in the compar-
ative judgments represented in that matrix. In contrast, if CR is
more than the acceptable value, inconsistency of judgments within
that matrix has occurred and the evaluation process should there-
fore be reviewed, reconsidered and improved.
3.2. TOPSIS method
The Technique for Order Preference by Similarity to Ideal
Solution (TOPSIS) was first developed by Hwang and Yoon
(1981). TOPSIS is relatively simple and fast, with a systematic pro-
cedure (Shanian Savadogo, 2006). It has been proved as one of
the best methods in addressing the rank reversal issue. The basic
idea of TOPSIS is that the best decision should be made to be clos-
est to the ideal and farthest from the non-ideal. Such ideal and
negative-ideal solutions are computed by considering the various
alternatives (Irfan Nilsen, 2009). The positive-ideal solution is a
solution that maximizes the benefit criteria and minimizes the cost
criteria, whereas the negative ideal solution maximizes the cost
criteria and minimizes the benefit criteria (Wang Chang, 2007;
Wang Elhag, 2006). Many researchers have proposed the TOPSIS
to solve the Multi Criteria Decision Making problem. Rao and
Davim (2008) proposed a combined TOPSIS and AHP logical proce-
dure for given engineering design. Ho, Xu, and Dey (2010) pro-
posed TOPSIS approaches for supplier evaluation and selection.
Wang, Cheng, and Cheng (2009) approached Fuzzy hierarchical
TOPSIS for supplier selection. Alemi, Jalalifar, Kamali, and Kalbasi
(2010) approached TOPSIS to present the best artificial lift method
selection for different circumstances of oil fields. Vetrivelsezhian,
Muralidharan, Nambirajan, and Deshmukh (2011) proposed an
integrated approach which employs AHP and TOPSIS to assess
the performance of three depots of a public sector of bus passenger
transport company. Peiyue, Qian, and Jianhua (2011) applied TOP-
SIS based on entropy weight to assess the performance of ground-
water quality. Rouhani, Ghazanfari, and Jafari (2012) presented
fuzzy TOPSIS for the evaluation of enterprise systems. Lin, Wang,
Chen, and Chang (2008) approached combined AHP and TOPSIS
method for customer driven product design process. The procedure
of TOPSIS method is as follows:
Step 1: Normalization of the evaluation matrix: the process is to
transform different scales and units among various criteria
into common measurable units to allow comparisons
across the criteria. Assume fij to be of the evaluation matrix
R of alternative j under evaluation criterion i then an
element rij of the normalized evaluation matrix R can be
calculated by many normalization methods to achieve this
objective.
rij ¼
fij
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
PJ
j¼1f2
ij
q j ¼ 1; 2; 3; . . . ; J; i ¼ 1; 2; 3; . . . ; n: ð5Þ
Step 2: Construction of the weighted normalized decision matrix:
The weighted normalized decision matrix can be calcu-
lated by multiplying the normalized evaluation matrix rij
with its associated weight wi to obtain the result
vij ¼ wi

rij j ¼ 1; 2; 3; . . . ; J; i ¼ 1; 2; 3; . . . ; n: ð6Þ
where wi is given by
Pn
i1wi ¼ 1.
Step 3: Determination of the positive and negative ideal solutions:
the positive ideal solution A⁄
indicates the most preferable
alternative and the negative ideal solution A
indicate the
least preferable alternative.
A
¼ fv1

; . . . ; vi

g ¼ maxjvij i 2 I0

; minjvij i 2 I00

ð7Þ
A
¼ v
1 ;:...;v
i

¼ minjvij i2I0

; maxjvij i2I00

: ð8Þ
Step 4: Calculation of the separation measure: the separation from
the positive and negative ideal for each alternative can be
measured by the n-criteria Euclidean distance.
D
j ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i¼1
viji
v
i
2
v
u
u
t ; j ¼ 1; 2; 3; . . . J: ð9Þ
D
j ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i¼1
ðviji
v
i Þ2
v
u
u
t ; j ¼ 1; 2; 3; . . . J: ð10Þ
Step 5: Calculation of the relative closeness to the ideal solution:
the relative closeness of the ith alternative with respect
to ideal solution A+
is defined as
CC
j ¼
D
j
D
j þ D
j
; j ¼ 1; 2; 3; . . . J: ð11Þ
Step 6: Ranking the priority: a set of alternatives then can be pref-
erence ranked according to the descending order of CC
j .
3.3. VIKOR method
The VIKOR method was developed for multi criteria optimiza-
tion of complex problems. Many researchers have proposed the
Table 2
Random Consistency Index (RCI).
No. 1 2 3 4 5 6 7 8 9 10
RCI 0 0 0.52 0.89 1.11 1.25 1.35 1.40 1.45 1.49

