Int. J. Materials and Product Technology, Vol. 53, Nos. 3/4, 2016
267
Selection of natural fibre reinforced composites using
fuzzy VIKOR for car front hood
Noordiana Mohd Ishak,
Sivakumar Dhar Malingam* and
Muhd Ridzuan Mansor
Faculty of Mechanical Engineering,
Universiti Teknikal Malaysia Melaka,
Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
Email: diedieku@yahoo.com
Email: sivakumard@utem.edu.my
Email: muhd.ridzuan@utem.edu.my
*Corresponding author
Abstract: Weight reduction of transportation vehicles is an important method
in improving fuel efficiency, reducing energy consumption and greenhouse gas
emissions. One of the solutions is through the application of green materials as
substitutes to conventional engineering materials. However, the selection of a
suitable substitute material for the intended application often imposes great
challenges due to the variety of alternative materials to choose from as well as
the need to satisfy multiple and conflicting requirements from various
stakeholders. Therefore, the aim of this study is to use fuzzy VIKOR, the
multiple criteria decision making method, to identify the appropriate type of
natural fibre for fibre reinforced composites to be applied on the fibre metal
laminate for car front hood to achieve the transportation weight reduction. The
result suggested that M3 (kenaf) has the best criteria. Kenaf has been selected
as the best natural fibre as it satisfies two compromise solutions. It has a least
VIKOR index value υ = 0.5. The results of the fuzzy VIKOR demonstrate the
potential of natural fibre to be applied on the fibre metal laminate structure as a
car front hood; this which could reduce vehicle weight and subsequently reduce
the overall vehicle CO2 gas emissions.
Keywords: materials selection; fibre metal laminate; FML; car front hood;
natural fibre; fuzzy VIKOR.
Reference to this paper should be made as follows: Ishak, N.M.,
Malingam, S.D. and Mansor, M.R. (2016) ‘Selection of natural fibre reinforced
composites using fuzzy VIKOR for car front hood’, Int. J. Materials and
Product Technology, Vol. 53, Nos. 3/4, pp.267–285.
Biographical notes: Noordiana Mohd Ishak received her Master’s in Technical
and Vocational Education from Universiti Tun Hussein Onn Malaysia in 2014.
She is currently a PhD student at Universiti Teknikal Malaysia Melaka,
Malaysia. Her research interests include in fibre metal laminate, natural fibre,
design selection and development.
Sivakumar Dhar Malingam is working as a Senior Lecturer in the Faculty of
Mechanical Engineering, Universiti Teknikal Malaysia Melaka. He received his
PhD in Mechanical Engineering from the Australian National University in
2012. His research interests include metal forming, composite forming, fibre
metal laminate and bio-composite.
Copyright © 2016 Inderscience Enterprises Ltd.
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N.M. Ishak et al.
Muhd Ridzuan Mansor is working as a Senior Lecturer in the Faculty of
Mechanical Engineering, Universiti Teknikal Malaysia Melaka. He received his
PhD in Mechanical Engineering from Universiti Putra Malaysia in 2015. His
research interests include concurrent design, bio composites and automotive
design.
1
Introduction
Nowadays, the environment is getting polluted due to rampant activities such as illegal
logging, open burning, oil spills and not forgetting air pollution by vehicles. The
International Aluminium Institute reported that approximately 23% of CO2 gas emissions
from fuel combustion are generated by the transportation sector which is continuously
growing. The energy required to power motor vehicles is four times more than the energy
required for producing them; consequently, over 80% of the transport sector’s
greenhouse-gas emissions are produced during the vehicle’s operating life (Helms and
Lambrecht, 2006). As a result, the reduction in vehicle weight is critical to reduce the
CO2 gas emissions.
Since there is a need to improve air quality, any engineering research that reduces
emissions by using materials is highly recommended. Material selection depends very
much on the skills, knowledge and experiences of the design team who work with a wide
range of materials although materials databases are now available to help in this process.
Mechanical and automotive engineers can select from a wide range of metals, as well as
polymers, composites and some ceramic materials as long as the materials meet the
specific requirements.
Figure 1
Schematic picture of FML
Source: Sivakumar et al. (2014)
Figure 1 shows a fibre metal laminate (FML) that consists of multiple thin layers of metal
alternately bonded to thin layers of fibre-reinforced polymers (Baumert et al., 2009). It is
a lightweight material, which has outstanding physical and mechanical properties
compared to monolithic metal structures (Li et al., 2015) as the FML takes advantage of
metal and fibre reinforced composites. According to Asundi and Choi (1997), FML is a
Selection of natural fibre reinforced composites using fuzzy VIKOR
269
low density weight saving structural material as it has epoxy-based polymer matrix and
low density aluminium sheets. Besides that, the replacement of metal with lower density
composite layer in FML leads to a reduction of overall density (Ferrante et al., 2016) and
directly contributes to the weight reduction of the material.
