The worldwide recycled aluminum generation is increasing quickly thanks to the environmental considerations and continuous growing of use demands. Aluminum dross recycling, as the 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 procedure for the proposed system selection as the MCDM problem. Here, an evaluation method, integrated FAHP, is presented to evaluate aluminum waste management systems. Therefore, we drive weights of each pair comparison matrix by the use of the goal programming (GP) model. The functional unit includes aluminum dross and aluminum scrap, which is defined as 1000 kilograms. The model is confirmed in the case of aluminum waste management in 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 one involving the primary aluminum ingot 99.5% including 200 kg and the secondary aluminum 98% (scrap) including 800 kg, and beneficiation activities are implemented, duplicate aluminum dross is recycled in the plant, and finally it is landfilled.
Nowadays, aluminum is used in industry, transportation, and construction and packaging industries, more increasingly. In aluminum industries, the secondary aluminum production grows rapidly due to the issues pertaining to the environmental considerations and the rise in the consumption demands. It is estimated that the production of this material will reach 2.60 × 107 t in 2015 [
This approach allowed us to numerically display vagueness and to reflect the decision-makers’ perception of the decision-making process as well.
This research is comprised of the following sections.
In Section
Total primary aluminum consumption in the world was of 50.2 Mt in 2013 [
The aim of this work is to offer a methodical and straightforward and simple to use method for the aluminum waste management system selection problem. MCDM methods were considered for this aim, including fuzzy logic, fuzzy comparison matrix, NWIA, the GP method, and the fuzzy AHP.
FN are one path to explain the ambiguity and be missing accuracy of data [ “
There are real numbers And
The set of all such fuzzy numbers is represented by
Typical triangular fuzzy number.
Consider the expert that prepares fuzzy opinion in place of exact opinion. It presumes trade to be with comparison matrix with triangular FN being the components of the matrix. We suppose a matrix whose components are FN as
In this section, we review an interval processor of FN, which is denoted by
In usage, the function
If
In this example
Triangular FN and its interval approximation.
The GP attempts to combine optimal logic and the preference of decision-maker in arithmetical programming in order to satiate several goals. The decision-making environment determines basic concepts including goal and system restrictions and aim function variables. This means that GP presents the way for concurrent goal attainment [
Weighted GP is a capable tool since it includes several factors simultaneously in the decision-making process and, at the same time, regards the system’s restriction. Of course using nonquantitative and intangible factors or criteria is out of the capability of this planning model. Therefore mix AHP and a supplementary tool capable of solving the shortcomings of weighted goal planning can shape a suitable model for organization decision-making such as optimizing the result mixture.
Regard the following problem:
In the routine situation, whenever a matrix
In the situation of inconsistence matrix, we should achieve the significance weights or equally
First by (
Therefore we present deviation variables
Regard
The result of ranking of proposed method.
Criterion | Weight | Rank |
---|---|---|
1 |
|
1 |
2 |
|
2 |
3 |
|
3 |
The AHP approach applies multicriteria decision analysis developed
The AHP method may not handle the ambiguity in determining the rankings of various attributes [
An algorithm to determine the most preferable aluminum waste management system selection among all possible alternatives, when data is fuzzy, by using GP and the NWIA, with the extended AHP method is given in the following.
To evaluate alternatives, an expert group comprised of researcher and managers should be formed.
Create a hierarchical structure of elements for problem solving. For this propose, it is necessary for decision-makers to determine criteria and subcriteria based on proposing the main target. See, for example, Figure
A hierarchical structure.
Build a set of fuzzy comparison matrices for each decision-maker.
We aggregate fuzzy comparison matrices constructed by decision-makers by using the geometric mean method and convert them to unit fuzzy comparison matrix,
For this purpose, we apply the following substeps.
We aggregate the weights and rank the alternatives and finally select the best aluminum waste management system. The priority weight of each option may be achieved by multiplying the matrix of assessment by the vector of characteristic weights and adding over all characteristics [
A case study on aluminum manufacturers and particularly aluminum remelter plants in Arak, an industrial city in Iran, is introduced. It illustrates how the proposed fuzzy AHP methodology according to the algorithm can be applied to selecting the best aluminum waste management system.