VIKOR to solve the Multi Criteria Decision Making problem. The
VIKOR method was developed by Opricovic (1998) to solve MCDM
problems with conflicting and non-commensurable criteria. The
method is focused on selecting and ranking from a set of alterna-
tives and a compromise solution is obtained with the initial
weights of a problem with conflicting criteria. Assuming that each
alternative is computed according to each criterion function, the
compromise ranking is performed by comparing the measure of
closeness to the ideal alternative. Mahmoodzadeh, Shahrabi, Paria-
zar, and Zaeri (2007) proposed the integration of FAHP and TOPSIS
in a project selection problem. But the TOPSIS methodology is not
considering the relative distances from the ideal and negative ideal
solution. The limitations can be overcome through VIKOR method-
ology. Only a few research papers have been found in the literature
in connection with VIKOR application for various fields. Opricovic
and Tzeng (2004) have given a detailed comparison of TOPSIS
and VIKOR and explained that the compromise solution (VIKOR)
gives a maximum group utility of the group majority and a
minimum individual regret of the opponent. Wu, Chen, and Chen
(2010) developed a hybrid fuzzy model application for the innova-
tion capital indicator assessment of Taiwanese Universities using
FAHP and VIKOR. Ilangkumaran and Kumanan (2012) applied
VIKOR based to select a suitable maintenance strategy for the
frame unit of a textile spinning mill. Rao(2008) proposed Improved
VIKOR for various case studies. Sanayei, Mousavi, and Yazdankhah
(2010) proposed Group decision making process for supplier selec-
tion with VIKOR under fuzzy an environment. Kuo and Liang
(2011) proposed a combining VIKOR with GRA techniques to
evaluate service quality of airports under fuzzy environment. San
Cristobal (2011) proposed VIKOR method for the selection of a
renewable energy project in Spain. This method focuses on ranking
and selecting from a set of alternatives, and determines the com-
promise solution obtained with the initial weights for a problem
with conflicting criteria. Assuming that each alternative is com-
puted according to each criterion function, the compromise rank-
ing is performed through comparing the measure of closeness to
the ideal alternative. The various alternatives are denoted as
A1,A2 . . .Am. For alternative Aj, the rating of the ith aspect is de-
noted by fij, i.e. fij is the value of ith criterion function for the alter-
native aj; n is the number of criteria. Development of VIKOR is
started with the following form of LP-metric:
Lpj ¼
X
n
i¼1
wiðf
i fijÞ=ðf
i f
i Þ
p
( )1=p
1 6 p 6 1; j ¼ 1; 2; . . . ; J:
In the VIKOR method L1,j (as Sj) and L1,j (as Rj) are used to
formulate ranking measure. The results are obtained by minj Sj is
with the maximum group utility (‘‘majority’’ rule), and the answer
obtained by minRj is with a minimum individual regret of the
‘‘opponent’’. The compromise ranking algorithm of VIKOR encom-
pass the following steps
Step 1: The purpose of normalizing the performance matrix is to
unify the unit of matrix entries. The determination of nor-
malized values of alternatives xij is the numerical score of
alternative j on criterion i. The corresponding normalized
value fij is defined as follows.
rij ¼
xij
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pm
i¼1X2
ij
q ; i ¼ 1; 2; 3 . . . m; j ¼ 1; 2; 3; . . . n: ð12Þ
Step 2: Determine the best f
i and the worst f
i values for each
criterion functions, i = 1,2,3,. . .n.
f
i ¼ maxjfij; f
i ¼ minjfij ð13Þ
Step 3: The utility measure and the regret measure for each
maintenance alternative are given as
Sj ¼
X
n
i1
wiðf
i fijÞ=ðf
i f
i Þ ð14Þ
Rj ¼ maxi½wiðf
i fijÞ=ðf
i f
i Þ ð15Þ
where Si and Ri represent the utility measure and the regret
measure, respectively and wj is the weight of the jth
criterion.
Step 4: Calculate the VIKOR index
Qj ¼
mðSj S
Þ
ðS
S
Þ
þ ð1 vÞ
ðRj R
Þ
ðR
R
Þ
ð16Þ
where, S⁄
= minjSj, S
= max jSj, R⁄
= min jRj, R
= max jRj and
m is introduced as weight of the strategy of ‘‘the majority
of criteria’’ (or ‘‘the maximum group utility’’), here m = 0.5.
Step 5: Rank the order of preference
The alternate with the smallest VIKOR value is determined to be
the best value. Propose as a compromise solution the alternate A0
,
which is ranked the best by the measure Q (Minimum) if the fol-
lowing two conditions are satisfied:
C1. Acceptable advantage:
QðA00
Þ QðA0
Þ P DQ
where A00
is the alternative with second position in the ranking list
by Q; DQ = 1/(m 1); m is the number of alternatives.
C2. Acceptable stability in decision making:
Alternative A0
must also be the best ranked by S or/and R. This
compromise solution is stable within a decision making process,
which could be ‘‘voting by majority rule’’ (when v 0.5 is needed),
or ‘‘by consensus’’ v 0.5, or ‘‘with veto’’ (v 0.5). Here, v is the
weight of the decision making strategy ‘‘the majority of criteria’’
(or ‘‘the maximum group utility’’). If one of the conditions is not
satisfied, then a set of compromise solutions is proposed, which
consists of:
Alternatives A0
and A00
if only condition C2 is not satisfied, or
Alternatives A0
; A00
. . . AðMÞ
if condition C1 is not satisfied; AðMÞ
is
determined by the relation QðAðmÞ
Þ QðA0
Þ DQ for maximum
M (the positions of these alternatives are ‘‘in closeness’’).
3.4. ELECTRE I Method
The ELECTRE I is one of most extensively used outranking meth-
ods reflecting the decision maker’s preferences in many fields. It
was first developed by Benayoun, Roy, and Sussman (1966). Sha-
nian, Milani, Carson, and Abeyarante (2008) have applied ELECTRE
for selecting a suitable material for the particular application of a
loaded thermal conductor. There is good agreement between the
results of the methods being used and available data in Cambridge
Engineering Selector (CES) databases. In addition, the materials
which are selected as the best choices by the ELECTRE I–II models
are in agreement with the Cambridge Engineering Selector (CES)
databases. Sevkli (2010) has proposed the application of fuzzy
ELECTRE on supplier selection. The proposed methods are applied
to a manufacturing company in Turkey. After determining the cri-
teria that affect the supplier selection decisions, the results for
both crisp and fuzzy ELECTRE methods are presented. The results
presented in that article have important implications for opera-
tions strategy and supply chain management research. Pang,

Zhang, and Chen (2011) have proposed a work on decision model
of reliability design scheme for computer numerical control
machine using ELECTRE I. They have proposed a novel AHP base
ELECTRE I method of reliability design scheme decision for
computer numerical control (CNC) machine. Based on the AHP
method combined with ELECTRE I, the decision model is built to
select the optimal design scheme. The results of computational
experiments indicated that the proposed algorithms possess good
application prospect. The procedural steps involved in ELECTRE I
are enlisted below:
Step 1: Normalization of the evaluation matrix: the process is to
transform different scales and units among various criteria
into common measurable units to allow comparisons
across the criteria. Assume fij to be of the evaluation matrix
R of alternative j under evaluation criterion i then an
element rij of the normalized evaluation matrix R can be
calculated by many normalization methods to achieve this
objective.
rij ¼
xij
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pm
j¼1x2
ij
q i ¼ 1; 2; 3; . . . ; n; j ¼ 1; 2; 3; . . . ; m: ð17Þ
Step 2: Construction of the weighted normalized decision matrix:
The weighted normalized decision matrix can be calcu-
lated by multiplying the normalized evaluation matrix rij
with its associated weight wi to obtain the result
vij ¼ wi

rij i ¼ 1; 2; 3; . . . ; n; j ¼ 1; 2; 3; . . . ; m: ð18Þ
where wi is given by
Pn
i1wi ¼ 1
Step 3: Ascertainment of Concordance and Discordance interval
sets: Let A = {a,b,c,. . .} denote a finite set of alternatives,
in the following formulation we divide the attribute sets
into two different sets of concordance interval set (Cab)
and discordance interval set (Dab). The concordance inter-
val set is applied to describe the dominance query if the
following condition is satisfied:
Cab ¼ fjjxaj P xbjg ð19Þ
On complementation of Cab, We obtain discordance interval
set (Dab)
Dab ¼ fjjxaj 6 xbjg ¼ j Cab ð20Þ
Step 4: Computation of concordance interval matrix:
Based on decision maker preference for alternatives, the
concordance interval matrix (Cab) between Aa and Ab can
be computed.
Cab ¼
X
j¼Cab
Wj ð21Þ
The concordance index indicated the preference of the assertion ‘‘A
outranks B’’. The concordance interval matrix can be formulated as
follows:
C ¼
cð1; 2Þ cð1; mÞ
cð2; 1Þ cð2; mÞ
.
.
. .
.
. ..
. .
.
.
cðm; 1Þ cðm; 2Þ

