Taguchi based fuzzy logic optimization of multiple quality characteristics of cobalt disulfide nanostructures

Article abstract of DOI:10.1016/j.jallcom.2014.03.124

Cobalt sulfide nanostructures, with a formula of Co_xS _y, have recently received considerable attention due to their unique catalytic, electric, magnetic, optical, and mechanical properties. In this study, cobalt disulfide (CoS₂) nanoparticles have been synthesized by the solvothermal method using cobalt chloride and sodium thiosulfate as the precursors. The Taguchi method has been implemented to investigate and optimize the affecting parameters involved in minimizing the band-gap energy. Then, the predictions used to model the anticipated results with fuzzy logic. It has been found that the reaction temperature and the precursor ratio are the most effective parameters when attempting to minimize the band-gap energy.

Full text of DOI:10.1016/j.jallcom.2014.03.124

Journal of Alloys and Compounds 607 (2014) 61–66
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Taguchi based fuzzy logic optimization of multiple quality
characteristics of cobalt disulfide nanostructures
T. Rajabloo a, , A. Ghafarinazari a,b, L. Seyed Faraji c, M. Mozafari d,1
⇑
a Materials Engineering Department, Islamic Azad University, Southern Branch, Tehran, Iran
b Department of Biotechnology, University of Verona, Strada Le Grazie 15, I-37134 Verona, Italy
c School of Mechanical & Aerospace Engineering, Oklahoma State University, 526 North Elgin Avenue, Tulsa, OK 74106, United States
d Bioengineering Research Group, Nanotechnology and Advanced Materials Department, Materials and Energy Research Center (MERC), P.O. Box 14155-4777, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history:
Cobalt sulfide nanostructures, with a formula of CoxSy, have recently received considerable attention due
to their unique catalytic, electric, magnetic, optical, and mechanical properties. In this study, cobalt disul-
fide (CoS2) nanoparticles have been synthesized by the solvothermal method using cobalt chloride and
sodium thiosulfate as the precursors. The Taguchi method has been implemented to investigate and opti-
mize the affecting parameters involved in minimizing the band-gap energy. Then, the predictions used to
model the anticipated results with fuzzy logic. It has been found that the reaction temperature and the
precursor ratio are the most effective parameters when attempting to minimize the band-gap energy.
Ó 2014 Elsevier B.V. All rights reserved.
Received 2 February 2014
Received in revised form 13 March 2014
Accepted 15 March 2014
Available online 3 April 2014
Keywords:
Cobalt disulfide
Band-gap
Solvothermal
Taguchi method
ANFIS
1. Introduction
importance of narrow band-gap characteristics and the unique
applications promised by many new features of these types of
Since the first attempts to introduce and apply nanostructured
materials in different aspects of science [1], many research groups
have paid attention to the controllable synthesis and optimized
characteristics of these materials [2]. An extraordinary range of
techniques and characteristics have been determined to control
the crystal form and size of nanostructured materials during the
crystallization process [3,4]. The transition metal disulfides are
normally crystalline with a pyrite structure [5], which have
received considerable attention due to their unique characteris-
tics [6]. Among these, cobalt disulfide (CoS2) is a promising nano-
material in terms of its catalytic and optoelectronic properties.
The band-gap energy is a critical criterion to illustrate the phys-
ical properties of this material [7]. The growing interest in nano-
structures has provided areas of application for the unique
properties of the narrow band-gap materials [8]. It has been
reported that the very small effective masses inherent in small
band-gap materials make them promising choices for observing
quantum confinement effects at larger dimensions (when compare
with the materials with wide-band-gaps) [9–11]. The technical
materials [12,13]. Indeed, a narrow band-gap is applicable in many
applications such as novel optoelectronic and solar energy devices.
Therefore, lower band-gap energy for CoS2 nanoparticles is set as
an ultimate goal for this research.
In this study, CoS2 nanoparticles have been successfully synthe-
sized via a moderate solvothermal method. Among different meth-
ods, solvothermal method has recently gained much attention due
to the advantages of simplicity, low temperature conditions, non-
vacuum process, low energy consumption, low cost, high efficiency
and high flexibility in selecting the process parameters [14–16].
