Eco-material selection using fuzzy TOPSIS method

Abstract

In the classical multiple attribute decision-making or MADM methods, the ratings and the weights of the criteria are known precisely. However, in eco-material selection exercises, the available data are typically inadequate because of the selection dual quantitative and qualitative natures. Some of the qualitative selection criteria can be rated in several classes rather being expressed by exact numerical values; hence the application of fuzzy concepts in decision-making seems attractive to deal with such kind of ratings. Thusly, the presented study attempts to propose an eco-material selection approach specific to the automobile body panels using a fuzzy technique for order preference by similarity to ideal solution (TOPSIS), to incorporate both numerical and rating-based criteria into one holistic sustainability model. TOPSIS and fuzzy logic can aid the material selection process in translating the design goals and parameters into usable numbers that in turn can be used to rank candidate materials in their closeness to the ideal solution. An additional uniqueness of this study stems from using the fuzzy-TOPSIS as a scoring tool without any assigned weights for the different selection attributes, in order to avoid the bias that is typically associated with other classical MADM, such as quality function deployment, analytical hierarchy process and digital logic.

Keywords:

• Automobile
• design for sustainability
• fuzzy logic
• material selection
• TOPSIS

1. Introduction

Sustainability in the transportation sector has been the subject of an increasing amount of research recently, knowing that 96% of the world’s transportation systems depend on petroleum-based fuels and products (Mayyas, Qattawi, and Omar 2012). Thus, reducing the amount of consumed fuel in the “use-phase” would be the main focus when researching a sustainable transportation system. Interestingly, the global transportation vehicles are the main consumer among other sectors; it accounts for about 40% of the world’s oil consumption of nearly 75 million barrels of oil per day based on 2003 statistics (McAuley 2003).

According to Mayyas et al. (2012), designing a sustainable automobile should be done from a holistic perspective that compromises the balance between social, economic and environmental issues as compared to economic factors within the product or service development process.

Several methodologies have been proposed for incorporating the environmental concerns in the material selection process. Some methods emphasize selecting materials based on a single phase of a product’s life cycle (e.g. use-phase or end-of-life); While others attempt to consider the entire life cycle, either qualitatively or quantitatively. For example, (Graedel and Allenby 1994) proposed a set of qualitative material selection guidelines (e.g. “use recycleable material”, “do not use toxic material”, etc.) to be applied in the early design stages. In fact, these material selection guidelines are simply “rules-of-thumb” in any design process, and should be used as a first screening effort in order to better focus the material selection scope (i.e. material space). Although using qualitative methods can also help in classifying the materials as desirable or un-desirable, still the prioritization of certain materials is difficult.

Alternatively, quantitative approaches for eco-material selection are proposed to rank the materials using single indicators including the Eco-Indicator, which is a single environmental indicator proposed by Wegst and Ashby (1998), the energy content over product’s entire lifetime as proposed and used by Ashby (2008, 2009) or a set of environmental indicators (e.g. CO₂, SO_x, NO_x, “recyclability and recycle fraction”, and resource scarcity) as suggested by Coulter et al. (1996). Another quantitative eco-material selection based on economic indicator is also proposed and used by Ermolaeva, Castro, and Kandachar (2004).

In selecting materials for a given component, one should consider all the design requirements simultaneously; however, it might be beneficial to combine some of these requirements. The performance indices proposed by Ashby (2008) and Kampe (2001) are useful in combining the technical requirements (strength, light weight, etc.). Still, material indices would only consider two major characteristics at a time; thus, the design process might be an iterative one.

Based on aforementioned discussions, there is still a necessity for developing a systematic method or procedure to model a sustainable material selection process using a holistic approach that covers economic, environmental and the societal aspects. Mayyas, Qattawi, and Omar (2012) proposed one embodiment of a design for sustainability model as applied to automobile structures, which can be considered comprehensive because it considers the design functional and aesthetics requirements; this proposed model employed a set of sustainability factors ranging between environmental, economic, societal factors and technical parameters (Mayyas, Qattawi, and Omar 2012; Mayyas et al. 2012). Figure 1 displays the structure of that model and identifies its hierarchy, which is built around material selection for “sustainable lightweight” designs rather than “traditional lightweight” designs. The main sustainability factors along with their importance are tabulated in Table 1. More details can be found in our previous work (Mayyas, Qattawi, and Omar 2012; Mayyas et al. 2012).

Figure 1. Design for sustainability model for auto-bodies.

Table 1. Sustainability factors and their importance.

Sustainability factor	Importance
Resource scarcity	A resource depletion index can perform as a proxy of resource scarcity which is a qualitative measure for scarcity level of depletion for natural resources
Water pollution index and water usage per kg of virgin material	Water pollution is any contamination of water with chemicals or other foreign substances that may adversely impact humans, plants or animals. Water pollution index has two measures: amount of water and toxicity of waste water used in each phase. Water usage index is a measure of amount needed to produce 1 kg of virgin material
Life cycle assessment (LCA)	Life cycle assessment is the study that assesses energy expenditures, materials used, and emissions release to the environment in the different life phases starting from pre-manufacturing to manufacturing, operation and maintenance and finally end-of-life phase
Recyclability	Recyclability is used as an indicator of environmental friendliness of materials and it is measured by percentage recycle fraction (ψ)
Durability	Mainly addresses the performance of the given part/product made of a given material under typical operating conditions. It is known that BIW acts as an outer shell for internal components of the vehicle and it is usually prone to harsh environment of salt water, and wear and scratch
Economic impact factors	This factor can be measured using life cycle cost analysis which mainly addresses the cost associated with life cycle phases and it is usually expressed in terms of $/kg or $/unit produced
Societal factors	Expressed as safety and health and wellness. Safety is an indirect measure for material properties (i.e. toughness and yield strength), while health and wellness is another indirect measure that is governed by noise-vibration-harshness performance (as controlled by dynamic stiffness of BIW structure and damping capacity of material) and emissions to the environment and their adverse effects like acid rain, global warming potential and ozone depletion
Technical factors	Technical factors address ease of manufacturing in terms of formability, joinability and paintability, of the given materials. Also, technical factors provide the designer and decision-makers with clearer view about “what if” analysis, if material X is to be used instead of material Y