ð22Þ
Step 5: Computation of discordance interval matrix:
First we consider the discordance index of d(a,b), which
can be viewed as the presence of discontent in decision
of scheme ‘a’ rather than ‘b’. More specifically, we define
dða; bÞ ¼
max
j2Dab
Vaj

Vbj

max
j2J;m;n2I
Vmj Vnj

ð23Þ
Here the scheme m, n is used to calculate the weighted normalized
value among all target attributes. Using this discordance set we can
find the discordance interval matrix.
D ¼
dð1; 2Þ dð1; mÞ
dð2; 1Þ dð2; mÞ
.
.
. .
.
. ..
. .
.
.
dðm; 1Þ dðm; 2Þ

ð24Þ
Step 6: Computation of concordance interval matrix
The Concordance index matrix for satisfaction measure-
ment problems are as follow as

c ¼
X
m
a¼1
X
m
b
cða; bÞ
mðm 1Þ
ð25Þ
Here
c is the critical value which is determined by average domi-
nance index. Thus Boolean matrix E is
eða; bÞ ¼ 1 if cða; bÞ P
c
eða; bÞ ¼ 0 if cða; bÞ
c
ð26Þ
Step 7: Determine the discordance index matrix:
The presence of dissatisfaction can be measured by discor-
dance index:

d ¼
X
m
a¼1
X
m
b
dða; bÞ
mðm 1Þ
ð27Þ
Based on the discordance index mentioned above, the discordance
index matrix (F) is given by
fða; bÞ ¼ 1 if dða; bÞ 6
d
fða; bÞ ¼ 0 if dða; bÞ
d
(
ð28Þ
Step 8: Computation of net superior and inferior value:
ca and da, the net superior and inferior values. ca be the sums to-
gether the number of competitive superiority for all alternatives.
ca ¼
X
n
b¼1
cða;bÞ
X
n
b¼1
cðb;aÞ ð29Þ
On the contrary, da is used to determine the number of inferiority
ranking the alternatives.
da ¼
X
n
b¼1
dða;bÞ
X
n
b¼1
dðb;aÞ ð30Þ
3.5. PROMETHEE methodology
Preference function-based outranking method is a special type
of MCDM tool that can provide a ranking ordering of the decision
options. The PROMETHEE method was developed by Brans and
Vincke (1985), which was further extended by Brans, Vincke, and
Mareschal (1986). PROMETHEE I method can provide a partial
ordering of the decision alternatives whereas PROMETHEE II meth-
od can derive the full ranking of the alternatives. It is suitable for
almost any kind of application having multiple criteria and various
alternatives when the designer needs to choose a most appropriate
alternative. Dagdeviren (2008) has proposed the AHP and PROM-
THEE method for an equipment selection problem. The real-time
facility location selection problem using PROMETHEE II method
has been illustrated by Athawale and Chakraborty (2010). Pirdashti

and Behzadian (2009) have proposed an application of AHP and
PROMETHEE for the selection of the best module design of ultra
filtration membrane in dairy industry. Boer, Wegen, and Telgen
(1998) have reported that an outranking approach (PROMETHEE)
is the best suitable tool for supplier selection problem. In this
paper, the PROMETHEE II method is employed to obtain the full
ranking of the network alternatives. The procedural steps involved
in PROMETHEE II are enlisted below:
Step 1: First of all, a committee of decision makers is formed. In
the decision making committee, there are three decision
makers; fuzzy rating of each decision maker can be repre-
sented as TFN with membership function.
Step 2: The appropriate crisp score is chosen for evaluating
network alternatives.
Step 3: Based on the questionnaire, the suitable crisp score is
assigned for alternative networks by each decision maker.
Then the decision matrix is formed.
Step 4: Normalize the decision matrix using the following
equation:
Rij ¼
½Xij min Xij
½max Xij min Xij
ði ¼ 1; 2 . . . n : j 1; 2 . . . mÞ ð31Þ
where Xij is the performance measure of ith alternative with respect
to jth Criterion.
For non-beneficial criteria, Eq. (31) can be rewritten as follows:
Rij ¼
½max Xij Xij
½max Xij min Xij
ð32Þ
Step 5: Calculate the evaluative differences of ith alternative with
respect to other alternatives. This step involves the calcu-
lation of differences in criteria values between different
alternatives pair-wise.
Step 6: Calculate the preference function Pj(i, i0
).
It may be very tough for decision makers to select the suitable
preference function for each criterion by Brans et al. (1986)
proposal. In order to reduce the overburden of decision makers,
the simplified preference function model by Athawale and
Chakraborty (2010) is implemented here.
pjði; i
0
Þ ¼ 0 if Rij 6 Ri0
j ð33Þ
pjði; i
0
Þ ¼ Rij Ri0
j if Rij Ri0
j ð34Þ
Step 7: Calculate the aggregated preference function taking the
criteria weights into account. Aggregated preference
function,
pði; i
0
Þ ¼
X
m
j¼1
½wj Pjði; i
0
Þ=
X
m
j¼1
Wj ð35Þ
where Wj is the relative importance (weight) of jth criterion.
Step 8: Determine the leaving and entering outranking flows as
follows:
Leaving (or positive) flow for ith alternative,
/þ
ðiÞ ¼
1
n 1
X
n
i¼1
pði; i
0
Þ ði–i
0
Þ ð36Þ
Entering (or negative) flow for ith alternative,
u
ðjÞ ¼
1
n 1
X
n
i¼1
pði; i
0
Þ ði–i
0
Þ ð37Þ
where n is the number of alternatives.
Here, each alternative faces (n 1) number of other alterna-
tives. The leaving flow expresses how much an alternative
dominates the other alternatives, while the entering flow denotes
how much an alternative is dominated by the other alternatives.
Based on these outranking flows, the PROMETHEE I method can
provide a partial pre-order of the alternatives whereas the PROM-
ETHEE II method can give the complete pre-order by using a net
flow, though it loses much information of preference relations.
Step 9: Calculate the net outranking flow for each alternative.
The net outranking flow is computed through the difference
between leaving flow and entering flow of each alternatives.
/
ði
0
Þ ¼ /þ
ði
0
Þ /
ði
0
Þ ð38Þ
Step 1: Determine the ranking of all the considered alternatives
depending on the values of u(i).The higher value of u(i),
the better is the alternative. Thus, the best alternative is
the one having the highest u(i) value.
3.6. Fuzzy set theory
A fuzzy set is a class of objects with grades of membership. It is
characterized by a membership function which assigns a grade of
membership ranging between zero and one to each object of the
class. Fuzzy sets theory has the capability of solving real world
problems by providing a wider frame than that of the classic sets
theory. Zadeh (1965) proposed the fuzzy set theory for the
scientific environment and later it has been made available to
other fields as well. Expressions such as ‘‘not very clear’’, ‘‘probably
so’’ and ‘‘very likely’’ represent some degree of uncertainty of hu-
man thought and are often used in daily life. In our daily life there
are different decision making problems of diverse intensity and if
the fuzziness of human decision making is not taken into account,
the results can be misleading. Fuzzy decision making turned out to
be a rational approach towards handling of decision making that
takes into account human subjectivity. Bellman and Zadeh (1970)
described the decision making methods in fuzzy environments.
The use of fuzzy set theory allows the decision-makers to
incorporate uncertain information into decision models (Kulak,
Durmusoglu, Kahraman, 2005). The fuzzy set theory resembles
human reasoning with the use of approximate information and
certainty to generate decisions and it is a better approach to
convert linguistic variables to fuzzy numbers under ambiguous
assessments. The fuzzy set theory which is incorporated with
AHP allows a more accurate description of decision making
process.
The uncertain comparison ratios are expressed as fuzzy num-
bers. It is possible to use different fuzzy numbers according to
the situation. In general, triangular and trapezoidal fuzzy numbers
are used. In common practice, the triangular form of the member-
ship function is used most often (Buyukozkan, Kahraman, Ruan,
2004; Ding Liang, 2005; Ilangkumaran Thamizhselvan, 2010).
The reason for using a triangular fuzzy number is to intuitively
easy for the decision-makers to use and calculate. In addition,
modeling using triangular fuzzy numbers has proved to be an
effective way for formulating decision problems where the infor-
mation available is subjective and imprecise (Buyukozkan et al.,
2004; Hsing Yeh, Deng, Hern Chang, 2000; Wang Chang,
2007). The evaluation criterion in the judgment matrix and weight
vector is represented by triangular fuzzy numbers. A fuzzy number

