I. NIKOLI] et al.: A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY AHP-TOPSIS APPROACH ...
147–157
A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY
AHP-TOPSIS APPROACH FOR PRIORITISING COPPER
SMELTING PROCESSES
NOV HIBRIDNI MODEL ZA ODLO^ITEV PREDNOSTNEGA
POSTOPKA PRETALJEVANJA BAKRA NA OSNOVI PRISTOPA Z
NAVIDEZNO LOGIKO AHP-TOPSIS
Ivica Nikoli}
*
, An|elka Stojanovi}, Milijana Mitrovi}
University of Belgrade, Technical Faculty in Bor, 12 Vojske Jugoslavije, 19210 Bor, Serbia
Prejem rokopisa – received: 2023-11-03; sprejem za objavo – accepted for publication: 2024-01-24
doi:10.17222/mit.2023.1037
The construction of a copper smelting facility and its undisturbed and profitable business undoubtedly contribute to the develop-
ment of each country’s economy. These facilities employ many workers and produce a large amount of copper, reducing imports
and dependence on this important raw material, thereby improving the economic situation in a given country. More than a hun-
dred copper smelters operate worldwide, many of which use different types of copper extraction processes. Strict legislation re-
lating to ecology and environmental protection as well as stakeholder involvement in selecting and constructing copper smelting
facilities limit the maximisation of short-term economic objectives. The prioritisation of technological processes for the extrac-
tion of copper must consider the impacts of often mutually opposing economic, technical and environmental objectives. No re-
search from the available literature analyses the economic, technical and environmental parameters systematically. Studies have
mainly dealt with exploring individual influences of factors through the use of one selection method. This paper presents the de-
velopment of a novel hybrid AHP-TOPSIS model in fuzzy environments that will provide both informative decisions and opti-
mum results of decision making.
Keywords: hybrid model, AHP, TOPSIS, fuzzy environment, copper smelting processes
Konstrukcija ter nato uspe{na izdelava in uporaba naprav za pretaljevanje bakra je nedvomno donosen posel, ki v celoti prispeva
k razvoju ekonomije vsake dr`ave. Te naprave zaposljujejo veliko ljudi in proizvajajo velike koli~ine strate{ke kovine kot je
baker, zmanj{ujejo uvoz in odvisnost od pomembnih osnovnih surovin ter tako izbolj{ujejo ekonomske razmere v dani dr`avi.
Ve~ kot sto talilnic bakra deluje po svetu in pri tem uporabljajo razli~ne postopke ekstrakcije bakra. Stro`ja ekolo{ka in okoljska
zakonodaja, kakor tudi vklju~evanje delni~arjev v izbiro vrste naprave za pretaljevanje bakra omejuje in skraj{uje roke za
ekonomske odlo~itve. Dajanje prednosti tehnolo{kim procesom ekstrakcije bakra je pogosto v nasprotju z ekonomskimi,
tehni{kimi in okoljskimi zahtevami, ko se ocenjuje realizacija projekta. Avtorji tega ~lanka v literaturi niso na{li ustrezne
analize, ki bi sistemati~no isto~asno upo{tevala ekonomske, tehni{ke in okoljske parametre. Obstoje~e {tudije se v glavnem
ukvarjajo z raziskovanjem posameznih vplivov z uporabo ene izbrane metode. V tem ~lanku avtorji predstavljajo razvoj novega
hibridnega modela AHP-TOPSIS v navideznem okolju, ki naj bi pripomogel tako do odlo~ilnih informacij za optimalne
rezultate odlo~anja v tako imenovanem »decision making« postopku.
Klju~ne besede: hibridni model, analiti~no hierarhi~ni proces (AHP), tehnika prednostne ureditve za idealno re{itev (TOPSIS),
zamegljeno oziroma navidezno okolje, proces pretaljevanja bakra
1 INTRODUCTION
Without a doubt copper represents one of the key
products needed for the economic development of any
country. Copper extraction dates back to prehistoric
times, to be more precise, to the Copper Age or Chalco-
lithic Age.
1
Although it is one of the oldest exploited
metals, its significance has not diminished. On the con-
trary, the significance of this metal is greater than ever,
and its positive growth trend continues. However, the in-
crease in the copper production has a negative impact on
the environment. This has led to a constant development
of new technological solutions for reducing the adverse
effects of copper extraction.
2–4
In the last half century,
there was progress in technological processes for extract-
ing non-ferrous metals, especially copper. Thus, produc-
tion capacities were increased, and the quality was im-
proved. However, the negative environmental impact re-
mained.
5,6
The manufacturing sector plays a significant role in
fostering sustainable economic growth in many devel-
oped economies. The study by Behun et al.