In essence, the material selection process in general and the eco-material selection in particular can be considered a multi-attribute decision-making (MADM) problem that usually include both quantitative and qualitative factors, where some of these factors might be conflicting in terms of their economic and environmental impacts. Hence, the design team should formulate their design mathematical function (penalty function, etc.) to include all conflicting objectives (e.g. cost vs. light weight; functionality vs. recyclability, etc.) and yet establish well-defined and accepted limits for each design requirement and constraint.

Recently, MADM methods along with artificial intelligence methods have been used extensively in the engineering materials selection filed as they prove to be efficient in handling multi-attribute selection problems. Examples of popular MADM methods are analytical hierarchy process (AHP), graph theory and matrix, quality function deployment (QFD)-based model, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), digital logic, etc. Artificial intelligence methods such as artificial neural networks, fuzzy logic and genetic algorithms have also been used in the material selection process over the past few decades. Most recently, hybrid approaches of MADM methods and artificial intelligence methods have been used to get more powerful decision-making models that can handle complex relationships in easy ways (e.g. fuzzy-AHP, fuzzy-QFD, fuzzy-TOPSIS, etc.). Further, this method may be difficult to deal with the large number of attributes. Manshadi et al. (2007) proposed a numerical method for materials selection combining nonlinear normalization with a modified digital logic method. Rao and Davim (2008) used two MADM methods for the benefit of material selection process, namely: AHP and TOPSIS. According to this study, the selection of AHP method over other MADM methods comes from the fact that AHP is a powerful and flexible decision-making process that helps people in setting priorities and makes the best decision when both tangible and nontangible aspects of a decision need to be considered (Rao and Davim 2008). Another advantage of AHP over other MADM methods is the ability of the AHP in dealing with tangible as well as nontangible attributes, especially where the subjective judgments of different individuals constitute an important part of the decision process. However, in some cases, the huge number of pair-wise comparisons of attributes and alternatives with respect to each of the attributes may result in longer computational times and efforts in assigning weights to all attributes and alternatives. On the other hand, our selection of TOPSIS method emerges as a novel decision-making method that is based on the matrix analysis and proves to be more efficient in dealing with the tangible attributes and the number of alternatives to be assessed (Hwang, Lai, and Liu 1993; Hwang and Yoon 1981; Olson 2004). However, the TOPSIS method proposed in this study did not take into consideration the qualitative factors of the material selection attributes. Another example of MADM methods that was used in the material selection process is ELCTRE (ELimination and Choice Expressing REality) which was used by Shanian and Savadogo (2006). However, this method utilizes the concept of outranking relationship and the procedure is rather lengthy. Another limitation of this process is the fact that ELECTRE can make a partial prioritization of alternative materials only rather than the whole set of the alternatives. As the number of alternatives increases, the amount of relationships rises quite rapidly and hence the computational time could increase very significantly. Rao (2008) presented a novel logical procedure for engineering material selection applications using an improved compromise ranking method. The proposed method considers the measures of the attributes and their relative importance, and hence provides an accurate evaluation of the alternative materials without giving more weights to one attribute over the others. In fact, this proposed method represents a simple mathematical MADM model and can be used with any material selection process when a large number of quantitative and qualitative material selection attributes need to be treated simultaneously.

In another work, Chakraborty and Chatterjee (2013) used three different MADM methods in order to establish a bias-free material selection process. In this study, five material selection problems from diverse domains of applications were examined to show the effect of the number of criteria on the ranking performance of VIKOR ((Vlse Kriterijumska Optimizacija Kompromisno Resenje), TOPSIS and PROMETHEE (Preference Ranking Organization METHod for Enrichment of Evaluations) methods. Interestingly, they found that the choices of the best and the worst materials solely depend on the most important criterion having the maximum priority weight. As a direct result of this study, Chakraborty and Chatterjee claim that the designers can eliminate the process of constructing the exhaustive material selection decision matrices and just focus on the most important selection criterion dictating the entire selection process. However, in our opinion, this conclusion should not be adopted until it is validated by conducting further analyses on other MADM methods.

Application of artificial intelligence tools for material selection purposes cannot be underestimated as they prove their efficiency in dealing with complex relationships and the power of the computation they possess compared to the traditional MADM methods. Examples of material selection processes based on artificial intelligence tools are the selection of winding materials for power transformers (Amoiralis, Georgilakis, and Gioulekas 2006), selection of sustainable materials using artificial neural networks and genetic algorithms (Zhou, Yin, and Hu 2009) and application of fuzzy logic for selection of the best performance materials (Khabbaz et al. 2009). Although artificial intelligence methods tend to have better performance and they need lesser amount of time in developing material selection problems, they require advanced knowledge that most of design teams lack. In fact, artificial intelligence methods are popular selection methods between academic and research communities.