Twenty-nine remelting facilities were incorporated in this research. The secondary aluminum remelting is considered as a unit function. As shown in Figure
Flowchart of the secondary aluminum remelting in proposed research.
All the results are based on the reference flow of 1 ton of aluminum batch, including new and old aluminum scraps and white and black aluminum dross (see Figure
Aluminum wastes in the proposed study.
New aluminum scrap
Old aluminum scrap
White aluminum dross
Black aluminum dross
In this study, firstly, a panel of experts as the decision-maker group was set up. The decision-makers were five experts: three engineers from the production managers of aluminum industries and two academics in the environment and management fields. Then, literature, financial documents, statistics of occupational accidents, the results of overviews, and the primary LCA, were evaluated by the decision-makers using fuzzy linguistic terms. This approach allowed us to mathematically represent uncertainty and vagueness and reflect the decision-maker’s perception of decision-making process. After this, a questionnaire was distributed to the decision-makers to evaluate and characterize the importance weights of the criteria and ratings of the options.
Once the answers were collected, the questionnaire results were studied and the discussions were directed to confirm the data reliability. Figure
The hierarchical structure in the proposed research.
Five management alternatives for aluminum waste management in Arak are presented as follows: Alternative “A”: aluminum crucible for remelting, aluminum batch, includes the primary aluminum ingot 99.5% including 200 kg and the secondary aluminum 96% (scrap) including 800 kg, beneficiation activities, related to input aluminum scrap such as washing, separating, and sorting, exporting aluminum black dross to another place, duplicate recycling, and landfill. Alternative “B”: aluminum crucible for remelting, aluminum batch, includes the primary aluminum ingot 99.5% including 200 kg and the secondary aluminum with a grade 96% (scrap) including 800 kg, remelting without beneficiation activities, exporting remaining aluminum black dross to another place and duplicate recycling, and release in the environment. Alternative “C”: aluminum crucible for remelting, aluminum batch, includes the primary aluminum ingot 99.5% including 200 kg and the secondary aluminum 96% (scrap) including 800 kg, beneficiation activities related to input aluminum black scrap such as washing, separating, and sorting, duplicate aluminum dross recycling in plant, and landfill. Alternative D, defined as the present current aluminum waste management system: aluminum crucible for remelting, aluminum batch, includes the primary aluminum ingot 99.5% including 200 kg and the secondary aluminum 96% (scrap) including 800 kg, remelting without beneficiation activities, exporting aluminum black dross to another place and duplicate recycling, and release in the environment. Alternative E: aluminum crucible for remelting, aluminum batch, includes the primary aluminum ingot 99.5% including 200 kg and the secondary aluminum 98% (scrap) including 800 kg, beneficiation activities related to input aluminum scrap such as washing, separating, and sorting, duplicate aluminum black dross recycling in plant, and 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 the 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 is exported to another place to duplicate recycling. Alternative E is defined as the environmentally friendly system.
Pairwise comparison concerning the main target is presented in Table
Criteria concerning the main target.
Main target | C1 | C1 | C1 |
---|---|---|---|
C1 | (1, 1, 1) | (4.22, 6.26, 8.28) | (4.72, 6.26, 8.28) |
C2 | (0.12, 0.16, 0.21) | (1, 1, 1) | (3, 5, 7) |
C3 | (0.12, 0.16, 0.21) | (0.14, 0.2, 0.33) | (1, 1, 1) |
Pairwise comparison matrix subcriteria concerning the basic criteria are presented in Table
Subcriteria concerning the main criteria.
Environmental (C1) | C11 | C12 | C13 |
---|---|---|---|
C11 | (1, 1, 1) | (1.18, 2.76, 3.56) | (0.84, 1.18, 1.91) |
C12 | (0.19, 0.36, 0.58) | (1, 1, 1) | (2.08, 2.92, 5.28) |
C13 | (0.52, 0.84, 1.18) | (0.18, 0.34, 0.48) | (1, 1, 1) |
Social (C2) | C21 | C22 |
---|---|---|
C21 | (1, 1, 1) | (2.08, 2.92, 3.66) |
C22 | (0.27, 0.34, 0.48) | (1, 1, 1) |
Economical (C3) | C31 | C32 |
---|---|---|
C31 | (1, 1, 1) | (2.08, 4.21, 6.26) |
C32 | (0.16, 0.24, 0.48) | (1, 1, 1) |
Comparison matrix subcriteria concerning the alternatives are as in Tables
Purposed options concerning GWP subcriteria.
