**Comparative Evaluation of Sustainable Design Based on Step-Wise Weight Assessment Ratio Analysis (SWARA) and Best Worst Method (BWM) Methods: A Perspective on Household Furnishing Materials**

#### **Sarfaraz Hashemkhani Zolfani <sup>1</sup> and Prasenjit Chatterjee 2,\***


Received: 17 December 2018; Accepted: 5 January 2019; Published: 10 January 2019

**Abstract:** For a few years, there has been an increasing consciousness to design structures that are concurrently economic and environmentally responsive. Eco-friendly inferences of building designs include lower energy consumption, reduction in CO2 emissions, assimilated energy in buildings and enhancement of indoor air quality. With the aim of fulfilling design objectives, designers normally encounter a situation in which the selection of the most appropriate material from a set of various material alternatives is essential. Sustainability has been developing as a new concept in all human activities to create a better balance between social, environmental and economic issues. Designing materials based on the sustainability concept is a key step to enable a better balance because there is no need to re-structure phases and procedures to make the system more efficient in comparison to previous models. Some of the most commonly used materials are household furnishing materials, which can be electrical devices, kitchen gears or general furnishing materials. The volume of production and consumption of these materials is considerable, therefore a newer sustainable plan for a better designed system is justifiable. In the literature, the application of multi-attribute decision-making (MADM) methods has been found to be very suitable for evaluating materials and developing general plans for them. This study contributes by applying two approaches based on MADM methods for weighting the criteria related to the sustainable design of household furnishing materials. Step-Wise Weight Assessment Ratio Analysis (SWARA) and Best Worst Method (BWM) are two specialized and new methods for weighting criteria with different approaches. This paper has not only investigated the weighting of important and related criteria for sustainable design but has also evaluated the similarities and differences between the considered weighting methods. A comparative study of SWARA and BWM methods has never been conducted to date. The results show that, except pairwise comparisons, SWARA and BWM are certainly similar and in some cases SWARA can be more accurate and effective.

**Keywords:** sustainable design; household furnishing materials; multi-attribute decision-making (MADM); step-wise weight assessment ratio analysis (SWARA); Best Worst Method (BWM)

#### **1. Introduction**

Rapid movements of a large number of populations from rural to urban areas and socio-economic changes that transform the agricultural human society into an industrial society, involving the extensive economic re-organization intensify the rate of resource deficiency and ecological contamination globally. Due to uncontrolled urbanization, environmental degradation has been occurring very quickly, causing land insecurity, water quality degradation and air and noise pollution, along with severe waste disposal

issues. However, due to urbanization and economic globalization, the manufacturing and construction industries are becoming the fastest developing sectors everywhere. Superior financial affordability of consumers led to an increased requirement for improved life, better aesthetics and comfort level, which ultimately asserts high demands for the interior features in terms of artifact materials [1]. Interior designers have incredible influence by deciding the types of materials and products to be used to make a viable, endurable and ecologically-clean living environment. A home designed for energy efficiency will have the advantage of the site, sunlight and natural breezes. Conventionally, the interior designing job has been confined to conformist practice, focusing only on style and extravagant design while ignoring energy savings, toxic emissions, the harmful effects on customers' psychophysical health, and environmental pollution. However, recent trends in interior design have seen a spectacular move towards design policies that not only focus on the creation of art, beauty and taste, but also a healthy and sustainable environment for consumers to live and work in [2]. Thus, sustainability is a big trend in today's construction industry for energy use, resource efficiency, material selection, safety and life-cycle management, for developing an environmentally responsible environment.

Green or sustainable household furnishing material selection plays a considerable role in the entire interior design process to ensure better product performance and diminished life-cycle impact to the surroundings and individuals' health. Green or sustainable household furnishing materials generally refer to all the physical substances that are accumulated to craft the building interior. The primary advantages of using sustainable household furnishing materials in indoor environments are the reduction of health costs, increased employee productivity in work areas and greater shrinkage in operation and maintenance costs. In addition, these materials also help to reduce the adverse impacts associated with their processing, fabrication, installation, recycling and removal. Today, most buildings are constructed from a variety of materials that have specific functionalities and multipart assembly requirements. However, selecting the most appropriate decoration material for a particular industrial application, considering multi-perspective criteria, is not an easy task and is a great challenge for the interior decorators. Architects need to consider a range of selection criteria including some basic requirements like visuals, acoustic, tactile along with environmental requirements including energy consumption, low carbon emission features, recyclability and regional reachability, reduction of cost, meeting legal requirements, accounting for operating conditions and making the new product more competitive. There are a number of reasons for the evaluation and selection of the best suited material for a given case study. These include making improvements in service performance, reduction of cost, meeting the new legal requirements, accounting for the operating conditions, making the new product more competitive, to name a few [3]. On the other hand, inappropriate material selection frequently leads to early product failure with reduced efficiency, recurrence of processes, substantial financial loss and pitiable product performance, there by negatively affecting the output, effectiveness, environment and status of the organization.

