Research Article  Open Access
The Integrated Fuzzy AHP and Goal Programing Model Based on LCA Results for Industrial Waste Management by Using the Nearest Weighted Approximation of FN: Aluminum Industry in Arak, Iran
Abstract
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.
1. Introduction
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 × 10^{7} t in 2015 [1]. In the following, FAHP methodology has been considered to evaluate the environmental, economical, and social impacts of the aluminum waste. To ameliorate the MCDM procedure and facilitate aluminum waste system choice process, the present research will use a fuzzy integrated approach to represent decisionmakers’ judgments, which is utilized to evaluate the weight of criteria and alternatives. Then, literature, the results of questionnaires, overviews, and the results of the primary life cycle assessment are evaluated by experts by the use of fuzzy linguistic terms.
This approach allowed us to numerically display vagueness and to reflect the decisionmakers’ perception of the decisionmaking process as well.
This research is comprised of the following sections.
In Section 2, we give some related literature concerning the proposed problem a onceover. In Section 3, as methodology, we review some basic concepts, and finally the proposed algorithm is explained. In Section 4, a case study related to the aluminum waste is presented. The study ends with a discussion and conclusion.
2. Literature Review
Total primary aluminum consumption in the world was of 50.2 Mt in 2013 [2]. The manufacture of aluminum from alumina demands much more energy than other metals and leads to major quantities of greenhouse gas pollutants [3]. Aluminum production is responsible for 1.1% of the annual greenhouse gas emissions [4]. It is about 75% of all the aluminum production as secondary aluminum (aluminum scrap and dross) since 1880s which 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 secondary aluminum compared to the production of primary aluminum [5]. Authors represented that the aluminum waste recycling is economically and environmentally friendly [6]. Opportunities for recovery and recycle of metals from wastes are high. Recovery of secondary resources such as Al, Fe, Cu, and Zn from these wastes is gaining increasing interest [7, 8]. Also, by recycling secondary aluminum, resources are saved, the need for landfill area could have been decreased, and the public opinion would be satisfied. A lot of dross is produced as a waste product during remelting or refining aluminum [9]. Although aluminum dross is a waste of current resources, in case of being landfilled without suitable treatment, it will lead to the secondary contaminants which would affect air, water, and soil [1]. Aluminum wastes, mainly, are disposed of in landfill sites, which may result in leaking of toxic metal ions into the ground water. Also, when aluminum waste comes in contact with water it emits poisonous gases as NH_{3}, CH_{4}, PH_{3}, H_{2}, and H_{2}S [10, 11]. The environmental effects of aluminum scrap from recycled 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 has been always considered as a problematic issue. The fuzzy set idea was used by [12] to manage uncertainty in the inventory data. Seppälä modified and compared the fuzzy approach presented in [13] to the “traditional” valuation method of LCA [14]. Since Van Laarhoven, Pedrycz, and Buckley [15, 16] offered their initial study in FAHP, numerous works have applied FAHP in disparate environment problems [17–20]. Also, some studies applied FAHP method concerning LCA thinking. For example, this methodology was applied by Zheng et al. in the building sector [21] and by Chan and Lin to evaluate green product design [19, 22]. Complex decisionmaking situations are relevant to the aluminum waste management system which needs the realization of different sections of the industry and community. However, little attention has been given to the environmental aspects of the processing output of aluminum dross and aluminum scrap as aluminum waste in MCDM methodologies.
3. Methodology
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.
3.1. Fuzzy Numbers (FN)
FN are one path to explain the ambiguity and be missing accuracy of data [23]. A fuzzy number is a fuzzy set that satisfied the following:“” is continuous. outside some interval .There are real numbers , , and so that . And, , is decreasing on , is increasing on .The set of all such fuzzy numbers is represented by . Fuzzy number with linear sides and the membership function having the following form (see Figure 1)is called triangular fuzzy number and is denoted by
3.2. Fuzzy Pair Comparison Matrix
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 where is a triangular FN; see [24]. It is supposed that is reciprocal, if the following term is satisfied [25]:
3.3. The Nearest Weighted Interval Approximations (NWIAs)
In this section, we review an interval processor of FN, which is denoted by . We apply a fuzzy weighted spacing quantity on the FN. Then, we acquire the interval approximations for FN [26].
function is as and functions , are not negative, are uniformly increasing, and satiate the undernormalization term:Now, let be a fuzzy number with and let be a weighted function. Then the interval is to FN .
In usage, the function may be selected pursuant to the real term.
If , which is a triangular FN, and , which is a weighting function, so
Example 1. In this example is a triangular FN; also, and are two weighting functions. Then, the nearest weighted interval to is as follows (Figure 2) [26]:
3.4. Goal Programming (GP)
The GP attempts to combine optimal logic and the preference of decisionmaker in arithmetical programming in order to satiate several goals. The decisionmaking environment determines basic concepts including goal and system restrictions and aim function variables. This means that GP presents the way for concurrent goal attainment [27].
Weighted GP is a capable tool since it includes several factors simultaneously in the decisionmaking 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 decisionmaking such as optimizing the result mixture.
Regard the following problem: where are goal functions and is not empty in an achievable region. Model (4) is now a significant area of MCDM mathematical programming. The conception of goal programming is to set up an aim level of gaining each indicator. This procedure needs the decisionmaker to consider a goal for each aim that someone wishes to obtain. A favored result is then explained as the one which reduces the deflections from set objectives to the smallest possible amount. After that, the GP may be presented asThe decisionmakers in their objectives set some acceptive dream levels for these objectives and attempt to obtain a collection of objectives as intimately as feasible. The aim of programming is to reduce the perversions between the attainment of objectives, , and these acceptive dream levels, (). In addition, and are up and down attainment of the th objective, respectively.
3.5. Deriving the Weights of Criteria
In the routine situation, whenever a matrix is reciprocal and consistent, afterwards the weights of criteria are computed as
In the situation of inconsistence matrix, we should achieve the significance weights or equally . Hence in the situation of ambiguity, for deriving the weights from inconsistence fuzzy matrix we do as [26].
Step 1. First by (8) we convert each fuzzy component of the comparison matrix to . Therefore, the fuzzy comparison matrix is transformed to an interval matrix .
Therefore we present deviation variables , and , , which lead to where deviation variables , and , are not negative real numbers but may not be positive concurrently, which is, and . Now we use the GP procedure. It is worthwhile that the deviation variables and remain to be as little as possible, which drive to the following GP model [26]:By the resolvent model (12), we acquire the optimal weight vector and display the significance of each indicator. We can use these weights in the course of solving a multiple criteria decisionmaking problem. To solve this problem, we apply the linear programming software .
Example 2 (matrix with triangular fuzzy number). Regard reciprocal matrix with FN: We apply the function . Afterwards, by applying equality (7), the interval approximation pairwise comparison matrix is acquired as We build the GP procedure for the mentioned interval approximation matrix asBy solving GP (15), we achieve the optimal vector . We may apply these weights in the process of solving a MCDM problem. In addition, these weights display that indicator 1 is more significant than others (see Table 1). In this case the grade arrangement of these indicators is as follows:The results of ranking these criteria are presented in Table 1.