7
showed that
changes in the manufacturing and sales sectors are al-
most immediately reflected in the gross domestic prod-
uct (GDP) changes. In a survey conducted by Vishal
Chandr Jaunky (2013), the influence of copper consump-
tion on the economic development of 16 countries was
analysed.
8
Based on this research and other relevant stud-
ies from the literature, it can be concluded that copper
consumption and production are crucial elements of a
country’s long-term economic development.
9–13
The fact
is that copper smelting facilities employ many workers
Materiali in tehnologije / Materials and technology 58 (2024) 2, 147–157 147
UDK 549.281:666.1.037.4 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 58(2)147(2024)
*Corresponding author's e-mail:
inikolic@tfbor.bg.ac.rs (Ivica Nikoli})

and produce a significant amount of copper, contributing
to a better economic situation in each country. The con-
struction of such industrial facilities contributes to reduc-
ing the import of this extremely important raw material
and improving the living standards in the environment
where a copper facility operates. Therefore, it is essential
to develop an adequate model for selecting the optimal
copper smelting process, taking into account the impor-
tance of these facilities for the local economy and the
economy of the country.
The modern environment is full of challenges and, in
such conditions, decision-makers often need quick and
efficient tools that help them quickly model and optimise
several alternative solutions, and then compare them
based on different prerequisites or performance crite-
ria.
14–16
This problem can be solved by using the
multi-criteria decision making methodology (MCDM),
which provides a wide range of mathematical models
that can give effective solutions.
In this paper, eight of the most effective and fre-
quently used technological processes for the pyro-
metallurgical extraction of copper were selected after
consulting experts. In a study conducted by Kapusta in
2004, over 50 active copper smelters worldwide were
analysed based on economic, ecological and technologi-
cal factors. The study provides an insight into the fre-
quency of a specific type of technological process used
for extracting copper.
17–21
Based on a broad literature review, it has been con-
cluded that no research systematically analyses the eco-
nomic, environmental and technical parameters for pri-
oritising copper smelting processes. There is mainly
available research on analysing separate effects of vari-
ous factors.
3,22,23
Therefore, the essence of this study was
to determine which current technological process
achieves the optimal pre-set economic goals while com-
plying with technological and environmental standards.
In addition to filling the literature gap, applying this sys-
tematic decision model would increase the cleaner “red
metal” production with technological efficiency and eco-
nomic justification. This approach determines the opti-
mal technological process for the given situation.
The hybrid AHP-TOPSIS method in a fuzzy environ-
ment was used to rank the analysed technological pro-
cesses for copper extraction according to the 11 men-
tioned parameters. The ranking was based on 11
economic, technological and environmental parameters
selected based on previous consultations with the experts
in the copper production field. The importance of the
chosen parameters for copper processing can be found in
the papers by Davenport et al.,
24
Moskalyk & Alfantazi,
17
Kapusta,
18
Schlesinger et al.,
19
Najdenov et al.,
25
and oth-
ers. These parameters represent the criteria for the model
proposed in this paper. The scientific contribution of this
paper is reflected in the integration of the economic as-
pect with technological and environmental parameters.
2 OVERVIEW OF THE CONSIDERED
TECHNOLOGICAL PROCESSES AND
PARAMETERS
Extracting copper from copper ores can be achieved
through pyrometallurgy and hydrometallurgy. The litera-
ture review shows that hydrometallurgical processes are
more environmentally friendly than pyrometallurgical
ones, but most copper smelting facilities use pyro-
metallurgical processes.
21
Pyrometallurgical processes
occur at high temperatures, leading to very rapid reac-
tions. Thus, by applying a pyrometallurgical process,
copper is obtained much faster than with the hydro-
metallurgical process. In this way, producing a larger
amount of copper within a much shorter period is possi-
ble. It also has a significant economic impact that re-
flects on a greater reversal of assets and the ability to
make a profit in a shorter time.
26–28
For the reasons men-
tioned above, the research focused only on pyrometallur-
gical processes. When selecting a specific technological
process for extracting copper, in addition to the techno-
logical, two other basic criteria were considered: eco-
nomic and environmental acceptability. The environmen-
tal acceptability of the technology was significantly
actualised at the end of the twentieth century. As the eco-
nomic parameter is the most influential when choosing
the technology, and it is prominent in pyrometallurgical
procedures, about 80 % of copper produced today is ex-
tracted primarily through pyrometallurgical pro-
cesses.
19,21
In addition, numerous improvements that oc-
curred in the previous period led not only to an increase
in the production infrastructure and capacity but also in a
reduction of the negative impact on the environment.
29–32
The parameters selected as the criteria in this paper
significantly impact the implementation of the techno-
logical process, its economic viability and the environ-
ment.