There are many material selection methods that can be applied and one of them is
multiple criteria decision making (MCDM). The MCDM method for material selections
includes the elimination and et choice translating reality (ELECTRE) method, Vlse
kriterijumska optimizacija kompromisno rejense (VIKOR) method, technique for order
preference by similarity to ideal solution (TOPSIS) method, analytical hierarchy process
(AHP), preference ranking organisation method for enrichment of evaluations
(PROMETHEE), etc.
Table 1
List of material selection using MCDM methods
Authors
Anojkumar et al. (2014)
Milani et al. (2011)
MCDM methods
Material selection
Fuzzy AHP, TOPSIS, VIKOR,
ELECTRE, PROMTHEE
Pipe in sugar industry
VIKOR
Plastic gear
Kaoser et al. (2014)
AHP, VIKOR
Metal for electroplating process
Rathod and Kanzaria
(2011)
TOPSIS, fuzzy TOPSIS, AHP
Solar domestic hot water system
Fuzzy VIKOR
Femoral knee component
TOPSIS
Thin-film solar cells
TOPSIS, VIKOR
Micro-electromechanical
systems
Mansor et al. (2014a)
WSM
Thermoplastic matrix for hybrid
polymer composite
Mansor et al. (2014b)
TOPSIS
Thermoset matrix for
automotive bumper beam
Kumar and Ray (2014)
Entropy, TOPSIS
Exhaust manifold
Bahraminasab and Jahan
(2011)
Gupta (2011)
Chauhan and Vaish
(2012a)
Shanian et al. (2008) used ELECTRE III in the material selection of a thermal loaded
conductor cover. However, the ELECTRE method uses the concept of outranking
relationship and the procedure is rather lengthy. Maity et al. (2012) presented a cutting
tool material selection using the COPRAS-G method which considers grey data in the
decision matrix. Mansor et al. (2013) used the AHP method to select the most suitable
natural fibre to be hybridised with glass fibre reinforced polymer composites for the
design of a passenger vehicle centre lever parking brake component. Chauhan and Vaish
(2012b) proposed the VIKOR and TOPSIS methods to select soft and hard magnetic
materials and the Ashby method to select hard coating materials (Chauhan and Vaish,
2013). Besides that, Jahan and Edwards (2013) proposed an extended TOPSIS and
comprehensive VIKOR for material selection in biomedical application. Chatterjee et al.
(2011) used two MCDM which is COPRAS and EVAMIX for material selection to select
the most appropriate material for a cryogenic storage tank for transportation of liquid
nitrogen. Çalışkan et al. (2013) addressed a structured model using five techniques,
VIKOR, TOPSIS, AHP, Entropy and PROMETHEE to select a material for the tool
270
N.M. Ishak et al.
holder used in hard milling. A list of material selection using MCDM methods are shown
in Table 1.
From the literature review, MCDM is recognised as a material selection method.
Fuzzy VIKOR is one of the MCDM methods which focuses on ranking and selecting
from a set of alternatives to determine the compromise solution in a complex system
(Opricovic and Tzeng, 2004). Extended VIKOR in fuzzy environments is to solve the
problems of uncertainty in expressing decision maker’s preferences (Opricovic, 2007)
where, it makes the ranking list, gives the weight and provides a compromise solution
(Ahmad et al., 2015a). Compromise solution is the attainable resolution which is closest
to the ideal. Obtaining the compromise solution will be done by comparing the degree of
closeness to the ideal alternative, where each alternative can be analysed by each criterion
function. Hence, applying the fuzzy VIKOR method which compares the degree of
closeness to the ideal alternative assists the selection of an appropriate material and this
includes the selection of natural fibre for reinforcement composites. Therefore, the aim of
this study is to use fuzzy VIKOR, which is one of the MCDM methods, to identify the
appropriate type of natural fibre for reinforcement composites in the fabrication of FML
which will be used as the car front hood product design specifications.
2
Case study
Reduction in the weight of transportation vehicles is an important method of improving
fuel efficiency as well as reducing both energy consumption and greenhouse gas
emissions. Other measures include improved engines, lower air friction, better lubricants,
etc. Another option is the application of FML in the car front hood. Various studies have
been conducted on FML. For example, Ahmad et al. (2015b) analysed FML in the form
of tubular structures and investigated the crush and energy absorption response. Tan and
Akil (2012) studied the impact response of FML sandwich composite structure with
polypropylene honeycomb core. Daghigh et al. (2016) studied the creep behaviour of
basalt FML.
Besides that, research has also focused on FML which has been combined with
natural fibre reinforced. Vasumathi and Murali (2013) studied carbon-jute reinforced
aluminium laminate (CAJRALL) and carbon-jute reinforced magnesium laminate
(CAJRMAL). Santulli et al. (2012) studied the damage characterisation of PP-hemp/
aluminium FML using acoustic emission. Hussain et al. (2016) analysed the tensile
performance of palm oil FML.