Therefore, the precursors came to reaction after dissolving in the
solvent media. The temperature was near the boiling point of the
solvent, which caused the production of nanoparticles. The imple-
mentation of stirring led to a shorter reaction time by increasing
the heat and the mass transfer rate. Additionally, the Taguchi
method as a robust technique to understand the effects of control-
lable factors on the nanostructured materials has been used. The
full factorial method is valuable because it aids in the analysis of
the reaction factors and their interactions, but the Taguchi method
reduces the number of reactions. As a case in point, for 5 factors in
4 levels, the Taguchi requires only 16 tests instead of 1024 (45)
tests. Since the Taguchi method cannot interpolate the data, an
adaptive neuro-fuzzy interface system (ANFIS) has been also
⇑
Corresponding author. Tel.: +98 3203089944.
E-mail addresses: t.rajabloo@unibs.it (T. Rajabloo), mozafari.masoud@gmail.com
(M. Mozafari).
1
utilized [17]. ANFIS provides
a better understanding of the
Co-corresponding author. Tel.: +98 21 22373717.
http://dx.doi.org/10.1016/j.jallcom.2014.03.124
0925-8388/Ó 2014 Elsevier B.V. All rights reserved.

62
T. Rajabloo et al. / Journal of Alloys and Compounds 607 (2014) 61–66
m
X
controllable impact factors that influence the band-gap energy.
Finally, the results of this program coincide with the experiments
at optimum conditions.
SST
¼
Y2i ꢀ mðYT Þ2
ð7Þ
j¼1
In Eq. (7), m represents the number of experiments; and, YT obtains from
P
m
YT
¼
iꢀ1Yi=m. The factorial sum of squares, SSF, can be calculated by Eq. (8):
2. Experimental procedures
L
X
m
SSF
¼
ðYFL ꢀ YT Þ2
ð8Þ
L
Cobalt chloride (CoCl2), sodium thiosulphate (Na2S2O3), and sodium dodecyl
sulfate (SDS) (an anionic surfactant with a polar group [18]) have been dissolved
in solvents. Moreover, pure ethanol and its mixtures have been prepared using dis-
tilled water in different v/v percentages as the solvents. These solvents are harmless
and readily available. Then, the content of the reactor has been filtered and the
black precipitates washed several times with distilled water. The final product
has been dried at 60 °C. Finally, the effect of heat treatment on some of the selected
samples has been investigated. The reaction parameters at different levels, shown
in Table 1, have been implemented using the Taguchi method. Then, the results
of 16 experiments have been applied into the formula of the Taguchi method to
anticipate the number of other tests.
k¼1
Here, YFK is the average value of the measurement results of a certain factor in
the kth level. Additionally, the variance of error, VEr, can be obtained by Eq. (9)
[26,27]:
P
D
SST
ꢀ
F¼ASSF
VEr
¼
ð9Þ
m
The Fuzzy Logic Toolbox of MATLAB is a proper tool for the ANFIS processing
section of the research. We implemented 1024 (45) tests, obtained from Eq. (4),
as the ANFIS inputs. Eq. (10) has been used to normalize all of the input data:
The final synthesized materials have been analyzed by X-ray powder diffraction
(XRD), Fourier Transform Infra-Red (FTIR), Ultraviolet Visible (UV–vis.), and Field
Emission Scanning Electron Microscope (FESEM). In addition, to calculate band-
gap energy of the final products, the Taus formula has been applied (Eq. (1)) [19,20]:
Xi ꢀ Xmin
Xn
¼
ð10Þ
Xmax ꢀ Xmin
In this stage, we should divide the initial data into the train, validation, and test
Bðhv
ꢀ Eg Þꢀn=2
sets. It is important to utilize the input selection method based on the special ANFIS
properties. The ANFIS model with the smallest root mean squared error (RMSE)
achieves a lower RMSE after one epoch of training when more epochs of training
are given. For this purpose, Jang’s method was selected. Some codes in MATLAB
have been used to make train/validation/test sets, and then these sets trained for
one epoch. The smallest RMSE among 1000 runs has been obtained after one epoch
of training. In addition, various kinds of membership functions (MFs) have been uti-
lized in order to find the optimum ANFIS parameters for the training data. One time,
MFs were the same and the numbers of MFs were equal. Then, the other procedure
with various kinds and different numbers of MFs has been implemented. Due to the
proven high training efficiency for ANFIS [29], bell shaped MFs and the hybrid
method as the learning algorithm have been selected. Finally, the ANFIS model
has been utilized for plotting the interaction effects.