The traditional material selection methods tend to be ineffective when dealing with qualitative-based criteria that are often imprecisely defined for the decision-makers, or used improperly as design guidelines instead of being objectives of the design problem; for example, designers may treat formability as a guideline in the material selection, while it should be treated as a design goal with defined constraints. Our selection of TOPSIS method is based on the fact that TOPSIS has proved its efficiency in modelling multi-attribute decision problems using a reliable mathematical algorithm, but lacks the flexibility to deal with a mixed nature of sustainability decision-making problems which is usually made up from large number of qualitative and quantitative attributes. However, TOPSIS method needs an efficient procedure to find out the relative importance of different attributes with respect to the objective and fuzzy logic provides such a framework. Hence, to take the advantages of both methods, a combined MADM (using TOPSIS and fuzzy logic) is developed in the current work to facilitate eco-material selection of the auto-bodies by considering all sustainability factors. This paper also discusses the importance of the fuzzy-TOPSIS technique as a material selection method because of its ability in displaying the complex relationships among design variables and constraints.

In our previous publications (Mayyas, Qattawi, and Omar 2012; Mayyas et al. 2012), we have focused on design for sustainability for auto-bodies and how to derive the material selection indices based on the functionality, required performance and constraints associated with design of the body panels. We also used several decision-making methods and statistical analyses to incorporate decision-making methods in the selection of light yet sustainable materials which can replace steel without affecting the functionality or load bearing of the body panels. However, we have found that the dual nature of sustainability selection criteria may need a powerful multi-attribute decision-making method that has the capabilities to deal with this dual nature and can be used to get bias-free reliable material selection method. For these reasons, this paper is an attempt to provide a framework for developing unbiased method for eco-materials selection for automobile body structures (panels) using an integrated fuzzy-TOPSIS method. A set of qualitative and quantitative materials selection attributes have been collected to cover all aspects of sustainability; economical, societal, and environmental factors. These factors are considered simultaneously in the selection process and they gain same weight to avoid any bias towards low-cost or lightweight materials. After that, a set of 21 candidate materials – those usually used to make auto-body structural panels – have been subjected to the selection criteria using TOPSIS method in order to rank them in their closeness to the ideal or semi-ideal sustainable design.

2. Design and material selection

Engineering design process usually passes into several consecutive stages starting by investigating ideas and brainstorming sessions and proceed to what so-called conceptual design stage where decisions are made towards selecting best design option(s), feasibility of making these new products using current infrastructure at the company or if there is any need for new equipment, followed by the economic or cost analysis. After that, designers may proceed to the embodiment design stage where they can use the functional structure to analyse the operation, sizing of components if necessary, do another materials screening, and determining of operational conditions and its allowable limits. The final stage of the engineering design process is the detailed design phase in which the specifications are written for all components; in addition to analysing several critical components to make decisions in regard to the production route and final cost analysis. General rule of thumb in material selection is to select materials, which after appropriate manufacturing processes, should have the ability to perform the required functions at the lowest cost in association with stability of dimensions and shape upon putting it in service. In the conceptual design stage, designers and engineers usually sit together to decide on the important design parameters in terms of the intended usage of the product, the design constraints and the governing mathematical equations for each design consideration. Typical material selection strategy starts by identifying the objective function as the first step, and ends up with a set of candidate materials that can meet the design requirements (Ashby 2008). The proposed study in this manuscript employs a conventional BIW of a small-size passenger vehicle as shown in Figure 2. The major panels considered in this study and their design functions are listed in Table 2.

Figure 2. Major panels of coupe car BIW with closures. Source of image: http://www.billwang.net/bbs/oldattach/2006/06/16/billwang_5085491-Alfa-Romeo-Villa-d-Este-body-in-white-lg-embed.jpg; Picture adopted from www.billwang.net.

Table 2. BIW major panels and their main design functions.

No.	Panel name	Main design functions
1	Roof	Dent resistance, lightweight, durability
2	Hood (inner)	Bending stiffness, lightweight, ease of manufacturing
3	Hood (outer)	Dent resistance, lightweight
4	Trunk (inner)	Bending stiffness, lightweight, ease of manufacturing
5	Trunk (outer)	Dent resistance, lightweight
6	Trunk pan	Bending stiffness, lightweight, durability
7	Engine cradle	Crashworthiness, temperature performance, NVH, durability
8	Strut towers	Bending stiffness, lightweight, durability
9	Splash wall	Temperature performance, lightweight, durability
10	Quarter panel	Dent resistance, lightweight
11	Front fender	Dent resistance, lightweight
12	Door (inner)	Bending stiffness, lightweight, ease of manufacturing
13	Door (outer)	Dent resistance, lightweight
14	Wheel house	Bending stiffness, lightweight, durability
15	A, B, C pillars	Bending stiffness, lightweight, ease of manufacturing, durability
16	Floor pan	Bending stiffness, lightweight, durability

3. Fuzzy TPOSIS

The term “fuzzy logic” was firstly introduced in 1965 by Lotfi Zadeh (Hajek 2002; Zadeh 1965). Since then, fuzzy logic has been applied in many fields including control theory, engineering analysis, artificial intelligence, medical analysis, etc. The idea behind using Fuzzy logic is to deal with reasoning that is approximate rather than dealing with exact numbers. Compared to traditional binary sets (where variables may take on true (1) or false (0) values), fuzzy logic variables treat all values as having a relative truth value that ranges in degree between 0 and 1. Fuzzy logic, in fact, has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false (Hajek 2002; Krohling and Campanharo 2011).

Coming paragraphs provide the basic definitions associated with fuzzy terminologies that are necessary in understanding the nature of fuzzy-TOPSIS model. These definitions are briefed from (Sodhi and Prabhakar 2012):

Definition 1: A fuzzy set in a universe of discourse X has a membership function (x) that maps each element x in X using a real number from the interval [0, 1]. The function value (x) measures the grade of membership of x in .

Definition 2: A triangular fuzzy number is a triple-point function that has  = (a₁, a₂, a₃). The membership function (x) of triangular fuzzy number can be calculated using the following equation:(1)

where a₁, a₂, a₃ are the real numbers. Constants a₁ and a₃ are the lower and upper bounds of the available area for the evaluation data. These constants reflect the fuzziness of the evaluation data. The narrower the interval [a₁, a₃] is, the lower the fuzziness of the evaluation data will be.

