Sustainable Manufacturing Evaluation Based on Enterprise Industry 4.0 Technologies

Abstract

Most studies in recent decades focused on transforming linear economics into circular through recovering and remanufacturing the products. Circular Economies (CE) aim to minimize the usage of resources by utilizing the waste in production as new or raw materials. Interconnectivity between parties in the industrial system provides decision-makers with rich information and anticipation of failure. Industry 4.0 technologies (I4.0) allow for handling such issues, protecting the environment by utilizing resources efficiently, and restructuring the industry to be smarter as well. This paper contributes to achieving cleaner production (CP), CE, and social for manufacturers through the linkage between 6R methodology with new technologies of I4.0 such as Blockchain technology (BCT) and big data analytical technology (BDA). In this paper, the authors proposed a Multi-criteria decision-making (MCDM) decision framework based on the best-worst method (BWM), Decision-Making trial and evaluation laboratory (DEMATEL), Technique for order of preference by similarity to ideal solution (TOPSIS), and Complex Proportional Assessment (COPRAS). The authors contributed to addressing the weaknesses and problems of these subjective MCDM methods through the cooperation of the neutrosophic theory with the usage of MCDM methods in this work. In the first stage, all criteria that influence sustainable manufacturer selection are specified using literature research on this topic. BWM-based neutrosophic theory was combined to get the criteria’s weights with the aid of DEMATEL-based neutrosophic to obtain the least and best criteria used in BWM in the second stage. The optimal sustainable manufacturer was selected based on TOPSIS and COPRAS under neutrosophic theory in the third and fourth stages, respectively. Furthermore, a case study performed indicated manufacturer 2 (A₂) is an optimal sustainable manufacturer in two ranking methods otherwise, manufacturer 4 (A₄) is the worst sustainable manufacturer. The contribution of this work is to propose a hybrid MCDM with an uncertainty theory of neutrosophic for sustainable manufacturer selection based BDA-BCT with 6R. Sensitivity analyses were carried out to show the decision’s flexibility in various scenarios. Finally, the consequences for management viewpoints were considered.

1. Introduction

Manufacturing enterprises suffer from the continuous pressure of changing manufacturing modalities to remain competitive in the market. Sustainability considers three pillars represented in the triple bottom line (TBL) economic, environmental, and social. The concept of 6R is introduced in [1] and highlights the reducing, reusing, recycling, redesigning, recovering, and remanufacturing activities. In the marketplace, remanufactured goods are sold at lower prices or numerous new product channels in the primary market [2]. Based on [3], implementing 6R enhances the end-of-use product for closed-loop as shown in Figure 1. It shows that implementing 6R leads to CP [3] and CE that support any manufacturer to achieve sustainability of the environment, economy, and society, respectively.

Cleaner Production (CP) [4] aims to increase efficiency during consumption by reducing or recycling waste in all production and operation phases. By adopting CP, the manufacturer in [5] can assess the phases of manufacturing. In (i) the usage of resources and their quality, (ii) the consumed energy, transport, and shipment to transfer products from manufacturing to distribution, (iii) the use of recyclable packaging for products, and (iv) the use of the product after the end of its useful life by recycling.

Circular economy (CE) is the catalyst for economically sustainable manufacturers [6,7]. It aims to optimize the use of resources, which in turn, eliminates waste [5]. Although manufacturers are keen to adopt concepts that contribute to achieving sustainability, they face obstacles. One of these obstacles is their lack of capabilities to take initiatives to upgrade technological processes and make them more competitive in a globalized market [8].

According to [9], I4.0 has contributed to transforming traditional manufacturing into digital and smart manufacturing. I4.0 motivator for the sustainability of CE and CP, social [10] as shown in Figure 2. According to [11] and Figure 2, I4.0 technologies with aides of 6R are contributing to transforming manufacturing approaches from a linear model to CE.

In manufacturing, data must be processed from different sources with real-time transparency and sharing for each partner inside manufacturers. BCT and BDA are I4.0 technologies [12] that can tackle these issues through distributed ledger technology. This ledger is shared by all participants in the manufacturer.

The importance of these technologies in manufacturing sustainability motivates us to apply the method of [13] to analyze research publications about applying BCT and BDA in achieving sustainable manufacturing. The Scopus database is searched for the relevant literature publications from 2017 to 2021. The query for two technologies resulted in 21 publications. These two technologies have been applied since 2017 to transform traditional manufacturing into smart manufacturing for sustainable manufacturing in business and industrial sectors. The number of researchers adopting these technologies in manufacturing and growth in 2018 and 2019 are four and six, respectively. This idea still applied in 2020 and early 2021. However, attention to using two technologies in the manufacturing sector and achieving sustainability is limited.

Therefore, this paper attempts to address the shortcomings of other research regarding adopting the I4.0 technologies in their manufacturing and operation by applying BCT and BDA with 6R for clarification as clarified in Section 3. Consequently, manufacturers who adopt these technologies in their operations should evaluate the effect of their use on achieving sustainability. Evaluation is performed based on methodologies’ criteria, and then the most sustainable one is selected by utilizing MCDM methods.

Many researchers have employed MCDM methods to evaluate the sustainability of manufacturers and then the most sustainable one (i.e., alternative) based on CE, CP, and social pillars are selected [14,15,16]. Generally, ref. [17] divided the methods of calculating weights of determined criteria of achieving sustainable manufacturing into three categories: subjective methods, objective methods, and hybrid methods combining subjective and objective methods.

Another shortcoming that this paper attempts to solve is the inability of MCDM methods to handle vagueness, impreciseness, and ambiguity [18]. This lead to imperfect and indeterminate decisions by experts.

This work contributes to improving and reinforcing these methods by operating them in an environment that can treat such problems and situations these methods suffer from. This environment represents a neutrosophic theory that can absorb various judgments for decision-makers by representing their judgments-based degrees of true, indeterminate, and false. The novelty of our approach appears in

Table 1. Methodologies and flaws of previous research.

Ref#	Methodology	Handling Uncertainty
Jamwal et al. [14]	The authors performed literature about applying various MCDM in sustainable supply chain management (SSCM) for analysis of barriers, challenges, drivers, enablers, criteria, outcomes, and practices of SSCM.	The literature observed that there are missing and limited opportunities in integrating optimization and simulation techniques with MCDM to handle imprecise.
Lin et al. [15]	TOPSIS was refined, and the so-called Non-orthogonal coordinates based TOPSIS (NOC-TOPSIS) was created for prioritizing industrial systems after a life cycle sustainability assessment.	Uncertainty problems could not be discussed in assessing sustainability for industrial systems
Keshavarz-Ghorabaee et al. [16]	Applied MEthod based on the Removal Effects of Criteria (MEREC) is a method of MCDM to determine the weights of criteria.	The scholars focus on a method of calculating weights of criteria, not covering the problem of ambiguity.
Büyüközkan et al. [18]	proposed a decision-making method for evaluating BC as an enterprise platform solution for businesses. The evaluation process performed based on VIKOR	any imprecise or vagueness information leads to incorrect judgments.

where none of the studied literature deals with the problem of uncertainty.

