Safety Risk Assessment of Lithium-Ion Batteries Through Fuzzy Multi-Criteria Decision Making Methods
Subject Areas : Fuzzy Optimization and Modeling JournalMohammad Rostami 1 * , Amir Sabripour 2
1 - Shahrood University of Technology
2 - Iran University of Science and technology
Keywords: Lithium-ion batteries, Risk management, EOL management, Fuzzy Multi-criteria decision making.,
Abstract :
Lithium-ion batteries (LIBs) can help support sustainability through electric vehicles. LIBS are now widely used and there are concerns about obtaining LIB metals such as cobalt and lithium. LIB end-of-life (EOL) management is essential to the sustainability of the LIB metal supply chain. Safety risks in EOL LIBs are potential malfunctions. The paper addresses the assessment of safety risks in the management of end-of-life lithium-ion batteries. It employs a combination of the Fuzzy Simplified Best-Worst Method (FSBWM) and a hybrid Multi-Criteria Decision-Making Method (MCDM) to both quantify and rank the sources of safety risks and their impact on activities. This paper introduces the Simplified Best-Worst Method (SBWM), a pairwise comparison-based technique. SBWM is developed using triangular fuzzy numbers (TFNs) to create a fuzzy extension known as the Fuzzy Simplified Best-Worst Method (F-SBWM). The study also introduces an approach based on fuzzy multi-criteria decision-making (F-MCDM) to assess scenarios and initial failure hazards effectively. Ultimately, the paper utilizes two fuzzy MCDM methods, in addition to the proposed FSBWM and hybrid MCDM approach. The objective is to identify and rank failure modes comprehensively, offering a robust framework for evaluating safety risks in EOL LIB management, considering various criteria and perspectives. This method blends risk analysis with fuzzy MCDM to provide initial visions into relative safety risk resource improvements.
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Safety Risk Assessment of Lithium-Ion Batteries Through Fuzzy Multi-Criteria Decision Making Methods
Mohammad Rostamia*, Amir Sabripoorb
a Department of Industrial Engineering and Management, Faculty of Industrial Engineering and Management, Shahrood University of Technology, Shahrood, Iran
bDepartment of Industrial Engineering and Advancement, Faculty of Industrial Engineering and Advancement, Iran University of Science and Technology, Tehran, Iran
A R T I C L E I N F O |
| A B S T R A C T Lithium-ion batteries (LIBs) are essential for the sustainability of electric vehicles (EVs), but their end-of-life (EOL) management is critical for maintaining the supply chain of valuable metals such as cobalt and lithium. Effective EOL management not only mitigates environmental risks but also supports economic stability and social well-being. This paper quantitatively assesses the safety risks associated with EOL LIB management using advanced methodologies. We introduce the Fuzzy Simplified Best-Worst Method (F-SBWM) along with a hybrid approach combining the Fuzzy Additive Ratio Assessment (F-ARAS) and Fuzzy Weighted Aggregated Sum Product Assessment (F-WASPAS) methods. Our objective is to identify and rank failure modes comprehensively, providing a robust framework for evaluating safety risks from multiple perspectives. This approach integrates risk analysis with fuzzy Multi-Criteria Decision Making (MCDM) to offer insights into relative safety risk resource improvements. The study identifies and ranks key safety risk sources based on their impact on EOL processes, highlighting significant environmental, economic, and social concerns. It emphasizes the need for effective strategies to reduce environmental harm, support economic sustainability by ensuring resource availability, and enhance public safety and trust. The results propose actionable improvements to increase the stability and sustainability of LIB supply chains, addressing the critical intersections of environmental protection, economic viability, and social responsibility.
|
Article history: Received 3 May 2024 Revised 16 August 2024 Accepted 1 Semptember 2024 Available online 12 October 2024 | ||
Keywords: Lithium-ion batteries Risk management EOL management, Fuzzy Sets Multi-criteria decision making |
1. Introduction
The use of lithium-ion battery (LIB) is expanding, especially with the recent growth of the electric vehicle market (Duffner et al. [16]). LIB technology is also used for aircraft, drones, grids, and storage (Jiang et al. [21]). This growth and multiplicity of applications has led to complex supply problems of LIB resources including lithium, nickel, manganese and cobalt. Resource and supply concerns have also arisen, making end-of-life (EOL) management of LIBs a global concern (Mossali et al. [27], Slattery et al., [35])— Because supply chain disruptions for these resources have been widely observed (Sun et al. [37]).