a
¼
ð1Þ
h
v
In this equation, the term hv is the photon energy, Eg stands for the band-gap
energy, and B is a constant that is related to the type of sample. The number n liaises
with the stimulated electron type. The other parameters of this equation were com-
puted by the Butler equations (Eq. (2)) [21,22]:
T ¼ expðꢀ
atÞ
ð2Þ
Here, T is the transition coefficient, and t shows the thickness of the sample
under radiation of UV–vis. All of the necessary calculations for the optimizations
and predictions have been performed based on the Taguchi method by related
equations [22], as shown below:
First, Eq. (3) gives the S/N ratio for the little better status [23–26]:
S=N ¼ ꢀ10log10ðy2Þ
ð3Þ
3. Results and discussion
In Eq. (3), y refers to the amount of band-gap energy. These 16 experiments are
representative of 1024 (45) tests, which will be estimated through the prediction
formula of the Taguchi method, Eq. (4) [24]:
3.1. Experimental results
n
X
The FTIR analysis has been implemented to determine the prod-
uct elements.
ðS=NÞp ¼ ðS=NÞm
þ
½ðS=NÞi ꢀ ðS=NÞm
ꢁ
ð4Þ
i¼1
The FTIR spectra of the samples without heat-treatment indi-
cate that there are no Co-O bond vibrations [25]. As shown in
Fig. 1, the appearance of one strong band (due to the S–O modes)
at about 970 cmꢀ1 is detectable, which is due to the formation of
CoS2.
The achieved XRD patterns showed that all of the materials
without calcinations were in an amorphous state because there
were no appropriate conditions for crystallization (see Fig. 2). On
the other hand, amorphous structures can be due to the atmo-
spheric conditions. The samples under heat-treatment were crys-
talline and the XRD pattern depicted the existence of CoS2
In Eq. (4), (S/N)m is the total mean of the S/N ratio. (S/N)i is the mean S/N ratio at
the predicted level, and n represents the number of main design parameters that
affect the quality characteristics. The analysis of the mean (ANOM) statistical
approach is necessary to construct the main effects. Therefore, we should calculate
the mean of the S/N ratio of each factor at a certain level [27,28]. For example,
v
el¼i
Eq. (5) shows Mlfeactor¼1, which is the mean of the S/N ratio of factor I at level i:
nIj
X
1
nIj
le
v
el¼i
level¼i
M
¼
½S=N
ꢁ
ð5Þ
factor¼1
factor¼1
j
j¼1
where nIi represents the number of appearances of factor I at level i, and ½S=Nlfeactor¼1ꢁ
v
el¼i
j
is the S/N ratio of factor I at level i. The mean of the S/N ratios of other factors at a
certain level, by Eq. (5), have been also determined. In addition to ANOM, the anal-
ysis of variance (ANOVA) statistical method has been used to analyze the influence of
each controllable factor on the band-gap energy of the products. Moreover, the for-
mula for the percentage contribution of each factor,
qF, is (Eq. (6)):
SSF ꢀ ðDOFF ꢀ VEr
Þ
qF
¼
ꢂ 100
ð6Þ
SST
In Eq. (6), DOFF represents the degree of freedom for each factor. DOFF was equal
to three for all factors in this research. The equation to calculate the total sum of
squares, SST, is shown here (Eq. (7)):
Table 1
Controllable factors and levels.
Factor
Description
Level 1
Level 2
Level 3
Level 4
A
B
C
D
E
Tr (°C)
S/Co
Solvent (%)
Surfactant (g)
Tc (°C)
60
0.25
70
0
70
1
80
5
75
4
90
10
330
80
8
100
20
0a
300
360
a
Without calcinations.
Fig. 1. FTIR spectrum of sample 8.