This paper benefits from the integration of BDA -BCT, as technologies of I4.0, with 6R to achieve CE, CP, and social pillars of TBL for sustainable manufacturing. In this paper, the authors are developing a decision framework to analyze the effect of BCT’s and BDA’s criteria-based 6R by calculating the weight for each criterion-based BWM which is more efficient and easier for pair comparisons compared with the AHP method [19]. In this decision framework, BWM integrates with neutrosophic theory to strengthen this framework which clarified in Section 3.

N-DEMATEL is aided by N-BWM to determine the most desirable or most important criterion (i.e., the criterion with the largest value of (${\mathrm{R}}_{\mathrm{i} }-{\mathrm{C}}_{\mathrm{j} }$) in the cause group). Moreover, the least desirable or least important criterion (i.e., the criterion with the smallest value of (${\mathrm{R}}_{\mathrm{i} }-{\mathrm{C}}_{\mathrm{j} }$) in the effect group) is determined. Finally, two ranking subjective methods, TOPSIS is clear and easy implementation and uses the positive and negative ideal solutions in DM [20,21]. This method cooperates with neutrosophic theory to generate N-TOPSI for ranking the manufacturers and selecting the most sustainable one as the best alternative based on its highest value of ${\mathrm{CC}}_{\mathrm{i}}$ compared with existing alternatives. Another ranking method is COPRAS is employed as a comparative ranking method based on neutrosophic theory to select the most sustainable manufacturer based ${\mathrm{U}}_{\mathrm{i}}$. The objective of this paper is as follows:

• A novelty idea in this paper is applying 6R with the integration of BCT and BDA to achieve sustainability. This integration is explained in Section 3.
• A committee of experts is formed to evaluate the most influential criteria of the two integrated methodologies. Criteria are evaluated based on N-BWM to obtain the criteria’s weights are used in N-TOPSIS and N-COPRAS for ranking manufacturers.
• The least and most important criteria required in N-BWM are determined via N-DEMATEL through values of (${\mathrm{R}}_{\mathrm{i} }-{\mathrm{C}}_{\mathrm{j} }$).
• N-TOPSIS is used to evaluate and rank the alternatives of manufacturers who adopt the idea in point one. The most sustainable manufacturer is selected.
• The evaluation and selection of sustainable manufacturer-based N-TOPSIS are compared with another method of MCDM represented in N-COPRAS.

This paper is structured as follows: theoretical background related to our paper is represented in Section 2. The methodology of applying two I4.0 technologies with 6R is shown and an evaluation of this integration through a developed decision framework is presented in Section 3. Using a case study, the hybrid mathematical approach is validated in Section 4. In Section 5 the discussion and possible implications on sustainability manufacturing in enterprises are highlighted. This is followed by the method analysis in Section 6, where sensitivity analysis is provided along with a comparative analysis between the proposed method and Bipolar Neutrosophic TOPSIS, VIKOR, and EDAS methods are conducted and discussed. The framework managerial implications are listed in Section 7. Finally, contributions, conclusions, and future work are highlighted in Section 8.

2. Historical Insights on Research-Relevant Concepts

This section discusses several recent surveys which focused on the new technologies of I4.0. For instance, ref. [22] described BCT as an electronic database system that can be recorded and distributed. These records are secured by cryptography and governed by a consensus among the participants involved in a system. Refs. [23,24] epitomized BCT and its characteristics as follows: (i) Transparency and synchronization: Every participant in the network can access the data of complete historical transactions in the ledger. (ii) P2P networks where Participants in the network work collectively with equal responsibility and no central authority. (iii) Smart contract and payment: Computer programming codes are utilized to formalize a contractual agreement that is verified by participants. It confirms pre-determined rules and penalties automatically before executing the terms of agreements. (iv) Immutability of data: Creation and modification processes are verified by the consensus of most of the participants.

The concept of BDA in [25] is related to the so-called 5v refers to (i) volume-specific for dimension of data, (ii) flow rate of data represented through velocity, (iii) variety that illustrates different formats of data, (iv) veracity that represents the uncertainty of data, and (v) value that means the quality of data. BDA based on [26] helps in making the right decision promptly based on analyzing data collected from various resources through new technologies of I4.0 such as IoT and CPS. Thus, according to [27], DBA is a beneficial technique that plays an important role in improving the domain of business and manufacturing. It helps manufacturers working in business and industrial sectors achieve their goals through (1) making appropriate decisions for the situation, (2) cost reduction, (3) earning revenue as in [2], (4) making decisions in real-time, and (5) enhancing quality through detecting and analyzing failures and defects in equipment or manufacturing. It enhances the management of the life cycle for products, detects and analyzes flaws in the chain of manufacturers, and predicts the profits of enterprises. Accordingly, it helps manufacturers achieve a competitive advantage, which makes them more sustainable in the business environment.

Many researchers seek to integrate intelligent technologies of I4.0 to take advantage of both. For instance, ref. [28] developed a framework consolidating BCT and BDA. The architecture of the developed framework consists of five layers. The first layer adopts Industrial Inter-net of Things (IIoT) equipment attached to things and people as sensors, wearable equipment, and radio frequency identification (RFID). This equipment collects data from several sources where they are attached. The collected data from the first layer are transmitted via Bluetooth, and ZigBee included in the second layer is represented in the communication layer. The transmitted data are analyzed in the third layer by BDA techniques. After the fourth layer data are analyzed, they are shared with participants or nodes in the BC network. Other researchers in [29] adopt the same idea as [28] where BDA and BCT are merging.

As a consequence of conducting literature works about integrating BCT-BDA and its benefits in the domains, the evaluation for applying these technologies in domains is vital. MCDM methods were employed in [30] to evaluate the adoption of BCT for the sustainability of agricultural SC. The AHP method was used to analyze the factors of BCT and determine their effect on agricultural SC through the value of factor’s weights and comparing SC that adopts BCT with traditional SC. Moreover, ref. [31] utilized VIekriterijumsko KOmpromisno Rangiranje (VIKOR) to evaluate alternatives and select the best among BCT platforms. BCT was integrated with the renewable energy systems via [18] to achieve sustainable energy grid management systems through CE. The goal of [32] is to evaluate the link between I4.0 and CE as it relates to supply chain management via a combination of the interpretative structural modeling (ISM) and cross-impact matrix multiplication applied to the classification (MICMAC) approach under a fuzzy environment. The fuzzy environment in [33] degree of membership of the elements in a universe is a single value that does not reveal any extra information about the elements’ incomplete ideas. So, our paper is seeking to strengthen MCDM by integrating it with neutrosophic theory to evaluate the sustainability of manufacturers. Because of, the ability of neutrosophic as in [34] to treat with three degrees of information which represent indeterminacy besides truth and falsity.