Under these circumstances, a mechanism is required to explore the alternative candidates and identify the best one. Although sustainable design has become a leading concern in the interior design business, evaluation and selection of sustainable materials in real practice is limited due to the complexities involved. The optimal solution must satisfy the decision maker's (DM's) objectives, which are often conflicting in nature. For this purpose, the DMs need to deal with a large amount of data to arrive at the decision with the most consensus. The complexity of an engineering difficulty can be eased with the development of a well-structured decision-support tool that can deliberate multiple conflicting criteria [4]. The existing literature is flooded with numerous applications of classical and trial and error-based methods while many engineering industries are reforming their evaluation and measurement systems by adopting advanced decision-making methodologies. A multi-attribute decision-making (MADM) method can thus be a useful approach to the process of material assessment and selection [5]. The MADM methods have the potential to determine a ranking pre-order of the considered material alternatives from the first ranked to the last ranked in the presence of several mutually confounding properties. As all MADM problems include multiple criteria that have different

importance levels due to the preferences of the DMs, the determination of criteria weights is one of the significant issues. The problem of choosing an appropriate technique for estimating criteria weights is very important as this directly affects the outcome of the entire evaluation and selection process. That is why numerous weight elicitation methods have been developed in order to confront this cognitive issue. The purpose of this paper is to compare the results of variability between the criteria priorities for Stepwise Weight Assessment Ratio Analysis (SWARA) and Best-Worst Method (BWM) for weight elicitation and to make suggestions about the conditions of using these two methods for sustainable material selection problems. It is the first time that SWARA is compared with BWM, and this makes the study different and unique.

The paper is organized as follows: Section 2 presents the literature review on sustainable material selection; Section 3 presents the research gap; in Section 4, detailed mathematical formulations of the considered methods have been presented; a comparative study between the considered methods for a sustainable household furnishing material selection problem has been discussed in Sections 5 and 6 concludes the paper.

#### **2. Literature Review**

Numerous studies have already been directed in addressing material selection problems using different ranking and optimization techniques. However, the literature shows many fewer works that deal with the problems on green materials' selection, particularly, there is no convincing ground of scientific research on comprehensive and holistic approaches used by design engineers for the assessment of household furnishing materials [6]. Thus, the aim of this section is to study past research on sustainable material selection to understand their weaknesses and enable the DMs to reduce subjectivity and uncertainty to ensure clearer support for a strong framework. Some basic models like the Leadership in Energy and Environmental Design (LEED), an extensively deployed building assessment system and Building Research Establishment Environmental Assessment Methods (BREEAM), the foremost sustainability evaluation strategy are vastly used for materials assessment and performance prediction. The LEED system boosts the utilization of materials that have a good amount of recycled content, fast renewable periods, accountable garnering management, low poisonous substance and proper solar reflectance and emissivity indices. Whereas the BREEAM system evaluates the environmental impacts of various construction materials and considers environmental issues. User-defined weighting is also incorporated to derive the values of different environmental impacts. However, due to the lack of flexibility and requirement of superior technical expertise, the use of LEED and BREEAM systems are limited and most designers and architects select such materials based on their past knowledge, experience and perception, thereby limiting the practical applications and result in considerable disappointment. Also these tools are only environment conscious and neglect economic and social concerns when selecting materials. Castro-Lacouture et al. [7] projected a mixed integer optimization (MIO) model incorporating different constraints to maximize the values achieved in the LEED rating system. Zhou et al. [8] developed a multi-objective optimization (MOO) model for sustainable material selection through an integrated artificial neural network (ANN) and genetic algorithm (GA) approach while considering mechanical properties, process, cost, performance and environment related factors. Rahman et al. [9] employed the technique of ranking preferences by similarity to the ideal solution (TOPSIS) method to develop an integrated model for optimizing the roof material selection process. Maniya and Bhatt [10] advocated the use of a preference selection index (PSI) method to search for an appropriate material that fits with the engineering requirements. Akadiri et al. [11] presented a fuzzy extended analytical hierarchy process (FEAHP) for building material selection. Florez and Lacouture [12] explored the applicability of a MIO framework while considering the potential impact of cost constraints, design considerations; environmental requirements along with some subjective factors to help the DMs in selecting the best green material for construction projects. Baharetha et al. [13] highlighted that durability, reuse, efficient energy usage, maintainability and lower negative environment impacts are the predominant factors for a sustainable material