(GWP) C11 | A | B | C | D | E |
---|---|---|---|---|---|
A | (1, 1, 1) | (1.44, 3.55, 5.6) | (0.34, 0.46, 0.58) | (1, 3, 5) | (0.15, 0.16, 0.19) |
B | (0.26, 0.30, 0.41) | (1, 1, 1) | (0.11, 0.14, 0.14) | (0.2, 0.33, 1) | (0.11, 0.14, 0.14) |
C | (1, 2.29, 5) | (7, 7, 9) | (1, 1, 1) | (3, 5, 7) | (0.16, 0.24, 0.48) |
D | (0.2, 0.33, 1) | (1, 3, 5) | (0.14, 0.2, 0.25) | (1, 1, 1) | (0.11, 0.14, 0.16) |
E | (4.22, 6.25, 8.27) | (7, 7, 9) | (2.08, 4.21, 6.26) | (5.6, 7, 9) | (1, 1, 1) |
Options concerning the ETP subcriteria.
(ETP) C12 | A | B | C | D | E |
---|---|---|---|---|---|
A | (1, 1, 1) | (1, 3, 5) | (0.21, 0.25, 0.3) | (1, 1, 3) | (0.13, 0.19, 0.30) |
B | (0.14, 0.24, 0.28) | (1, 1, 1) | (0.11, 0.14, 0.14) | (0.23, 0.48, 1) | (0.11, 0.14, 0.14) |
C | (2.08, 4.21, 6.26) | (7, 7, 9) | (1, 1, 1) | (5, 7, 9) | (0.21, 0.23, 0.36) |
D | (0.33, 1, 1) | (1, 2.08, 4.22) | (0.12, 0.16, 0.24) | (1, 1, 1) | (0.11, 0.14, 0.16) |
E | (1.91, 3.97, 6.08) | (6.25, 7, 9) | (2.08, 4.21, 6.26) | (6.25, 7, 9) | (1, 1, 1) |
Options concerning LU subcriteria.
(LU) C13 | A | B | C | D | E |
---|---|---|---|---|---|
A | (1, 1, 1) | (4.22, 6.25, 8.26) | (0.33, 1, 1) | (1.44, 3.55, 5.6) | (0.18, 0.28, 0.69) |
B | (0.13, 0.18, 0.28) | (1, 1, 1) | (0.11, 0.14, 0.14) | (0.33, 1, 1) | (0.11, 0.14, 0.14) |
C | (1, 1, 3) | (7, 7, 9) | (1, 1, 1) | (3, 5, 7) | (0.23, 0.48, 1) |
D | (0.18, 0.28, 0.69) | (1, 1, 3) | (0.14, 0.2, 0.33) | (1, 1, 1) | (0.11, 0.14, 0.14) |
E | (1.44, 3.55, 5.59) | (7, 7, 9) | (1, 2.08, 4.21) | (7, 7, 9) | (1, 1, 1) |
Options concerning H&S subcriteria.
H&S (C21) | A | B | C | D | E |
---|---|---|---|---|---|
A | (1, 1, 1) | (0.24, 0.28, 0.52) | (0.24, 0.28, 0.52) | (0.11, 0.14, 0.14) | (0.11, 0.14, 0.18) |
B | (2.08, 4.21, 6.26) | (1, 1, 1) | (0.33, 1, 1) | (0.14, 0.2, 0.33) | (0.24, 0.48, 1) |
C | (2.08, 4.21, 6.26) | (1, 1, 3) | (1, 1, 1) | (0.24, 0.33, 0.58 |
(0.33, 1, 1) |
D | (7, 7, 9) | (3, 5, 7) | (1, 3, 5) | (1, 1, 1) | (11.44, 3.55) |
E | (6.25, 7, 9) | (1, 2.08, 4.2) | (1, 3, 5) | (0.4, 0.7, 0.7) | (1, 1, 1) |
Options concerning regulation subcriteria.