Definition 3: Let  = (a₁, a₂, a₃) and = (b₁, b₂, b₃) be two triangular fuzzy numbers. Then, the operation with these fuzzy numbers is defined as follows (Krohling and Campanharo 2011):(2)

Linguistic variables in fuzzy set theory, coercion scales are applied to transform the linguistic terms into fuzzy numbers. In this paper, a scale of 1–9 has been used to transform the qualitative linguistic selection criteria into triangular fuzzy numbers (Figure 3). The intervals (Table 3) are chosen to get a uniform representation from 1 to 9 for the fuzzy triangular numbers used for the five linguistic ratings (very poor, poor, fair, good and very good). Vertex method can be used to measure the distance between two triangular fuzzy numbers. Let  = (a₁, a₂, a₃) and = (b₁, b₂, b₃) be two triangular fuzzy numbers; then, the distance between is:(3)

Figure 3. Fuzzy membership used to transform linguistic variables into fuzzy numbers.

Table 3. Fuzzy ratings for linguistic qualitative selection criteria.

Assessment	Qualitative ratings	Fuzzy number
Very poor	Very low (VL)	(1,1,3)
Poor	Low (L)	(1,3,5)
Fair	Medium (M)	(3,5,7)
Good	High (H)	(5,7,9)
Very good	Very high (VH)	(7,9,10)
Excellent	Extremely high	(9,10,10)

Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Situation) can be used to evaluate multiple alternatives with respect to the selected criteria. In the TOPSIS model, an alternative that has the nearest distance to the Fuzzy Positive Ideal Solution (FPIS) and farthest from the Fuzzy Negative Ideal Solution (FNIS) is chosen as an optimal solution. FPIS represents the best performance values for each alternative, whereas the FNIS represents the worst performance values (Hung and Chen 2009).

Assuming a decision group that has K members; if the fuzzy rating and importance weight of the k_th decision-maker, about the i_th alternative on j_th criterion, are: and respectively, where i = 1, 2, …, m, and j = 1,2, …, n, then the aggregated fuzzy ratings of alternatives (i) with respect to each criterion (j) can be made by  = (a_ij, b_ij, c_ij) such that (Sodhi and Prabhakar 2012):

(4)

The aggregated fuzzy weights () of each criterion are calculated as where:(5)

A fuzzy multi-attribute decision-making problem can be expressed in matrix format as (Sodhi and Prabhakar 2012):(6) (7)

where ∀_i,j and ; i = 1,2,…, m, j = 1,2, …, n are the linguistic variables that can be described by triangular fuzzy numbers for qualitative properties or by actual numbers for quantitative properties, and . Each criterion is characterized by a weight w_j which must be previously assigned by the decision-maker, frequently adopting a pair-wise-comparison approach. The weights should satisfy the following relation .

To keep the normalization formula simple, the linear scale transformation is used to transform various criteria scales into a comparable scale. Thus, the normalized fuzzy decision matrix as:(8)

where(9)

associated with maximization goal of the given attribute; and(10)

associated with minimization goal of the given attribute.

The above normalization method preserves the property that the ranges of normalized triangular fuzzy numbers belong to [0, 1].

A weighted triangular fuzzy decision matrix can be computed by multiplying the weight vector () of evaluation criteria and the normalized fuzzy decision matrix as:(11)

The FPIS and FNIS can be computed as follows:(12) (13)

where and

The distance () of each weighted alternative i = 1,2, … , m from the FPIS and the FNIS can be calculated using the following equations:(14) (15)

where d_v is the distance measurement between two fuzzy number and .

The closeness coefficient CC_i represents the distances to fuzzy positive ideal solution, A⁺, and the fuzzy negative ideal solution, A⁻, simultaneously. The closeness coefficient of each alternative can be calculated as follows:(16)

Alternative with highest closeness coefficient represents the best alternative and is closest to the FPIS and farthest from the FNIS.

4. Eco-material selection procedure using fuzzy TOPSIS

The methodology used in the present study is a framework that can be used in the conceptual design stage where a ranking method is conducted to yield a set of ranked materials for a given body panel. This is achieved by incorporating fuzzy logic with TOPSIS model as a decision-aid tool to rank candidate materials in the order of their closeness to the ideal solution that fits design goals.

However, some sustainability factors are qualitative in nature, for example, materials are classified as having high, medium and low corrosion resistance; the same is true for wear resistance and thermal performance. Also, the same idea is applicable to rate some societal factors (i.e. safety, and health and wellness) that lack any quantifiable measures; thus should be scaled to show the relative performance of the different materials; unless some of these factors, such as safety, are assumed to be mainly governed by a material property such as the yield strength, or the material toughness. Hence, this will further add another degree of complexity to the calculations for having dependent and independent factors. Additionally, health and wellness can be related to the vehicles’ emissions and its toxicity. For these reasons, rating is used here to first quantify some of the descriptive sustainability factors; these factors might not have a well-defined mathematical objective function. Table 4 illustrates the rating method used to rank different engineering materials based on their performance with respect to corresponding sustainability factors. This proposed scale is used to be consistent with the fuzzy ratings (Table 3) assigned for some of the factors related to durability, societal and technical issues.

Table 4. Scaling method used for rating some sustainability factors and fuzzy functions used to rate these properties.