Common circularity Re practices include recycling, remanufacturing, repurposing, repairing, and reusing (Richa et al. [31])— each of which may have different operational implications in closing the circular material flow loop. Economic and environmental value is achieved by proper management of EOL LIB and has been studied. (Pagliaro and Meneguzzo [29]).
Social and safety concerns regarding spent LIBs have received limited attention and are virtually absent from circular economy research, despite being a critical issue in practice (Wrålsen et al. [42]). The safety of LIB EOL management can be influenced by the battery's chemical composition, operating environment, and usage conditions (Chen et al. [9]).
The lifecycle of LIBs is summarized in Figure 1 and is based on the Ellen MacArthur Foundation's (EMF) circular economy license model (Foundation [17]). Raw metals are extracted for LIB production, which are then used to manufacture the final product delivered to users. Used LIBs are eventually collected from users for EOL management, allowing for the recovery of valuable materials. Collecting spent LIBs from users is a prerequisite for circular economy actions (Bird et al. [5]). Figure 1 illustrates the complexity and risks of the circular economy process by showing the various operators involved in different activities, the component loop, and the technology loop.
Figure 1. A butterfly model of a circular economy for lithium-ion batteries based on EMF (Chen et al. [13]).
Remanufacturing and repurposing can be considered as two similar CE technical methods (Alaoui et al. [2], Kampker et al. [22]). They involve changing a major component or aspect of batteries and using them. The difference between remanufacturing and reuse is that remanufacturing means returning spent LIBs to products for the same purpose. (Chen et al. [8]), and changing the usage is changing the use of batteries by changing the battery management system (Alaoui et al. [2], Yang et al. [43]). Batteries obtained from electric vehicles can be repurposed for energy storage—as an example. Recycling is the last technical CE loop for LIBs and may represent the CE final EOL LIB loop. (Chen et al. [8]).
Recycling represents the final technical CE loop for LIBs and is considered the ultimate EOL process in the circular economy framework (Chen et al. [8]). Batteries and battery residues that are deemed unfit for secondary use can be recycled to recover valuable materials for reuse in battery manufacturing and other applications (Shekhar et al. [33], Wang et al. [40]). However, safety risks associated with various EOL activities can lead to supply chain and material flow disruptions in CE-based LIB material management (Mossali et al. [27]). We have added more detailed examples of specific safety risks encountered in the EOL management of lithium-ion batteries (LIBs) to better contextualize the problem and emphasize its significance. The examples provided include:
· Thermal runaway: Improper handling and storage of used rechargeable batteries can result in thermal runaway, which can cause the battery temperature to rise uncontrollably, potentially causing a fire or explosion (Börger et al. [7]).
· Chemical exposure: Damaged or leaking batteries can release toxic chemicals such as lithium solvents, cobalt, and electrolytes, posing health risks to workers and environmental hazards (Zeng et al. [46]).
· Electrical hazards: Even at the end of their useful life, rechargeable batteries can retain a significant electrical charge. Short circuits or improper disassembly can result in electric shock or sparks, causing injury or fire (Blum & Long Jr [6]).
· Mechanical damage: Crushing, puncturing, or shredding a rechargeable battery without proper safety precautions can create flammable gases or thermal runaway (Shukla & Shankul. [34]).
· Environmental pollution: Improper disposal or recycling of LIBs can lead to soil and water pollution with toxic metals and chemicals, affecting local ecosystems and human health (Kilgo [23]).
Assessing supply chain disruptions due to safety risks can mitigate barriers to CE-based LIB management. The goals of this study include:
· Identify the sources of safety risks in LIBs CE technical loop practices.
· Assessing and ranking the impact of safety risk sources in LIBs EOL process activities that form the technical loop practices.
· Provide participants with insight into reducing safety risks in EOL LIB management and improving supply chain stability for circular economy activities for LIBs.
To address these challenges, this study introduces a comprehensive approach to assessing and managing safety risks in LIB EOL processes. The main research questions this study aims to resolve are:
· What are the specific sources of safety risk?
· What are the specific sources of safety risks in the EOL management of LIBs within a circular economy framework?
· How can these safety risks be quantified and ranked based on their impact on various EOL activities?
· What strategies can be employed to mitigate these risks and enhance the stability and sustainability of LIB supply chains?