From a conducted survey on literary works, we are upgrading the framework in [27] by merging 6R with BDA-BCT to encourage CP, CE, and social in manufacturing. Also, we are evaluating the sustainability of manufacturers who adopt this notion based on neutrosophic theory with MCDM methods.

3. Methodology

This section is divided into two subsections. The first subsection describes the integration between two technologies (e.g., BDA-BCT) and 6R that are established in the manufacturing sector, and how this integration supports achieving CP, CE, and social pillars for improving sustainability. The second subsection is the mathematical decision methods that are represented in MCDM methods supported by the neutrosophic environment. The proposed decision framework’s most important advantage is its ability to treat an uncertain environment and analyze incomplete information. This framework is used to evaluate the sustainability of manufacturers who adopt the integration in Figure 3. The evaluation is performed by a panel of experts. This panel analyzes and evaluates the determined criteria. Posteriorly, these manufacturers are ranked based on their valuations, and the best is selected.

3.1. Manufacturing Lifecycle Based on I4.0 Technologies and 6R

The architecture in Figure 3 describes the life cycle of digitizing the manufacturing process through developing a framework that applies to the manufacturing chain. The framework illustrates how BCT-BDA with IIOT-based 6R is employed for the manufacturer to be a robust competitor in the business environment through five phases.

The role of the framework for achieving sustainability in manufacturing is illustrated by answering research questions (RQs):

RQ-1. 

How does manufacturing apply 6R, whether inbound/outbound, to achieve the pillars of sustainability?

The first phase in Figure 3 illustrates the chain for inbound/outbound manufacturing. This chain starts from laborers who are responsible for manufacturing products at the operation level to the customer who consumes the product. The 6R permits labor to produce products with the following properties [35]: (i) reduce the use of resources and materials (i.e., waste management); (ii) reduce the use of new materials to produce new products by reusing existing products; (iii) reuse waste products in production rather than new materials; (iv) products can be disassembled, sorted, and recovered as raw materials; and (v) new generation of products designed from disassembled and recovered products.

RQ-2. 

How does IIoT transform traditional objects and partners of the chain in Phase one into smart objects/partners?

IIoT equipment, as in Phase 2 in Figure 3, is attached to objects and partners to help managers and stakeholders track and monitor labor via wearable devices. Such sensors are attached to machines to enable engineers and designers to monitor the conditions of the machines. Detection devices with materials and equipment are used to detect any defect. This equipment aids DMs by gathering data, transmitting data for analysis, and recording the collected data and transactions using BDA techniques.

RQ-3. 

How does BDA help DMs and stakeholders in the manufacturing sector make decisions?

The collected data from Phase 2 via IIoT’s equipment passes through several processes as in Phase 3. When data is collected, eliminating and filtering any observations that could include errors or are not useful for the analysis is crucial. Famous algorithms such as logistic regression, naïve Bayes, and decision trees are usually used to classify data into various groups, extract pattern recognition and new information, and utilize them to support diverse applications through using specialized techniques like machine learning [36]. Finally, visualization methods [37] are used for representing and clarifying information such as charts, diagrams, and graphs.

RQ-4. 

What is the effect of BCT on achieving security and transparency of the information and new patterns extracted from BDA techniques?

The information and new patterns obtained from applying BDA techniques in the previous layer are stored in blocks in the network of BC. Each block in the chain consists of: Block number, Data may refer to transactions, Previous hash indicates the hash of the previous block, and hash, where each block has its hash (e.g., fingerprint). The BCT ensures transparency and enhances trust over the network through the record of each block’s previous hash [38].

RQ-5. 

What are various applications and services for adopting BCT in the manufacturing sector?

The application of IIoT and BCT technologies in the manufacturing sector in our framework is shown in Figure 3. (i) CP and CE are achieved through resource waste management by tracking the processes of production and controlling the resource usage. (ii) Energy used in the shipment is controlled by tracking the truck and its itinerary in real-time. Tracking helps manufacturers detect problems of defective raw materials. (iii) Each participant in the chain can access information via utilization of distributed ledger in BCT. Thus, information becomes transparent among participants. No one can modify or add information without the agreement or consensus of other participants in the chain. (iv) Incidents and hazards are reduced working hours, and wages are stored and retrieved through BCT to guarantee the rights of workers, working hours, and wages are stored and retrieved through BCT to guarantee the rights of workers.

3.2. Decision Framework Based on Neutrosophic Theory

Questionnaires and interviews are conducted to collect the criteria. Specialists from various manufacturers are given questionnaires to fill in. Answers are analyzed using MCDM methods under neutrosophic theory to assess the criteria and their influence on achieving sustainability.

In Figure 4, the steps of developing a hybrid framework based on neutrosophic theory for evaluating manufacturers are provided. In the following, the mathematical framework is defined in steps.

• Stage 1: Deciding and evaluating the most effective criteria

Based on [29], a set of criteria {$c_{1, }{c}_{2 },\dots , c_8\}$ with the main role in the sustainability of manufacturers can be identified, as shown in Figure 5.

Table 2. Achieving sustainability-based criteria of 6R and BCT-BDA.

Criteria	I4.0 Technologies in This Study			Pillars of Sustainability Achieved Based 6R and I4.0 Technologies
	IIoT	BCT	BDA	CE	CP	Social
C1	√		√	√	√
C2	√		√	√	√
C3	√	√	√	√		√
C4	√		√	√	√
C5		√	√	√		√
C6		√	√	√		√
C7	√	√	√	√		√
C8	√	√	√	√		√

shows the extent of their effect on achieving sustainability based on 6R and I4.0 technologies. This process is performed through the following steps:

• Step 1: Form a committee of experts and specialists interested in this domain.
• Step 2: Evaluate the criteria based on a questionnaire approach to collect data. The interview is another approach used by the expert panel to obtain and analyze information for assessing the influence of criteria on achieving sustainable manufacturing.

• Stage 2: Using the subjective MCDM method to determine the weights of criteria

At this stage, the BWM method is applied according to [17,39]. BWM is a subjective method for obtaining weights for identified criteria. We chose this method for reasons [19] mentioned in the introduction. This paper aims to strengthen BWM through a neutrosophic environment to take its advantages in dealing with uncertain situations as mentioned in the Introduction.