T. Rajabloo et al. / Journal of Alloys and Compounds 607 (2014) 61–66
63
Table 2
nanocrystals [30]. As can be seen, the peaks at 37.7, 45.6 and 54.8
Band-gap energy outcomes with related S/N.
degrees supported the crystalline structure of CoS2. In fact, the
heat-treatment process affects the structure of the final products
and induces crystallization. The band-gap energy of each sample
is listed in Table 2 as the main output of this study.
No.
Tr
S/Co
Sol.
Surf. (g)
Tc
Gap energy
S/N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
60
60
60
60
70
70
70
70
75
75
75
75
80
80
80
80
0.25
1
4
8
0.25
1
4
8
0.25
1
4
8
0.25
1
4
8
70
80
90
100
80
70
100
90
90
100
70
80
0
5
0
3.38
3.25
3.26
2.92
3.13
2.87
3.01
2.97
3.92
3.44
3.34
3.17
3.35
3.18
3.04
2.88
ꢀ10.58
ꢀ10.24
ꢀ10.26
ꢀ9.31
300
330
360
360
330
300
0
10
20
10
20
0
3.2. Optimization
ꢀ9.91
ꢀ9.16
ꢀ9.57
The Taguchi formulas have been applied to minimize the band-
gap and optimize the reaction conditions. Thus, the main effect of
the S/N ratio of each controllable factor at a certain level ANOM has
been calculated by Eq. (5), presented in Table 3. The boldfaced
numbers in Table 3 refer to the best values of the S/N ratio.
Therefore, Table 4 shows the optimum conditions for having
minimum band-gap energy.
There is some difference in the S/N ratio between the optimum
conditions and Test 6, while the S/Co ratio substantially increases
from 1 to 8. Furthermore, the calcination temperature increases
from 330 to 360 °C. Actually, a bigger S/Co ratio and a higher calci-
nation temperature correspond to a better band-gap energy when
a minimum energy is required.
5
ꢀ9.46
20
10
5
0
5
0
20
10
300
0
ꢀ11.87
ꢀ10.73
ꢀ10.47
ꢀ10.02
ꢀ10.5
360
330
330
360
0
100
90
80
ꢀ10.05
ꢀ9.66
70
300
ꢀ9.19
Table 3
The main effect of each factor of reaction.
Lev
el
Level
Factor/level
½ðS=NÞFactorꢁj
j = 1
ðMÞFactor
j = 2
j = 3
j = 4
3.3. Percentage of contribution
Tr/60
Tr/70
Tr/75
Tr/80
ꢀ10.58
ꢀ9.91
ꢀ10.24
ꢀ9.16
ꢀ10.73
ꢀ10.05
ꢀ9.91
ꢀ9.46
ꢀ9.57
ꢀ9.46
ꢀ9.16
ꢀ9.91
ꢀ9.46
ꢀ9.57
ꢀ9.57
ꢀ9.46
ꢀ9.91
ꢀ9.16
ꢀ9.46
ꢀ9.57
ꢀ9.16
ꢀ9.91
ꢀ10.26
ꢀ9.57
ꢀ9.31
ꢀ9.46
ꢀ10.02
ꢀ9.19
ꢀ10.02
ꢀ10.5
ꢀ9.66
ꢀ9.19
ꢀ9.19
ꢀ9.66
ꢀ10.05
ꢀ10.5
ꢀ10.05
ꢀ10.5
ꢀ9.19
ꢀ9.66
ꢀ9.66
ꢀ9.19
ꢀ10.5
ꢀ10.05
ꢀ10.1
ꢀ9.52
ꢀ10.77
ꢀ9.85
ꢀ10.6
ꢀ10.17
ꢀ9.99
ꢀ9.49
ꢀ9.85
ꢀ9.96
ꢀ10.41
ꢀ10.03
ꢀ10.05
ꢀ10.17
ꢀ10.31
ꢀ9.99
ꢀ10.11
ꢀ10.21
ꢀ9.98
ꢀ9.94
Initially, Table 5 shows the amounts of YFK (the average value of
the measurement results of a certain factor in the level of K). The
values of SSF for each factor have been calculated by substituting
YFK and YT = 3.19 into Eq. (8). These values are listed in Table 6.