(Reg) C22 | A | B | C | D | E |
---|---|---|---|---|---|
A | (1, 1, 1) | (3, 5.7) | (0.33, 1, 1) | (1, 3, 5) | (0.2, 0.33, 1) |
B | (0.14, 0.2, 0.33) | (1, 1, 1) | (0.11, 0.14, 0.14) | (1, 1, 1) | (0.11, 0.14, 0.14) |
C | (0.7, 1, 2) | (7, 7, 9) | (1, 1, 1) | (3, 5.7) | (1, 1, 1) |
D | (0.2, 0.33, 1) | (1, 1, 1) | (0.14, 0.2, 0.33) | (1, 1, 1) | (0.11, 0.14, 0.14) |
E | (1, 3, 5) | (7, 7, 9) | (1, 1, 1) | (7, 7, 9) | (1, 1, 1) |
Options concerning turnover subcriteria.
(Turnover) C31 | A | B | C | D | E |
---|---|---|---|---|---|
A | (1, 1, 1) |
|
(0.33, 1, 1) | (1, 3, 5) | (0.13, 0.24, 0.28) |
B | (0.14, 0.2, 0.33) | (1, 1, 1) | (0.11, 0.14, 0.14) | (0.33, 1, 1) | (0.11, 0.14, 0.14) |
C | (1, 1, 3) | (7, 7, 9) | (1, 1, 1) | (3, 5.7) | (1, 1, 1) |
D | (0.2, 0.33, 1) | (0.69, 1, 1) | (0.12, 0.16, 0.24) | (1, 1, 1) | (0.11, 0.14, 0.14) |
E | (3.55, 4.18, 7.61) | (7, 7, 9) | (1, 1, 1) | (7, 7, 9) | (1, 1, 1) |
Options concerning gain subcriteria.
(Gain) C32 | A | B | C | D | E |
---|---|---|---|---|---|
A | (1, 1, 1) | (0.58, 1.4, 2.92) | (0.28, 0.69, 1) | (1.21, 2.02, 3.66) | (2.08, 4.21, 6.25) |
B | (0.34, 0.69, 1.7) | (1, 1, 1) | (1.09, 1.7, 2.5) | (1, 2.08, 4.21) | (6.25, 7, 9) |
C | (1, 1, 3) | (0.39, 0.58, 0.92) | (1, 1, 1) | (0.18, 0.28, 0.69) | (1, 1, 1) |
D | (0.27, 0.49, 0.82) | (0.2, 0.33, 1) | (1, 3, 5) | (1, 1, 1) | (5, 7, 9) |
E | (0.13, 0.24, 0.28) | (0.11, 0.14, 0.2) | (1, 1, 1) | (0.13, 0.14, 0.19) | (1, 1, 1) |
The results of interval approximation of pairwise comparison matrices are presented in Tables
The interval approximation main target concerning the gain criteria.
Main target | C1 | C2 | C3 | Obtained weights |
---|---|---|---|---|
C1 | [ |
[5.7, 6.8] | [5.7, 6.8] | 0.84507 |
C2 | [0.15, 0.18] | [ |
[4.5, 5.5] | 0.126761 |
C3 | [0.15, 0.18] | [0.18, 0.23] | [ |
0.028169 |
The interval approximation subcriteria concerning the main criteria.
Environment | C11 | C12 | C13 | Obtained weights |
---|---|---|---|---|
C11 | [ |
[2.36, 2.96] | [1.09, 1.37] | 0.633438 |
C12 | [0.32, 0.42] | [ |
[2.71, 3.51] | 0.267838 |
C13 | [0.76, 0.93] | [0.30, 0.38] | [ |
0.098724 |
Social | C21 | C22 | Obtained weights |
---|---|---|---|
C21 | [ |
[2.7, 3.1] | 0.754717 |
C22 | [0.32, 0.47] | [ |
0.245283 |
Economic | C31 | C32 | Obtained weights |
---|---|---|---|
C31 | [ |
[3.68, 4.73] | 0.821693 |
C32 | [0.22, 0.3] | [ |
0.178307 |
The interval approximation purposed choices referring to GWP subcriteria.