Copper ores contain a relatively small percentage of
copper. Therefore, copper ores must be enriched by flo-
tation before further processing in smelting facilities to
achieve optimal conditions for a copper production. The
product of copper flotation operation is copper concen-
trate.
24
The amount of concentrate that will be processed
should be taken into account when choosing the appro-
priate technological process. An economical copper pro-
duction can be achieved if larger quantities of concen-
trate are processed during the day. For this reason, a
higher value of this parameter positively affects the busi-
ness.
Furnaces for copper metallurgy work at high temper-
atures, so they must be protected from the inside since
they are in contact with the reaction medium and smelt-
ing products. The inside of a furnace is made of refrac-
tory bricks, which isolate high-temperature zones and re-
duce heat losses, thus ensuring the static stability of the
furnace, etc. In certain parts of the furnace (for chemical
reaction) that are used for the separation of matte from
slag as well as for the separation of gases, different tech-
I. NIKOLI] et al.: A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY AHP-TOPSIS APPROACH ...
148 Materiali in tehnologije / Materials and technology 58 (2024) 2, 147–157

nological conditions prevail, so a variety of refractory
materials and different ways of protecting the device by
water-cooling are required. The wall lining in all types of
autogenic furnaces is mainly made of chrome-magnesite
bricks. The exception is the Inco flash furnace, which
reaches extremely high temperatures, so copper-cooling
water jackets for flash furnaces are built into its walls.
Previously, the chimney for flash smelting was made of
refractory bricks. Over the last decades, there has been a
tendency to entirely cool chimneys with water-cooling
off-gas devices to change dust into a solid before enter-
ing the boiler. While assigning ranking based on this pa-
rameter, priority should be given to smelters with a lon-
ger lining lifetime. This reduces the direct costs arising
from the lining change and the time workers spend on
the lining change. Moreover, the indirect costs of pro-
duction stagnation are reduced, as is the negative impact
on the environment, reflected through dust resulting
from poor cooling of the off-gases.
17–19,24,33
A significant parameter is also the percentage of sul-
phur and copper recovery. The sulphur and copper recov-
ery should be maximised to increase the economy of the
technological process. In addition to economic reasons,
environmental ones have become dominant in selecting a
technological process.
Also, it has been noticed that the content of Fe in
copper is always low so that the content of copper is
high, and thus, a smaller extent of further refining is
needed. Also, the content of Cu in the slag should be at
the lowest possible level so that the copper recovery is
better. Copper technological processes have the advan-
tage of being capable of smelting poor concentrates, thus
increasing the number of potential concentrate suppli-
ers.
21,34,35
Copper smelting facilities worldwide use many
different pyrometallurgical processes to extract cop-
per.
3,17,24
Each technology exhibits different positives and
negatives based on the above-described parameters and
characteristics. The eight most current and representative
technological processes were selected for further consid-
eration (Table 1). The technological processes represent
alternatives in this study.
According to the data from the USGS website (the
data are for 2023), there are over a hundred operational
copper smelters worldwide. The largest number of cop-
per smelters are located in China (19 smelters), Russia
(10 smelters), Chile (7 smelters) and Japan (6 smelters).