The value of VEr was 4.94 ꢂ 10ꢀ15 obtained from substituting SSF
and SST = 2.13 into Eq. (9). Finally, the percentage contribution of
ꢀ11.87
ꢀ10.5
ꢀ10.47
ꢀ9.66
(S/Co)/0.25
(S/Co)/1
(S/Co)/4
(S/Co)/8
Sol./70
Sol./80
Sol./90
Sol./100
Surf./0
Surf./5
Surf./10
Surf./20
Tc/0
ꢀ10.58
ꢀ10.24
ꢀ10.26
ꢀ9.31
ꢀ11.87
ꢀ10.47
ꢀ10.47
ꢀ10.02
ꢀ10.47
ꢀ10.02
ꢀ11.87
ꢀ10.73
ꢀ10.02
ꢀ10.47
ꢀ11.87
ꢀ11.87
ꢀ10.73
ꢀ11.87
ꢀ10.02
ꢀ10.47
ꢀ10.58
ꢀ10.24
ꢀ10.26
ꢀ9.31
each factor,
qF, by the substitution of SSF, SST, VEr, and DOFF has
been calculated by Eq. (6) (Table 6). Among the examined factors,
the reaction temperature and the S/Co ratio have the most influ-
ence on the band-gap energy.
ꢀ10.58
ꢀ10.24
ꢀ10.26
ꢀ9.31
3.4. Structural investigation
ꢀ10.58
ꢀ10.24
ꢀ10.26
ꢀ9.31
Tc/300
Tc/330
Tc/360
The FESEM images of the samples show the appearance of the
produced nanoparticles (see Fig. 3). The results illustrate different
shapes in the case of the presence of surfactant. For example, at the
tests with numbers 4 (Fig. 3b) and 6 (Fig. 3c), when 20 g of surfac-
tant was used, which caused the production of nanorod structures.
The surfactant, because of its growth control behavior, causes a
mixture of nanosphere and nanorod shaped particles. In fact, the
surfactant molecules cover the product particles and poison the
growth surfaces in certain axes, causing a one-dimensional growth
of the particles. The surfactant leads to the advent of nanorod
structures [31], and the products exhibit less band-gap energy. It
is obvious that nanorods are more evident in test 6 in comparison
with test 4 (with equal amounts of surfactant). The main reason for
this difference lies in the reaction temperature. Indeed, the effect of
Table 4
Comparison S/N ratio of the best results of Table 2 with the optimum conditions.
Tr
S/Co Sol. Surf. Tc
Gap energy S/N
Test 6
70
1
8
70
70
20
20
330 2.87
360 2.79
ꢀ9.16
ꢀ8.91
Optimization condition 70
Table 5
The average of the measurement results of a certain factor in the level of K.
YKT
YKT
YSKurf
YSK=Co
YSKol
r
C
Level
1
2
3
4
3.20
2.99
3.47
3.11
3.44
3.18
3.16
2.98
3.12
3.15
3.33
3.18
3.18
3.23
3.18
3.19
3.21
3.26
3.16
3.14
Tr is stronger than the effect of the surfactant. This is additional
evidence to be considered in the ranking of the importance of
the parameters.
Overall, after heat-treatment besides the formation of crystal-
line phase, the sizes of the particles increase slightly, while the
band-gap energy decreases. In test 1 (Fig. 3a), no heat-treatment
is implemented. Therefore, the sizes of the particles are very fine,
Fig. 2. XRD pattern of the samples under heat-treatment.

64
T. Rajabloo et al. / Journal of Alloys and Compounds 607 (2014) 61–66
Table 6
Table 7
SSF and the contribution percentage of each factor.
Normalized amounts of optimum conditions based on Taguchi method.
Factor
SSF
qF (%)
Parameters
Tr
S/Co
1
Sol.
0
Surf.
1
Tc
Tr
0.97
0.86
0.22
0.01
0.07
45.42
40.41
10.27
0.57
Normal optimum parameters
0.5
1
S/Co
Sol.
Surf.
TC
ANFIS model. After modeling of the results in ANFIS, and selecting
dual parameters, their functions have been obtained as surfaces.