Sustainability group	Sustainability factor	Qualitative scale	Fuzzy scale
Societal factors	Safety (Crashworthiness rating)	These properties are classified into six different levels which rate the performance of the material with respect to this sustainability factor: very poor; poor, fair, good, very good and excellent.	Triangular fuzzy function with six classes (Very Low; Low, Medium, High, Very High, Extremely High)
	Health and wellness (NVH and emissions adverse impact)
Durability factors	Corrosion resistance
	Wear resistance
	Thermal performance
Technical factors	Formability
	Joinability
	Paintability

In this study, the sustainability attributes are represented as points (vectors) in a multi-dimensional space, where each dimension represents a distinct attribute (variable, measurement) describing the object. Thus, a set of objects is represented as an mXn matrix, where m rows represent the candidate materials and n columns represent the selection attributes.

It is often difficult for decision-makers or designers to assign a precise performance rating to a candidate material for the criteria under consideration. The merit of using a fuzzy approach is to assign the relative importance of the selection attributes using fuzzy numbers instead of precise numbers. The following steps summarize fuzzy-TOPIS approach employed in this study (see Figure 4 for the flow chart of this fuzzy-TOPSIS model):

Figure 4. Flow chart for eco-material selection model using fuzzy-TOPSIS.

Step 1: Collect and classify sustainability attributes which will act as selection criteria afterwards. In this study, 20 different sustainability attributes are used to cover all sustainability aspects from economics, environmental, societal and technical perspectives (see Table 5).

Table 5. Sustainability factors and material properties correspond to each factor.

Material properties and	General		Mechanical					Technical			Durability			Environmental					Societal
	Density (g/cc)	Price ($/kg)	E Modulus (GPa)	Yield Strength (MPa)	Ultimate tensile strength (MPa)	Shear modulus (GPa)	Total Elongation (%)	Formability^a^,^b	Joinability^a	Paintability^a	Corrosion resistance^a	Wear resistance^a	Thermal performance^a	Resource scarcity index	Water usage (L/kg)	Life cycle energy (MJ/kg)	Life cycle CO2 footprint (kg/kg)	Recycle fraction (ψ), %	Crashworthiness^a	Health and Wellness^a
Direction of improvement	↓	↓	↑	↑	↑	↑	↑	↑	↑	↑	↑	↑	↑	↓	↓	↓	↓	↑	↑	↑
Carbon steel AISI 1015 (as rolled)	7.87	25.36	210.00	312.50	420.00	81.50	39.00	0.80	0.90	0.90	0.70	0.80	1.00	0.000	0.227	0.719	45.75	6.75	0.45	90.00
Carbon steel AISI 1015 (annealed)	7.87	25.09	210.00	285.00	387.50	81.50	37.00	0.80	0.90	0.90	0.70	0.80	1.00	0.100	0.210	0.726	45.75	6.95	0.45	90.00
Carbon steel AISI 3140	7.87	25.09	210.00	440.00	700.00	80.00	25.00	0.80	0.90	0.90	0.70	0.80	1.00	0.100	0.378	0.726	45.75	6.95	0.45	90.00
Dual Phase steel 280/600	7.87	25.24	210.00	280.00	600.00	80.00	34.00	0.60	0.80	0.90	0.70	0.80	1.00	0.000	0.524	0.726	45.75	6.95	0.45	90.00
HSLA 462/524	7.87	25.08	210.00	462.00	524.00	80.00	40.00	0.70	0.80	0.90	0.90	0.80	1.00	0.000	0.283	0.726	45.75	6.95	0.45	90.00
Martensite steel 950/1200	7.87	25.26	210.00	950.00	1200.00	80.00	7.00	0.40	0.70	0.90	0.90	0.80	1.00	0.000	0.649	0.726	45.75	6.95	0.45	90.00
Stainless steel AISI 201; Austenitic	7.87	29.85	197.00	845.00	1120.00	77.50	15.00	0.50	0.70	0.80	0.90	0.90	1.00	0.000	0.605	0.596	224.50	7.88	0.55	90.00
Stainless steel, ferritic, AISI 405	7.72	27.37	200.00	223.00	448.00	78.00	21.00	0.50	0.70	0.80	0.90	0.90	1.00	0.000	0.242	0.730	224.50	6.65	0.45	90.00
Aluminium alloy AA5005	2.70	25.93	71.30	145.00	160.00	26.00	11.00	0.60	0.50	0.80	0.90	0.60	1.00	0.008	0.087	0.908	992.50	5.14	0.36	95.00
Aluminium alloy AA2424	2.78	25.29	70.00	79.00	185.00	27.00	20.00	0.70	0.50	0.80	0.90	0.60	1.00	0.008	0.100	1.000	992.50	4.60	0.33	95.00
Aluminium alloy AA6060	2.70	25.93	70.00	90.00	160.00	26.00	20.00	0.70	0.50	0.80	0.90	0.60	1.00	0.008	0.086	0.950	992.50	4.93	0.34	95.00
AZ61 Mg alloy	1.80	28.55	45.00	193.50	295.00	17.00	12.00	0.40	0.40	0.70	1.00	0.60	1.00	1.00	0.159	0.766	3750.00	5.90	0.42	95.00
Mg–Li(12%) as cast	1.77	32.41	45.50	70.00	150.00	17.50	8.00	0.40	0.40	0.70	1.00	0.60	1.00	1.00	0.081	0.882	4950.00	5.27	0.37	95.00
Ti/3Al/8 V/6Cr/4Zr/4Mo	4.80	98.02	103.00	1130.00	1220.00	38.00	9.00	0.60	0.50	0.70	0.90	0.90	1.00	0.00	0.659	0.431	1000.00	11.00	0.75	80.00
Epoxy-carbon fibre (SMC)	1.55	47.43	100.00	250.00	300.00	50.00	3.00	0.80	0.70	0.30	0.30	0.70	0.80	1.00	0.162	0.209	865.50	19.35	1.56	0.00
High-strength C- fibre/epoxy composite, 0° unidirectional lamina	1.55	68.43	140.00	550.00	1850.00	5.00	1.30	0.80	0.70	0.30	0.50	0.70	0.80	1.00	1.000	0.209	865.50	19.35	1.56	0.00
High-strength C- fibre/epoxy composite,90° unidirectional lamina	1.55	68.43	8.50	45.00	32.00	5.00	0.55	0.80	0.70	0.30	0.50	0.70	0.80	1.00	0.017	0.209	865.50	19.35	1.56	0.00
High-strength C- fibre/epoxy composite, Isotropic	1.55	68.43	55.00	300.00	300.00	20.00	0.35	0.70	0.70	0.30	0.50	7.00	0.80	1.00	0.162	0.209	865.50	19.35	1.56	0.00
Epoxy-glass fibre (SMC)	1.65	29.45	20.70	151.50	190.00	8.00	1.25	0.80	0.70	0.30	0.30	0.70	0.30	1.00	0.103	0.209	207.50	19.35	1.56	0.71
High strength glass fibre composite (GF 40–60%), unidirectional lamina	1.78	45.04	40.00	700.00	700.00	16.55	2.50	0.60	0.70	0.30	0.30	0.70	0.40	1.00	0.378	0.209	207.50	19.35	1.56	0.71
S-Glass Fibre/epoxy composite, 0/90° biaxial lamina (30–60%GF)	1.86	54.64	26.40	455.50	455.50	4.90	1.78	0.70	0.70	0.30	0.30	0.70	0.30	1.00	0.246	0.209	207.50	19.35	1.56	0.71