GWP | A | B | C | D | E | Obtained weights |
---|---|---|---|---|---|---|
A | [ |
[3.02, 4.06] | [0.33, 0.4] | [2.5, 3.5] | [0.15, 0.17] | 0.090862 |
B | [0.28, 0.31] | [ |
[0.13, 0.14] | [0.3, 0.5] | [0.14, 0.14] | 0.026054 |
C | [1.96, 2.96] | [ |
[ |
[4.5, 5.5] | [0.23, 0.27] | 0.195402 |
D | [0.3, 0.5] | [2.5, 3.5] | [0.18, 0.21] | [ |
[0.13, 0.14] | 0.036345 |
E | [5.7, 6.76] | [ |
[3.68, 4.72] | [6.8, 7.5] | [ |
0.651339 |
The interval approximation choices referring to ETP subcriteria.
ETP | A | B | C | D | E | Obtained weights |
---|---|---|---|---|---|---|
A | [ |
[2.5, 3.5] | [0.22, 0.21] | [ |
[0.18, 0.22] | 0.041578 |
B | [0.42, 0.61] | [ |
[0.13, 0.15] | [0.42, 0.61] | [0.14, 0.14] | 0.024023 |
C | [3.68, 4.72] | [ |
[ |
[6.5, 7.5] | [0.23, 0.27] | 0.180174 |
D | [0.83, |
[1.8, 2.6] | [0.15, 0.18] | [ |
[0.13, 0.14] | 0.027719 |
E | [3.5, 4.5] | [6.8, 7.5] | [3.68, 4.72] | [6.8, 7.5] | [ |
0.726506 |
The interval approximation choices referring to LU subcriteria.
LU | A | B | C | D | E | Obtained weights |
---|---|---|---|---|---|---|
A | [ |
[5.74, 6.67] | [0.83, |
[3.02, 4.06] | [0.25, 0.38] | 0.173079 |
B | [0.17, 0.2] | [ |
[0.13, 0.15] | [ |
[0.13, 0.15] | 0.030116 |
C | [ |
[ |
[ |
[4.5, 5.5] | [0.5, 0.6] | 0.223084 |
D | [0.25, 0.38] | [ |
[0.18, 0.23] | [ |
[0.13, 0.15] | 0.042567 |
E | [ |
[ |
[1.8, 2.6] | [ |
[ |
0.531153 |
The interval approximation choices referring to H&S subcriteria.
H&S | A | B | C | D | E | Obtained weights |
---|---|---|---|---|---|---|
A | [ |
[0.21, 0.25] | [0.27, 0.34] | [0.13, 0.14] | [0.13, 0.15] | 0.037196 |
B | [3.68, 4.72] | [ |
[0.83, |
[0.18, 0.23] | [0.42, 0.61] | 0.109401 |
C | [3.68, 4.72] | [ |
[ |
[0.13, 0.14] | [0.83, |
0.164101 |
D | [ |
[4.5, 5.5] | [2.5, 3.5] | [ |
[1.3, 1.97] | 0.492303 |
E | [6.8, 7.5] | [1.8, 2.6] | [ |
[0.62, 0.69] | [ |
0.197 |
The interval approximation choices referring to the regulation subcriteria.
Regulation | A | B | C | D | E | Obtained weights |
---|---|---|---|---|---|---|
A | [ |
[4.5, 5.5] | [0.83, |
[2.5, 35] | [0.3, 0.5] | 0.247475 |
B | [0.18, 0.23] | [ |
[0.13, 0.14] | [ |
[0.13, 0.14] | 0.045455 |
C | [0.92, 1.3] | [ |
[ |
[4.5, 5.5] | [ |
0.318182 |
D | [0.3, 0.25] | [ |
[0.18, 0.23] | [ |
[0.13, 0.14] | 0.070707 |
E | [2.5, 3.5] | [ |
[ |
[ |
[ |
0.318182 |
The interval approximation choices referring to turnover subcriteria.
Turnover | A | B | C | D | E | Obtained weights |
---|---|---|---|---|---|---|
A | [ |
[5.08, 6.09] | [0.83, |
[2.5, 3.5] | [0.15, 0.17] | 0.224165 |
B | [0.32, 0.42] | [ |
[0.13, 0.14] | [0.92, |
[0.13, 0.14] | 0.044833 |
C | [ |
[6.81, 7.5] | [ |
[5.74, 6.76] | [ |
0.336247 |
D | [0.30, 0.38] | [0.92, |
[0.15, 0.17] | [ |
[0.13, 0.14] | 0.058508 |
E | [4.43, 5.44] | [ |
[ |
[ |
[ |
0.336247 |
The interval approximation options concerning gain subcriteria.