In this work, the focus is on single-valued triangular neutrosophic merged with BWM to generate N-BWM for accommodating various points of view for experts and DMs. A single-valued triangular neutrosophic set is represented in [40] as $\tilde{a}$ = $\left(a_1, a_2, a_3\right);{\alpha }_{\tilde{a}}, {\theta }_{\tilde{a}}, {\beta }_{\tilde{a}}$, where $a_1, a_2, \mathrm{and} a_3$ represents the lower, middle, and upper parts of the neutrosophic number.$\tilde{a}$ set is classified into membership functions as truth-membership function $\left(T_{\widetilde{a }}\right)$, indeterminacy-membership function $\left(I_{\tilde{a}}\right)$, and falsity-membership function $\left(F_{\tilde{a}}\right)$ and formed as follows:

$$T_{\tilde{a}}=\left\{\begin{array}{l}{\alpha }_{\tilde{a}}\left(\frac{x-a_1}{a_2-a_1}\right)\hspace{1em}\hspace{1em}\hspace{1em}{a}_1\le x\le a_2\\ {\alpha }_{\tilde{a}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}x=a_2\\ {\alpha }_{\tilde{a}}\left(\frac{a_3-x}{a_3-a_2}\right)\hspace{1em}\hspace{1em}\hspace{1em}{a}_2\le x\le a_3\\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathit{\text{otherwise}}\end{array}\right.$$

(1)

$$I_{\tilde{a}}=\left\{\begin{array}{l}{\theta }_{\tilde{a}}\left(\frac{a_2-x}{a_2-a_1}\right)\hspace{1em}\hspace{1em}\hspace{1em}{a}_1\le x\le a_2\\ {\theta }_{\tilde{a}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}x=a_2\\ {\theta }_{\tilde{a}}\left(\frac{x-a_3}{a_3-a_2}\right)\hspace{1em}\hspace{1em}\hspace{1em}{a}_2\le x\le a_3\\ 1\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathit{\text{otherwise}}\end{array}\right.$$

(2)

$$F_{\tilde{a}}=\left\{\begin{array}{l}{\beta }_{\tilde{a}}\left(\frac{a_2-x}{a_2-a_1}\right)\hspace{1em}\hspace{1em}\hspace{1em}{a}_1\le x\le a_2\\ {\beta }_{\tilde{a}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}x=a_2\\ {\beta }_{\tilde{a}}\left(\frac{x-a_3}{a_3-a_2}\right)\hspace{1em}\hspace{1em}\hspace{1em}{a}_1\le x\le a_3\\ 1\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathit{\text{otherwise}}\end{array}\right.$$

(3)

Weights for eight criteria identified in Figure 5 are obtained based on N-BWM as follows:

Figure 5. Description of determined criteria of the utilization of 6R-based BCT-BDA based on [29].

Figure 5. Description of determined criteria of the utilization of 6R-based BCT-BDA based on [29].

• Step 3: Determine the best (i.e., most important) and worst (i.e., least important) criteria. DEMATEL method united with single-valued triangular of neutrosophic theory as N-DEMATEL is applied as follows:

  3.1 

  Form a panel of DMs and experts to express their judgments for eight criteria identified in Figure 5 using the Saaty scale—based NTS in [40].

  3.2 

  Produce pairwise comparison matrices based on the relation between criteria by DMs, as shown in matrix $X^{ex}$ in Equation (4). Then deneutrosophic these matrices as in Equation (5):

  $$X^{ex}=\left(\begin{array}{ccc}{r}_{11}^{ex}& r_{12}^{ex}\cdots & r_{1n}^{ex}\\ ⋮& \ddots & ⋮\\ r_{m1}^{ex}& r_{m2}^{ex} \cdots & r_{mn}^{ex}\end{array}\right)$$

  (4)

  where $m,n$ refers to the number of alternatives and criteria and $ex$ refers to number of experts.

  $$\mathrm{s}\left({\mathrm{r}}_{ij}\right)=\frac{\left(l_{ij}+m_{ij}+u_{ij}\right)}{9}\ast \left(2+\mathrm{T}-\mathrm{I}-\mathrm{F}\right)$$

  (5)

  where $i=1,2,3,\dots ,m;n=1,2,3,\dots ,j$; $l,m,u$ refer to the lower, middle, and upper values and $\mathrm{T},\mathrm{I},\mathrm{F}$ refers to the truth, indeterminacy, and falsity values.

  3.3 

  Perform aggregation according to Equation (6). Construct a direct relationship for matrix $Z$ as formed in Equation (7).

  $$x_{ij}=\frac{{{\displaystyle \sum }}_{ex=1}^{ex}{r}_{ij}}{ex}$$

  (6)

  $$Z=\left(\begin{array}{ccc}{x}_{11}& x_{12}\cdots & x_{1n}\\ ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}\cdots & x_{mn}\end{array}\right).$$

  (7)

  3.4 

  Utilize Equations (8) and (9) to normalize the direct relation matrix $Z$.

  $$Nor=K\ast X$$

  (8)

  $$K=\frac{1}{ ma{x}_{1\le i\le n}({{\displaystyle \sum }}_{j=1}^n{x}_{ij})}\left(i,j=1,2,\dots ,n\right),$$

  (9)

  3.5 

  Produce total relation matrix T as in Equation (11) by using identity matrix I as formed in Equation (10).

  $$I=\left(\begin{array}{ccc}1& \cdots & 0\\ ⋮& \ddots & ⋮\\ 0& \cdots & 1\end{array}\right)$$

  (10)

  $$T=Nor{\left(I-Nor\right)}^{-1}$$

  (11)

  3.6 

  Determine the most effective criterion with the highest value of (${\mathrm{R}}_{\mathrm{i}}-{\mathrm{C}}_{\mathrm{j}}$). Determine the least important/desired criterion with the least value of (${\mathrm{R}}_{\mathrm{i}}-{\mathrm{C}}_{\mathrm{j}}$) among the eight criteria.