is a special fuzzy set F = {(x, lF(x), x € R} where x takes its value on
the real line R1: 1 x + 1 and lF(x) is a continuous mapping
from R1 to the close interval [0,1]. A Triangular Fuzzy Number
(TFN) can be denoted as M = (l, m, u). The TFN can be represented
as follows:
lAðxÞ ¼
0; x; l;
xl
ml
; l 6 x 6 m;
ux
um
; m 6 x 6 u;
0; x u
8

:
According to the nature of TFN, it can be defined as a triplet
(l, m, u). The TFN can be represented as e
A ¼ ðL; M; UÞ, where L and
U represent the fuzzy probability between the lower and upper
boundaries of evaluation. The triangular fuzzy number is shown
in Fig. 1. The two fuzzy numbers e
A ¼ ðL1; M1; U1Þ and
e
A2 ¼ ðL2; M2; U2Þ are assumed.
e
A1
e
A2 ¼ ðL1; M1; U1Þ ðL2; M2; U2Þ ¼ ðL1 þ L2; M1 þ M2; U1 þ U2Þ
e
A e
A ¼ ðL1; M1; U1Þ ðL2; M2; U2Þ ¼ ðL1L2; M1M2; U1U2Þ
~
A1 ~
A2 ¼ ðL1; M1; U1Þ ðL2; M2; U2Þ ¼ ðL1 L2; M1 M2; U1 U2Þ
e
A e
A ¼ ðL1; M1; U1Þ ðL2; M2; U2Þ ¼ ðL1=U2; M1=M2; U1=L2Þ
~
A1
1 ¼ ðL1; M1; U1Þ1
¼ ð1=U1; 1=M1; 1=L1Þ
4. Proposed methodology
The proposed methodology consists of three basic stages: (1)
Identification of the criteria to be used in the model (2) FAHP com-
putation (3) Ranking the alternatives using VIKOR, TOPSIS, ELEC-
TRE, and PROMTHEE. The schematic diagram of the proposed
methodology for the selection of opt material is shown in Fig. 2.
In the first stage, material alternatives and the evaluation criteria
are identified and a decision hierarchy is framed. The FAHP model
is structured such that the objective is at the first level of hierar-
chy; criteria at the second level and alternate materials are at the
third level. The decision hierarchy is approved by decision-making
team at the end of the first stage. After the approval of decision
hierarchy, criteria used in material selection are assigned with
weights using FAHP in the second stage. In the second phase, in
order to determine the criteria weights, pair-wise comparison
matrices are formed. The experts from decision-making team make
evaluations using the Satty’s scale to determine the values of the
elements of pair-wise comparison matrices. The geometric mean
of the values obtained from the evaluations is computed. A consen-
sus is arrived at on a final pair-wise comparison matrix that is
formed. Based on this final comparison matrix, the weights of the
criteria are calculated. These weights are approved by a decision-
making team towards the completion of this phase. Material ranks
are determined by using VIKOR, TOPSIS, ELECTRE and PROMTHEE
methods in the third stage.
4.1. A numerical application of the proposed model
The proposed models have been applied to solve a real problem
in the sugar industry located at southern part of the India. The
sugarcane crushing capacity of the industry is 19,000 tonnes per
day. This unit is the only sugar factory in India which could pro-
duce superfine grade of sugar corresponding to the international
standard measured at grade 35 and below by International
Commission for Uniform Method of Sugar Analysis (ICUMSA).The
cane sugar production processes involves various stages like recep-
tion, cleaning, extraction, juice clarification, evaporation,
crystallization, centrifugation, drying, storing and packing. The
piping has a major role to bridge the various stages of the produc-
tion process. The acid nature of the sugar cane juice is corrode the
inner surface of the pipe. It leads to the frequent maintenance of
the pipe lines and which may interrupt the production. The indus-
trial persons are taking an effort to overcome the aforementioned
problem to replace the existing material with suitable one. The
engineers and designers proposed five alternate stainless steel
grade materials for evaluating the optimum material to minimize
the corrosive wear.
4.2. Criteria for selecting an optimum material
In this article, the evaluation criteria are identified for selection
of optimum material through literature (Peter Smith, 2005; Prado
et al., 2010; Pravin et al., 2007; Wesley et al., 2012) and experts
in the industry. After the identification of the evaluation criteria,
alternate materials are investigated and decision-making team
determines five possible alternates and the seven influencing
criteria for the evaluation process. The identified evaluation
criteria are described as follows:
(1) Yield strength (YS): Yield strength is a very important value
for use in piping design. It must support a force during in use
and does not plastically deform.
(2) Ultimate tensile strength (UTS): It helps to provide a good
indication of a material’s toughness and necessary to ensure
the failure with range of applied load.
(3) % of Elongation (E): It measures the percentage change in
length before fracture takes place. It is essential to withstand
the operating load.
(4) Hardness (H): It enables to resist plastic deformation, pene-
tration, indentation, and scratching, when a force is applied
during the working process.
(5) Cost (C): The value of money that has been used to purchase
the material.
(6) Corrosion resistance (CR): It is a natural process that seeks to
reduce the binding energy in metals. It has a major role to
improve the life time of the material.
(7) Wear resistance (WR): The ability of a metal to resist the
gradual wearing away caused by abrasion and friction.
4.3. FAHP computations
The decision hierarchy diagram is established using identified
evaluation criteria and the alternate materials are shown in the
Fig. 3. There are three levels in decision hierarchy structure for
material selection process. The overall goal of the decision process
is to determine as the selection of optimal material at the first level
of the hierarchy. The criteria are at the second level and the
alternate materials are at the third level of the hierarchy. After
µÃ(X)
Fig. 1. Triangular fuzzy numbers.

