Integrated fuzzy MCDM based on LCA results for industrial waste management
R. Zare*1 J. Nouri1, M. A. Abdoli2, M. Alavi3 , F. Atabi1
1Department of environment management, faculty of energy and environment, science and research
Branch, Islamic Azad University, Tehran, Iran;
2Faculty
of environment, university of Tehran;
of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran
3Department
* Corresponding Author: E-mail: r.zare@srbiau.ac.ir
Abstract:
The global secondary aluminum production grows rapidly because of the environmental considerations
and continuous growing of the consumption demands as well. Aluminum dross recycling, as secondary
aluminum process has been always considered as a problematic issue in the world. The aim of this work
is to propose a methodical and easy-to-use algorithm for the proposed system selection as a MCDM
problem. In this study, an integrated fuzzy AHP model is developed in order to assess aluminum waste
management systems. For this purpose, we drive weights of each pairwise comparison matrix by the use
of the goal programming model. The functional unit includes aluminum dross and aluminum scrap, which
is defined as 1,000 kg. The model is confirmed in the case of aluminum waste management in the
industrial city of Arak. For the proposed integrated fuzzy AHP model, five alternatives are investigated.
The results showed that, according to the selected attributes, the best waste management alternative is the
alternative involving the primary aluminum ingot 99.5% include 200 kg and the secondary aluminum
98% (scrap) include 800 kg. So the beneficiation activities are implemented, aluminum dross is recycled
again in the plant and finally it is landfilled.
Key words: Aluminum waste, Dross, FAHP
1. Introduction:
Nowadays, aluminum is used in industry, transportation, construction and packaging industries, more
increasingly. In aluminum industries, the secondary aluminum production grows rapidly due to the
pertaining to the environment considerations and growing of the consumption demands. It is estimated
that the production of this material will reach 2.60x107 t in 2015 (Hong et al., 2010). In this paper, FAHP
methodology has been considered to evaluate the environmental, economic, and social impacts of the
aluminum waste.
This approach allowed us to mathematically represent the uncertainty to reflect the decision maker’s
perception to decision making process as well. The arrangement of the rest of this study is as follows:
In section two, we review some literatures about the proposed problem. In section three, as methodology,
we review some basic concept and finally the proposed algorithm is explained. In section four, we present
a case study related to the aluminum waste is provided. The study ends with a discussion and conclusion.
2. Literature review:
The production of aluminum from bauxite needs much more energy than other metals and leads to large
quantities of greenhouse gas emissions (Norgate and Jahanshahi, 2011). Aluminum production is
1
responsible for 1.1% of the annual greenhouse gas emissions (Liu et al., 2013). It is about 75% of all the
aluminum production as secondary aluminum since 1880s is still in generative use. The findings of these
studies indicated that the emissions and energy consumption of aluminum were decreased in the
production of the secondary aluminum compared to the production primary aluminum (Liu and Müller,
2012). Authors represented that the aluminum waste recycling is an economic and environment friendly
(Shinzato and Hypolito, 2005). By recycling the secondary aluminum, resources are saved, the need for
landfill area could have been decreased and the public’ thought would be satisfied. Although aluminum
dross is a waste of current resources but on the condition it is landfilled without suitable treatment and it
causes the secondary contaminants which would effect on air, water and soil (Hong et al., 2010). The
environmental impact by aluminum dross from the secondary aluminum should be minimized. That is
why in this study, the effects and impacts of aluminum waste management systems are evaluated. In
addition, aluminum dross recycling is always considered as a problematic issue. Fuzzy set idea was used
by (Weckenmann and Schwan, 2001) to manage uncertainty in the inventory data. Since Van Laarhoven
and Pedryezand (Van Laarhoven and Pedrycz, 1983) presented their initial study in FAHP, many works
applied FAHP in different environment problems (Weck et al., 1997, Abdi, 2009, Chan et al., 2013,
Wang et al., 2012). Also, some studies applied FAHP method concerning LCA thinking. For example,
this methodology applied by Zhang in the building sector (Zheng et al., 2011), and by Hing and Lin to
evaluate green product design (Hing Kai et al., 2013) (Lin et al., 2013). Complex decision-making
situations are relevant to the aluminum waste management system which needs the understanding of
different sectors within the industry and society. However, little attention has been given to the
environmental aspects of the processing output of aluminum dross and aluminum scrap as aluminum
waste in the MCDM methodologies.