selection process. Ribeiro et al. [14] suggested a comprehensive life cycle assessment (LCA) model for four commercial biodegradable polymers. Hosseinijou et al. [15] proposed social-LCA process for building material selection. The proposed methodology was also capable for comparative products assessment. Van der Velden et al. [16] employed a material selection model based on LCA for a wearable smart textile device to promote sustainability while considering resource diminution cost, carbon footprint and human health as the major indicators. However, LCA is very intricate to implement in real life applications, attributable to the complexities involved in data acquisition and data quality control. Zhao et al. [17] used an integrated MADM approach encompassing AHP and Grey relational analysis (GRA) methods for sustainable design of a plastic pipe. Ma et al. [18] used a combined Entropy, TOPSIS and LCA approach for an automotive material selection application. Bhowmik et al. [19] also adopted Entropy-TOPSIS model to evaluate energy-efficient materials considering some predefined material properties. Criteria weights were calculated using the Entropy method, whereas TOPSIS was applied to rank the alternative materials.

The material selection process frequently considers some archetypal factors like light weight, economic manufacturing, product function, quality, performance and aesthetics and customer satisfaction. Less attention has been paid to the environmental and social impacts of the building materials. Nowadays, the advancement of the material selection process has moved towards social and sustainable criteria. Even though the principal material selection is the same for both sustainable and regular materials, the presence of a diverse range of criteria makes the selection process quite complex and time consuming. Table 1 shows that criteria for selecting sustainable materials can be grouped into three major dimensions or criteria levels. The first dimension (economic sustainability) indicates planned designs, which can avoid the requirements of major future restorations and thus reduce costs associated with energy use, water use and maintenance. The second dimension (social sustainability) mainly helps to prevent injuries through incorporating built-in safety attributes to provide adjustability and consolation for people of alternative capabilities in distinct life phases. The third and last dimension (environmental sustainability) is intended to reduce greenhouse gas emissions, proper utilization of water and energy along with reduced waste. However, the relative significance of these attributes is very challenging to estimate.


**Table 1.** Comprehensive list of sustainable material selection criteria.


**Table 1.** *Cont.*

#### **3. Research Gap**

By summarizing and exploring the existing literature, two major conclusions can be drawn. First of all, a comprehensive hierarchical structure for sustainable material criteria has never been developed by the earlier researchers and also several social and environmental dimensions have been overlooked. Secondly, for estimating criteria weights for sustainable material selection issues, previous studies have mainly adopted the Entropy and AHP methods for different assessment rationales [11,17–19]. However, a weighting method like AHP uses pairwise comparisons for preference input and it is based on the DM's knowledge about the problem. DMs usually have different persuasion, background, and knowledge levels and can hardly arrive at conformity on the relative importance of criteria which ultimately lead to deviations of criteria weights due to the involvement of subjective factors. While the objective weighting method, Entropy, is based on inherent criteria information, which has the ability to reduce man-made errors and make results in more accord with facts. The smaller the entropy value is, the smaller the disorder degree of the system is small. The Entropy method is particularly suitable for those situations in which either decision matrix is purely cardinal, or the ordinal values are converted to the comparable numbers or appropriate scales.

Since criteria weight has an enormous influence on the outcome of any MADM method, the sole pivotal dilemma is to evaluate the weights of different material characteristics. Additionally, the rationality of the weight estimation has an evidential effect on the consistency and precision of the computational results. Therefore, there is a need for an unambiguously acceptable methodology to guide the DMs to determine the criteria weights. Thus, this research aims to evaluate the sustainable material selection design and planning more objectively and realistically by introducing a hierarchical structure of the sustainable material selection criteria, as shown in Figure 1.