Determination of final rank
Selecting the best material
Stage 3
Establish Pair-wise comparison matrix
Direct eigenvector max eigen value
Derive consistency index(CI)
CI is acceptable or not
Criteria weight
by FAHP
Stage 2
Expert Experience
Determination of alternative Materials
Identification
Structuring decision hierarchy
Approval of
Decision
Literature
Survey
Stage
PROMTHEE
VIKOR
TOPSIS
ELECTRE
Fig. 2. Schematic diagram of the proposed model for material selection.
Material Selection
Yield
Strength
Ultimate Tensile
Strength
Percentage
Elongation
Hardness Cost Corrosion
Rate
Wear Rate
M1 M2 M3 M4 M5
Fig. 3. Decision hierarchy of material selection.

the construction of the hierarchy diagram the weights of the crite-
ria to be used in evaluation process are computed using FAHP
method. The questionnaire design is presented in Appendix A to
form a pair-wise comparison matrix. The FAHP methodology
requires the pair-wise comparison of the criteria in order to deter-
mine their relative weights. In the pair wise comparison process,
each criterion is compared with others using satty’s nine point
scale. The fuzzy comparison judgments of the seven criteria with
respect to the overall objective are shown in Table 3. The geometric
mean of the values obtained from the evaluations is computed. A
consensus is arrived at on a ﬁnal pair-wise comparison matrix that
is formed. Based on this ﬁnal comparison matrix, the weights of the
criteria are calculated. Then consistency index, consistency ratio
are calculated to check whether the importance given to the crite-
ria in pair wise comparison matrix is correct or not. The weights
are approved by a decision-making team towards the completion
of this phase. The obtained relative weights, consistency index,
consistency ratio of criteria are tabulated in Table 4.
4.4. TOPSIS computations
The TOPSIS method has proposed for the selection of a suitable
material. The obtained data are tabulated in Table 5 and are nor-
malized using Eq. (5). The normalized data are tabulated in Table
6. The FAHP criteria weights are considered to compute the
weighted normalized decision matrix using Equation (6) and tabu-
lated in Table 7. The positive and negative ideal solutions are
calculated using Eqs. (7) and (8) and are tabulated in Table 8. Sep-
aration measures of each alternate are computed using Eqs. (9) and
(10) and are tabulated in Table 9. The Calculation of the relative
closeness to the ideal solution are done by Eq. (11) and tabulated
in Table 10. Finally, according to the relative closeness to the ideal
solution value, the ranks are preferred to the materials and the ob-
tained results are tabulated in Table 10.
4.5. VIKOR computations
The VIKOR method has also proposed for selecting the optimum
material among the alternate materials. The normalized decision
matrix is calculated same as TOPSIS methodology, the resulting
normalized decision matrix is shown in Table 6. The best and worst
values of the each criterion are calculated by using Eq. (13) and the
obtained values are tabulated in Table 11. The values of utility
measure and regret measure are calculated using the Eqs. (14)
and (15) are tabulated in Table 12. Finally, the VIKOR Index value
is calculated using an Eq. (16) and are tabulated in Table 13. Based
on the VIKOR Index value the ranks are assigned for the materials
and the obtained results are tabulated in Table 13.
Table 3
Pair wise comparison matrix for criteria.
YI UTS %E H C CR WR
YI (1, 1, 1) (1, 3, 5) (1, 1, 3) (0.33, 1, 1) (0.11, 0.14, 0.2) (0.14, 0.2, 0.33) (0.2, 0.33, 1)
UTS (0.2, 0.33, 1) (1, 1, 1) (0.33, 1, 1) (0.14, 0.2, 0.33) (0.11, 0.11, 0.14) (0.11, 0.11, 0.14) (0.11, 0.14, 0.2)
%E (0.33, 1, 1) (1, 1, 3) (1, 1, 1) (0.2, 0.33, 1) (0.11, 0.11, 0.14) (0.11, 0.14, 0.2) (0.11, 0.14, 0.2)
H (1, 1, 3) (3, 5, 7) (1, 3, 5) (1, 1, 1) (0.11, 0.14, 0.2) (0.2, 0.33, 1) (0.33, 1, 1)
CO (5, 7, 9) (7, 9, 9) (7, 9, 9) (5, 7, 9) (1, 1, 1) (1, 1, 3) (1, 1, 3)
CR (3, 5, 7) (7, 9, 9) (5, 7, 9) (1, 3, 5) (0.33,1,1) (1, 1, 1) (1, 1, 3)
WR (1, 3, 5) (5, 7, 9) (5, 7, 9) (1, 1, 3) (0.33, 1, 1) (0.33, 1, 1) (1, 1, 1)
Table 4
Results obtained with FAHP.
Criteria Weights kmax
,
CI, RCI CR
YI 0.060162 kmax ¼ 7:35 0.043226
UTS 0.027215
%E 0.036882 CI = 0.058355
H 0.093839
C 0.348038
CR 0.249222 RCI = 1.35
WR 0.184642
Table 5
Materials properties.
Material Properties
Yield strength Ultimate tensile strength % Of elongation Hardness Cost Corrosion rate Wear rate
J4 382 728 48 98 112 0.16 2.75
JSLAUS 420 790 58 97 210 0.31 2.63
204Cu 415 795 55 96 120 0.05 2.5
409 M 270 455 32 78 184 0.4 4
304 256 610 60 86 89 0.01 2.59
Table 6
Normalized decision matrix (rij).
Material Criteria
Criteria weights 0.060162 0.027215 0.036882 0.093839 0.348038 0.249222 0.184642
J4 0.5138 0.4993 0.4196 0.4897 0.3334 0.3001 0.4173
JSLAUS 0.4170 0.4253 0.4895 0.4398 0.6252 0.5814 0.3990
204Cu 0.5582 0.5453 0.4807 0.4797 0.3573 0.0938 0.3793
409 M 0.3632 0.3121 0.2797 0.3898 0.5478 0.7502 0.6069
304 0.3444 0.4184 0.5244 0.4298 0.2650 0.0188 0.3930