The corresponding output diagrams for the fuzzy approach for Tr,
solvent, and S/Co ratio are shown in Fig. 4. Among Tr, solvent,
and S/Co ratio, the percentage of the solvent is less important than
the other two factors. As shown in Fig. 4a, the temperature of the
reaction plays a key role in the band-gap energy. Therefore, at
the optimum amount of 0.5 for Tr, the solvent does not play a sig-
nificant role in the size of the band-gap energy. It is noticeable that
the solvent has an overall effect on the properties of the final prod-
uct, but it has less influence than the other two parameters. Since
the solvents in this study are pure ethanol and its mixtures with
water are polar in nature, there is no significant difference between
these four levels of solvents. Thus, the solvent type has no influ-
ence on the results. As Fig. 4b depicts, the solvent affects the
band-gap energy as compared to optimum amount of S/Co. This
is due to less difference of the solvent levels, as explained earlier.
Fig. 4d depicts the effect of the reaction temperature and surfac-
tant on the band-gap energy. In Fig. 4d, two parameters, Tr and sur-
factant, are the most and least important parameters, respectively,
based on the main effect calculations of the Taguchi method. The
best of our results occurred with Tr at level 2 and with the surfac-
tant at level 3. Moreover, it is clear in Fig. 4 that the surfactant does
not have any important effect on the results. In other words, we
found that when Tr is optimum, equal to 0.5, all quantities of the
surfactant are reliable. We detected that the effect of Tr on
the band-gap energy of the products is obviously greater than the
effect of the surfactant.
3.32
with an average diameter of 30 nm and a band-gap energy of
3.38 eV. In the absence of the surfactant, spherical shape morphol-
ogy has been observed (Fig. 3a). In contrast, the samples of 7 and
12 produced bigger sizes and lower band-gap energies. In these
two samples, the surfactant was not used, which reveals that the
presence of the surfactant affects the product structure. Finally,
other tests were performed at optimum conditions, as shown in
Fig. 3f. The FESEM image of the optimum test shows a mixture of
nanorod and nanosphere particles with a band-gap energy equal
to 2.79 eV.
3.5. ANFIS modeling
In this stage, ANFIS modeling has been applied. The white color
ranges on the surfaces were related to the smallest amount of
band-gap energy and illustrated the lowest amounts of band-gap
energy. The normal amounts of the optimum conditions from the
Taguchi method are available in Table 7.
Initially, the modeling was based on consideration of all the
reaction factors; and, results were depicted as some surfaces.
According to Section 3.4., the percent contributions of the surfac-
tant factor and the calcination temperature on the band-gap
energy are clearly less than the contributions of the other factors.
In addition, modeling gives the same results. Therefore, the surfac-
tant factor and the calcinations temperature have been omitted,
and the main focus has been paid on three other factors in our
Referring to Fig. 4c, an increase in the reaction temperature up
to level 2 corresponds to a dramatic decrease in the band-gap
Fig. 3. FESEM images of the samples from Taguchi tests; test number of: (a) 1; (b) 4; (c) 6; (d) 7; (e) 12 and (f) optimum conditions (microbar is 300 nm).

T. Rajabloo et al. / Journal of Alloys and Compounds 607 (2014) 61–66
65
Fig. 4. General performances of ANFIS outputs by 3D plots on Band-gap energy as color bar, x and y axes are: (a) Tr – solvent, (b) S/Co – solvent, (c) Tr – S/Co ratio and (d)
reaction temperature – surfactant.
in: 1st Middle East Conference on Biomedical Engineering, MECBME 2011,
Sharjah, United Arab Emirates, 21 February 2011. Article number 5752075, p.
100–103.
energy. As the reaction temperature increments above level 2, the
band-gap energy increases. Thus, at the amount of 0.5 for the reac-
tion temperature, the band-gap has its least value. Furthermore,
the optimum S/Co ratio for a lower band-gap lies at amounts of
0.5 and 1. Hence, the optimum S/Co ratio obtains the normal
amount of one. This means that we should choose an S/Co ratio
equal to one in order to cover the best S/Co ratio for both graphs
(Fig. 4b and c). An S/Co ratio equal to one is explanatory for amount
of eight. Therefore, the fuzzy concept from the outcome surface for
the S/Co ratio and the temperature of reaction proves the signifi-
cance of these two influences. Overall, the results indicate a strong
interaction between the reaction parameters.
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between the temperature of the reaction and the S/Co ratio. There-
fore, both investigations and modeling are vital to gain reliable
results.
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