**Figure 1.** Proposed hierarchical criteria structure for evaluation of sustainable materials.

#### **4. Comparative Methodologies**

MADM has been developing new perspectives and methods. Mostly, new contributions on methods can be categorized in two sections. The first section mainly focuses on developing criteria weighting techniques, while the other section is centering on the ranking of alternatives. The most commonly used methods for estimating criteria weights are AHP (Saaty [41]) and the Analytic Network Process (ANP) (Saaty [42,43]), whereas, among the new criteria weight determination approaches, SWARA (Kersuliene et al. [44]), Factor Relationship (FARE) (Ginevicius, [45]), BWM (Rezaei, [46]), Extended SWARA (Hashemkhani Zolfani et al. [47]), and Full Consistency Method (FUCOM) (Pamucar et al. [48]) are worth mentioning. There are also some studies that focused on the applications of different MADM methods in sustainability challenges and decisions [49–53]. This section highlights some of the key factors for product comparison or selection and provides a tangible basis for fixing priorities with a view to tarnish the environmental footprint of any building. Generically, product-to-product demarcations are likely to be ambiguous when it deals with construction and casing or envelope materials. Product-to-product comparisons are more pragmatic for interior finishes, outfit products and interior decorations. For instance, springy or pliable floor coverings can freely be analyzed and compared with each other as far as installation materials, product cleaning, expected service life and end of a product's life are pondered. Window systems are usually mobilized to a construction site as pre-assembled elements that can be mutually compared in terms of thermal performance and other criteria, without too much regard for eclectic system speculations. However, this strategy will fail when scores are assigned to evaluate building materials in different rating systems. This is due to the fact that material scores germinate from a concurrent apprehension of environmental issues that does not necessarily go with the objective analysis. For example, according scores for recycled content in products presumes reduced environmental hazards. However, it may not always stand practical, and recycling for any specific application may have congenial impacts. It is well established that reuse or recycling can conserve hazardous waste dump, but at the same time, there is a likelihood of consuming more energy and detrimental upsets on air and water quality. The center of interest on recycling defines these unfavorable footprints and utterly gives additional weightage to solid waste and resource depletion issues as compared to global warming traits. Early conceptual design decisions are mostly concentrated to the initial material related environmental consequences of a building due to the considerations of fundamental structure and envelope elements. These are customarily the towering mass elements with remarkable manufacturing and transportation domination. Thus, it makes acceptable perception to allocate higher weightage to the environmental implications of materials at the initiation of the design procedure.

Except SWARA, other methods are based on pairwise comparisons, although there are big differences in the way of calculating the criteria weights. For example, the original BWM method, based on a non-linear model, is used only for the estimation of criteria weights [46,54]. Also, there is a simplified BWM method based on a linear model. SWARA is a policy-based method which works on weighting criteria depending up on their priority. This priority can be arranged by policy makers on the basis of descriptive future scenarios and current regulations and strategic plans [55–58].

BWM and SWARA have similar ideas with different perspectives and have not been reported yet. The notion of identifying the best and worst criterion in the BWM method is very similar to the first step of the SWARA method. When criteria are prioritized on a policy basis, a preference order emerges, which helps in identifying the best and worst criteria. When these two criteria are identified, the same pairwise comparisons as used in the SWARA method are accomplished due to similar expert opinions. BWM somehow is also a link to connect these two perspectives in weighting criteria and this research study attempted to work on this idea to check the results of SWARA and BWM methods in a single framework. During the past few years, there have been a significant number of studies associated with the applications of SWARA and BWM implementations which can be found in References [59,60].

#### *4.1. Best Worst Method (BWM)*

As one of the latest MADM methods, BWM can efficiently tackle the inconsistency derived from pairwise comparisons. This method is more consistent in comparison to the AHP, ANP, FARE and Simple Multi-Attribute Rating Technique (SMART) methods [61,62]. The BWM method has been cited 249 times-based on Google scholar information (until 19 November 2018). BWM has been applied in different studies and fields including supplier selection and development [63]; water management [64]; complex bundling configurations [65]; urban sewage sludge application [66]; social sustainability of

supply chains [54]; measuring logistics performance [67]; identifying success factors [68]; cloud service selection [69]; evaluating university-industry doctoral projects [70].

The structure and basic steps of BWM method is as follows [46,71]:

Step 1: Selecting and identifying criteria in a common way; literature review, expert ideas and other probable ways.

Step 2. Identifying and selecting the best and worst criteria based on experts' ideas and opinions.

Step 3. Designing the preferences matrix based of comparing best criterion over all others by applying numbers ranging between 1 and 9.

$$A\_b = (a\_{1B\_1} a\_{2B\_2} a\_{3B\_3} \dots a\_{nB\_s})\tag{1}$$

Step 4. Designing the preferences matrix based of comparing worst criterion over all others by applying numbers between 1 and 9.

$$A\_b = (a\_{1\heartsuit}, a\_{2\heartsuit}, a\_{3\heartsuit}, \dots, a\_{n\heartsuit}) \tag{2}$$

Step 5. Finding the relative importance of criteria through calculation of final and optimal weights (*w*<sup>1</sup> \* , *w*<sup>2</sup> \* , *w*<sup>3</sup> \* ,... .*w*n \* ) by solving the following optimization model.

$$\text{Minmax}\_{\circ} \left\{ \left| \left( \left( w\_{B} / w\_{\circ} \right) - a\_{B\circ} \right|, \left| \left( w\_{\circ} / w\_{w} \right) - a\_{jw} \right| \right. \right. \tag{3}$$