^a Indicates factors that are fuzzy in nature and where fuzzy logic were used to transform these characteristics into fuzzy numbers.

^b Formability is defined as the ability of making complicated shapes using designated material.

Step 2: Score a set of 21 candidate materials that are commonly used in automotive applications; these scores have been collected from different sources and stored in the same table for further analysis (CES 2008; Davies 2004; Mayyas, Qattawi, and Omar 2012; Mayyas et al. 2012). In this study, eight classes of engineering materials have been considered, namely: forming grade steels, advanced high strength steels, aluminium alloys, magnesium alloys, titanium, and carbon fibre-reinforced plastics (CFRP) and glass fibre-reinforced plastics (GFRP).

Step 3: Choose the linguistic ratings and for attributes and weights selection, respectively. The fuzzy linguistic rating ensures that the ranges of the normalized triangular fuzzy numbers belong to [0, 1]. To avoid any bias towards lighter or lower cost materials, thus it is decided to set where all factors get the same weight in the proposed model. Hence, matrix (Equation 11(11) ) is same as matrix (Equation 8(8) )

Step 4: Construct the weighted normalized fuzzy decision matrix (the term ‘fuzzy decision matrix’ here refers to the matrix that has mixed numbers, i.e. fuzzy numbers and numerical values that come from intrinsic materials properties (e.g. density, yield strength, etc.)). The weighted normalized values are obtained using Equation (9(9) ) if the goal is to maximize the selection attribute (e.g. formability and corrosion resistance) and Equation (10(10) ) if the goal is to minimize selection attribute (e.g. density and cost).

Step 5: Identify the set of positive ideal (A*) and negative ideal (A⁻) solutions; for the order of selecting the fuzzy positive ideal solution (FPIS; A⁺) and the fuzzy negative ideal solution (FNIS; A⁻) using Equations (12(12) ) and (13(13) ), respectively. Table 6 summarizes these calculations.

Table 6. Distance () of each sustainability factors i = 1,2, … , 21 from FPIS and FNIS.

Attributes	DIFS (Ai, A*)	DIFS(Ai, A^−)
Density (g/cc)	0.065	0.331
LCCA ($/kg)	0.124	0.484
E modulus (GPa)	0.329	0.013
YS (MPa)	0.512	0.020
UTS (MPa)	0.575	0.010
Shear modulus (GPa)	0.337	0.020
Total elongation (%)	0.441	0.004
Formability	0.262	0.131
Joinability	0.286	0.127
Paintability	0.282	0.094
Corrosion resistance	0.291	0.032
Wear resistance	0.265	0.177
Heat Performance	0.243	0.073
Reserve	0.333	0.000
Safety (crashworthiness)	0.559	0.010
Health and wellness	0.341	0.071
Water usage (L/kg)	0.007	0.732
Energy	0.080	0.338
CO2 footprint (kg/kg)	0.073	0.349
Recycle frac.(ψ), %	0.279	0.000

Step 3.1: Calculate δ-index using Equations 17(17) :(17)

where

Step 6: Calculate distance between δ-index and in weighted fuzzy normalized decision matrix by Equations (11(11) ) and (17(17) ).

Step 7: Calculate the similarity coefficient CC_i from the ideal solutions using Equations 16(16) (Table 7).

Table 7. Relative closeness and rank of all candidate materials.

Material^a	Relative closeness ()	Rank	Group
Carbon steel AISI 1015 (as rolled)	0.569	8	High
Carbon steel AISI 1015 (annealed)	0.582	6	High
Carbon steel AISI 3140	0.614	3	VH
Dual Phase steel 280/600	0.613	4	VH
HSLA 462/524	0.609	5	VH
Martensite steel 950/1200	0.660	1	VH
Stainless steel AISI 201; Austenitic	0.653	2	VH
Stainless steel, ferritic, AISI 405	0.556	10	High
Aluminium alloy AA5005	0.481	14	Low
Aluminium alloy AA2424	0.495	11	Medium
Aluminium alloy AA6060	0.491	12	Medium
AZ61Mg alloy	0.413	18	Very low
Mg–Li (12%) as cast	0.374	21	Very low
Ti/3Al/8V/6Cr/4Zr/4Mo	0.578	7	High
Epoxy-carbon fibre (sheet moulding compound)	0.436	16	Low
High-strength C-fibre/epoxy composite, 0° unidirectional lamina	0.568	9	High
High-strength C-fibre/epoxy composite,90° unidirectional lamina	0.380	20	Very low
High-strength C-fibre/epoxy composite, Isotropic	0.413	19	Very low
Epoxy-glass fibre (sheet moulding compound)	0.427	17	Very low
High strength glass fibre composite (GF 40–60%), unidirectional lamina	0.490	13	Medium
S-glass fibre/epoxy composite, 0/90° biaxial lamina (30–60%GF)	0.446	15	Low

^a HSS: high-strength steel; HSLA: high-strength low-alloy steel; AHSS: advance high-strength steel.