3. Methodology
The aim of this work is to present a systematic method for the aluminum waste management option
selection problem. Methods were evaluated for this purpose, including as follows: fuzzy logic, group
decision making, goal programming method and the fuzzy AHP.
3.1 Fuzzy number (FN)
FN is a method to illustrate the ambiguity and the missed crisp data (Zadeh, 1965). The decision makers
present fuzzy opinion in place of crisp opinion for a pairwise comparison.
3.2 The nearest weighted interval approximations ( NWIAs )
We achieve the interval approximations for a FNs (Izadikhah, 2012).
3.3 Group Decision making
A group of experts who have high levels of awareness and experience in the proposed waste management
systems were used to propose the criteria. Then, a survey was conducted through the distribution of a
questionnaire among the decision makers group to determine the importance weights of the criteria and
ratings of the alternatives. Decision makers are five experts from the production managers of the proposed
industries and academic centers in the Environment and Management fields who contribute to the
decision-making process. The relative importance of each attributes and the preferences of the decision
makers are transformed to the triangular fuzzy numbers. We use 0-1 and 0-10 scale to express their
opinions independently on the rating of the criteria and alternatives with respect to the criteria.
3.5 Goal Programming
The goal programming attempts to combine optimal logic and the preference of decision makers in the
arithmetical programming in order to satiate the several goals. This means that, the goal programming
presents the way for concurrent goal attainment (Tzeng and Huang, 2013).
3.6 Driving the Weight of Criterion
In case of ambiguity, and for driving the weight of each criterion from the inconsistent fuzzy matrix, we
act as the following method (Izadikhah, 2012).
Step 1: We transform the fuzzy matrix A to an interval matrix A .
2
Step 2: We achieve the optimum weight vector W   w1 , w2 , w3  showing the importance of each
criterion. In order to solve the problem, we apply the linear programming software LINGO 11.
The detailed mathematics are found in Appendix A
3.7 FAHP method
AHP approach applies multi-criteria decision analysis developed and presented by Saaty (Saaty, 1988)) to
compute the weighting factor of the criteria. The AHP method cannot handle the uncertainty in deciding
the ratings of different attributes (Chan and Kumar, 2007). In FAHP method, the judgments are made
using linguistic parameters which are characterized by fuzzy membership functions. If there is more than
one expert involved in judging process, the different matrices are combined together to form one synthetic
matrix.
3.8 Proposed algorithm
The proposed integrated AHP, goal programing and NWIA algorithm determine the most preferable
aluminum waste management system selection among all possible alternatives, when data is fuzzy, is
given as follows:
Step 1: Set up the expert group. To evaluate alternatives, an expert group comprised of researchers and
managers should be established;
Step 2: Create a hierarchical structure of the elements for the problem solving. For this propose, it is
necessary for the decision makers to determine criteria and sub-criteria based on the proposed main target.
Step 3: Build a set of fuzzy pairwise comparison matrices for each decision maker;
Step 4: Aggregate fuzzy pairwise comparison matrices. We aggregate fuzzy pairwise comparison
matrices constructed by the decision makers by using geometric mean method and to convert them to unit
fuzzy pairwise comparison matrix.
Step 5: Derive the weights of each matrix. For this purpose, apply the following sub steps:
Sub-step 5.1: Convert each fuzzy matrix to an interval fuzzy matrix.
Sub-step 5.2: Calculate the weight of each pairwise comparison matrix;
Step 6: Aggregate the weights and rank the alternatives. We aggregate the weights and rank the
alternatives to select the best aluminum waste management system.
4. Case study:
A case study on aluminum industries and particularly aluminum remelter plants in Arak industrial area
center of the Islamic Republic of Iran is presented. It illustrates how the proposed fuzzy AHP
methodology according to above descripted algorithm can be applied to selecting the best aluminum
waste management system. Twenty-nine re-melting facilities were incorporated in this research. The
secondary aluminum re-melting is considered as a unit function. As shown in figure 1, this process unit
includes the storage in place (1), beneficiation activities (2) related to input aluminum scrap such as
washing, separating and sorting (or without beneficiation activities (3)), remelting in aluminum crucible
furnace (4), duplicate aluminum black dross recycling in plant (5) (or export aluminum black dross to
other place and duplicate recycling (6)), and final waste landfill (7) (or release in the environment (8)).