Subject to ∑ *j wj* = 1

Model (3) can easily be converted to Model (4) to find out the optimal weights (*w*<sup>1</sup> \* , *w*<sup>2</sup> \* , *w*<sup>3</sup> \* , ... .*w*n \* ) and the optimal value of reliability level (*ξ\** ):

$$\begin{array}{l} \text{Min}^{\mathbb{Z}}\_{\mathbb{S}}\\ \left| \begin{array}{l} \frac{w\_{B}}{w\_{j}} - \mathbf{a}\_{Bj} \\ \frac{w\_{j}}{w\_{w}} - \mathbf{a}\_{jw} \end{array} \right| \leq \xi \text{ for all } j\\ \left| \begin{array}{l} \frac{w\_{j}}{w\_{w}} - \mathbf{a}\_{jw} \end{array} \right| \leq \xi \text{ for all } j\\ w\_{j} = 1 \end{array} \\ w\_{j} \geq 0 \text{ for all } j \end{array}$$

where *wB* and *ww* indicate the weights of the best and the worst criteria respectively. a*Bj* is the preference of the most important (best) criterion over criterion *j* and a*jw* is the preference of criterion *j* over the least important (worst) criterion.

Step 6. Estimating the consistency ratio (*Ksi*) to verify the reliability level of the pairwise comparisons using Equation (4).

Similar to the AHP method, a consistency index (*CI*), as shown in Table 2, helps to determine the *Ksi* value. A smaller *Ksi* value (close to zero) indicates superior consistency, whereas, a higher *Ksi* value (close to one) indicates inferior consistency made during pairwise comparisons [46].

$$K\_{\rm si} = \frac{\xi^\*}{\underline{\dot{C}}I} \tag{4}$$


aBW in Table 2 indicates the preference of the best criterion over the worst criterion. It is important to mention that *CR* in the AHP method is basically used to substantiate the validity of comparisons, but in BWM, its main function is to find the degree of reliability of the pairwise comparisons, thus provides more conformable results. Also, BWM employs many fewer comparisons (2n − 3) by forming comparison-vectors. This phenomena assures more reliability of the weights obtained by BWM as compared to the weights of AHP method. These advantages of BWM method have led the foundation of selecting it for sustainable material selection assessment. In addition to this, in BWM, no fractional numbers are used which makes the computation easier for the DMs. Rezai [46,71] statistical validated that BWM computes criteria weights appreciably better than AHP in terms of *CR*, total divergence and agreement.

#### *4.2. Step-Wise Weight Assessment Ratio Analysis (SWARA)*

In this method, DMs have an essential portrait of evaluations and calculation of criteria weights. The basic characteristic of this method is the assessment of expert opinion on the importance of the considered criteria for estimating their weights. Experts select the importance of each criterion and rank them in order of preference by employing their inherent experience, understanding and information. Based on this method, criterion having the highest importance is given rank 1, while the criterion with the least importance attains the last rank. The overall ranks to the group of experts are determined according to the average values. Based on Google scholar information, this method (Kersuliene et al. [44]) has been cited 210 times (until 13 December 2018). The application of the SWARA method has been developing and some of latest studies based on the SWARA method application include the evaluation of chemical wastewater purification [72]; investigating supply chain management competitive strategies [73]; evaluating construction projects [74]; flood susceptibility assessment [75]; sustainable third-party reverse logistics provider evaluation [76]; pharmacological therapy selection [77]; assessment of the railway management [78]; competency-based IT personnel selection [79].

SWARA steps are summarized as follows [80–82]:

Step 1. Sorting of criteria based on policy and expert opinion or some standards.

Step 2. Providing relative importance between criteria:

Initiating from the second criterion, experts exhibit the corresponding importance of *j* th criterion in congruence with the previous (*j* − 1) criterion through comparative importance of average value (*sj*) ratio.

Step 3. Computation of coefficient *kj*:

$$k\_{\hat{j}} = \begin{cases} 1 & j = 1 \\ s\_{\hat{j}} + 1 & j > 1 \end{cases} \tag{5}$$

Step 4. Determination of recalculated weight *wj*:

$$w\_j = \begin{cases} 1 & j = 1\\ \frac{x\_{j-1}}{k\_j} & j > 1 \end{cases} \tag{6}$$

Step 5. Calculation of final criteria weights:

$$q\_{\dot{j}} = \frac{w\_{\dot{j}}}{\sum\_{k=1}^{n} w\_{\dot{j}}} \tag{7}$$

#### **5. Comparative Results**

This research focuses on a comparative study on criteria weight estimation using SWARA and BWM methods for sustainable household furnishing material selection problem. This part is designed according to the available literature and adopted methodologies to assess the outputs of SWARA and BWM methods. Accordingly, five experts with at least five years of experience have been selected. To be very specific, as the main intention of this comparative analysis is to check the model of thinking of the DMs for the two different weight elicitation methods; therefore, questionnaires of SWARA and BWM methods were delivered to the experts at the same time. The most critical points of their ideas have been presented in the Appendix A. In brief, all five experts had to answer the questionnaires at the same time, but they could select one to answer first. Also, they had the opportunity to change their opinions after finishing the first questionnaire if required. Sustainable development needs a great balance between its economic, social and environmental dimensions, therefore, the proper integration between these three dimensions is an imperative need for policy-making. The main idea is to meet the boundaries and the best scenario which is aligning with 2030 agenda for sustainable development and 17 related goals [83].