3.6. FAHP Method
The AHP approach applies multicriteria decision analysis developed presented by Saaty [28], to compute the weighting factor of attribute. The AHP method is constructed on the pairwise comparison to compute the weight of each criterion. The AHP permits experts to determine the significance of each criterion during comparing other criteria from 1 to 9, from “same importance” to “completely more important” . Building a decision tree, decisionmaker is permitted to first describe weights of the main criteria, and then decisionmaker can describe the lower level subcriteria that exactly describe the tested multicriteria issue [28].
The AHP method may not handle the ambiguity in determining the rankings of various attributes [29]. Also, it is usually hard to evaluate various factors because of a lack of suitable data. In FAHP method, quid pro quo of allocating definite quantities, the adjudications are built by applying linguistic parameters and are characterized by fuzzy membership functions. The fuzzy geometric mean method is the most accepted method to construct the matrix. The relict procedures are just routine AHP.
3.7. Proposed Algorithm
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.
Step 1 (set up the expert group). To evaluate alternatives, an expert group comprised of researcher and managers should be formed.
Step 2. Create a hierarchical structure of elements for problem solving. For this propose, it is necessary for decisionmakers to determine criteria and subcriteria based on proposing the main target. See, for example, Figure 3.
Step 3. Build a set of fuzzy comparison matrices for each decisionmaker.
Step 4 (aggregate fuzzy comparison matrices). We aggregate fuzzy comparison matrices constructed by decisionmakers by using the geometric mean method and convert them to unit fuzzy comparison matrix, is the important opinion of the th decisionmaker.
Step 5 (deriving the weights of each matrix). For this purpose, we apply the following substeps.
Step 5.1. By using (7), we convert each fuzzy matrix to an interval fuzzy matrix.
Step 5.2. By resolving model (12), we can achieve the weight of each comparison matrix.
Step 6 (aggregate the weights and rank the alternatives). 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 [30].
4. Case Study
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.
Twentynine remelting facilities were incorporated in this research. The secondary aluminum remelting is considered as a unit function. As shown in Figure 4, this process unit includes the storage in place , beneficiation activities related to input aluminum scrap such as washing, separating, and sorting (or without beneficiation activities ), remelting in the crucible furnace , duplicate aluminum black dross recycling in plant (or exporting aluminum black dross to another place and duplicate recycling ), and final waste landfilling (or release in the environment ).
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 5). The upkeep and repair of the plant and equipment materials are provided to this life cycle stage from both primary and secondary aluminum processing. Also, the secondary remelters have a diversity of melting furnaces: toploaded closed, rotary, and side wellfeeding melting. They have different competence. In this study, the crucible furnace for the secondary aluminum remelting is used.
(a) New aluminum scrap
(b) Old aluminum scrap
(c) White aluminum dross
(d) Black aluminum dross
In this study, firstly, a panel of experts as the decisionmaker group was set up. The decisionmakers 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 decisionmakers using fuzzy linguistic terms. This approach allowed us to mathematically represent uncertainty and vagueness and reflect the decisionmaker’s perception of decisionmaking process. After this, a questionnaire was distributed to the decisionmakers 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 6 shows the decision hierarchy for the decisionmaking issue. In the upper ranks of the hierarchy we have the general aim which in this instance is the choice of an aluminum waste management system. We presented the main criteria including environmental, social, and economic aspects at level 2. The associated common attributes or subcriteria (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 five management options.
Five management alternatives for aluminum waste management in Arak are presented as follows:(i)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.(ii)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.(iii)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.(iv)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.(v)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 2.