Gain | A | B | C | D | E | Obtained weights |
---|---|---|---|---|---|---|
A | [ |
[1.22, 1.81] | [0.59, 0.77] | [1.82, 2.43] | [3.68, 4.72] | 0.322223 |
B | [0.60, 0.95] | [ |
[0.028, 0.169] | [1.81, 2.61] | [6.81, 7.5] | 0.305145 |
C | [0.18, 0.23] | [0.54, 0.67] | [ |
[0.25, 0.38] | [ |
0.159262 |
D | [ |
[0.3, 0.5] | [0.30, 0.38] | [ |
[6.5, 7.5] | 0.168588 |
E | [0.21, 0.28] | [0.13, 0.15] | [2.36, 2.96] | [0.14, 0.16] | [ |
0.044782 |
The calculating of weighted approximation related to Table
As shown in Table
The results of ranking aluminum waste management system options.
Alternatives | Final obtained weights | Rank of alternatives |
---|---|---|
A | 0.090549 | 3 |
B | 0.036346 | 5 |
C | 0.198146 | 2 |
D | 0.070878 | 4 |
E | 0.594161 | 1 |
Ranking order | E > C > A > D > B |
In addition, the fuzzy AHP methods in the literature are compared [
The comparison of various FAHP models [
Sources | Basic specifications | Positives (P)/negatives (N) |
---|---|---|
[ |
Direct extension of Saaty’s AHP model with triangular fuzzy numbers | (P) The judgments of multiple experts may be modeled in the reciprocal matrix |
Lootsma’s logarithmic least square model is used to derive fuzzy weights and fuzzy performance scores | (N) Evermore there is no solution to the linear equations | |
(N) The calculational demand is great, even for a low problem | ||
(N) It permits only triangular FN to be applied | ||
|
||
[ |
Direct extension of Saaty’s AHP model with trapezoidal fuzzy numbers | (P) It is simple to extend to the fuzzy term |
Uses the geometric mean model to derive fuzzy weights and performance scores | (P) It guarantees an alone solution to the reciprocal comparison matrix | |
(N) The calculational demand is great | ||
|
||
[ |
Modifies van Laarhoven and Pedrycz’s model | (P) The judgments of multiple experts may be modeled |
Shows a more robust method to the normalization of the local priorities | (N) The calculational demand is great | |
|
||
[ |
Synthetical degree values | (P) The calculational demand is partly low |
Layer simple sequencing | (P) It follows the steps of crisp AHP; it does not involve additional process | |
Composite total sequencing | (N) It permits only triangular FN to be applied | |
|
||
[ |
Creates fuzzy standards | (P) The calculational demand is not great |
Illustrates performance numerals by membership functions | (N) Entropy is applied when probability distribution is known. The model is based on both probability and possibility measures | |
Uses entropy concepts to calculate aggregate weights | ||
|
||
|
|
|
|
||
|
|
The comparison of results of proposed method and Chang’s fuzzy AHP method.