Eventually, economic dimension received a weight of 0.333, social dimension received a weight of 0.333 and environment dimension received a weight of 0.334 and final weights of the sub-criteria under the three dimensions have been calculated and tabulated. The final results based on each sustainable material selection dimension are presented below. Detail calculations of SWARA and BWM methods have been added in the Appendix B.

#### *5.1. Economic Dimension*

In this section, final weights for main economic dimension as calculated using the SWARA and BWM methods-based on the opinions of the five experts are first presented in Tables 3–7 respectively. Computations of final weights based on each expert's idea are presented separately as this study intents to analyze the similarities and differences of the two above mentioned methods. From Tables 3–7, it is observed that there are no differences in sub-criteria priorities in the SWARA and BWM methods for economic dimension. In both the cases, C1-1 (initial costs) and C1-4 (maintenance cost) emerge out as the most and least important criteria under economic dimension.


**Table 3.** Final weights of economic dimension based on comparative study (Expert 1).

**Table 4.** Final weights of economic dimension based on comparative study (Expert 2).


Weight C1-1 C1-2 C1-3 C1-4 C1-5 C1-6 SWARA 0.075 0.068 0.043 0.037 0.059 0.051 BWM 0.125 0.078 0.026 0.014 0.052 0.039 Priority based on SWARA 1 2 5 6 3 4 Priority based on BWM 1 2 5 6 3 4 *Ksi* (BWM) 0.089

**Table 5.** Final weights of economic dimension based on comparative study (Expert 3).

**Table 6.** Final weights of economic dimension based on comparative study (Expert 4).


**Table 7.** Final weights of economic dimension based on comparative study (Expert 5).


#### *5.2. Social Dimension*

Similar to the economic dimension, calculations and final weights of all sub-criteria in social dimension are exhibited in Tables 8–12 which reflect no alterations in the priorities of the different sub-criteria under this dimension, as opined by the five experts. These tables also indicate that among the four sub-criteria, C2-1 (safety and security) becomes the most prominent criteria, whereas C2-4 (functionality) is the least important criteria.

**Table 8.** Final weights of social dimension based on comparative study (Expert 1).



**Table 9.** Final weights of social dimension based on comparative study (Expert 2).

**Table 10.** Final weights of social dimension based on comparative study (Expert 3).


**Table 11.** Final weights of social dimension based on comparative study (Expert 4).


**Table 12.** Final weights of social dimension based on comparative study (Expert 5).


#### *5.3. Environmental Dimension*

Finally, the necessary information and final weights based on both the BWM and SWARA methods for the considered sub-criteria of environmental dimension are presented in Tables 13–17. It is observed that that there are no considerable differences in the sub-criteria priorities as provided by the group of experts through the SWARA and BWM methods. It is also perceived that C3-6 (decomposition) and C3-7 (upgrades possibility) criteria received the maximum and minimum weights respectively.