Step 8: Rank the candidate materials relative to their proximity to the ideal solution (i.e. the material with lowest CC_i value gets the rank 1, followed by the second closest value, and so on for other materials). Table 7 shows final CC_i values and ranking of all candidate materials; the relative qualitative ranking of candidate materials is also shown in the last column of Table 7. The classification is based on dividing the span of CC_i into five equal intervals, then grouping the materials into the corresponding cluster (Figure 5).

Figure 5. Relative qualitative ranking of candidate materials.

The distance, i.e. the relative closeness coefficient, and the corresponding ranking of all candidate materials are tabulated in Table 7. Therefore, one can see that the rank of these candidate materials is: Martensite steel followed by austenitic Stainless steel AISI 201, then Carbon steel AISI 3140 in the third position. Table 7 also shows that the first six preferred choices are different grades of steels, which means that steel is still competitive from the sustainability point of view. The second material group that is likely to meet the sustainability goals is the stainless steel; however, aluminium and magnesium alloys get medium relative ranks, which means that aluminium and magnesium alloys have the ability to reduce energy and emissions during the vehicles’ use phase, but they are less preferable from economical and technical point of views (Mayyas et al. 2012). Unsurprisingly, it can be said that plastic-reinforced composites are among the materials that have lower relative scores; making them less preferred from the sustainability perspective due to several reasons; including its high initial cost combined with almost zero recyclability as well as their low durability, low formability and the manufacturing infrastructure needed to form these materials into auto-body panels; these factors might hinder the mass penetration of plastic composites in automotive applications.

Generally speaking, low-density materials such as aluminium, magnesium and reinforced plastic composites have low performance values in terms of their cost, modulus of elasticity, shear modulus, joinability, paintability, heat performance; however, the plastic-reinforced composites also have poor performance in terms of their total elongation, heat resistance, life cycle energy and CO₂ assessments, recycle fraction, and health and wellness (Mayyas, Qattawi, and Omar 2012; Mayyas et al. 2012). Another interesting conclusion can be drawn from correlations between safety (crashworthiness) and yield and ultimate tensile strengths, which show high correlation values, and proves that the crashworthiness is highly dependent on these characteristics. However, this correlation matrix contains several pieces of hidden knowledge and can be used as a tool to extract useful trends and effects between different selection attributes; but it has to be used with caution and only for generalization purposes and not for getting empirical equations among the different selection attributes.

5. Comparison with other multi-attribute decision-making methods

Interestingly enough, it has been found that the relative fuzzy-TOPSIS ranks are in agreement with other ranking methods used previously by authors (Mayyas, Qattawi, and Omar 2012), but with slight changes. These methods include the multi-attribute decision-making tools; namely the analytical hierarchy process (AHP), the quality function deployment (QFD), preference selection index (PSI); principal component analysis (PCA) and clustering method for same set of candidate materials.

The comparison between several decision-making methods (namely QFD, AHP, PSI, PCA and clustering methods) shows that all of these decision-making methods are efficient in terms of selecting sustainable materials for body-in-white, but each one has its own pros and cons as shown in Table 8. For example, quality function deployment (QFD) and analytical hierarchy process (AHP) can assess all alternatives through algorithms that evaluate different alternatives and then ranking them based on their abilities to meet customer expectations. AHP algorithm includes a pair-wise comparison between all of the selection criteria and candidate materials among themselves and among each other which adds a degree of complexity to the computing process. On the other hand, QFD has the ability to translate customer needs into the final product through the technical ranks. Moreover, AHP has the ability to adjust its weights if any inconsistency is found as it has inherited inconsistency checking formulas. However, such inconsistency index could be used in QFD, even though no established role of this inconsistency index is present in the literature.

Table 8. Comparison between several multi-attribute decision-making methods used in the eco-material selection.

Method	Pros	Cons
Analytical hierarchy process (AHP)	Pair-wise comparison between all of the selection criteria and candidate materials allows users in adjusting their relative scoring and tuning up their selection process	Complexity and time associated with assigning scores during pair-wise comparison and then adjusting these scores to get acceptable consistency value
Quality function deployment (QFD)	QFD has the ability to incorporate customer requirements in the product design and then rank these requirements. This allows design team to make changes in the early stage of the design process	Complexity and time associated with assigning weights to all materials with relative to the selection criteria
		Bias towards certain materials as QFD does not have a well-established consistency check
Preference selection index (PSI)	No weighting is necessary to evaluate candidate materials, rather, evaluation is solely made through assessing performance of each alternative by calculating their relative score to the best solution	This method utilizes scaling schemes for qualitative factors, which usually associated with higher degree of bias towards certain materials in the mind of the user
Principal component analysis (PCA)	No weighting is necessary to evaluate candidate materials, rather, evaluation is solely made through assessing performance of each alternative by calculating their relative score to the best solution	Similar to PSI, this method utilizes scaling schemes for qualitative factors, which usually associated with higher degree of bias towards certain materials in the mind of the user
		PCA is considered as advanced statistical method which requires advanced statistics knowledge by users and that might not be the case in most design cases
Cluster analysis (CA)	No weighting is necessary to evaluate candidate materials. This approach groups similar materials together (through sequence of iterative calculations) based on their similarities	Cluster analysis is a sorting method that can be used to classify materials in a qualitative mode and does not give relative ranking for each material within the same group
		CA is considered as advanced statistical method which requires advanced statistics knowledge by users and that might not be the case in most design cases
Fuzzy-TOPSIS	Has the ability to treat qualitative factors in very easy and yet reliable way to avoid any bias from the people towards certain materials	Fuzzy-TOPSIS is considered as artificial intelligence method and most of the classical design teams do not have enough experience in dealing with it