Given the multi-stakeholder and multi-criteria nature of the problem context, our study introduces a combined methodology that integrates the Fuzzy Set-Based Weighting Method (FSBWM), Fuzzy Additive Ratio Assessment (F-ARAS), Fuzzy Weighted Aggregated Sum Product Assessment (F-WASPAS), and a hybrid approach of F-ARAS and F-WASPAS. This combined methodology aims to evaluate the concerns and support the goals of this study. The research is structured into four sequential phases:
· Identification of Safety Risks: The first step involves identifying six major sources of safety risks throughout the end-of-life (EOL) process activities, based on a literature review and expert input.
· Risk Weighting: The second step uses FSBWM to exemplify the weighting of these sources of safety risk.
· Performance Assessment: The third step involves evaluating the performance of these sources across different EOL activities using F-ARAS, F-WASPAS, and the proposed hybrid Multi-Criteria Decision-Making (MCDM) method.
· Validation: The final stage is to validate the methodology and results through feedback from experts.
Below, we address the potential limitations and assumptions made during our analysis:
Data Diversity and Quantity: Our study examines safety risks in the end-of-life (EOL) management of lithium-ion batteries (LIBs) using a blend of FSBWM, F-ARAS, and F-WASPAS methods. However, the range and volume of data collected, including expert opinions, may be restricted. This limitation could influence the accuracy and applicability of the results, as a more extensive dataset and a wider array of expert feedback might yield more thorough insights.
Fuzzy Methodology Constraints: Employing fuzzy methods such as F-SBWM, F-ARAS, and F-WASPAS adds inherent complexity and relies on theoretical models. The effectiveness of these fuzzy multi-criteria decision-making (MCDM) techniques is contingent upon the accuracy of the input data and the subjective judgments of the experts. Any variations in these inputs may impact the robustness and reliability of the risk assessments. Expert Feedback Limitations: While validating our results through expert feedback is essential, it may be influenced by the experts' personal interpretations and biases. Despite seeking input from a diverse group of experts, their individual perspectives and experiences could affect the validation process and, consequently, the outcomes.
We assume that the expert opinions obtained are both representative and reliable for assessing safety risks in LIB EOL management. This assumption relies on the experts' experience and expertise in the field; however, individual biases and limited knowledge in specific areas could influence the results. Additionally, the integration of FSBWM, F-ARAS, and F-WASPAS methods presumes that these methods are compatible and provide a coherent approach for evaluating and ranking safety risks.
The remainder of this research begins with a review of papers related to LIBs, safety risk sources, and methods in Section 2. Section 3 provides more details on the study methodology. Section 4 shows the results obtained from sample field data using the proposed method with expert input. Conclusions, limitations and future study steps are summarized in Section 5.
2. Background and literature
2.1. EOL activities of lithium-ion batteries
The supply of raw materials is one of the important issues facing the widespread use of LIBs. There are numerous social, economic and environmental issues in the supply chain of metals used for LIB production (Liu et al. [26]). Based on this situation, CE has become an important topic in the field of LIB (Mossali et al. [27]). CE is a system that combines reduction, reuse and recycling that supports the reduction of raw material consumption, reduction of environmental impact and improvement of economic efficiency (Kampker et al. [22]).
Figure 2. Research process flowchart.
Table 1 summarizes previous studies on LIB EOL management activities. These EOL activities include collection, testing, sorting, discharge, disassembling, crushing, sieving, reassembling, and recycling technologies (Alaoui et al. [2], Chen et al. [11], Kampker et al. [22], Hua et al. [20], Shekhar et al. [33], Wang et al. [40], Yang et al. [43]). Safety issues in these activities are listed in Table 1 in several studies (Chen et al. [10], Christensen et al. [14], Wang et al. [40]). Christensen et al. [14] discusses the safety challenges of LIBs, pointing out that their quick integration into everyday life has surpassed our understanding of their risks. It highlights deficiencies in current safety practices and stresses the importance of improved education and regulations to address these risks as we move towards low-carbon energy and transportation solutions. Similar research addresses the safety and management challenges of LiBs in electric vehicles (EVs) throughout their lifecycle. It highlights risks such as thermal runaway, fire, and explosion incidents, emphasizing the need for effective safety plans. The study also examines the environmental impacts of LiBs, focusing on creating a resource-efficient recycling system (Shukla & Shankul [34]). In review paper examines the environmental impacts of LIBs from production through usage and recycling, emphasizing the growing need for sustainable recycling as LIB waste increases. It highlights that reusing recovered materials in battery manufacturing can reduce environmental footprints, greenhouse gas emissions, and energy consumption. The study provides an overview of the environmental effects of LIBs across their lifecycle and underscores the importance of recycling for metal replenishment (Liu et al. [26]). However, measurement of safety issues and inclusion in decision-making has been neglected. The aim of our study is to evaluate and quantitatively analyze the sources of different safety risks and their impact on EOL activities, based on the importance of safety issues for CE of LIBs and the sustainability of the battery metal supply chain. This approach and results provide initial evidence for safety measures and management in this closed-loop system, but also evidence for a broader CE safety assessment.