3
(3)
(1)
Aluminum Industries
Skimming
Aluminum
dross Storage
(7)
Aluminum
Ingot
(4)
(2)
(5)
(emission to air)
(6)
(8)
(emission to water)
(emission to watersoil)
Figure 1: Flowchart of the secondary aluminum re-melting in proposed research
All the results are based on the reference flow of 1 ton of aluminum batch include new and old aluminum
scraps and dross. The upkeep and repair of the plant and equipment materials are provided to this lifecycle stage from both primary and secondary aluminum processing. Also, the secondary remelters have a
diversity of melting furnaces: top-loaded closed, rotary, and side well-feeding melting. They have
different competences. In this study, the crucible furnace for the secondary aluminum re-melting is used.
In this study, firstly, a panel of experts as decision maker group was set up. The decision makers were
five experts: Three engineers from the production managers of the aluminum industries, and two
academics in the Environment and Management fields. Then, the documents including literature, financial
documents, statistics of the occupational accidents and diseases, the results of overviews and primary life
cycle assessment were evaluated by the decision makers using fuzzy linguistic terms. This approach
allowed us to mathematically represent the uncertainty and vagueness and reflect the decision maker’s
perception to decision making process. After this, a questionnaire was distributed to decision makes to
evaluate and determine the importance weights of the criteria and ratings of the alternatives.
Once the responses were received, the questionnaire results were checked and interviews were conducted
to ensure the data validity. Figure 2 shows the decision hierarchy for the decision making problem. In the
upper ranks of the hierarchy we have the general objective that in this case is the selection of an
aluminum waste management system. We presented the main criteria including environmental, social and
economic aspects at level 2. The associated general attributes or sub-criteria (level 3) are the main criteria.
These general attributes are broken-down into global warming (GWP), human toxicity (HTP), land use
(LU), health and safety at work (H&S), regulation (Reg), turnover and gain. At level 4, we showed the
five management alternatives.
aluminum waste management system selection
Criterion C1
Criterion C3
TurnoverC31
GWP C11
Gain C32
Alternative E
Alternative D
LU C12
Alternative C
Criterion C2
ETP C13
Alternative B
H&S C21
Reg C22
Alternative A
Figure 2: The hierarchical structure in the proposed research
Five management alternatives for aluminum waste management in the city of Arak are presented as
follows:
 Alternative A aluminum crucible for re-melting aluminum batch include the primary aluminum ingot
99.5% include 200 kg and the secondary aluminum 96% (scrap) include 800 kg, beneficiation
4




activities related to input aluminum scrap such as washing, separating and sorting, export aluminum
black dross to other place and duplicate recycling, landfill.
Alternative B aluminum crucible for re-melting, aluminum batch include the primary aluminum
ingot 99.5% include 200 kg and the secondary aluminum with grade 96% (scrap) include 800 kg, remelting without beneficiation activities, export remain aluminum black dross to other place and
duplicate recycling, release in environment.
Alternative C aluminum crucible for re-melting aluminum batch include the primary aluminum ingot
99.5% include 200 kg and the secondary aluminum 96% (scrap) include 800 kg, beneficiation
activities related to input aluminum black scrap such as washing, separating and sorting, duplicate
aluminum dross recycling in plant, landfill.
Alternative D is defined as the present current aluminum waste management system: aluminum
crucible for re-melting, aluminum batch include the primary aluminum ingot 99.5% include 200 kg
and the secondary aluminum 96% (scrap) include 800 kg, re-melting without beneficiation activities,
export aluminum black dross to other place and duplicate recycling, release in environment.
Alternative E aluminum crucible for re-melting, aluminum batch include the primary aluminum
ingot 99.5% include 200 kg and the secondary aluminum 98% (scrap) include 800 kg, beneficiation
activities related to input aluminum scrap such as washing, separating and sorting, duplicate
aluminum black dross recycling in plant, landfill.
Alternative A is defined as the 'intermediate' waste management system. Alternative B is defined as the
current waste management system. It is similar to alternative A, but instead of landfill method, the
aluminum waste is released in environment. Alternative C represents 'business' option where economic
benefits are more important. Alternative D represents 'waste export' where approximately 70% of
aluminum waste that is normally landfilled, are exported to other place for duplicate recycling.
Alternative E is defined as the environment friendly aluminum waste management system.
The results interval approximation matrices were presented in tables 1-5.