Thus, FML has been chosen as a potential lightweight material to be used as the car
front hood. The suitable natural fibre for reinforced composites material will be defined
using the fuzzy VIKOR method. The natural fibre for reinforced composites material to
be selected are designated as jute (M1), hemp (M2), kenaf (M3), flax (M4) and sisal
(M5). These five materials have been selected based on the analysis of relevant literature
regarding the use of natural fibre in the automotive industry. Natural fibres such as kenaf,
hemp, flax, jute and sisal provide automobile part reinforcement due to drivers as
reductions in weight, cost and CO2, less reliance on foreign oil sources, recyclability and
the added benefit that these fibre resources are green or eco-friendly (Holbery and
Houston, 2006).
Data was obtained via discussions and a questionnaire which was administered to a
decision makers group that consists of five experienced composite and FML
Selection of natural fibre reinforced composites using fuzzy VIKOR
271
practitioners. The preference for one measure over another was decided by the available
research and the experience of the experts involved (Akadiri et al., 2013). The
questionnaire was administered to assess the relative importance of the criteria and later
aggregate them into seven independent assessment factors.
3
Requirement for car front hood
The front hood is the main component of a car which covers the engine of motor vehicles
and allows access to the engine compartment for maintenance and repair. Factors
involved in the selection of a material for the car front hood are as follows:
3.1 Stiffness
Stiffness is the resistance of a fibre or material to bending when under load. In the case of
front hood stiffness, it is not the case of whether more is better or less is better. Instead,
there is an optimum: too stiff, and the front hood is injurious; not stiff enough, the
pedestrian’s head bottoms out, that is, strike the very stiff structure in the engine
compartment (Hutchinson et al., 2011).
3.2 Density
The density of a material is a physical property that is directly related to the component
weight. The structure should be of great strength and should have high mechanical
strength under high temperature. The material should have the capability to withstand
heavy force and high impact (Girubha and Vinodh, 2012).
3.3 Cost
One of the most important consumer driven factors in the automotive industry is cost.
Cost includes three components: actual cost of the raw material, manufacturing value
added and the cost to design and test the product (Cole and Sherman, 1995). Since the
cost of a new material is always compared to that presently employed in a product, it is
one of the most important variables that determine whether any new material has an
opportunity to be selected for a vehicle component.
3.4 Water absorption
Water absorption is the capability of a material to absorb water when immersed in water
for a stipulated period of time. Water molecules can diffuse into the network of
composites to affect the mechanical properties (Li, 2000). Therefore, it is crucial to
determine the appropriate natural fibre that has a low water absorption capability to be
utilised with the FML
3.5 Availability
Availability is one of the important factors to be considered when selecting the potential
material. According to Gunnarsdóttir and Valdimarsdóttir (2012), material availability is
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N.M. Ishak et al.
measured by the probability that the material is available for use at any given instant.
Availability would consider the local and international production, industries applicable
and large scale. Therefore, material availability in the right requirement and quantities is
important to make sure that the potential material is suitable.
4
Application steps of fuzzy VIKOR
4.1 Input data collection
The compromise solution method, also known as VIKOR has been developed for
multi-criteria optimisation in a complex system to determine the compromise solution
and best solution from a set of values (Opricovic and Tzeng, 2004). In fuzzy VIKOR, it is
suggested that decision makers use linguistic terms to evaluate the ratings of alternatives
with respect to criteria as shown in Table 2 and Table 3.
Table 2
Linguistic terms and corresponding fuzzy numbers for each criterion
Linguistic variable
Fuzzy number
Very poor (VP)
(0.0, 0.0, 0.1, 0.2)
Poor (P)
(0.1, 0.2, 0.2, 0.3)
Medium poor (MP)
(0.2, 0.3, 0.4, 0.5)
Fair (F)
(0.4, 0.5, 0.5, 0.6)
Medium good (MG)
(0.5, 0.6, 0.7, 0.8)
Good (G)
(0.7, 0.8, 0.8, 0.9)
Very good (VG)
(0.8, 0.9, 1.0, 1.0)
Table 3
Linguistic terms and corresponding fuzzy numbers for each material
Linguistic variable
Very low (VL)
Fuzzy number
(0.0, 0.0, 0.1,0.2)
Low (L)
(0.1, 0.2, 0.2, 0.3)
Fairly low (FL)
(0.2, 0.3, 0.4, 0.5)
Medium (M)
(0.4, 0.5, 0.5, 0.6)
Fairly high (FH)
(0.5, 0.6, 0.7, 0.8)
High (H)
(0.7, 0.8, 0.8, 0.9)
Very high (VH)
(0.8, 0.9, 1.0, 1.0)
A trapezoidal fuzzy number can be defined as {(n1, n2, n3, n4)| n1, n2, n3, n4 ∈ R;
n1 ≤ n2 ≤ n3 ≤ n4} which denotes the smallest possible, most promising and largest
possible values (Shemshadi et al., 2011) and the membership function as equation (1) and
it is shown in Figure 2. Triangular fuzzy numbers and trapezoidal fuzzy numbers are the
most commonly used in the theory and practice of number (Liu et al., 2012; Girubha and
Vinodh, 2012) as the trapezoidal fuzzy number can encompass more uncertainty than the
triangular fuzzy number (Shemshadi et al., 2011).