• Step 4: Determine the judgments and preferences of the expert panel by using Table 2 to evaluate the best ${\mathrm{criterion}}_B$ over other ${\mathrm{criteria}}_j$. Ref. [41] explained the relation between best to other criteria as $\widetilde{criterio{n}_B}=\left(\widetilde{criterio{n}_{B1}}, \dots ,\widetilde{criterio{n}_{B8}}\right)$.
• Step 5: Determine the judgments and preferences of the expert panel by using the scale in [41] to evaluate ${\mathrm{criteria}}_j$ over least desired/important ${\mathrm{criterion}}_W$. Ref. [40] explained the relation between other criteria to ${\mathrm{criterion}}_W$ as $\widetilde{ criterio{n}_W}=\left(\widetilde{criterio{n}_{1W}}, \dots ,\widetilde{criterio{n}_{8W}}\right)$.
• Step 6: Perform deneutrosophic process to convert the evaluations and judgments in steps 4 and 5 for the expert panel from NTS to crisp values based on Equation (5). Then, aggregate the judgments of the expert panel according to Equation (6).
• Step 7: Utilize Equations (12) and (13) to find the optimal weights for determining criteria.

  $$\begin{array}{c}minma{x}_j=\left\{\left|\frac{w_B}{w_j}-{\mathrm{criteria}}_{Bj}\right|,\left|\frac{w_j}{w_w}-{\mathrm{criteria}}_{jw}\right|\right\}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ s.t\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ {{\displaystyle \sum }}^{ }{w}_j=1\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ w_j\ge 0 for all j\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \end{array}$$

  (12)

  $$\begin{array}{c}minma{x}_j \mathit{\text{is converted to a linear model as}}:\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ min{\epsilon }^L\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ s.t\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ \left|w_B-{\mathrm{criteria}}_{Bj}{w}_j\right|\le {\epsilon }^L, for all j\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ \left|w_j-{\mathrm{criteria}}_{jw}{w}_w\right|\le {\epsilon }^L, for all j \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ {{\displaystyle \sum }}^{ }{w}_j=1\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \\ w_j\ge 0 for all j\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hfill \end{array}$$

  (13)

  where $w_B$ is the weight of best criterion. $w_w$ is the weight of worst criterion.

• Stage 3: Ranking manufacturers who adopt 6R based on I4.0 technologies for sustainability

Apply TOPSIS as a subjective MCDM method to evaluate and rank alternatives of manufacturers based on the established framework in their chain of inbound and outbound manufacture. Rank various manufacturers according to closeness coefficient (${\mathrm{CC}}_{\mathrm{i}}$), and the manufacturer with the highest ${\mathrm{CC}}_{\mathrm{i}}$. value is the best alternative. TOPSIS utilizes weights generated from N-BWM to produce the weighted decision matrix.

• Step 8: Form a committee of DMs to perform interviews and questionnaires for evaluating a set of alternatives.
• Step 9: Construct a decision matrix based on the preferences of the committee for alternatives according to NTS in [40].
• Step 10: Repeat procedure 3.2 of step 3 in stage 2 to deneutrosophicate constructed decision matrices in the previous step for alternatives. Also, repeat 3.3 in stage 2 to aggregate deneutrosophicate matrices.
• Step 11: Normalize aggregated decision matrix according to Equation (14).

  $$Nor{m}_{ij}=\frac{x_{ij}}{\sqrt{{{\displaystyle \sum }}_{j=1}^m\left(x^2{}_{ij}\right)}}$$

  (14)
• Step 12: Producing the weighted decision matrix as in Equation (15).

  $$w{z}_{ij}=w_i\ast Nor{m}_{ij}$$

  (15)

  where $w_i$ is weights of N-BWM in the previous stage.
• Step 13: Compute positive ideal solution and negative ideal solution based on Equations (16) and (17), respectively.

  $$A^{*}=\left(w{z}_1{}^{*},w{z}_2{}^{*},\dots ,w{z}_n{}^{*} \right),w{z}_j{}^{*}=ma{x}_{i }\left\{w{z}_{ij}\right\}$$

  (16)

  $$\overline{A}=\left(w{z}_1{}^{-},w{z}_2{}^{-},\dots ,w{z}_n{}^{-} \right),w{z}_j{}^{-}=mi{n}_{i }\left\{w{z}_{ij}\right\}$$

  (17)

  where $w{z}_1{}^{*}\dots w{z}_n{}^{*},w{z}_1{}^{-}\dots w{z}_n{}^{-}$ are max and min values of weighted normalized criteria per column respectively.
• Step 14: Compute the distance between the positive ideal solution and negative ideal solution to each alternative via Equations (18) and (19) respectively.

  $$d_i{}^{*}={\displaystyle \sum }_{j=1}^{n}d\left(w{z}_{ij},w{z}_j{}^{*} \right)$$

  (18)

  $$d_i{}^{-}={\displaystyle \sum }_{j=1}^{n}d\left(w{z}_{ij},w{z}_j{}^{-} \right)$$

  (19)
• Step 15: Determine the ranking and arrangement of alternative by calculating the closeness coefficient (${\mathrm{CC}}_{\mathrm{i}}$) based on Equation (20). The most sustainable alternative/manufacturer has the highest value of ${\mathrm{CC}}_{\mathrm{i}}$.

  $${\mathrm{CC}}_{\mathrm{i}}=\frac{d_i{}^{-} }{d_i{}^{*}+d_i{}^{-}}$$

  (20)

• Stage 4: Ranking manufacturers based on N-COPRAS.

Apply the subjective method to rank the alternatives of manufacturers such as COPRAS based on NTS as a comparative MCDM ranking method to assess set of alternatives through the following steps.

• Step 16: Repeat Step 8 in Stage 3 for cooperating committee of DMs for evaluating alternatives.
• Step 17: Follow Steps 9 and 10 in Stage 3 to develop an aggregated decision matrix for DMs as in Equations (6) and (7).
• Step 18: Normalize an aggregated decision matrix based on Equation (21).

  $$\mathrm{NormAgg}={\left[{\mathrm{r}}_{\mathrm{ij}}\right]}_{\mathrm{m}\times \mathrm{n}}=\frac{{\mathrm{h}}_{\mathrm{ij}}}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{h}}_{\mathrm{ij}}}$$

  (21)
• Step 19: Produce the weighted decision matrix ($wz$) as in Equation (15). Sum of weighted decision matrix calculated according to Equations (22) and (23).

  $${\mathrm{S}}_{+\mathrm{i}}={\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{n}}w{z}_{+\mathrm{ij}}, \mathrm{for} \mathrm{beneficial} \mathrm{criteria}$$

  (22)

  $${\mathrm{S}}_{-\mathrm{i}}={\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{n}}w{z}_{-\mathrm{ij}}, \mathrm{for} \mathrm{nonbeneficial} \mathrm{criteria}$$

  (23)
• Step 20: Utilize Equation (24) to determine the relative importance of alternatives. Calculate quantity utility ${\mathrm{U}}_{\mathrm{i}}$ for each alternative based on Equation (25) to rank the alternatives.

  $${\mathrm{Q}}_{\mathrm{i}}={\mathrm{s}}_{+\mathrm{i}}+\frac{{\mathrm{s}}_{-\min } {{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{s}}_{-\mathrm{i}}}{{\mathrm{s}}_{-\mathrm{i}} {{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}({\mathrm{s}}_{-\mathrm{m}/}{\mathrm{s}}_{-\mathrm{i}})}$$

  (24)

  where i = 1, 2,…,m, and ${ \mathrm{s}}_{-\mathrm{m}}$=${ \mathrm{s}}_{-\mathrm{i}}$ all criteria are beneficial.

  $${\mathrm{U}}_{\mathrm{i}}=\left[\frac{{\mathrm{Q}}_{\mathrm{i}}}{{\mathrm{Q}}_{\max }}\right]\times 100\%,$$

  (25)

  where the alternative with the highest ${ \mathrm{U}}_{\mathrm{i}}$ is the best one.