**Table 13.** Final weights of environment dimension based on comparative study (Expert 1).


**Table 14.** Final weights of environment dimension based on comparative study (Expert 2).


**Table 15.** Final weights of environment dimension based on comparative study (Expert 3).


**Table 16.** Final weights of environment dimension based on comparative study (Expert 4).


**Table 17.** Final weights of environment dimension based on comparative study (Expert 5).


#### **6. Discussion and Conclusions**

Conventional engineering optimization and statistical approaches are applied often on the basis of a well-developed and structured problem. Solution of engineering problems with only one objective or criterion is very easy to acquire, however, most of the real life problems consist of conflicting objectives and multiple criteria, making the process more perplexed and time consuming. It is well accepted that the weight calculation methods used for solving different MADM problems have a vital contribution to defining the criteria importance and obtaining the best and satisfying results for the DMs. In this paper, two different approaches—namely SWARA and BWM—with similar methodological structures have been adopted for computation of criteria weights for sustainable housing material selection design. The main idea is to see the differences in results. In this regard, five separated ideas based on expert opinion have been compared directly. Accordingly, after finishing the questionnaires by the experts, authors examined the general inklings of them about the two different questionnaires. In SWARA method, experts have more options to show the weightage of each criterion in comparison to the other more important criteria. The DMs can probably have a clearer idea about what they want to demonstrate in terms of criteria weights. BWM first identifies the most preferable and the least favorable criteria to make pairwise comparisons between each of them and the other considered criteria. Finally, it solves a linear optimization model to deduce the criteria weights. In BWM, the DMs probably follow the same structure as SWARA specially when there are not so many criteria for evaluation. This research is carried out with specific goals, descriptions and surveys since it endeavors to reckon the key elements in sustainable housing material evaluation process development. Moreover, in real time situations, DMs or the experts have limited domain of knowledge and expertise to present and express their ideas precisely. In case of having so many criteria, it will be certainly complicated to express the differences and priorities based on some linguistic variables or qualitative numbers. In brief, it can be said that although SWARA and BWM have different mathematical approaches, there are some similarities between them and there are some advantageous in SWARA method when the general approach (pairwise comparison or policy based) is not a big challenge and deal. SWARA and BWM methods more preferable than the AHP method which requires n(n − 1)/2 pairwise criteria comparisons, thus complicating the application of this method. Especially, when the number of criteria is large, it becomes practicality unfeasible to perform such huge consistent pairwise comparisons in the AHP method. Also, as mathematical transitivity in the pairwise criteria comparisons is extremely important to consider the deviation from transitivity results in an increase in inconsistency in case of AHP method. However, the major issue in any decision-making process is not only finding the best alternative or criteria priorities, rather more emphasis should be given on appropriately guiding the DMs toward identifying the critical components, and proper structuring of the problem considering relevant criteria and decision alternatives. Therefore, the establishment of a comprehensive appraisal system and defining crucial decision-making points is an important and necessary step. As in this paper, equal weights for the three major three sustainable dimensions have been assumed which may also be changed as per the requirements of the DMs and the effects may also be observed in further research. Furthermore, comparative studies with other weight elicitation approaches like decision making trial and evaluation laboratory (DEMATEL), the resistance to change method and full consistency method (FUCOM) may be carried out for exploration of knowledge-base.

**Author Contributions:** Main idea, conceptualization, methodology, identifying criteria, interviews, appendix, calculations, discussion and editing and writing–original draft by S.H.Z.; Introduction, literature review, research gap, conclusion, editing and writing-original draft by P.C.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

#### **Experts' opinions:**

#### **Expert 1**

It feels like this research is doing something similar. The idea is tricky and hard to say whether the idea is completely same or not, but it seems for comparing limited criteria, one has to follow the same route. It is hard to say someone will do it for 100% but definitely for limited criteria, it should be common.

#### **Expert 2**

It seems you have two different perspectives which can lead you to a wider area. It is harder to make a proper decision in complex and larger problems based on pairwise comparisons. I think normal decisions aren't challenging and both ideas are really practical and helpful. When you have more chance to show that the exact differences of criteria, I guess you can manage a better decision while pairwise comparison is also interesting.

#### **Expert 3**

In the case of creating a ranking for the criteria, I could definitely have enough concentration of the topic and lastly, I knew what probably will happen as results.

#### **Expert 4**

When you have so many criteria, it will be really hard to do a pairwise comparison. You don't have so many differences based on a scale like 1–9.

#### **Expert 5**

Feel more concentrated when you are making decision based on a priority. How can I be sure about my assessment while I just have limited numbers to compare all criteria based on a pairwise comparison.