Table 1: The interval approximation main target concerning the gain criteria
Main target
C1
C2
C3
Obtained Weights
C1
[1,1]
[5.7,6.8]
[5.7,6.8]
0.84507
C2
[0.15,0.18]
[1,1]
[4.5,5.5]
0.126761
C3
[0.15,0.18]
[0.18,0.23]
[1,1]
0.028169
Table 2: The interval approximation sub-criteria concerning the environmental criterion
Environment
C11
C12
C13
Obtained Weights
C11
[1,1]
[2.36,2.96]
[1.09,1.37]
0.633438
C12
[0.32,0.42]
[1,1]
[2.71,3.51]
0.267838
C13
[0.76,0.93]
[0.30,0.38]
[1,1]
0.098724
Social
C21
C22
Table 3: The interval approximation sub-criteria concerning the main criteria
C21
C22
Weights
Economic
C31
C32
[1,1]
[2.7,3.1]
0.754717
C31
[1,1]
[3.68,4.73]
[0.32,0.47]
[1,1]
0.245283
C32
[0.22,0.3]
[1,1]
Weights
0.821693
0.178307
Table 4: The interval approximation options concerning the sub-criteria of environmental criterion
sub-criteria
GWP
ETP
LU
Alternatives
A
0.090862
0.041578
0.173079
B
0.026054
0.024023
0.030116
C
0.195402
0.180174
0.223084
D
0.036345
0.027719
0.042567
5
E
0.651339
0.726506
0.531153
Table 5 The interval approximation options concerning the sub-criteria of social and economic criteria
sub-criteria
H&S
regulation
turnover
gain
Alternatives
A
0.037196
0.047475
0.224165
0.322223
B
0.109401
0.045455
0.044833
0.305145
C
0.164101
0.318182
0.336247
0.159262
D
0.492303
0.070707
0.058508
0.168588
E
0.197
0.318182
0.336247
0.044782
The results of ranking alternatives were shown in table 6. Alternative E is assigned as the most preferred
choice with a weight of 0.594161, followed by alternative C with a value of 0.198146, alternative A with
a value of 0.090549, alternative D with a value of 0.070878 and alternative B with a value of 0.036346.
Table 6: The results of ranking the aluminum waste management system options
alternatives
A
B
C
D
E
Ranking order
Final obtained Weights
0.090549
0.036346
0.198146
0.070878
0.594161
E˃C˃A˃D˃B
Rank of alternatives
3
5
2
4
1
5. Comparison with other existing methods
The fuzzy AHP methods in the literature were compared (Büyüközkan et al., 2004, Ayağ and Özdemir,
2006) in table 7. There are important differences in their theoretical structures. The comparison includes
advantages and disadvantages of each method. Main characteristics and advantages proposed method
were referred at the bottom of table 8 and were denoted with the gray color. In addition, for evaluating
proposed method, we applied Chang’s method(Chang, 1996) in order to assess the aluminum waste
management systems. The obtained results show that the ranking of the alternatives in two methods are
similar (See table 8).
Table 7: The comparison of various fuzzy AHP methods (Büyüközkan et al., 2004) (Ayağ and Özdemir, 2006)
Sources
Main characteristics
Advantages (A)/Disadvantages (D)
Van
Direct extension of Saaty’s AHP method with
(A) The opinions of multiple decision-makers can be
Laarhove triangular fuzzy numbers
modeled in the reciprocal matrix
n
Lootsma’s logarithmic least square method is used to (D) There is not always a solution to the linear
and
derive fuzzy weights and fuzzy performance scores
equations
Pedrycz
(D) The computational requirement is tremendous,
(1983)
even for a small problem
(D) It allows only triangular fuzzy numbers to be used
Buckley
Direct extension of Saaty’s AHP method with
(A) It is easy to extend to the fuzzy case
(1985)
trapezoidal fuzzy numbeds
Uses the geometric mean method to derive fuzzy
(A) It guarantees an unique solution to the reciprocal
weights and performance scores
comparison matrix
(D) The computational requirement is tremendous
Boender
Modifies van Laarhoven and pedrycz’s method
(A) The opinions of multiple decision-makers can
et
be modeled
al.(1989) Presents a more robust approach to the normalization (D) The computational requirement is tremendous
6
of the local priorities
Synthetical degree values
Chang
(1996)
(A) The computational requirement is relatively
low
(A) It follows the steps of crisp AHP. It does not
involve additional operation
(D) It allows only triangular fuzzy numbers to be used
Layer simple sequencing
Composite total sequencing
Cheng
(1996)
Proposed
method
Builds fuzzy standards
Represents performance scores by membership
functions
(A) The computational requirement is not tremendous
(D) Entropy is used when probability distribution is
known. The method is based on both probability and
possibility measures
Uses entropy concepts to calculate aggregate weights
Uses interval approximation to defuzzfication
(A) It allows all fuzzy numbers to be used
(A) It keeps uncertainty of fuzzy number in itself
Uses goal programming procedure to obtain weights
(A)It is easy to do, especially, with a software such as Lingo
Table 8: The comparison of results of proposed method and Chang’ fuzzy AHP method
Alternatives
Weights
(proposed)
A
0.090549
B
0.036346
C
0.198146
D
0.070878
E
0.5941
Ranking order (the proposed method)