4. Validation of Hybrid Mathematical Approach: An Empirical Case Study

This section aims to validate the proposed mathematical decision framework by applying it on different manufacturers (alternatives). We are surveying thirty manufacturers in the 10th of Ramadan city which is a big manufacturing city in Egypt. From this number we find out four manufacturers who adopt these new technologies of I4.0 in their departments.

Manufacturer one (A₁) is a home appliances manufacturer (i.e., electrical equipment). Manufacturer two (A₂) is a ceramic manufacturer operating for more than 20 years. Manufacturer three (A₃) and manufacturer four (A₄) are textile manufacturers who have a strong long-term commitment to enhancing management techniques for eco-friendly manufacturing, in addition to optimizing the operations through saving usage resources, energy, and finances to support manufacturers to be more competitive in the marketplace.

• First, deciding and evaluating the most effective criteria

In this stage, a panel of four experts from the above four alternative manufacturers. Manufacturers three and four are producing the same type of product.

We conducted a questionnaire via an expert panel who participated in evaluating the alternatives for BDA–BCT-based 6R methodology, as well as how this integration can achieve CE, CP, and social.

Table 3. Profile of expert panel.

DMs	Department	Years of Experience	Qualification	Specialization
DM1	Sales and purchasing	15	B. Sc	Textile Manufacturing
DM2	Planning and production	20	MBA	Electronic Manufacturing
DM3	Product quality control	18	B. Sc	Ceramic Manufacturing
DM4	Information Technology	12	Professional Diploma	Textile Manufacturing

describes their departments, years of experience, qualification, and industry specialization. These experts hold managerial positions in their departments with broad data access.

• Step 1: Determine the most effective criteria related to the proposed framework.
• Step 2: The panel of experts expresses their opinions and preferences for the decided criteria. Their expressions are performed based on NTS, as shown in [40].

• Second, utilizing the subjective method of MCDM for valuing criteria’s weights

N-BWM is used to compute the weights of criteria.

• Step 3: Apply the N-DEMATEL to compute the relation between criteria as:

  3.1 

  Build the comparison matrix

  3.2 

  Deneutrosophicate a pairwise comparison matrix for criteria using Equation (5).

  3.3 

  Aggregate the pairwise comparison into one matrix to obtain the direct relation matrix by Equations (6) and (7) as in Table 4.

  3.4 

  Obtain the sum of each row, and the maximum value for the sum of each row is 33.3. Next, utilize Equations (8) and (9) to normalize the direct relation.

  3.5 

  Produce the total relation matrix according to Equation (11).

  3.6 

  C₆ is considered the most effective or most important criterion, and C₁ is the least important or least effective for BWM.

  Table 4. The aggregated pairwise comparison matrix.

  Criteria	C1	C2	C3	C4	C5	C6	C7	C8
  C1	0.50	4.82	5.56	5.18	4.30	5.98	2.88	4.08
  C2	0.22	0.50	5.77	5.56	5.84	6.30	2.00	3.30
  C3	0.19	0.18	0.50	4.97	5.56	5.03	5.98	5.56
  C4	0.20	0.19	0.21	0.50	5.03	5.98	4.16	4.16
  C5	0.23	0.18	0.19	0.21	0.50	6.51	6.93	6.93
  C6	0.18	0.16	0.21	0.18	0.15	0.50	0.85	0.85
  C7	0.83	0.86	0.18	0.24	0.14	1.18	0.50	4.27
  C8	0.24	0.42	0.19	0.24	0.14	1.18	0.31	0.50

  Table 4. The aggregated pairwise comparison matrix.

  Criteria	C1	C2	C3	C4	C5	C6	C7	C8
  C1	0.50	4.82	5.56	5.18	4.30	5.98	2.88	4.08
  C2	0.22	0.50	5.77	5.56	5.84	6.30	2.00	3.30
  C3	0.19	0.18	0.50	4.97	5.56	5.03	5.98	5.56
  C4	0.20	0.19	0.21	0.50	5.03	5.98	4.16	4.16
  C5	0.23	0.18	0.19	0.21	0.50	6.51	6.93	6.93
  C6	0.18	0.16	0.21	0.18	0.15	0.50	0.85	0.85
  C7	0.83	0.86	0.18	0.24	0.14	1.18	0.50	4.27
  C8	0.24	0.42	0.19	0.24	0.14	1.18	0.31	0.50

• Step 4: Determine the judgments and preferences of the expert panel using the scale in [41] to evaluate C₆ over other criteria.
• Step 5: Determine the judgments and preferences of the expert panel using the scale in [41] to evaluate criteria over C₁.
• Step 6: Convert the evaluations and judgments in steps 4 and 5 for the expert panel from NTS to crisp values as in procedures 3.2 and 3.3 in the previous step.
• Step 7: Find the optimal weights for determined criteria-based Equation (12) on Equation (13). Figure 6 show that C₆ has the largest weight $w_1=0.103274226, w_2=0.076431404,w_3=0.0558155,w_4=0.0964963,w_5=0.049269274,w_6=0.310396423,w_7=0.153813887,w_8=0.154502948$.

• Third, the ranking of stages for sustainable manufacturers based on N-TOPSIS

The evaluation for manufacturing enterprises that adopt the framework (Figure 3) in their operation and chain, whether inbound/outbound, is vital a process. Subsequently, ranking and selecting the most appropriate one is a critical process. This stage aims to integrate TOPSIS with neutrosophic theory to produce N-TOPSIS and work together to rank alternatives (four manufacturers), as shown in the following steps:

• Step 8: Repeat step 2 for evaluating four alternatives of manufacturers in this case study.
• Step 9: Build the decision matrices by the opinions of experts. Convert decision matrices constructed in the previous step for alternatives into crisp values through the deneutrosophic process by employing Equation (5), as represented in Step 10. Aggregate the matrix deconstruct according to Equations (6) and (7), as shown in

  Table 5. The aggregated decision matrix.