Regarding the application of technology, the most wide-
spread is the reverberatory furnace (31 smelters use this
technology), followed by Outokumpu flash smelting
(Outotec) (24 smelters use this technology). In contrast,
the least applied technologies are Inco Flash (one smelter
in the USA and one in Canada) and Vanyukov (one
smelter in Russia and one in Kazakhstan). The techno-
logical process called Ausmel/Isasmelt lance is currently
utilised by seven smelters worldwide, El Teniente by six
smelters, while Noranda and Mitsubishi are each used in
I. NIKOLI] et al.: A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY AHP-TOPSIS APPROACH ...
Materiali in tehnologije / Materials and technology 58 (2024) 2, 147–157 149
Table 1: Brief overview of the considered processes of pyrometallurgical extraction of copper
Type of the process Major positives Literature review
Outokumpu flash
smelting (Outotec)
adaptability, low energy consumption, high sulphur
recovery, more efficient use of sulphide energy from
concentrates, higher utilisation of metals and much
better protection of the atmosphere against pollution
by SO
2
and other harmful substances
Higgins et al., 2009;
36
Vra~ar, 2010;
33
Schlesinger et al., 2011;
19
Liu et al., 2014;
37
Outokumpu, 2023;
38
Outotec, 2023;
39
USGS,
2023;
40
Ausmel/Isasmelt lance highly efficient process, low production costs, com-
pliance with strict environmental standards
Davenport et al., 2002;
24
Schlesinger et al.,
2011;
19
Najdenov et al., 2012;
25
USGS, 2023;
40
Isasmelt, 2023;
41
Inco Flash using technical oxygen instead of air reduces the
amount of gases produced;
however, this method is still quite costly with a large
consumption of electricity
42
Queneau and Marcuson, 1996; Moskalyk and
Alfantazi, 2003;
17
Kapusta, 2004;
18
Vra~ar,
2010;
33
Inco, 2023;
43
Mitsubishi high utilisation of SO
2
, reduction of the emission of
harmful gases, high flexibility, ability to process re-
verse and secondary materials, reduced consumption
of electricity
Shibasaki et al., 1993;
44
Iida et al., 1997;
45
Asaki
et al., 2001;
46
Davenport et al., 2002;
24
Fthenakis
et al., 2009;
47
Schlesinger et al., 2011;
19
Wang et
al., 2013;
48
Noranda small amount of fuel, possibility to achieve complete
autogenic smelting with 40% of oxygen, but with a
negative economic effect
Veldbuizen and Sippel, 1994;
49
Davenport et al.,
2002;
24
Cui and Zhang, 2008;
50
Vra~ar, 2010;
33
Schlesinger et al., 2011;
19
El Teniente better energy use, economic, but it requires a more
complicated and complex control
Bergh et al., 2005;
51
Valencia et al., 2006;
52
Schaaf et al., 2010;
53
Najdenov et al., 2012;
25
Najdenov, 2013;
20
Vanyukov (semi)autogenic smelting of copper concentrates with
various additives, large-folded and selectively di-
gested rich copper ore, return materials and the sol-
vent
Davenport et al., 2002;
24
Moskalyk and
Alfantazi, 2003;
17
Schlesinger et al., 2011;
19
Najdenov et al., 2012;
25
Reverberatory furnace
it is often replaced by some of the previous ones be-
cause it does not have many positives and it requires
high energy consumption
Diaz et al., 1991;
54
Ullmann, 1995;
55
Stankovi},
2000;
56
Davidovi} et al., 2009;
57
Najdenov et al.,
2013;
20
Mohagheghi and Askari, 2016;
58
USGS,
2023;
40

four smelters. Based on the data from Kapusta’s
18
study,
which depicts roughly half of the smelters with different
types of technological processes, it can be concluded that
the ratio of the applied copper extraction technological
processes has not significantly changed in the past 20
years.
18,40
3 METHODOLOGY
The aim of this research was to select the optimal
technological process of copper extraction in complex
conditions. To fulfil this aim, authors developed a hybrid
fuzzy AHP-TOPSIS model. The FAHP method was used
to assess the weight of factors based on the experts’eval-
uation of each criterion’s significance, while the TOPSIS
method was used to rank the technological processes.
The prioritisation process used in this research is pre-
sented in Figure 1. The applied methods are briefly de-
scribed below.
3.1 Fuzzy AHP
AHP is one of the most used MCDA methods. This
method was introduced in 1980 by Saaty, and since then,
the number of studies in which this method was applied
has continually increased. The main reason for this pop-
ularity is its ease of operation and application as well as
its great flexibility. Thanks to these characteristics, this
method is applied in many areas, such as economics,
manufacturing, social science, education, etc.
59–64
How-
ever, problems in applying this method may arise from
using experts’ subjective judgments during evaluations.
65
In fact, experts use exact values when comparing criteria
or alternatives and therefore cannot express their prefer-
ences.
66
This problem was recognised by Laarhoven and
Pedrycz (1983), who proposed the FAHP (fuzzy analyti-
cal hierarchy process) method as the solution to this
problem. The FAHP uses the principles of fuzzy logic
within the AHP method.
67,68
There are many variants of the FAHP method. In this
research, modified Chang’s extent analysis was applied
to prioritise copper smelting processes. This modifica-
tion includes using triangular fuzzy numbers (TFNs) for
the pairwise comparison scale and the extent analysis
method for the synthetic extent value of Si of the
pairwise comparison.
69
The main flaw of modified
Chang’s extent analysis is that determined weights can-
not be used as priorities because they do not represent
the relative importance of decision criteria or alterna-
tives. Wang and Chen (2007) corrected the normalisation
formula to solve this problem.
70,71
The FAHP method
used in this research is described in several steps.
Step 1: Defining the problem and developing a fuzzy
comparison matrix. A hierarchical structure of an AHP
problem consists of at least three levels. At the top of
this structure, there is an overall goal of the problem, in
the middle, there are multiple criteria, while at the bot-
tom there are decision options.