Ranking order (Chang’s method)
Rank of
alternatives
3
5
2
4
1
Weights
(Cang’s method)
0.094855
0.006343
0.305851
0.01511
0.409039
E˃C˃A˃D˃B
E˃C˃A˃D˃B
Rank of
alternatives
3
5
2
4
1
6. Discussion:
Over 200 Kg of aluminum black dross as waste are produced for each ton of secondary aluminum. Black
dross is either duplicate recovered as by-products or landfilled. However, releasing this quantity in
environment can produce considerable negative consequences from air, water and soil pollution point of
view. The presented model for industrial waste management alternatives was implemented in the case of
aluminum waste systems in the industrial city of Arak.
6.1 proposed method
The life-cycle thinking is a unique way of addressing environmental problems from a system perspective.
In addition, no single solution is available as each industry in each country has different characteristics in
terms of geographical environmental as well as social and economic aspects. Several management
decisions are required to provide efficient aluminum waste management systems. The aim of this paper is
proposing a method for application fuzzy AHP in aluminum waste management system. This model,
which integrates social, economic and environmental aspects, is a fuzzy multiple-criteria decision-making
problem. It can systematically evaluate and contains interdependency relationship among criteria under
uncertainty. The results of the present study illustrates that the procedure is simple in calculations and set
priorities. For the proposed integrated fuzzy AHP model, five alternatives are investigated. In this study
we applied the NWIA-of-FNs to convert each fuzzy element of the pairwise comparison matrix to an
interval. Then, we applied goal programming model for driving the weights and LINGO11 to solve the
problems. In the present study, we apply environmental, social and economic criteria to evaluate and
support decision-making within the aluminum industry as a MCDM problem. On the other hand, the
fuzzy AHP used not only as a way to handle the inner dependences within a set of aspects and criteria, but
7
also as a way of producing more valuable information for decision making. We have considered seven
sub-criteria from a group of three main criteria, namely: environmental, social and economic. Firstly, the
decision makers evaluated each waste management alternative for the selected criteria and sub-criteria.
Secondly, these evaluation results take into account the weight of each criteria and sub-criteria. Also we
have transformed the collected data into fuzzy version. Finally, a real MCDM problem has been applied
for the proposed decision making method which aims to rank the aluminum waste management system
alternatives. According to the results of the expert judgment, the most influential environmental subcriteria are determined as global warming potential (GWP), human toxicity potential (HTP) and land use
(LU). On the other hand, the most important social indicator is indicated as Health and Safety at work
(H&S) and regulation (Reg.) and the most influential economic sub-criteria are determined as turnover
and gain. As each of the presented alternatives represents a hypothetical scenario, any preference obtained
and rank calculated will be under those circumstances for the case of the impacts and the participation of
each decision makers.
6.2 Fuzzy AHP and LCA
The primary response collected from our involved Group Decision making showed that they felt difficulty
in linking environmental sub-criteria and proposed aluminum recycling process. Therefore, we used
SimaPro LCA software (www.pre-sustainability.com/simapro) to generate quantitative information. The
primary LCA results incorporate into the decision making process as a guide by experts group.
6.3 Comparing the five aluminum waste management alternatives:
Table 6 shows that alternative E has the highest ranking compared to other alternatives. Also the
alternative C and alternative A are ranked the third and fourth, respectively. Apart from these three
alternatives, the other alternatives of the aluminum waste management system like alternative D and
alternative B, ranked the fourth and fifth. Each alternative presents a solution for the aluminum waste
management system with a certain degree of trade-off between benefit and its consequences related to the
environmental, social and economic aspects. For example, the selection choice of alternative C could be
increased by increasing amount of new aluminum scraps related to the primary aluminum production
process. Also, the alternative D represents the export of aluminum waste to other places in the form of
aluminum black dross with less metallurgic aluminum. In this way, the environmental and social impacts
related to the recycling process transit to other place with less commitment to reduce them.