  Criteria	C1	C2	C3	C4	C5	C6	C7	C8
  A1	3.744444	4.344444	4.666667	3.788889	1.9	2.316667	6.933333	5.844444
  A2	2.666667	4.577778	3.955556	0.822222	2.983333	6.722222	5.633333	1.9
  A3	3.166667	1.872222	4.894444	4.344444	6.722222	4.027778	0.794444	3.15
  A4	3.927778	5.844444	1.111111	3.194444	4.027778	1.944444	4.133333	1.8

  .
• Step 11: Utilize Equation (14) to normalize aggregated matrix.
• Step 12: Produce the weighted decision matrix, by employing the weights obtained from N-BWM to obtain $w_i$ in Equation (15) with the normalized matrix.
• Step 13: Compute positive ideal solution and negative ideal solution as in

  Table 6. Ranking alternatives of manufacturers based on N-TOPSIS.

  Alternatives	d*	d−	CCi	Rank
  A1	0.165864	0.14217	0.46154	2
  A2	0.106345	0.194545	0.646565	1
  A3	0.15421	0.104559	0.404063	3
  A4	0.204862	0.074798	0.26746	4

  .
• Step 14: Compute the distance between the positive ideal solution and negative ideal solution for each alternative via Equations (18) and (19). This step helps obtain the value of (${\mathrm{CC}}_{\mathrm{i}}$) based on Equation (20), whereas ${\mathrm{CC}}_{\mathrm{i}}$ values determine and rank alternatives from the most appropriate (A₂) to the least appropriate (A₄) as Table 6.

• Fourth, the ranking method stage-based on N-COPRAS.

• Step 15–16: Start with the aggregated decision matrix in Table 5.
• Step 17: Normalized an aggregated matrix based on Equation (21)
• Step 18: Follow Step 13 in Stage three to derive the weights based on N-BWM. These weights contribute to producing the weighted decision matrix through Equation (15).
• Step 19: Determine the sum of the weighted normalized decision matrix. In this paper, eight identified criteria are considered beneficial. Thus, Equation (22) is applied to find the values of ${\mathrm{S}}_{+\mathrm{i}}$. The value of ${\mathrm{S}}_{-\mathrm{i}}$ is zero. Subsequently, the value of S-min/S-i is zero, where S-min is zero. So, the relative importance of alternatives $\left({\mathrm{Q}}_{\mathrm{i}}\right)$ based on Equation (24), ${\mathrm{Q}}_1$ = 0.282470383$. {\mathrm{Q}}_2$ = 0.284099748$. {\mathrm{Q}}_3$ = 0.235788938$, {\mathrm{Q}}_4$ = 0.197640932.

• Step 20: Calculating quantitative utility $({\mathrm{U}}_{\mathrm{i}})$ based on Equation (25). The values of ${\mathrm{U}}_{\mathrm{i}}$ clarify that A₂ is the most appropriate manufacturer, and A₄ has the least rank.

5. Implications of Results

This paper validates the efficiency of a developed neutrosophic-based mathematical approach through applying an empirical case study. This work has a vital role in evaluating the extent of achieving sustainability for manufacturers who adopt the two methodologies (i.e., BCT-BDA with the concept of 6R. The integration contributes to proposing a framework as shown in Figure 3. The objective of this merger is to support manufacturing enterprises based on the fulfillment of the three pillars of sustainability.

Cooperation and communication with a related panel of experts and DMs working in this field are performed in (Section 3). This panel has given a set of determined criteria (Figure 5). The panel expresses their opinions and judgments for evaluating the criteria. These criteria are the results of the said merger to support manufacturers in maintaining a competitive edge in the marketplace for survival and sustainability (Table 2). Various judgments are performed and aggregated through integrating MCDM methods (i.e., DEMATEL-BWM) based on a neutrosophic environment. N-DEMATEL determines the best and worst criteria-based values ${\mathrm{R}}_{\mathrm{i} }-{\mathrm{C}}_{\mathrm{j} }$.

The determination of the best and worst criteria in N-BWM is the initial and main step to obtaining the weights for the identified criteria (Figure 5). The weights obtained from N-BWM are used as inputs to be multiplied with the normalized decision matrix to produce the weighted decision matrix in Stage Three. This stage aims to evaluate and rank the alternatives of manufacturers who adapt BCT and BDA of I4.0 technologies with 6R to achieve sustainable manufacture. This paper applies N-TOPSIS to four manufacturers in an empirical case study. The values of ${\mathrm{CC}}_{\mathrm{i}}$ in N-TOPSIS (Table 6) indicate that A₂ > A₁ > A₃ > A₄. Moreover, Figure 7 shows manufacturers’ ${\mathrm{CC}}_{\mathrm{i}}$ values, which present that A₂ is the most appropriate, sustainable manufacturer, and A₄ is the least sustainable one.

In this paper, the ranking of alternatives via N-TOPSIS is compared with another subjective method of MCDM as COPRAS based on neutrosophic environment and is represented in the fourth stage. This stage entails cooperation with different DMs as mentioned in Table 2, to rate and judge the same four alternatives in the third stage through NTS in [41]. Various rates and scores of DMs are aggregated. Then, these scores are analyzed and calculated to produce the weighted decision matrix through employing weights of criteria obtained from N-BWM that are multiplied with the normalized matrix according to Equation (15). The produced weighted decision matrix contributes to producing the sum of the weighted decision matrix. Therefore, the values of ${ \mathrm{S}}_{+\mathrm{i}}$ and ${ \mathrm{S}}_{-\mathrm{i}}$, which contribute to producing values of ${\mathrm{U}}_{\mathrm{i}}$ that are responsible for ranking of alternatives, are easy to obtain. The values of ${\mathrm{U}}_{\mathrm{i}}$ indicate that A2 > A1 > A3 > A4, as shown in Figure 8. Based on this, A₂ is the most appropriate and sustainable manufacturer and A₄ is the least appropriate and sustainable manufacturer.

6. Discussion

6.1. Sensitivity Analysis

In this section, we introduce five cases to change the weights of criteria and then see the rank of alternatives N-TOPSIS.

Table 7. Five cases in the change of weights of criteria.

	Case 1	Case 2	Case 3	Case 4	Case 5
C1	0.125	0.2	0.1	0.1	0.1
C2	0.125	0.1	0.2	0.1	0.1
C3	0.125	0.1	0.2	0.2	0.1
C4	0.125	0.1	0.1	0.2	0.1
C5	0.125	0.1	0.1	0.1	0.1
C6	0.125	0.1	0.1	0.1	0.2
C7	0.125	0.1	0.1	0.1	0.2
C8	0.125	0.2	0.1	0.1	0.1

shows the five cases. From case 1 to case 4 no change in the rank of alternatives where A₁ is the best alternative and A₄ is the worst alternative. But in case 5 the best alternative is A₂ and the worst alternatives is A₄. Figure 9 shows the rank of N_TOPSIS under five cases in changes of weights.