Selection of natural fibre reinforced composites using fuzzy VIKOR
273
⎧ x − n1
x ∈ [n1 , n2 ]
⎪n − n ,
⎪ 2 1
x ∈ [n2 , n3 ]
⎪1,
μ A ( x) = ⎨
⎪⎛ n4 − x ⎞ x ∈ [n3 , n4 ]
⎪⎜⎝ n3 − n4 ⎟⎠
⎪
Otherwise
⎩0
Figure 2
Table 4
(1)
Trapezoidal fuzzy number
Importance weight of criteria assessed by decision makers (linguistic variable)
C1 (stiffness)
C2 (density)
C3 (cost)
C4 (water
absorption)
C5
(availability)
D1
VG
G
G
G
G
D2
VG
VP
VP
VG
VG
D3
G
MG
F
G
MG
D4
MG
G
MG
MG
G
D5
VG
VG
VG
VG
VG
Table 5
Importance weight of criteria assessed by decision makers (fuzzy set)
C1
C2
C3
C4
C5
D1
(0.8, 0.9, 1.0,
1.0)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
D2
(0.8, 0.9, 1.0,
1.0)
(0.0, 0.0, 0.1,
0.2)
(0.0, 0.0, 0.1,
0.2)
(0.8, 0.9, 1.0,
1.0)
(0.8, 0.9, 1.0,
1.0)
D3
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.4, 0.5, 0.5,
0.6)
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
D4
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
D5
(0.8, 0.9, 1.0,
1.0)
(0.8, 0.9, 1.0,
1.0)
(0.8, 0.9, 1.0,
1.0)
(0.8, 0.9, 1.0,
1.0)
(0.8, 0.9, 1.0,
1.0)
274
N.M. Ishak et al.
Table 2 and Table 3 show the linguistic terms and their corresponding fuzzy numbers.
The linguistic variables and corresponding fuzzy set value for each criterion is shown in
Tables 4 and 5 while the respective terms for describing the importance of material with
respect to criteria assessed by decision makers are shown in Tables 6, and 7. Let the
fuzzy ratings for the criterion and importance of weight of the kth decision maker be
Xijk{Xijk1; Xijk2; Xijk3; Xijk4;} and Wjk1{Wjk1; Wjk2; Wjk3; Wjk4}.
Table 6
Importance of material with respect to criteria assessed by decision makers (linguistic
variable)
D1
C1
C2
C3
C4
C5
M1
M
H
FH
H
VH
M2
H
FH
FH
FH
FH
M3
FH
H
H
VH
VH
M4
H
FH
FH
H
M
M5
FH
H
FH
FH
FH
D2
C1
C2
C3
C4
C5
M1
H
VH
VH
VL
VH
M2
M
VH
M
FL
FL
M3
FH
VH
VH
FH
VH
M4
H
VH
L
FL
M
M5
M
H
M
VL
M
D3
C1
C2
C3
C4
C5
M1
M
M
FH
M
H
M2
M
M
FH
M
FH
M3
FH
M
FH
M
H
M4
H
FH
FL
H
M
M5
FH
M
FH
M
FH
D4
C1
C2
C3
C4
C5
M1
FH
H
FH
H
H
M2
FH
H
FH
H
H
M3
H
FH
FH
FH
FH
M4
FH
H
H
H
FH
M5
FH
H
H
FH
H
D5
C1
C2
C3
C4
C5
M1
FH
H
M
M
VH
M2
FH
H
M
M
VH
M3
FH
H
M
M
VH
M4
FH
H
M
M
VH
M5
FH
H
M
M
VH
Selection of natural fibre reinforced composites using fuzzy VIKOR
Table 7
275
Importance of material with respect to criteria assessed by decision makers (fuzzy set)
D1
C1
C2
C3
C4
C5
M1
(0.4, 0.5, 0.5,
0.6)
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.8, 0.9, 1.0,
1.0)
M2
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
M3
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
(0.8, 0.9, 1.0,
1.0)
(0.8, 0.9, 1.0,
1.0)
M4
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.4, 0.5, 0.5,
0.6)
M5
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
D2
C1
C2
C3
C4
C5