4.6. ELECTRE computations
The ELECTRE method has proposed for the selection of a suit-
able material. The obtained data are tabulated in Table 1 and are
normalized using Eq. (17). The normalized data are tabulated in
Table 6. The FAHP criteria weights are considered to compute the
weighted normalized decision matrix using Eq. (18) and tabulated
in Table 7. Based on the concept of concordance and discordance
interval set, the concordance and discordance interval sets ascer-
tained using Equations and tabulated in Table 14. Then the concor-
dance interval index and discordance interval index is computed
using Eqs. (21) and (23) and are tabulated in Tables 15 and 16. Con-
cordance indexes and discordance indexes can be calculated using
Eqs. (25) and (27) and tabulated in Tables 17 and 18. Finally, the
net superior value and the net inferior values are calculated using
Eqs. (29) and (30) and tabulated in Table 19. Based on the superior
and inferior values, the ranking order for the materials is
ascertained.
4.7. PROMTHEE computation
This phase begins with the formation of evaluation matrix
based on the value of evaluation criteria with respect to material
Table 7
Weighted normalized decision matrix (vij).
Material Criteria
J4 0.0309 0.0136 0.0155 0.0460 0.1161 0.0748 0.0770
JSLAUS 0.0251 0.0116 0.0181 0.0413 0.2176 0.1449 0.0737
204Cu 0.0336 0.0148 0.0177 0.0450 0.1243 0.0234 0.0700
409 M 0.0218 0.0085 0.0103 0.0366 0.1907 0.1870 0.1121
304 0.0207 0.0114 0.0193 0.0403 0.0922 0.0047 0.0726
Table 8
Positive ideal solution (A⁄
) and negative ideal solution (A
).
Criteria Positive ideal solution A⁄
Negative ideal solution A
YI 0.0336 0.0207
UTS 0.0148 0.0085
%E 0.0193 0.0103
H 0.0460 0.0366
C 0.0922 0.2176
CR 0.0047 0.1870
WR 0.0700 0.1121
Table 9
Distance of alternatives from PIS and NIS (D
j , D
j ).
Alternatives D
j D
j
J4 0.074540525 0.1560966
JSLAUS 0.188418513 0.0579066
204Cu 0.037213019 0.1937972
409 M 0.212208843 0.0269642
304 0.01468039 0.2249737
Table 10
Closeness coefﬁcient of alternatives ðCC
j Þ and ranking of alternatives.
Alternatives CC
j Rank
J4 0.6768 3
JSLAUS 0.2351 4
204Cu 0.8389 2
409 M 0.1127 5
304 0.9387 1
Table 11
Best value and worst value for VIKOR.
Criteria ~
f
i
~
f
i
YI 420 256
UTS 795 610
%E 60 32
H 98 78
C 89 210
CR 0.01 0.4
WR 2.5 4
Table 12
Si and Ri values of alternatives.
Alternative Si Ri
J4 0.227894 0.095854566
JSLAUS 0.662298 0.34803752
204Cu 0.132532 0.089166637
409 M 0.920079 0.273252598
304 0.142353 0.06016242
Table 13
Qi values for v = 0.5.
Alternative Qi Rank
J4 0.1225 3
JSLAUS 0.8363 4
204Cu 0.0504 2
409 M 0.8701 5
304 0.0062 1
Table 14
Cab Concordance interval sets.
C(1,2) 1, 2, 4, 5, 6 D(1,2) 3, 7
C(1,3) 4, 5 D(1,3) 1, 2, 3, 6, 7
C(1,4) 1, 2, 3, 4, 5, 6, 7 D(1,4) 0
C(1,5) 1, 2, 4 D(1,5) 3, 5, 6, 7
C(2,1) 3, 7 D(2,1) 1, 2, 4, 5, 6
C(2,3) 3 D(2,3) 1, 2, 4, 5, 6, 7
C(2,4) 1, 2, 3, 4, 6, 7 D(2,4) 5
C(2,5) 1, 2, 4 D(2,5) 3, 5, 6, 7
C(3,1) 1, 2, 3, 6, 7 D(3,1) 4, 5
C(3,2) 1, 2, 4, 5, 6, 7 D(3,2) 3
C(3,4) 1, 2, 3, 4, 5, 6, 7 D(3,4) 0
C(3,5) 1, 2, 4, 7 D(3,5) 3, 5, 6
C(4,1) 0 D(4,1) 1, 2, 3, 4, 5, 6, 7
C(4,2) 5 D(4,2) 1, 2, 3, 4, 6, 7
C(4,3) 0 D(4,3) 1, 2, 3, 4, 5, 6, 7
C(4,5) 1 D(4,5) 2, 3, 4, 5, 6, 7
C(5,1) 3, 5, 6, 7 D(5,1) 1, 2, 4
C(5,2) 3, 5, 6, 7 D(5,2) 1, 2, 4
C(5,3) 3, 5, 6 D(5,3) 1, 2, 4, 7
C(5,4) 2, 3, 4, 5, 6, 7 D(5,4) 1