68
Decision-makers evalu-
ate the relative significance of particular criteria and al-
ternatives at each hierarchical level in pairs, with the
help of linguistic variables. In this way, paired compari-
son matrices are defined, whose values are translated
into TFNs in accordance with Table 2 to obtain a fuzzy
pairwise comparison matrix. This completes the first step
of Chang’s (1996) extent analysis method.
69,72,73
Table 2: Linguistic variables for pairwise comparison of each
criterion
73,74
Linguistic
variables
Triangular fuzzy
scale
Triangular fuzzy re-
ciprocal scale
Equally strong (1, 1, 1) (1, 1, 1)
Moderately strong (2, 3, 4) (1/4, 1/3, 1/2)
Strong (4, 5, 6) (1/6, 1/5, 1/4)
Very strong (6, 7, 8) (1/8, 1/7, 1/6)
Extremely strong (9, 9, 9) (1/9, 1/9, 1/9)
Intermediate values
(1, 2, 3) (1/3, 1/2, 1)
(3, 4, 5) (1/5, 1/4, 1/3)
(5, 6, 7) (1/7, 1/6, 1/5)
(7, 8, 9) (1/9, 1/8, 1/7)
Step 2: Determining the fuzzy synthetic extent # with
respect to criteria i that is carried out according to Kabir
and Sumi, 2014:
~~ ~
,,..., S
li j
j
n
ij
j
n
i
n
CCi =⊗
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ =
== =
−
∑∑ ∑
11 1
1
12 , n
(1)
I. NIKOLI] et al.: A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY AHP-TOPSIS APPROACH ...
150 Materiali in tehnologije / Materials and technology 58 (2024) 2, 147–157
Figure 1: Proposed approach

where n represents the size of the fuzzy judgment ma-
trix.
75
An inverse vector from the preceding equation can be
calculated using the following formula:
~
, C
um
ij
j
n
i
n
ij
j
n
i
n
ij
j
n
i
= =
−
=== =
∑ ∑
∑∑∑
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ =
1 1
1
111 1
11
n
ij
j
n
i
n
l
∑∑ ∑
= =
⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ,
1
1 1
(2)
However, as already stated, Wang and Chen (2007)
70
corrected the normalisation formula according to the fol-
lowing form:
~
,
C
lu
ij
j
n
i
n
ij
i
n
ij
y
n
kki
n
= =
−
== =≠
∑ ∑
∑∑ ∑
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ =
+
1 1
1
11 1
1
⎛ ⎝ ⎜ ⎜ ⎜ ⎜ +
⎞ ==== =≠
∑ ∑∑∑ ∑
,
,
,
11
1111 1
mu l
ij
j
n
i
n
kj
y
n
kj
y
n
kki
n
⎠ ⎟ ⎟ ⎟ ⎟ (3)
Since normalised degrees of probability can indicate
the extent to which a given TFN is greater than any other
TFN, but not their relative significance, Liou and Wang
(1992)
76
proposed a total integral value with an index of
optimism a, which gives priorities to the synthetic extent
values according to the following equation:
75
I s a m u a l m au m a l
T
a
li ii ii i
(
~
)()() () () =+ +−+=+ + −
1
2
1
2
1
1
2
1 [] i
)
(4)
The optimism index a, in fact, represents the degree
of optimism of the decision maker and ranges from 0 to
1. If the optimism index is closer to 1, the decision
maker is more optimistic, and the opposite; if the index
of optimism index is closer to 0, the decision maker is
more pessimistic.
77
Step 3: Determination of the normalised weight vec-
tor W=( w
1
, w
2
, ..., w
n
)
T
fuzzy judgment matrix is done
using the following formula:
77
w
IS
IS
x
T
a
x
T
a
k
k
n
=
=
∑
(
~
)
(
~
)
1
(5)
where w
x
represents a non-fuzzy number.
3.2 TOPSIS
Another MCDM method used in this research is the
technique for order of preference by similarity to ideal
solution (TOPSIS). This method was introduced by
Hwang and Yoon in 1981. The main characteristic of this
method is that the best alternative has the shortest dis-
tance from the positive ideal solution (PIS) and the lon-
gest distance from the negative ideal solution (NIS).
78
A
positive ideal solution represents a solution that maxi-
mises the benefit attributes and minimises cost attributes.
On the other hand, a negative ideal solution maximises
the cost attributes and minimises the benefit attributes.
79
The TOPSIS method has been widely used to solve the
ranking problems in real-life situations, thus providing
an easily understandable and programmable calculation
process. This method has the ability to consider different
criteria with different units simultaneously.
80
In addition,
to enable the application of this method, the values of the
chosen criteria used for the selection must be numeri-
cally, monotonically rising or decreasing, and they must
also be organised in the form of proportional units.