M1
(0.7, 0.8, 0.8,
0.9)
(0.8, 0.9, 1.0,
1.0)
(0.8, 0.9, 1.0,
1.0)
(0.0, 0.0, 0.1,
0.2)
(0.8, 0.9, 1.0,
1.0)
M2
(0.4, 0.5, 0.5,
0.6)
(0.8, 0.9, 1.0,
1.0)
(0.4, 0.5, 0.5,
0.6)
(0.2, 0.3, 0.4,
0.5)
(0.2, 0.3, 0.4,
0.5)
M3
(0.5, 0.6, 0.7,
0.8)
(0.8, 0.9, 1.0,
1.0)
(0.8, 0.9, 1.0,
1.0)
(0.5, 0.6, 0.7,
0.8)
(0.8, 0.9, 1.0,
1.0)
M4
(0.7, 0.8, 0.8,
0.9)
(0.8, 0.9, 1.0,
1.0)
(0.1, 0.2, 0.2,
0.3)
(0.2, 0.3, 0.4,
0.5)
(0.4, 0.5, 0.5,
0.6)
M5
(0.4, 0.5, 0.5,
0.6)
(0.7, 0.8, 0.8,
0.9)
(0.4, 0.5, 0.5,
0.6)
(0.0, 0.0, 0.1,
0.2)
(0.4, 0.5, 0.5,
0.6)
D3
C1
C2
C3
C4
C5
M1
(0.4, 0.5, 0.5,
0.6)
(0.4, 0.5, 0.5,
0.6)
(0.5, 0.6, 0.7,
0.8)
(0.4, 0.5, 0.5,
0.6)
(0.7, 0.8, 0.8,
0.9)
M2
(0.4, 0.5, 0.5,
0.6)
(0.4, 0.5, 0.5,
0.6)
(0.5, 0.6, 0.7,
0.8)
(0.4, 0.5, 0.5,
0.6)
(0.5, 0.6, 0.7,
0.8)
M3
(0.5, 0.6, 0.7,
0.8)
(0.4, 0.5, 0.5,
0.6)
(0.5, 0.6, 0.7,
0.8)
(0.4, 0.5, 0.5,
0.6)
(0.7, 0.8, 0.8,
0.9)
M4
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.2, 0.3, 0.4,
0.5)
(0.7, 0.8, 0.8,
0.9)
(0.4, 0.5, 0.5,
0.6)
M5
(0.5, 0.6, 0.7,
0.8)
(0.4, 0.5, 0.5,
0.6)
(0.5, 0.6, 0.7,
0.8)
(0.4, 0.5, 0.5,
0.6)
(0.5, 0.6, 0.7,
0.8)
D4
C1
C2
C3
C4
C5
M1
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
M2
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
M3
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
(0.5, 0.6, 0.7,
0.8)
M4
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
M5
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.7, 0.8, 0.8,
0.9)
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
276
N.M. Ishak et al.
Table 7
Importance of material with respect to criteria assessed by decision makers (fuzzy set)
(continued)
D5
C1
C2
C3
C4
C5
M1
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.4, 0.5, 0.5,
0.6)
(0.4, 0.5, 0.5,
0.6)
(0.8, 0.9, 1.0,
1.0)
M2
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.4, 0.5, 0.5,
0.6)
(0.4, 0.5, 0.5,
0.6)
(0.8, 0.9, 1.0,
1.0)
M3
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.4, 0.5, 0.5,
0.6)
(0.4, 0.5, 0.5,
0.6)
(0.8, 0.9, 1.0,
1.0)
M4
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.4, 0.5, 0.5,
0.6)
(0.4, 0.5, 0.5,
0.6)
(0.8, 0.9, 1.0,
1.0)
M5
(0.5, 0.6, 0.7,
0.8)
(0.7, 0.8, 0.8,
0.9)
(0.4, 0.5, 0.5,
0.6)
(0.4, 0.5, 0.5,
0.6)
(0.8, 0.9, 1.0,
1.0)
4.2 Aggregation
The aggregated fuzzy ratings, Xij of alternatives with respect to each criterion can be
calculated as:
X ij = { X ij1 ; X ij 2 , X ij 3 , X ij 4 }
where
X ij1 = min { X ijk1}
X ij 2 =
1
k
X ijk 3 =
1
k
∑X
ijk 2
∑X
ijk 3
X ijk 4 = max { X ijk 4 }
The calculation of alternative (M1) with respect to criterion (C1) is as follows:
D1M 1 = (0.4, 0.5, 0.5, 0.6), D2 M 1 = (0.7, 0.8, 0.8, 0.9),
D3 M 1 = (0.4, 0.5, 0.5, 0.6), D4 M 1 = (0.5, 0.6, 0.7, 0.8),
D5 M 1 = (0.5, 0.6, 0.7, 0.8)
k = decision maker (D), k = 5.