alternatives are tabulated in Table 5. In the first step of the PROM-
ETHEE, material alternative values with respect to each criterion
are normalized using Eqs (31) (32) from Table 20. The weighted
normalized decision matrix is tabulated in Table 7. Then the
preference functions are calculated for all the pairs of material
alternatives, using Eqs. (33) and (34), and are tabulated in Table
21. The Table 22 exhibit the aggregated preference function values
for all the paired material alternatives, as calculated using Eq. (35).
The leaving and the entering flows for different material alterna-
tives are computed using Eqs. (36) and (37) respectively, and
obtained values are tabulated in Table 23. The net outranking flow
values for different material alternatives are tabulated in Table 24
using Eq. (38).
5. Result and discussion
The results of proposed methodology are tabulated in Table 25.
The comparative results of various methodologies for selecting
suitable material for pipe applications are described below.
5.1. Comparing VIKOR results with other MCDM methods
The obtained results of VIKOR method are compared with TOP-
SIS, ELECTRE and PROMTHEE. The ranking order of materials ob-
tained from VIKOR is 304 204Cu J4 JSLAUS 409 M.
5.2. VIKOR with TOPSIS
This ranking order is positioned in descending order based on
VIKOR index (304 = 0.0062 204Cu = 0.0504 J4 = 0.1225 JSL-
AUS = 0.8363 409 M = 0.8701). The ranking order from TOPSIS is
based on closeness coefficient (304 = 0.9387 204Cu = 0.8389
J4 = 0.6768 JSLAUS = 0.2351 409 M = 0.1127). In VIKOR the
aggregate functions are always closest to ideal values. In TOPSIS,
the closeness coefficients of materials are not always closest to
ideal solution. For example, in VIKOR 304 is obtained at the first
position with aggregate function of 0.9938(1–0.0062), which is
very closest to ideal value 1. But in TOPSIS, the same 304 is posi-
tioned at first rank with the closeness coefficient value of 0.9387,
which is not closest to ideal value 1 as compared to VIKOR aggre-
gate function.
5.3. VIKOR with ELECTRE
Ranking results by ELECTRE (304 204Cu J4 JSL-
AUS 409 M) are very similar to VIKOR results since they are based
on the similar decision foundation by considering both maximum
group of utility and minimum individual regret. The compromise
solution by ELECTRE method provides a balance between a maxi-
mum group utility of the majority, obtained by concordance that
represents the utility measure Si (J4 = 0.2279, JSLAUS = 0.6623,
204Cu = 0.1325, 409 M = 0.9201, 304 = 0.1424) and a minimum of
individual regret of the opponent, obtained by discordance that
represents the regret measure Ri (J4 = 0.0959, JSLAUS = 0.3480,
204Cu = 0.0892, 409 M = 0.2733, 304 = 0.0602). But in ELECTRE,
computations are very complex and consume more time as com-
pared to VIKOR method.
5.4. VIKOR with PROMTHEE
The ranking results by PROMTHEE having net outranking flow
(204Cu = 0.3142 J4 = 0.2372 304 = 0.1678 JSLAUS = 0.0.0098
409 M = 0.0294) which is differed as obtained from VIKOR.
This net outranking flow is computed by considering the max-
imum group of utility only, whereas the VIKOR method inte-
grates maximum group utility as utility measure Si
(J4 = 0.2279, JSLAUS = 0.6623, 204Cu = 0.1325, 409 M = 0.9201,
304 = 0.1424) and minimum individual regret as regret mea-
sure Ri (J4 = 0.0959, JSLAUS = 0.3480, 204Cu = 0.0892,
409 M = 0.2733, 304 = 0.0602).For example, the ranking results
by net outranking flow (204Cu J4 304 JSLAUS 409 M) in
PROMTHEE are the same as ranking results by utility measure
Table 16
Discordance interval index (Dab).
– 0.0331 1.0000 0.0000 1.0000
1.0000 – 1.0000 0.6404 1.0000
0.1612 0.0027 – 0.0000 1.0000
1.0000 1.0000 1.0000 – 1.0000
0.1454 0.0312 0.4006 0.0062 –
Table 17
Concordance index (E).
0 1 0 1 0
0 0 0 1 0
1 1 0 1 0
0 0 0 0 0
1 1 1 1 0
Table 18
Discordance index (F).
0 0 1 0 1
1 0 1 1 1
0 0 0 0 1
1 1 1 0 1
0 0 0 0 0
Table 19
Net inferior and net superior values (ca da).
ca Ranking order da Ranking order
J4 0.8031 3 0.2736 3
JSLAUS 1.8168 4 0.2668 4
204Cu 1.7742 2 2.2367 2
409 M 3.1836 5 3.3534 5
304 2.4231 1 3.4166 1
Table 20
Normalized decision matrix for PROMTHEE.
J4 JSLAUS 204Cu 409 M 304
YS 0.7925 0.3396 1 0.0881 0
UTS 0.8029 0.4853 1 0 0.4559
%E 0.5714 0.8571 0.8214 0 1
H 1 0.5 0.9 0 0.4
C 0.8099 0 0.7438 0.2149 1
CR 0.6154 0.2308 0.8974 0 1
WR 0.8333 0.9133 1 0 0.94
Table 15
Concordance interval index (Cab).
– 0.7785 0.4419 1.0000 0.1812
0.2215 – 0.0369 0.6520 0.1812
0.5581 0.9631 – 1.0000 0.3659
0 0.3480 0 – 0.0602
0.8188 0.8188 0.6341 0.9398 –