Table 1. Studies of lithium-ion battery end-of-life management.
Author | Subject | Collection | Test | Sort | Discharge | Disassemble | Crush | Sieve | Reassemble | Hydrometallurgical, Pyrometallurgical, Direct physical process | Safety mention | Safety evaluations | |
EOL | √ |
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| √ |
| √ |
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LIBs |
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2021) | EOL | √ |
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| √ | √ |
| √ |
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| |
LIBs |
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| ||||||
|
2018) | EOL |
|
| √ | √ | √ |
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| √ | √ |
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| |
LIBs |
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|
2019) | EOL |
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| √ |
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LIBs |
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|
2020) | EOL |
| √ |
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| √ |
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LIBs | |||||||||||||
EOL | √ |
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| √ |
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LIBs |
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LIBs |
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| √ |
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2018) |
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2019) | LIBs |
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| √ |
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2021) | LIBs |
| √ |
| √ |
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| √ |
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LIBs | √ | √ |
| √ | √ | √ |
| √ | √ | √ |
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2015) | EOL | √ |
| √ |
| √ | |||||||
LIBs | |||||||||||||
|
2020) | EOL |
| √ |
| √ | √ | √ | √ |
| √ | |||
LIBs | |||||||||||||
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2019) | EOL | √ | √ |
| √ | √ | √ |
| √ | √ |
| √ | |
LIBs | |||||||||||||
(Christensen et al., 202) | EOL LIBS |
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| √ | √ |
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| √ | |
(Ren et al., 2023) | EOL LIBS | √ | √ |
| √ | √ | √ |
| √ |
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| √ | |
( Shukla & Shankul, 2024) | EOL LIBS | √ | √ |
| √ | √ |
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| √ |
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(Liu et al., 2024) | EOL LIBS |
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| √ | √ | √ |
| √ | √ |
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2023) | EOL | √ | √ | √ | √ | √ | √ | √ | √ | √ |
| √ | |
Current | LIBs | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ √ | ||
LIBs | |||||||||||||
Figure 3. IDEF system for end-of-life management for lithium-ion batteries (Zeng et al. [47]).
To further describe some EOL LIB management activities and their interrelationships - which will be examined later in this research - an IDEF systems design and analysis process model is introduced (Bankole et al. [4]) shown in Figure 3. The six rectangles show specific EOL activities. Entering activities are the inputs and arrows exiting the activities show the outputs. Arrows from the top represent controls that would include standards, specifications, and management methods. The arrows going into the rectangle from the bottom up are mechanisms, such as equipment, machine, and people, which are used to transform inputs into outputs.
Initially, proper collection is the first activity usually performed in the management of EOL LIBs. The widespread use, different capacities, and compositions in a wide variety of LIBs make collection an important topic (Zeng et al. [47]). Testing and sorting of EOL batteries is the next step - especially considering the quality of the collected materials and the estimation of battery lifetime is a significant challenge at this stage (Zhang et al. [49]).
EOL LIBs typically have internal energy storage, which leads to an important and relatively unique EOL LIB activity - battery discharge. (Bankole et al. [49], Liao et al. [25], Zhang et al. [48]). Battery pack disassembly is an important activity and obstacle in achieving CE for LIBs. This requires the separation of the battery's main components, such as the body, cathode material, diaphragm, and electrolyte. (Sommerville et al. [36]). Batteries and parts that cannot be further reused are crushed in a crusher and screened through a screen before being recycled. (Liu et al. [26], Vel´ azquez-Martínez et al. [39], Yang et al. [43], Zhong et al. [50], Zolfani & Chatterjee [5]). Recycling technologies include hydrometallurgical, pyrometallurgical and direct physical processes, the last material conversion activity in CE technologies. (Ciez and Whitacre, [15], Olivetti et al. [28]). In each stage, especially in the final stage, handling and transportation - outbound logistics - batteries and various materials are carried out after the completion of all activities.