Therefore,
X ij1 = min { X ik1} = 0.4
X ij 2 =
1
k
∑X
ijk 2
1
= (0.5 + 0.8 + 0.5 + 0.6 + 0.6) = 0.6
5
X ij 3 =
1
k
∑X
ijk 3
1
= (0.5 + 0.8 + 0.5 + 0.7 + 0.7) = 0.64
5
(2)
Selection of natural fibre reinforced composites using fuzzy VIKOR
277
X ij 4 = max { X ik 4 } = 0.9
X ij = (0.4, 0.6, 0.64, 0.9)
The aggregated fuzzy weight Wj of each criterion can be calculated as:
W j = {W j1 ; W j 2 , W j 3 , W j 4 }
(3)
where
W j1 = min {W jk1}
Wj2 =
1
k
∑W
jk 2
W j3 =
1
k
∑W
jk 3
W j 4 = max {W jk 4 }
The calculation of criterion (C1) is as follows:
D1 = (0.8, 0.9, 1.0, 1.0), D2 = (0.8, 0.9, 1.0, 1.0),
D3 = (0.7, 0.8, 0.8, 0.9), D4 = (0.5, 0.6, 0.7, 0.8),
D5 = (0.8, 0.9, 1.0, 1.0)
k = decision maker (D), k = 5.
Therefore,
W j1 = min {W jk1} = 0.5
Wj2 =
1
k
∑W
jk 2
1
= (0.9 + 0.9 + 0.8 + 0.6 + 0.9) = 0.82
5
W j3 =
1
k
∑W
jk 3
1
= (1.0 + 1.0 + 0.8 + 0.7 + 1.0) = 0.9
5
W j 4 = max {W jk 4 } = 1.0
W j = (0.5, 0.82, 0.9, 1.0)
The aggregated matrix for criterion weights and material ratings are calculated using
equation (2) and equation (3) and it is shown in Table 8. Thus, it leads to the formation of
the decision matrix of criterion.
N.M. Ishak et al.
278
Table 8
Aggregated fuzzy value of material ratings and criterion weights
C1
C2
C3
C4
C5
W
(0.5, 0.82, 0.9,
1.0)
(0.0, 0.62,
0.68, 1.0)
(0.0, 0.56,
0.62, 1.0)
(0.5, 0.80,
0.86, 1.0)
(0.5, 0.80,
0.86, 1.0)
M1
(0.4, 0.6, 0.64,
0.9)
(0.4, 0.76,
0.78, 1.0)
(0.4, 0.64,
0.72, 0.8)
(0.0, 0.52,
0.54, 0.9)
(0.7, 0.86,
0.92, 1.0)
M2
(0.4, 0.6, 0.64,
0.9)
(0.4, 0.72,
0.76, 1.0)
(0.4, 0.56,
0.62, 0.8)
(0.2, 0.54,
0.58, 0.9)
(0.2, 0.64,
0.72, 1.0)
M3
(0.5, 0.64,
0.72, 0.9)
(0.4, 0.72,
0.76, 1.0)
(0.4, 0.68,
0.74, 1.0)
(0.4, 0.62,
0.68, 1.0)
(0.5, 0.82,
0.90, 1.0)
M4
(0.5, 0.72,
0.76, 0.9)
(0.5, 0.74,
0.80, 1.0)
(1.0, 0.48,
0.52, 0.9)
(0.2, 0.64,
0.66, 0.9)
(0.4, 0.60,
0.64, 1.0)
M5
(0.4, 0.58,
0.66, 0.8)
(0.4, 0.74,
0.74, 0.9)
(0.4, 0.60,
0.64, 0.9)
(0.0, 0.44,
0.50, 0.8)
(0.4, 0.68,
0.74, 1.0)
4.3 Defuzzification
Defuzzify the fuzzy decision matrix and fuzzy weight of each criterion into crisp value
using equation (4) (Shemshadi et al., 2011; Girubha and Vinodh, 2012). The attained
crisp values are shown in Table 9.