#### **Appendix B**

#### **Detail calculations:**

#### **Economic dimension:**


**Table A1.** Final weights of economic dimension based on SWARA (Expert number 1).

**Table A2.** Best criterion to other criteria for economic dimension based on BWM method (Expert number 1).



**Table A3.** Other criteria to the worst criterion for economic dimension based on BWM method (Expert number 1).

**Table A4.** Final results and weights of main criteria for economic dimension based on BWM method (Expert number 1).


**Table A5.** Comparative results (Expert number 1).


**Table A6.** Final weights of economic dimension based on SWARA (Expert number 2).


**Table A7.** Best criterion to other criteria for economic dimension based on BWM method (Expert number 2).



**Table A8.** Other criteria to the worst criterion for economic dimension based on BWM method (Expert number 2).

**Table A9.** Final results and weights of main criteria for economic dimension based on BWM method (Expert number 2).


**Table A10.** Comparative results (Expert number 2).


**Table A11.** Final weights of economic dimension based on SWARA (Expert number 3).


**Table A12.** Best criterion to other criteria for economic dimension based on BWM method (Expert number 3).



**Table A13.** Other criteria to the worst criterion for economic dimension based on BWM method (Expert number 3).

**Table A14.** Final results and weights of main criteria for economic dimension based on BWM method (Expert number 3).


**Table A15.** Comparative results (Expert number 3).


**Table A16.** Final weights of economic dimension based on SWARA (Expert number 4).


**Table A17.** Best criterion to other criteria for economic dimension based on BWM method (Expert number 4).



**Table A18.** Other criteria to the worst criterion for economic dimension based on BWM method (Expert number 4).

**Table A19.** Final results and weights of main criteria for economic dimension based on BWM method (Expert number 4).


**Table A20.** Comparative results (Expert number 4).


**Table A21.** Final weights of economic dimension based on SWARA (Expert number 5).


**Table A22.** Best criterion to other criteria for economic dimension based on BWM method (Expert number 5).



**Table A23.** Other criteria to the worst criterion for economic dimension based on BWM method (Expert number 5).

**Table A24.** Final results and weights of main criteria for economic dimension based on BWM method (Expert number 5).


**Table A25.** Comparative results (Expert number 5).


#### **Social dimension:**

**Table A26.** Final weights of social dimension based on SWARA (Expert number 1).


**Table A27.** Best criterion to other criteria for social dimension based on BWM method (Expert number 1).


**Table A28.** Other criteria to the worst criterion for social dimension based on BWM method (Expert number 1).


**Table A29.** Final results and weights of main criteria for social dimension based on BWM method (Expert number 1).


**Table A30.** Comparative results (Expert number 1).


**Table A31.** Final weights of social dimension based on SWARA (Expert number 2).


**Table A32.** Best criterion to other criteria for social dimension based on BWM method (Expert number 2).


**Table A33.** Other criteria to the worst criterion for social dimension based on BWM method (Expert number 2).



**Table A34.** Final results and weights of main criteria for social dimension based on BWM method (Expert number 2).



**Table A36.** Final weights of social dimension based on SWARA (Expert number 3).


**Table A37.** Best criterion to other criteria for social dimension based on BWM method (Expert number 3).


**Table A38.** Other criteria to the worst criterion for social dimension based on BWM method (Expert number 3).


**Table A39.** Final results and weights of main criteria for social dimension based on BWM method (Expert number 3).



**Table A40.** Comparative results (Expert number 3).

**Table A41.** Final weights of social dimension based on SWARA (Expert number 4).


**Table A42.** Best criterion to other criteria for social dimension based on BWM method (Expert number 4).


**Table A43.** Other criteria to the worst criterion for social dimension based on BWM method (Expert number 4).


**Table A44.** Final results and weights of main criteria for social dimension based on BWM method (Expert number 4).


**Table A45.** Comparative results (Expert number 4).



**Table A46.** Final weights of social dimension based on SWARA (Expert number 5).

**Table A47.** Best criterion to other criteria for social dimension based on BWM method (Expert number 5).


**Table A48.** Other criteria to the worst criterion for social dimension based on BWM method (Expert number 5).


**Table A49.** Final results and weights of main criteria for social dimension based on BWM method (Expert number 5).


#### **Table A50.** Comparative results (Expert number 5).


#### **Environmental dimension:**


**Table A51.** Final weights of environment dimension based on SWARA (Expert number 1).

**Table A52.** Best criterion to other criteria for environment dimension based on BWM method (Expert number 1).


**Table A53.** Other criteria to the worst criterion for environment dimension based on BWM method (Expert number 1).


**Table A54.** Final results and weights of main criteria for environment dimension based on BWM method (Expert number 1).



**Table A55.** Comparative results (Expert number 1).


**Table A56.** Final weights of environment dimension based on SWARA (Expert number 2).

**Table A57.** Best criterion to other criteria for environment dimension based on BWM method (Expert number 2).


**Table A58.** Other criteria to the worst criterion for environment dimension based on BWM method (Expert number 2).


**Table A59.** Final results and weights of main criteria for environment dimension based on BWM method (Expert number 2).


**Table A60.** Comparative results (Expert number 2).



**Table A61.** Final weights of environment dimension based on SWARA (Expert number 3).

**Table A62.** Best criterion to other criteria for environment dimension based on BWM method (Expert number 3).


**Table A63.** Other criteria to the worst criterion for environment dimension based on BWM method (Expert number 3).


**Table A64.** Final results and weights of main criteria for environment dimension based on BWM method (Expert number 3).


**Table A65.** Comparative results (Expert number 3).



**Table A66.** Final weights of environment dimension based on SWARA (Expert number 4).

**Table A67.** Best criterion to other criteria for environment dimension based on BWM method (Expert number 4).


**Table A68.** Other criteria to the worst criterion for environment dimension based on BWM method (Expert number 4).


**Table A69.** Final results and weights of main criteria for environment dimension based on BWM method (Expert number 4).


**Table A70.** Comparative results (Expert number 4).



**Table A71.** Final weights of environment dimension based on SWARA (Expert number 5).

**Table A72.** Best criterion to other criteria for environment dimension based on BWM method (Expert number 5).


**Table A73.** Other criteria to the worst criterion for environment dimension based on BWM method (Expert number 5).


**Table A74.** Final results and weights of main criteria for environment dimension based on BWM method (Expert number 5).


**Table A75.** Comparative results (Expert number 5).


#### **References**


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