Pairwise comparison matrix subcriteria concerning the basic criteria are presented in Table 3.
(a)  
 
(b)  
 
(c)  

Comparison matrix subcriteria concerning the alternatives are as in Tables 4–10.







The results of interval approximation of pairwise comparison matrices are presented in Tables 11–19.

(a)  
 
(b)  
 
(c)  








The calculating of weighted approximation related to Table 12 is presented in Example 2.
As shown in Table 20, alternative “E” is assigned as the most preferable choice, with a weight of 0.594161; 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 are in next order, respectively.

5. Comparison with Other Existing Methods
In addition, the fuzzy AHP methods in the literature are compared [30, 31] as shown in Table 21. There are significant differences in their hypothetical forms. The comparison includes positives and negative points of each method. Main positives of proposed method were assigned at the bottom of Table 21 and were denoted with bold font. For evaluation of proposed method, we applied Chang’s method [32] in order to assess the aluminum waste management systems (see Table 22).


6. Discussion
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 byproducts 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 decisionmaking 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 decisionmaking. 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 decisionmaking 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, decisionmakers 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 decisionmaking 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 tradeoff 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.
7. Conclusions
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 abovementioned consideration, uncertainty in the LCA results and limitations of the current method should be taken into account by decisionmakers. 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.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
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Copyright
Copyright © 2016 Ramin Zare et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.