Defuzz ( X ij ) =
∫ μ( x).xdx
∫ μ( x)dx
⎛ x−x
∫ ⎜⎝ x − x
⎞
⎟ .xdx +
xij1
ij 2
ij1 ⎠
=
xij 2 ⎛ x − x
ij1 ⎞
⎜ x − x ⎟ dx +
xij1
⎝ ij 2 ij1 ⎠
xij 2
∫
=
xij 4 − x ⎞
⎜
⎟ .xdx
xij 2
xij 3
⎝ xij 4 − xij 3 ⎠
xij 3
xij 4 ⎛ x − x
ij1 ⎞
dx +
⎜ x − x ⎟ dx
xij 2
xij 3
⎝ ij 2 ij1 ⎠
∫
ij1
xij 3
∫
xdx +
∫
xij 4 ⎛
∫
(4)
1
1
( xij 4 − xij 3 )2 − ( xij 2 − xij1 )2
3
3
− xij1 − xij 2 + xij 3 + xij 4
− xij1 xij 2 + xij 3 xij 4 +
The calculation of crisp value for criterion (C1) with material (M1) is as follows:
C1M 1 = (0.4, 0.6, 0.64, 0.9)
Defuzz ( X ij ) =
1
1
( xij 4 − xij 3 )2 − ( xij 2 − xij1 )2
3
3
− xij1 − xij 2 + xij 3 + xij 4
− xij1 xij 2 + xij 3 xij 4 +
1
1
(−0.4)(0.6) + (0.64)(0.9) + (0.9 − 0.64) 2 − (0.6 − 0.4) 2
3
3
=
= 0.64
−0.4 − 0.6 + 0.64 + 0.9
Then, the best value ( fi* ) and worst value ( fi − ) of crisp material values are identified
and they are shown in Table 10.
Selection of natural fibre reinforced composites using fuzzy VIKOR
Table 9
279
Crisp value for weight and material ratings
C1
C2
C3
C4
C5
W
0.79
0.55
0.53
0.78
0.78
M1
0.64
0.72
0.63
0.48
0.87
M2
0.64
0.71
0.60
0.55
0.63
M3
0.69
0.71
0.70
0.68
0.79
M4
0.71
0.76
0.50
0.58
0.67
M5
0.61
0.68
0.64
0.42
0.70
Table 10
Calculated best and worst values
C1
C2
C3
C4
C5
f i*
0.71
0.76
0.70
0.68
0.87
ƒ i−
0.61
0.68
0.50
0.42
0.63
4.4 Measurement of utility index
The utility index (Si), which refers to the separation measure of ith alternative with fuzzy
best value, can be calculated using equation (5) and (6). Wj is the fuzzy weight of the jth
criteria.
n
Si =
∑
j =1
w j ( fi* − fij )
( f i* − f i − )
(5)
The calculation of Si value for (M1) is as follows:
WC1 = 0.79, fi*C1 = 0.71, fi − C1 = 0.61, fij = 0.64
⎛ w j ( fi* − fij ) ⎞
Si = ⎜⎜
⎟⎟
*
−
⎝ ( fi − fi ) ⎠
0.79(0.71 − 0.64)
=
= 0.56
(0.71 − 0.61)
The value of the each criterion (C) with respect to material (M1) is:
∑S
i
= 0.56 + 0.25 + 0.18 + 0.61 + 0.01 = 1.61
4.5 Measurement of regret index
Calculation of the regret index (Ri), refers to the separation measure of ith alternative to
the fuzzy worst value. Wj is the fuzzy weight of the jth criteria.
⎛ w j ( fi* − fij ) ⎞
Ri = max i ⎜⎜
⎟⎟
*
−
⎝ ( fi − fi ) ⎠
(6)
280
N.M. Ishak et al.
The solution obtained by Ri is with the maximum individual regret while the solution
obtained by Si is with a maximum group utility (Ahmad et al., 2015a; Sanayei et al.,
2010). Therefore, the Ri value for material (M1) is:
Ri = 0.61
4.6 Measurement of the VIKOR index
The value of VIKOR index (Qi) can be calculated using equation (7) where Qi represents
the ith alternative VIKOR. v is introduced as a weight for the strategy of ‘the majority of
criteria’ or ‘the maximum group utility’, whereas 1–v is the weight of the individual
regret (Girubha and Vinodh, 2012; Shemshadi et al., 2011; Ahmad et al., 2015a;
Opricovic, 2011; Kaya and Kahraman, 2011). The smallest alternative VIKOR value is
determined to be the best solution. The alternative sorting is ranked by the Si, Ri and Qi
values in ascending order as shown in Table 11. As shown in Table 12, the values of Si,
Ri and Qi are ranked in an ascending order to determine the best material.
⎛ v ( s − s* ) ⎞ (1 − v) ( Ri − R* )
Qi = ⎜ −i * ⎟ +
R − − R*
⎝ s −s ⎠
(7)
The calculation of the Qi value for (M1) is as follows:
Si = 1.61, S * = 0.70, S − = 2.83, Ri = 0.51, R* = 0.32, R − = 0.81, v = 0.5
⎛ v ( s − s* ) ⎞ (1 − v) ( Ri − R* )
Qi = ⎜ −i * ⎟ +
R − − R*
⎝ s −s ⎠
⎛ 0.5(1.61 − 0.70) ⎞ (1 − 0.5)(0.51 − 0.32)
=⎜
= 0.51
⎟+
0.81 − 0.32
⎝ 2.83 − 0.70 ⎠
Table 11
Calculation of utility, regret measure and VIKOR index
S
R
Q(0.5)
M1
1.61
0.61
0.51
M2
2.31
0.78
0.85
M3
0.70
0.32
0
M4
1.45
0.64
0.50
M5
2.83
0.81
1.00
Table 12
Ranking of material
1
2
3
4
5
S
M3
M4
M1
M2
M5
R
M3
M1
M4
M2
M5
Q (0.5)
M3
M4
M1
M2
M5
Selection of natural fibre reinforced composites using fuzzy VIKOR
281
4.7 Proposing compromise solution
The alternative (A(1)) i.e., the alternative with highest rank by arranging Si, Ri and Qi in
ascending order is considered to be the compromise solution if and only two conditions
C1 and C2 are satisfied.