Alternatives | Weights (proposed) | Rank of alternatives | Weights (Chang’s method) | Rank of alternatives |
---|---|---|---|---|
A | 0.090549 | 3 | 0.094855 | 3 |
B | 0.036346 | 5 | 0.006343 | 5 |
C | 0.198146 | 2 | 0.305851 | 2 |
D | 0.070878 | 4 | 0.01511 | 4 |
E | 0.5941 | 1 | 0.409039 | 1 |
Ranking order (the proposed method) | E > C > A > D > B | |||
Ranking order (Chang’s method) | E > C > A > D > B |
As was previously noted, the secondary aluminum production increases quickly due to environmental issues and continuous growing of use demands. In this case, over 200 kilograms of aluminum black dross as waste is 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 consequences from the air, the water, and the soil pollution point of view. Recovery, recycle, and disposal of aluminum wastes including aluminum dross and aluminum scrap are a global issue in terms of environmental, social, and economic aspects. The presented model for industrial waste management alternatives was implemented in the case of aluminum waste systems in the industrial city of Arak. The application of LCA to the aluminum waste management system will be a feasible way. However, LCA works have commonly an intrinsic ambiguity due to different categories. In addition, no single solution is available as each industry in each country has different characteristics in terms of geographical and environmental as well as social and economic aspects. Several management decisions are required to provide efficient aluminum waste management systems. The objective of this research is to propose an integrated FAHP in the aluminum waste management system. The model for the aluminum waste management system, which integrates social, economic, and environmental aspects, is the MCDM problem. This study has presented a model, based on the fuzzy concept, to compare aluminum waste management systems. It may mainly evaluate and contains interdependence relationship amongst the criteria under ambiguity. The results of the research represent that the method is easy in computation and setting priorities. Hence, it is mainly appropriate for solving MCDM problems. At this research we apply environmental, social, and economic criteria for evaluation and support decision-making within the aluminum industry as the MCDM problem. On the other hand, the fuzzy AHP can be utilized not only as a method to handle the interdependence within a collection of criteria, but also as a method of generating more noteworthy data for decision-making. The model also has disadvantages. For example, FAHP model uses the aggregated categories’ data that several subcategories are evaluated under the same main category. This will increase the uncertainty in FAHP based on LCA results that can be solved by using more specific life cycle data for several steps of aluminum waste. It is significant to regard that the weights of subcriteria 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. Seven subcriteria are considered from a group of three main criteria, namely, environmental, social, and economic. First, decision-makers evaluated each waste management alternative for selected criteria and subcriteria. Second, we obtained these evaluation results taking into account the weight of the criteria and subcriteria. Also, we transformed collected data into the fuzzy intuitionistic version. Finally, we applied a real MCDM problem for the proposed decision-making method. The model aims to rank waste management alternatives. Relevant to the outcomes of expert judgment, the most important environmental subcriteria are determined as global warming, human toxicity, and land use. The most influential social indicator is indicated as health and safety at work and regulation, and the most influential economic subcriteria are determined as turnover and gain.
The results showed that alternative E has the highest ranking compared to other alternatives. Also, alternative C and alternative A are ranked third and fourth, respectively. Apart from these three, other alternatives of aluminum waste management system, as alternative D and alternative B, ranked fourth and fifth, respectively. 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 environmental, social, and economic issues. For example, the choice of alternative C could be increased by the increasing amount of aluminum scraps, related to the primary aluminum production process. Also alternative D represents the export of aluminum waste to other places in the form of black dross or aluminum dross with less metallurgic aluminum. From the application perspective, this research will provide a valuable insight for managers to attempt to improve the environmental, social, and economic condition all together at the same time.
Nowadays, thanks to increased awareness and important environmental pressures from various stakeholders, environmental issues in daily activities are considered by industries. However, so far, little attention has been given to environmental aspects of processing output of aluminum dross and aluminum scrap as aluminum waste. All the information collected was related to LCA result, written documents, and findings from interviews. For the proposed integrated fuzzy AHP model, the five alternatives are investigated. In this study we applied the NWIA of FN to transform each fuzzy component of the pairwise matrix to its NWIA. Then, we applied the GP model for weighting and LINGO 11 to resolve. 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. In alternative E, aluminum batch includes primary aluminum ingot 99.5–20% and secondary aluminum (aluminum scrap 98–80%), beneficiation activities related to input aluminum scrap such as washing, separating, and sorting, duplicate aluminum dross recycling in plant, and landfill, while in alternative B aluminum batch includes primary aluminum ingot 99.5–20% and secondary aluminum (aluminum scrap 96–80%), remelting without beneficiation activities, exporting remaining aluminum dross to other places, and duplicate recycling and release in the environment.
According to above-mentioned consideration, uncertainty in the LCA results and limitations of the current method should be taken into account by decision-makers. First of all, the methodology may be utilized for similar problems where multiple criteria are present. This research will supply a valuable insight for the directors to try to improve the environmental, social, and economic condition all together simultaneously. In future research, current fuzzy approach can be developed and applied for different MCDM problems in industry where conflicting criteria exist.
The authors declare that there is no conflict of interests regarding the publication of this paper.