2.2. An EOL system conceptualization of safety risk sources
As the management of end-of-life (EOL) lithium-ion batteries (LIBs) increases, so do safety risks (Liu et al., 2018). Two primary factors contribute to the safety risks associated with EOL LIB management. First, EOL LIBs enter the waste stream in various states and with different defects, which complicates safety management. These conditions include leakage, swelling, internal short circuits, external coating damage, and corrosion (Winslow et al. [41]). Second, the complexity and variability of EOL management activities make it challenging to monitor and control safety risks (Harper et al. [19]). Safety issues such as spontaneous combustion and explosions that occur during EOL management activities can disrupt the circular economy (CE) processes for LIBs (Chen et al., [13]). The final sources of safety problems including electrical, chemical, mechanical, environmental, inter-organizational, and managerial risks may arise from EOL activities, as illustrated in the IDEF model in Figure 3, which is based on the literature review.
The main sources of safety risk during EOL LIB CE management activities are shown in Table 2. This table is based on secondary literature search (see previous sections) and extracted from research by) Chen et al. [12]). For further consideration, electrical, chemical and mechanical safety risk sources are categorized as technical safety risk sources and environmental, inter-organizational and management dimensions as non-technical safety risk sources. Technical resources indicate safety risks due to the immaturity and uncertainty of LIB design and manufacturing technology. Non-technical safety risks arise from internal and external circular economy activities.
Table 2. Safety risk sources during the end-of-life activities from a circular economy perspective.
Safety Risk Sources | Explanation | Reference | |
Technical | Electrical (EL) | Electrical hazard sources are identified such as over-discharge, and isolation concerns that can arise risks in different end-of-life activities. | (Christensen et al., 2021; Slattery et al., 2021) |
Chemical (CH) | The application of chemicals could cause hazardous pollutants and occurrence injury. | (Adeola, 2018; Chen et al., 2019; Harper et al., 2019; Vieceli et al., 2018; Waldmann et al., 2016; Zhou et al., 2020) | |
Mechanical (ME) | The mechanical source is including physical damage, vibration, and ambient pressure change during EOL management. | (McDowall et al., 2007; Slattery et al., 2021; Xie et al., 2020) | |
Non- technical | Environmental (EN) | External physical environment, for example, ambient temperature, humidity, and air composition is an important source of LIBs safety risks. | (Chen et al., 2017; Fan et al., 2020; Harper et al., 2019; Lyu et al., 2020; Moreno-Camacho et al., 2019; Wang et al., 2019; Zhang et al., 2018) |
Inter-Organizational (OR) | Risks occur across organizations, such as lack of regulation by government, emergency response for fire protection departments, fire detection systems and labeling for all non-government organizations and companies. | (Ciez and Whitacre, 2019; Hua et al., 2020; Huo et al., 2017; Yu et al., 2021) | |
Managerial (MA) | Managerial safety risk sources include the risks caused by inadequate managerial governance such as lack of safety design, manufacturer emergency response, overstock, lack of inventory coordination, insufficient operational training, and staff limited safety skills that might create safety risks. | (Fan et al., 2020; Huang et al., 2018; Moreno-Camacho et al., 2019; Slattery et al., 2021; Sommerville et al., 2020; Waldmann et al., 2016; Zhou et al., 2020) | |
3. Research methodology
In this research, a four-step method to evaluate the sources of safety risks and their impact on EOL activities from the perspective of CE practices has been carried out. The first step is to recognize the main safety risk sources and EOL management activities from a literature review. A questionnaire for the F-SBWM and F-ARAS and F- WASPAS and proposed hybrid MCDM methodology data acquisition is presented after determining an initial set of criteria informed by a literature review. Three experts are specified for preparing answers to the questionnaire during this initial stage; the characteristics of these experts are given in section 4.1. The outputs of the questionnaire are demanded for the latter steps of F-SBWM and F-ARAS and F- WASPAS and proposed hybrid MCDM execution. F-SBWM is used to obtained the weights of each safety risk source, and F-ARAS and F- WASPAS and the proposed hybrid MCDM approach are used to find their impact on each EOL activity.