Preference selection index (PSI) and principal component analysis (PCA) are another interesting set of decision-making methods where no weighs are necessary to evaluate selection alternatives; however, these methods can evaluate performance of each alternative by calculating their relative score to the best solution (best solution is calculated based on the highest value of each selection criteria). The good thing in using PSI and PCA decision-making methods is the bias-free calculation algorithms where no weights or judgments are required by designer to perform the calculations. Similarly, fuzzy-TOPSIS is another efficient decision-making method that can be used to evaluate different alternatives and compare them to the ideal solution; however, this method may require some weighting inputs from designer which may create a kind of bias towards some alternatives over other alternatives. This bias can be eliminated by assigning same weight to all selection criteria as we have done in this study.

Generally speaking, all of the above-mentioned decision-making methods are efficient tools for eco-material selection and give similar results. Even though some deviations in the rank were found among these methods, but still within acceptable level. This means that as many candidate materials considered in the selection process, slight change in rank would arise due to weights assigned by different persons. Another issue in using some of these methods (e.g. QFD, PSI and PCA) is that no typical scaling has been established so that scaling can be subjective. This subjectivity can limit the discriminating ability of these methods; for instance, one might use a scale from 1 to 3 and another from 1 to 5. This variation can be avoided using a wide range scale (e.g. 1–10 scale as that one used in AHP). Besides that, bias arises when dealing with such tools can be avoided by establishing a customer-oriented questionnaire and by incorporating a team that has members from engineering, marketing, research and development departments in the firm.

Results of these MADM methods are summarized in Table 9 which summarizes the first six ranked materials that can meet most of the sustainability attributes without compromising functionality of the auto-bodies, and hence perform better from sustainability point of view.

Table 9. Ranking of the first six materials using several multi-attribute decision-making methods used in the eco-material selection for auto-bodies.

Method	First ranked materials^a
Analytical hierarchy process (AHP)	AHSS Martenistic 950/1200
	Carbon steel AISI 1015 (annealed)
	HSS AISI 3140
	HSLA 462/524
	Carbon steel AISI 1015 (as rolled)
	High-strength Carbon fibre/Epoxy composite (0° unidirectional lamina)
Quality function deployment (QFD)	AHSS Martenistic 950/1200
	HSS AISI 3140
	HSLA 462/524
	Carbon steel AISI 1015 (annealed)
	Carbon steel AISI 1015 (as rolled)
	Dual phase steel 280/600
Preference selection index (PSI)	HSLA 462/524
	Carbon steel AISI 1015 (annealed)
	Carbon steel AISI 1015 (as rolled)
	Dual phase steel 280/600
	Carbon steel AISI 3140
	Martensite steel 950/1200
Principal component analysis (PCA)	HSLA 462/524
	Carbon steel AISI 1015 (annealed)
	Carbon steel AISI 1015 (as rolled)
	Dual phase steel 280/600
	Carbon steel AISI 3140
	Martensite steel 950/1200
Cluster Analysis (CA)	Advanced high strength steels, Carbon steels, Aluminium alloys
Fuzzy-TOPSIS	AHSS Martenistic 950/1200
	Stainless steel AISI 201; Austenitic
	Carbon steel AISI 3140
	Dual phase steel 280/600
	HSLA 462/524
	Carbon steel AISI 1015 (annealed)

^a HSS: high-strength steel; HSLA: high-strength low-alloy steel; AHSS: advance high-strength steel.

6. Conclusions

This study discussed a sustainability model for eco-material selection as applied to the automobiles’ body panels; using the fuzzy TOPSIS approach. The fuzzy-TOPSIS output can be used to rank candidate materials so that it meets a set of sustainability indices, without compromising its functional or technical requirements. This study also reinforced the rank of the different steel grades as best choice for automobile load bearing panels; thusly explaining the growing trends of alloying even stronger steel grades such as the ultra-strong high-strength steels and its different deviations including; the dual phase (DP), the transformation-induced plasticity (TRIP) and complex phase (CP) steels.

Because of the dual qualitative and quantitative natures of the sustainability characteristics, the fuzzy logic seems to be an efficient tool to integrate the qualitative factors along with numerical values of the quantitative characteristics into a TOPSIS model (Technique for Order Preference by Similarity to Ideal Solution). This manuscript showed that TOPSIS and fuzzy logic can aid the material selection process to translate the design goals and parameters into usable numbers; that in turn can be used to rank candidate materials in their closeness to an ideal solution. Additional novelty of the proposed approach is in using the fuzzy-TOPSIS as a scoring tool without assigning weights for different selection attributes; in order to avoid any bias typically associated with classical multi-attribute decision-making methods like quality function deployment, analytical hierarchy process, digital logic, etc.

Future work of this paper will cover integration of fuzzy-TOPSIS with other multi-attribute decision-making methods like AHP and QFD. Also, we will use fuzzy-TOPSIS model as the main approach in developing knowledge-based system as fuzzy-TOPSIS seems to be more efficient than other multi-criteria decision-making methods in coding qualitative and quantitative factors. Future work may be also expanded to include more sustainability factors to evaluate their effect on the overall eco-material selection process.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This study has been supported by the Masdar Institute of Science and Technology Research.