81
However, despite its popularity and simplicity, this
method is often criticised for its inability to adequately
handle the uncertainty and imprecision in value assign-
ment by the decision maker.
82
As a solution, the TOPSIS
method has undergone numerous upgrades to adequately
solve the problems of ranking and justification of the re-
sults obtained.
83,84
The procedure of the TOPSIS methodology is de-
scribed by Hwang and Yoon (1981) and shown in Fig-
ure 2.
4 RESULTS AND DISCUSSION
The previous section describes the multi-criteria deci-
sion-making tools as well as mathematical methods that
I. NIKOLI] et al.: A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY AHP-TOPSIS APPROACH ...
Materiali in tehnologije / Materials and technology 58 (2024) 2, 147–157 151
Figure 2: Stepwise procedure of TOPSIS
78

were used to support this research. In this way, the basis
for solving the defined research problem in this study is
established. The next step is the implementation of the
defined methodology, which creates a possibility of
achieving the basic goal of this research, i.e., determin-
ing which of the current technological processes for cop-
per extraction is the best at achieving the optimal pro-
duction goals.
The implementation of the proposed methodology
consists of six steps, as shown in Figure 1. Due to a lim-
ited space, it does not show the procedure and calcula-
tions for each step, but it provides general information so
that research and its results can be followed more easily.
The first step of the proposed methodology consists
of defining the hierarchical structure of the problem. The
hierarchical structure of the problem is shown in Fig-
ure 3.
At the top of the hierarchical structure is the goal for
the problem solution. In this case, it is identifying the op-
timum technological process for copper extraction. The
criteria used in the ranking are at the second level. The
evaluation was carried out based on three types of crite-
ria: economic, technological and environmental. The se-
lection of these three criteria was based on the literature
that deals with the impact of these factors on copper
smelters.
85–87
Perez et al.,
85
in their research conducted in
Chile, one of the leading countries in copper production
in the world, made the same division of criteria into envi-
ronmental, economic and technological factors affecting
Chilean copper smelters. There are several sub-criteria at
the third level used for defining each criterion. Since
some sub-criteria can be included in more than one crite-
rion, the division in our work was done based on the pos-
sibility that certain sub-criteria significantly influence
certain segments of the chosen criteria. Thus, certain
sub-criteria are classified as economic, even though they
are technological in nature because they significantly af-
fect the profitability of a copper smelter. On the other
hand, other sub-criteria undoubtedly belong to the de-
fined criteria. The order of criteria and their sub-criteria
is as follows:
ECONOMIC CRITERIA
C
1
– Concentrate amount in charge (t/day)
C
2
– Production of copper matte (t/day)
C
3
– Campaign life (year)
C
4
– Copper recovery (%)
C
5
– Cu content in waste slag (%)
TECHNOLOGICAL CRITERIA
C
6
– Cu content range in the concentrate
C
7
– Cu content in copper matte (%)
C
8
– Fe content in matte (%)
C
9
– Minimal Cu content in the concentrate
ENVIRONMENTAL CRITERIA
C
10
– Production of waste slag (t/day)
C
11
– Sulfur recovery (%)
Based on a comprehensive literature review con-
ducted by Nikoli} et al.
21
and relevant secondary sources
listed in Table 1, data was collected for a complete rank-
ing of the eight copper extraction technologies based on
the proposed criteria as presented in Table 3.
18,21
In the next step of the analysis, a group of experts
composed of several university professors and engineers
dealing with copper smelters was formed to define the
initial matrices of the pairwise comparison criteria con-
cerning the defined goal and the sub-criteria relative to
the criteria. In this way, group decision-making using the
AHP allows multiple stakeholders to express their opin-
I. NIKOLI] et al.: A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY AHP-TOPSIS APPROACH ...
152 Materiali in tehnologije / Materials and technology 58 (2024) 2, 147–157
Figure 3: Hierarchical structure of the problem

ions on the importance of the chosen criteria. To deter-
mine individual preferences, decision-makers provide
pairwise comparison matrices. These matrices are used
for obtaining independent preferences in the first round.
These preferences are then aggregated, using aggregation
through consensus voting on judgments in the second
round.
88
This method of aggregating individual prefer-
ences was chosen to simplify the judging process as it
can better reflect real-world decision-making.
89
Addi-
tionally, the consistency of all aggregated matrices of the
pairwise comparison was checked when all matrices
showed consistency with values of CR<0.1 (level of cri-
teria CR=0, environmental level CR=0, technological
level CR=0.0810 and economic level CR=0.0291). Then,
fuzzification of the pairwise comparison matrix was
done. The results of this step are shown in Tables 4 to 7.
In these tables, L represents the smallest possible value,
M represents the expected value, and U represents the
highest possible value that describes the TFN.