Si (204Cu 304 J4 JSLAUS 409 M) in VIKOR. From this re-
sult, it is conclude that PROMTHEE is based on maximum
group of utility.
The comparative results show that application of VIKOR provid-
ing valuable assistance for material selection decision-making
problems. The results of the proposed methodologies are tabulated
in Table 25. The material alternative 304 has obtained as the firsts
position in all the methodologies except PROMETHEE for pipes in
sugar industry. Pravin et al. (2007) reported that the grade 304
has better corrosion resistance as compared to other material
grades. The results are obtained based on many number of exper-
imental data with use of trial and error methods. J4 and 204Cu is
suitable material when the cost factor is also considered for the
evaluation factor. In this research work, the optimum material is
evaluated with consideration of various conflicting nature of the
criteria using MCDM technique. The results obtained has 304 is
the best suitable material as like previous researchers. It is evident
that the proposed model is to support significantly for selecting
suitable material in sugar industry applications.
6. Conclusion
Sugar industry plays a vital role towards an economic develop-
ment of the nation. The sugar industry is a challenging and repair-
able engineering industry which comprises of various systems
including feeding, juice extraction, steam generation, refining,
and crystallization. The efficient operation of the industry needs
to mitigate or reduce and provide prolonged life of the pipes. The
proper material selection plays a predominant role for reducing
the corrosion and failures of the pipes in sugar industry. This study
has presented a novel hybrid MCDM methods based on combining
FAHP, TOPSIS, VIKOR, ELECTRE and PROMTHEE to evaluate suitable
material for pipes. FAHP is used to compute the weights of evalu-
ation criteria. The FAHP weights are given as the input for TOPSIS,
VIKOR, ELECTRE and PROMTHEE for ranking the material alterna-
tives. A case example is illustrated for examining the results of
the proposed model. The obtained results of the proposed models
are same as compared to previous researchers. This study involves
various evaluation criteria like cost, corrosion rate, wear rate, yield
Table 21
Preference function for all pair of materials.
p1, p2 0.4528 0.3177 0 0.5 0.8099 0.3846 0 0.0272 0.0087 0 0.0469 0.2819 0.0959 0
p1, p3 0 0 0 0.1 0.0661 0 0 0 0 0 0.0094 0.0230 0 0
p1, p4 0.7044 0.8029 0.5714 1 0.5950 0.6154 0.8333 0.0424 0.0219 0.0211 0.0938 0.2072 0.1534 0.1539
p1, p5 0.7925 0.3471 0 0.6 0 0 0 0.0477 0.0095 0 0.0563 0 0 0
p2, p1 0 0 0.2857 0 0 0 0.08 0 0 0.0105 0 0 0 0.0148
p2, p3 0 0 0.0357 0 0 0 0 0 0 0.0013 0 0 0 0
p2, p4 0.2516 0.4853 0.8571 0.5 0 0.2308 0.9133 0.0151 0.0132 0.0316 0.0469 0 0.0575 0.1686
p2, p5 0.3396 0.0294 0 0.1 0 0 0 0.0204 0.0008 0 0.0094 0 0 0
p3, p1 0.2076 0.1971 0.25 0 0 0.2821 0.1667 0.0125 0.0054 0.0092 0 0 0.0703 0.0308
p3, p2 0.6604 0.5147 0 0.4 0.7438 0.6667 0.0867 0.0397 0.0141 0 0.0375 0.2589 0.1662 0.0160
p3, p4 0.9119 1 0.8214 0.9 0.5289 0.8974 1 0.0549 0.0272 0.0303 0.0845 0.1841 0.2237 0.1846
p3, p5 1 0.5441 0 0.5 0 0 0.06 0.0602 0.0148 0 0.0469 0 0 0.0111
p4, p1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
p4, p2 0 0 0 0 0.2149 0 0 0 0 0 0 0.0748 0 0
p4, p3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
p4, p5 0.0881 0 0 0 0 0 0 0.0053 0 0 0 0 0 0
p5, p1 0 0 0.4286 0 0.1901 0.3846 0.1067 0 0 0.0158 0 0.0662 0.0959 0.0198
p5, p2 0 0 0.1429 0 1 0.7692 0.0267 0 0 0.0053 0 0.3480 0.1917 0.0049
p5, p3 0 0 0.1786 0 0.2562 0.1026 0 0 0 0.0066 0 0.0892 0.0256 0
p5, p4 0 0.4559 1 0.4 0.7851 1 0.94 0 0.0124 0.0369 0.0375 0.2733 0.2492 0.1736
Table 22
Aggregate preference function.
p1, p2 0.460544
p1, p3 0.032395
p1, p4 0.693477
p1, p5 0.113424
p2, p1 0.025309
p2, p3 0.001317
p2, p4 0.333027
p2, p5 0.030617
p3, p1 0.128137
p3, p2 0.532294
p3, p4 0.78922
p3, p5 0.132968
p4, p1 0
p4, p2 0.074785
p4, p3 0
p4, p5 0.005297
p5, p1 0.197512
p5, p2 0.54994
p5, p3 0.121314
p5, p4 0.782863
Table 23
Leaving and entering flows.
Materials Leaving flow Entering flow
J4 0.324960086 0.087739588
JSLAUS 0.097567622 0.087739588
204Cu 0.39565484 0.081412319
409 M 0.020020577 0.049378079
304 0.217191564 0.049378079
Table 24
Net outranking flows.
Materials Net outranking flow Ranking
J4 0.237220498 2
JSLAUS 0.009828034 4
204Cu 0.314242521 1
409 M 0.0293575 5
304 0.167813484 3
Table 25
Result of proposed methodologies.
Materials TOPSIS VIKOR ELECTRE PROMTHEE
J4 3 3 3 2
JSLAUS 4 4 4 4
204Cu 2 2 2 1
409 M 5 5 5 5
304 1 1 1 3

strength, ultimate tensile strength, percentage of elongation and
hardness for the evaluation process. The MCDM techniques are
producing significant results and also a bridge the gap in between
the past research in sugar industry for material selection problem.
The proposed models are simple, convenient, precise and efficient
tool to help the decision makers to choose the suitable material
among the alternative materials. These novel MCDM method has
a capability for other material selection issues in the sugar industry
and the method can also be applied to other decision making prob-
lems. Thus, a further research have an attempt to access the opt
material for other parts of the sugar industry like cane carrier side
plates, juice pump body and impeller, juice tank, etc. In the future,
this article may helpful to the scholars work based on the sugar
industry issues and the researchers involved in the field of material
selection through MCDM methods.
Appendix A
A.1. Questionnaire design for the development of FAHP model for
material selection process
Read the following questions and put check marks on the pair-
wise comparison matrices. If a criterion on the left is more impor-
tant than the matching one on the right, put the check mark to the
left of the importance ‘Equal’ under the importance level. If a crite-
rion on the left is less important than the matching one on the
right, put your check mark to the right of the importance ‘Equal’
under the importance level.
With respect to yield strength (C1)
Q1. How important is the yield strength (C1) when it is com-
pared with ultimate tensile strength (C2)?
pared with percentage of elongation (C3)?
pared with hardness (C4)?
pared with cost (C5)?
pared with corrosive rate (C6)?
pared with wear rate (C7)?
With respect to criterion ultimate tensile strength (C2)
Q1. How important is the ultimate tensile strength (C2) when it
is compared with Percentage of elongation (C3)?
is compared with hardness (C4)?
is compared with cost (C5)?
is compared with corrosion rate (C6)?
is compared with Wear rate (C7)?
With respect to main criterion percentage of elongation (C3)
Q1. How important is the percentage of elongation (C3) when it
is compared with Hardness (C4)?
is compared with cost (C5)?
is compared with corrosion rate (C6)?
is compared with wear rate (C7)?
With respect to hardness (C4)
Q1. How important is the hardness (C4) when it is compared
with cost (C5)?
with corrosion rate (C6)?
with wear rate (C7)?
Q4. With respect to criterion cost (C5)
Q5. How important is the cost (C5) when it is compared with
corrosion rate (C6)?
Q6. How important is the cost (C5) when it is compared with
wear rate (C7)?
With respect to criterion corrosion rate (C6)
Q1. How important is corrosion rate (C6) when it is compared
with wear rate (C7)?
With respect to best Importance (or) preference of one criterion over another
Question Criteria Extreme Very
strong
Strong Moderate Equal Just
equal
Equal Moderate Strong Very
strong
Extreme Criteria
Q1 Yield strength
(c1)
Ultimate tensile
strength (c2)
Q2 Yield strength
(c1)
Percentage of
elongation (c3)
Q3 Yield strength
(c1)
Hardness (c4)
Q4 Yield strength
(c1)
Cost (c5)
Q5 Yield strength
(c1)
Corrosion rate
(c6)
Q6 Yield strength
(c1)
Wear rate (c7)
(continued on next page)

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With respect to best Importance (or) preference of one criterion over another
Question Criteria Extreme Very
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Percentage of
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Hardness (c4)
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Cost (c5)
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Corrosion rate
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Q11 Ultimate tensile
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Corrosion rate
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Q15 Percentage of
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Q19 Cost (c5) Corrosion rate
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Q21 Corrosion rate
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