6.2. Comparative Analysis

A comparative analysis is shown to demonstrate the suggested method’s applicability. In this section, we compare the proposed model with the Bipolar Neutrosophic TOPSIS, VIKOR, and EDAS methods. We used the same weight.

Table 8. Rank of comparative methods.

Proposed Ranking Methods	A1	A2	A3	A4
Proposed TOPSIS	2	1	3	4
Proposed COPRA	2	1	3	4
Bipolar TOPSIS	2	1	3	4
Bipolar VIKOR	4	1	2	3
Bipolar EDAS	2	1	4	3

shows in detail the rank of comparative methods. From Table 7, we find all methods accepted. A₂ is the best alternative. But in the worst alternative, we find two proposed methods and Bipolar TOPSIS accepted. A₄ is the worst alternative. Bipolar VIKOR has A₁ as the worst alternative. Bipolar EDAS has A₃ as the worst alternative.

Table 9. The Spearman’s rank correlation.

	Proposed TOPSIS	Proposed COPRA	Bipolar TOPSIS	Bipolar VIKOR	Bipolar EDAS
Proposed TOPSIS	-	1	1	0.4	0.8
Proposed COPRAS	1	-	1	0.4	0.8
Bipolar TOPSIS			-	0.4	0.8
Bipolar VIKOR				-	0.2
Bipolar EDAS					-

shows the Spearman’s rank correlation between methods. From Table 8, we find Proposed TOPSIS and COPRA as highly correlated. The correlation between proposed TOPSIS, Bipolar TOPSIS, and Bipolar EDAS is high but the Bipolar VIKOR is the smallest.

6.3. Limitations

Our paper aims to explore how to achieve sustainability for manufacturers and to be a competitor in the global marketplace through utilizing new technologies with the 6R methodology into operations and manufacturing whether inbound and outbound manufacturers (see Figure 3).

Although the paper has achieved significant results by applying various decision techniques in developing a decision framework (see Figure 4). The research has several limitations. First, this research does not discuss other dimensions which influence the sustainability of manufacturers as political, technical, and risk dimensions. Second, we did not discuss the challenges that may face the manufacturers and how to treat them to adopt and apply these technologies. Hence, their sustainability is threatened.

7. Managerial Implications

This study makes two significant managerial contributions that we sum up below:

• The study highlights the possible results of sustainability-focused I4.0 projects which can persuade managers and decision-makers to consider implementing sustainable I4.0 programs due to their economic and socio-environmental benefits. While the potential impacts of certain I4.0 technologies (such as IoT, automation, Cloud computing, BC, and BDA) on green practices and manufacturing are well-known in [41]. The integrative framework proposed by the authors enables managers to calibrate their involvement and assess their willingness to engage in terms of sustainability and the potential effects of such initiatives. The study assists firms in determining their readiness to incorporate sustainability into their I4.0 deployment.
• The findings emphasize the critical significance of management support and dedication in adopting I4.0 in a sustainable manner which is another managerial contribution of this work. Management should be prepared to build an environment conducive to incorporating sustainable practice within I4.0 implementation (including proper investments, staff involvement, resource deployment, and governance). Thus, firms may be able to expand the breadth and impact of externalities generated by sustainability-focused I4.0 efforts.
• Numerous experts have stated that employees are frequently hesitant to participate in I4.0 activities and perceive smart technologies as a threat. The findings of this study emphasize the critical role of management in resolving employee problems. Indeed, managers’ active participation in educating, informing, and elevating employees’ understanding of I4.0’s positive social externalities might assuage numerous of their reservations about such efforts. Managers’ support for such measures would increase staff engagement and success with a sustainability-focused I4.0 implementation.

8. Conclusions

Manufacturers have an important role in building the country’s economy. Hence, they continuously seek innovations and methodologies to achieve economic sustainability. However, the concept of sustainability and its realization is not only limited to the economy but also related to other pillars, the environment and society. These pillars belong to the so-called TBL. This paper seeks to apply various methodologies and technologies to achieve the sustainability of manufacturers and evaluate the sustainability performance of manufacturers who adopt these methodologies.

8.1. Theoretical Contributions

Our paper is a ground-breaking investigation into how to transform traditional linear economics into CE. The concept of circular products aims to return, remanufacture, and reuse products for end consumers to their initial form to reduce the consumption of raw materials and energy. Subsequently, CE can solve the problem of scarcity of resources by reducing waste emissions to the environment. Thus, the environment becomes clean and CP is achieved.

CE is achieved through applying 6R which extends to remanufacturing, reusing, redesign, recycling, recovery, and reduction of the product. 6R is a strong supporter to achieve CE and CP for manufacturers.

Another innovative representation in I4.0 and its technologies such as virtual reality, BCT, and BDA. These technologies are employed to improve the performance of manufacturers for gaining a global competitive advantage in the market to be sustainable CE, CP, and social.

So, this paper provides a contribution by merging with 6R methodology with BDA and BCT to improve manufacturers monitoring and traceability in the context of social sustainability and manufacturer become eco-friendly for the environment whether inbound and outbound manufacturing enterprise chain, as explained in Figure 3.

The evaluation process for manufacturers who adopt the merging in Figure 3 is vital. This process is performed based on scores and judgments for a set of criteria for applying 6R and I4.0 technologies by the DMs panel. Eight criteria used for evaluating the sustainability of manufacturing enterprises are determined as shown in Figure 5.

Another contribution discussed is utilizing the technique that can treat incomplete and imprecision data as neutrosophic theory combines with MCDM methods as BWM with the support of DEMATEL to obtain weights for criteria. These weights are utilized in N-TOPSIS and N-COPRAS, as illustrated in Stages Three and Four for evaluating and ranking the manufacturing enterprises and selecting the best one (see Figure 4).

The integrated decision framework is applied to an empirical case study for four manufacturers on the 10th of Ramadan city in Egypt to validate its efficiency, as mentioned in the section on the validation of the hybrid decision framework. The key findings of the empirical case study application clarify the following:

• C₆ is the most beneficial criterion and C₁ is the least benefit-based N-DEMATEL to use these criteria in N-BWM to obtain the final weights for eight determined criteria, as shown in Figure 6.
• The sustainability performances of four alternatives are evaluated and ranked in this case study through DMs.
• A₂ is the most sustainable alternative and A₄ is the least sustainable one according to N-TOPSIS and N-COPRAS as in Figure 7 and Figure 8.

8.2. Future Direction

In future work, this framework can be used by a public or private manufacturer from various industries. That can apply various forms of neutrosophic sets, such as Single-Valued, Bipolar, and Type-2 sets which can also be used in such a framework to represent uncertainty in other ways. Other multi-criteria decision-making strategies, depending on their structure, can be used to analyze and weigh the sustainability of manufacturing based on I4.0.