In the next step, using the above FAHP methodology,
the local and overall significance of the sub-criteria and
criteria are determined. The results of this part of the
analysis are shown in Table 8.
The obtained overall significance of the sub-criteria
represents the weight coefficient of the criteria used in
ranking the technological processes with TOPSIS, which
I. NIKOLI] et al.: A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY AHP-TOPSIS APPROACH ...
Materiali in tehnologije / Materials and technology 58 (2024) 2, 147–157 153
Table 3: Values of parameters for ranking copper extraction technologies
3
Criterion
Alternatives
Concentrate
amount
used (t/day)
Cu content range in
the concentrate (%)
Cu content in copper
matte (%)
Fe content in matte
(%)
Production of waste
slag (t/day)
Production of copper
matte (t/day)
Campaign life (year)
Sulphur recovery
(%)
Copper recovery (%)
Cu content in waste
slag (%)
Minimal Cu content
in the concentrate
(%)
Outokumpu flash 2750 5 65 11.5 2025 1500 9 96 97 0.65 26
Ausmelt/Isasmelt
lance
2250 4 67 14 1210 1200 2.1 97 97 0.6 25
Inco flash 3000 9 50 15 1350 935 15 93.6 97.5 0.65 20
Mitsubishi 2150 6 71.5 7.75 1375 1209 3 99.5 97 0.75 28
Noranda 2250 9 72.5 4.5 1500 975 1.75 94 95 0.75 28
El Teniente 2300 7 73 4.5 1725 962.5 1.5 90 96 0.325 26
Vanyukov 2150 8 59.5 10.5 1750 1300 4.5 90 98 0.6 26
Reverberatory 2000 16 40 27.5 1050 1450 3.5 50 93 0.75 19
Table 4: Level of criteria
Level of criteria
Environmental Technological Economic
LMULMULMU
Environmental 111123123
Technological 1/3 1/2 1111111
Economic 1/3 1/2 1111111
Table 5: Sub-criterion level: environmental level
Environmental level
Production of waste slag (t/day) Sulphur recovery (%)
LMULMU
Production of waste slag (t/day) 1 1 1 1/6 1/5 1/4
Sulfur recovery (%) 456111
Table 6: Sub-criterion level: technological level
Technological level
Cu content range in the
concentrate
Cu content in copper
matte (%)
Fe content in matte
(%)
Minimal Cu content in
the concentrate
LMULMULMULMU
Cu content range in
the concentrate
1 1 1 1/4 1/3 1/2 1/4 1/3 1/2 1 2 3
Cu content in copper
matte (%)
234111234234
Fe content in matte
(%)
2341 / 41 / 31 / 2111234
Minimal Cu content in
the concentrate
1/3 1/2 1 1/4 1/3 1/2 1/4 1/3 1/2 1 1 1

is also the next step of the analysis. Table 9 gives the
weights of the selected criteria and their directions. Dur-
ing this ranking, a complete ranking of all the technolog-
ical processes was performed.
Table 10: Ranking of technological processes based on relative close-
ness to the ideal solution
Criterion Alternatives CI * RANK
Outokumpu flash 0.7268 4
Ausmelt/Isasmelt lance 0.7081 5
Inco flash 0.7079 6
Mitsubishi 0.7554 1
Noranda 0.7528 2
El Teniente 0.7350 3
Vanyukov 0.6843 7
Reverberatory 0.2051 8
After applying all the steps of the TOPSIS methodol-
ogy, described in the previous section, to the data set pro-
vided in Tables 3 and 9, a list of the technological pro-
cesses based on determining the relative closeness to an
ideal solution is shown in Table 10. The alternative with
a higher value is ranked better with this methodology.
Based on Table 10, it can be concluded that the best
ranked technology is Mitsubishi. It is followed by
Noranda, El Teniente, Outokumpu flash, Ausmelt/
Isasmelt lance, Inco flash and Vanyukov, in that order.
Reverberatory is at the bottom of the ranking. As can be
noticed through the evaluation of the significance by the
experts, the greatest priority was given to one environ-
mental parameter, "Sulphur recovery", which was signif-
icantly higher than any economic or technological pa-
rameter. All technologies based on autogenous processes
are more environmentally acceptable and economically
justified. On the other hand, the reverberatory furnace
has become out of date, so it should no longer be used.
In the case of high-tech technology, sulphur recovery has
the major impact, which is 99.5 %.