C1
C2
Acceptable advantage: Q(A(2)) – Q(A(1)) ≥ 1/(m – 1), where A(2) is the second
position in the alternatives ranked by Q.
Acceptable stability in decision making: alternative A(1) must also be the best ranked
by S or/and R. When one of the conditions is not satisfied, a set of compromise
solutions is selected. The set of compromise solutions is composed of:
1 Alternatives A(1) and A(2) if only condition C2 is not satisfied.
2 Alternatives A(1), A(2),…, A(m) if condition C1 is not satisfied. A(M) is calculated
using the relation Q(A(M)) – Q(A(1)) < 1/(m – 1) for maximum M.
The calculation of proposing compromise solution is as follows:
•
Condition C1: Q(A(2)) – Q(A(1)) ≥ 1/(m – 1), 0.50 – 0.00 ≥ 1/(5 – 1), 0.50 ≥ 0.25
(condition C1 satisfied).
•
Condition C2: M3 is the best rank by S and R (condition C2 satisfied).
Both the conditions are satisfied in this context, therefore, the material with the least
VIKOR index which is M3 is selected as the best material.
5
Results and discussion
Based on the result of the fuzzy VIKOR analyses shown in Figure 3, the ascending rank
suggested that M3 (kenaf) has the best criteria among the other 5 candidate materials. M3
(kenaf) has been selected as the best natural fibre by satisfying both conditions (C1) and
(C2) with validation using least VIKOR index value v = 0.5 as shown in Table 11 and
Table 12, where the M3 has the lowest VIKOR index (Qi) value which is 0.00. M4 (flax)
was in second ranking with 0.50 scores, followed by M1 (jute) with 0.51 scores. M2
(hemp) and M5 (sisal) are the second last and last choice of natural fibre in the
application of FML for the car front hood with the scores of 0.85 and 1.00 respectively.
Figure 3
Graph ranking of S, R and Q (see online version for colours)
282
N.M. Ishak et al.
Studies have been conducted on the suitability of kenaf as the best natural fibre for
automotive application. For example, Mansor et al. (2013) found that kenaf is the best
natural fibre for parking brake lever. Madeswaran et al. (2016) research on brake pads
using natural fibre with organic ingredients showed that kenaf fibre could improve heat
resistance and strength of the brake pad. Yahaya et al. (2014) discovered that kenaf in
woven and unidirectional structure in hybrid composite has the potential to improve the
ballistic application for vehicle spall. Research on the ballistic impact properties of
woven kenaf-aramid hybrid composite with 14 layers of Kevlar and 2 layers of kenaf
fibre show a superior ballistic performance (Yahaya et al., 2016). Besides that, Davoodi
et al. (2010) applied the hybrid kenaf composite on the bumper beam to improve impact
property by optimising the structural design parameters. Davoodi et al. (2012) study to
improve the impact property of hybrid kenaf/glass fibre epoxy composite shows that
polybutylene terephthalate toughening with the modified SMC process can improve the
impact properties.
6
Conclusions
The MCDM methods are gaining importance as potential tools for analysing complex
real world problems due to their inherent ability to judge different alternatives on various
criteria for possible selection of the best or suitable alternatives. Selection of natural fibre
reinforced composite for the car front hood was executed using the fuzzy VIKOR based
on the car front hood requirements. Through the fuzzy VIKOR method, kenaf fibre was
determined as the potential material which has the suitable criteria to be applied on the
FML structure and meets the car front hood design requirements compared to the other
candidate natural fibres. Besides that, this study has proven fuzzy VIKOR can be applied
for multi criteria decision making particularly for the conceptual design stage. This
method includes a multi criteria optimisation of complex systems that focuses on ranking
and selecting from a set of alternatives among conflicting criteria. As a result, the use of
natural fibre-reinforced FML for automotive components may reduce vehicle weight and
subsequently reduce the overall vehicle CO2 gas emissions.
Acknowledgements
We would like to acknowledge the Faculty of Mechanical Engineering, Universiti
Teknikal Malaysia Melaka and MyBrain15 scholarship by the Ministry of Higher
Education of Malaysia (MOHE) for making this study possible.
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