Table 4 shows that alternative B has the highest environmental impact with weight values 0.026054,
0.024023 and 0.030116 concerning global warming potential (GWP), human toxicity potential (HTP) and
land use (LU), respectively. However, this is predictable because the beneficiation activities such as
sorting are not accomplished and final waste is released in environment without regarding the legal
requirements and regulations. In this case, alternative D with values 0.036345, 0.027719 and 0.042567
and alternative A with values 0.090862, 0.041578, 0.173079 are ranked the third and fourth, respectively.
Also alternative E, generally, has the lowest impacts to all environmental sub-criteria compared to the
other alternatives (See table 4). This is not surprising because the finished alloy is composed of the
secondary aluminum (include aluminum scrap and aluminum dross) with 99.5% pure aluminum and the
primary aluminum with grade 98% is known. In this option and also alternative C as the second
preference, the beneficiation activities such as washing, separating and sorting are applied and aluminum
black dross are duplicate recycled in plant, and as a result, the final waste is landfilled healthy. On the
other hand, this comparison shows that alternative A has the highest score for gain as the economic subcriteria with a value equal to 0.322223. This trend may be, because of the importance of income rather
than health, safety and with of the environmental consideration. In this alternative, weight score to health
and safety as social sub-criteria is 0.109401. It has lowest value compared to the other alternatives.
Regulation as other social sub-criteria has similar condition. Generally, observing regulations including
health and safety and environmental requirements increases costs and decreases incomes. Also turnover
8
as other economic sub criterion has a different situation and its scores are in opposite point of gain
criterion. For example, as shown in table 5, the decision makers for alternative B concerning gain and
turnover sub-criteria considered values 0.044833 and 0.305145, respectively. In this case, generally the
small industries in Iran with less turn over and more gain have more environmental issues compared to
the large industries. This case needs deep study. Alternatives that regard health and safety regulations at
work and expose less accident and occupational diseases, have been found to be high ranked compared to
the other alternatives. However, alternative D has the highest score to health and safety, though it is the
fourth preference compared to the other alternatives in the point of the decision makers’ view. Also
alternative C concerning health and safety with relatively low value 0.164101 is the third preference
compared to the other alternatives. This result is surprising and should be analyzed deeply. This
comparison shows that the alternatives which have the high health and safety levels as social subcriterion, do not necessarily have been found to be high ranked compared to the other options.
6.4 limitations and future research
This model, also have disadvantages. For example, FAHP model uses aggregated categories data in which
several subcategories are evaluated under the same main category. This will increase the uncertainty in
FAHP that can be solved by using more specific life cycle data for several steps of aluminum waste. It is
important to note that the weights of sub-criteria obtained from expert judgment are also subject to
uncertainties. With changing weights, a Fuzzy MCDM decision making method might give different
results for the ranking of aluminum waste management alternatives. From the application perspective, this
research will provide a valuable insight for managers to make their attempts for improving the
environmental, social and economic conditions, all together at the same time.
7. Conclusions:
Until now slight attention has been given to the environmental aspects of processing output of aluminum
dross and aluminum scrap as aluminum waste. This paper proposed a methodical and easy-to-use method
for the proposed system selection as a MCDM problem. All the information collected was related to the
literature, statistics, the primary LCA result, the written documents and findings from interviews. For the
proposed integrated fuzzy AHP model, five alternatives are investigated. This study applied the NWIAof-FNs to convert each fuzzy element of the pairwise comparison matrix to an interval. Then, we applied
the goal programming model for weighting and LINGO11 to solve the problems. The results showed that
alternative E and alternative B are assigned as the best and the worst preferred choice with weights of
0.594161 and 0.036346, respectively. This comparison shows that alternative A has the highest score for
gain with a value equal to 0.322223. Turnover as other economic sub-criterion has a different situation
and its scores are in opposite point of the gain criterion. Alternative C concerning health and safety with
relatively low value 0.164101 was the third preference compared to the other alternatives. This result was
surprising and should be analyzed deeply. The proposed methodology can be utilized for similar problems
where the multiple criteria are present. This study will provide a valuable insight for managers to make
their attempts to improve the environmental, social and economic conditions all together at the same time.
In future research, current fuzzy approach can be developed and applied for different MCDM problems in
industry where the conflicting criteria exist.
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