I. NIKOLI] et al.: A NOVEL HYBRID DECISION-MAKING MODEL: FUZZY AHP-TOPSIS APPROACH ...
154 Materiali in tehnologije / Materials and technology 58 (2024) 2, 147–157
Table 7: Sub-criterion level: economic level
Economic level
Concentrate amount
used (t/day)
Production of cop-
per matte (t/day)
Campaign life
(year)
Copper recovery
(%)
Cu content in waste
slag (%)
LMULMULMULMULMU
Concentrate amount
used (t/day)
1112342341 / 41 / 31 / 21 / 31 / 21
Production of copper
matte (t/day)
1 / 41 / 31 / 21111111 / 41 / 31 / 21 / 41 / 31 / 2
Campaign life (year) 1/4 1/3 1/2 1111111 / 61 / 51 / 41 / 41 / 31 / 2
Copper recovery (%) 234234456111111
Cu content in waste
slag (%)
123234234111111
Table 8: Local and overall significance of criteria and sub-criteria
Criterion Criterion significance Sub-criterion
Local sub-criterion sig-
nificance
Overall sub-criterion
significance
Environmental 0.492
C10 0.1690 0.0831
C11 0.8310 0.4086
Technological 0.254
C6 0.1629 0.0414
C7 0.4206 0.1069
C8 0.3144 0.0799
C9 0.1021 0.0259
Economic 0.254
C1 0.2100 0.0534
C2 0.0837 0.0213
C3 0.0802 0.0204
C4 0.3575 0.0909
C5 0.2686 0.0683
Table 9: Weights of selected criteria and their directions
Crite-
rion
Alterna-
tives
Concen-
trate
amount
used
(t/day)
Cu con-
tent range
in the
concen-
trate (%)
Cu con-
tent in
copper
matte (%)
Fe content
in matte
(%)
Produc-
tion of
waste slag
(t/day)
Produc-
tion of
copper
matte
(t/day)
Campaign
life (year)
Sulphur
recovery
(%)
Copper
recovery
(%)
Cu con-
tent in
waste slag
(%)
Minimal
Cu con-
tent in the
concen-
trate (%)
w-weight 0.0534 0.0414 0.1069 0.0799 0.0831 0.0213 0.0204 0.4086 0.0909 0.0683 0.0259
Min/Max Max Max Max Min Min Max Max Max Max Min Min

5 CONCLUSIONS
Copper production represents one of the crucial in-
dustrial sector activities that contributes to each coun-
try’s economic development. When constructing a cop-
per extraction plant, implementing a technological
process that will give the best economic effects and be
environmentally acceptable is required. The decision on
the optimal copper extraction process that will be applied
is very complex due to a number and the nature of crite-
ria that must be considered. Also, numerous participants
in the decision-making process can have different inter-
ests, so priorities and the weight of the selected criteria
should be differentiated. All of the above conditions
should be respected and in compliance with the com-
pany’s strategy. As Pivodová et al.
90
stated, a lack of a
systematic approach is the main cause of shortcomings
in achieving the set goals. This research provides a basis
for systematically managing a new copper extraction
plant.
Based on this research, a very efficient model for
solving the above problems was created. Namely, the
presented complex methodology enables a detailed anal-
ysis of the problems and significantly accelerates the de-
cision-making process when constructing this kind of
plant.
The best-positioned technological process in this
study is Mitsubishi. This technological process is domi-
nant over the others based on the criteria such as sulphur
and copper recovery. The values of these two parameters
are very high, but the other observed criteria are optimal.
In addition to the values of the criteria adopted for the fi-
nal prioritisation, expert preferences also have a signifi-
cant impact since group decision-making based on sub-
jective assessments of decision-makers is not free from
bias. Different expert preferences on the criteria can give
different results. Hence, the final prioritisation of the
smelting processes may be different in another research
based on the experts’ preferences and adopted criteria.
However, an increased interest in the ecology of smelting
facilities is also reflected in the results of this research.
Comparing the obtained results with the results of some
previous studies published by Moskalik and Alfantazi,
17
Kapusta,
18
Nikoli},
21
Perez et al.,
85
Aleksandar et al.
86
and Sourabh et al.,
87
we can see that the trend of adopt-
ing technologies that are environmentally acceptable and
economically justifiable continues.
Using this model to decide on the application of a
new technological process gives us an overall picture of
all the advantages of one alternative over the other, tak-
ing into account all the criteria considered. However, de-
spite the implementation of the model, the final decision
remains with the decision-makers. The goal of this
model is to make the management mechanism and deci-
sion-making process more efficient and the solutions op-
timal.
In the future, the authors will work on further im-
provements of this kind of methodology, which com-
bines several approaches and tools, integrating positive
impacts of each approach and neutralising the shortcom
mings. In this way, decision-makers are given the oppor-
tunity to justify their decision about the advantages of a
particular alternative over the others with more argu-
ments.
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