Section 3.1 focuses on investigating the extent of a study that initially aims to tackle uncertainties in the external environment. The study achieves this by exploring the principles of fuzzy logic. The second stage analyzes the safety risk sources by applying F-SBWM and is further detailed in Section 3.2. The data for F-SBWM was obtained from the questionnaire developed in step 1 and from the experts' responses. The third stage excavates the EOL activities using a hybrid method of risk analysis and F-ARAS and F- WASPAS and the proposed hybrid MCDM methods as detailed in Section 3.3. The data severity of effect (S) and the likelihood of occurrence (O) data—obtained from the questionnaire responses from the experts—are used in the F-ARAS and F- WASPAS and the proposed hybrid MCDM approach. The results of Step 3 are ranked safety scores that indicate the safety impact of safety risk sources throughout the EOL activities.
3.1. Fuzzy Logic
In 1965, Professor L. A. Zadeh introduced the fuzzy set theory. This theory, extending classical set theory, proves beneficial in addressing practical challenges within uncertain environments.
A fuzzy set, denoted as
, is defined as a pair (U, m), where U represents a set, and m: U → [0, 1] serves as the membership function, denoted as
. The functionallows the mapping of each element x within a universe of discourse X to a real number in the range [0, 1].
Definition 1. If 
and 
When two triangular fuzzy numbers are subjected to addition, the resultant fuzzy number, as described in Eq. (1), will also exhibit a triangular shape.
|
|
where 
and 
are the middle value and right-side value of the triangular fuzzy number 
, respectively.
Definition 2. If 
and 
are two triangular fuzzy numbers, then their distance, denoted by d(A,B), is a triangular fuzzy number 
whose values 
can be calculated using the following Eq. (2):
|
|
where in Eq. (3), (4):
| (3) |
| (4) |
Furthermore, the membership function is illustrated in Eq. (5).
| (5) |
Fuzzy numbers can represent linguistic variables. The relationship between linguistic variables and TFN are presented in Tables 3.
Table 3. Relationships between linguistic variables and triangular fuzzy numbers (Sabripoor et al., [32]).
Linguistic Terms | Fuzzy Scales |
Equally importance (EI) | (1,1,1) |
Weakly important (WI) | (1,2,3) |
Moderate importance (MI) | (2,3,4) |
Moderate plus importance (MP) | (3,4,5) |
Strong importance (SI) | (4,5,6) |
Strong plus importance (SP) | (5,6,7) |
Very strong importance (VS) | (6,7,8) |
Extreme importance (EX) | (7,8,9) |
3.2. Obtain weights for safety risk sources using F-SBWM
BWM is widely applied in operations and supply chain management (Bai et al. [3], Gupta and Barua [18], Kusi-Sarpong et al. [24], Liao et al. [25], Zolfani and Chatterjee [51]). This tool was developed as an alternative decision support tool to MCDM (Rezaei [30]) to address some of the complexities of the AHP method related to pairwise comparisons, but it is based on mathematical programming optimization and multi-objective optimization approaches. Similar to the traditional BWM, F-SBWM involves the identification of a set of criteria as a foundational step in the decision-making process. The decision maker then designates the most and least important criteria. Subsequently, fuzzy reference comparisons, involving linguistic terms and TFNs, are performed. The expert's fuzzy preferences vector is established, and the significance of each criterion is computed through straightforward calculations and fuzzy operators, eliminating the need for mathematical programming models.
During the fuzzy comparisons of the best criterion to the other criteria, the importance of the best criterion is determined. Utilizing the weight of the best criterion, the weights of the remaining criteria are also computed, forming the best-to-others vector. Additionally, in the fuzzy comparisons of the other criteria to the worst criterion, the importance of the worst criterion is determined. The weights of the other criteria are then derived using the weight of the worst criterion, resulting in the others-to-worst vector. Finally, these two vectors are amalgamated to derive the ultimate weights of the decision criteria. This approach substantially streamlines the decision-making process, reducing the time required. Importantly, and since there are no mathematical programming models in this method, the decision maker does not need to use software packages.
Proceeding further, the stages of the F-SBWM method are outlined as follows:
Step 1: This step nvolves defining decision criteria in the format of and selecting both the most significant and least significant criteria.
Step 2: The preference of the best criterion over each of the other criteria is established using linguistic terms and Triangular Fuzzy Numbers (TFNs) in the structure of 
.
Step 3: The preference of each criterion over the least important criterion is determined using linguistic terms and TFNs in the format of 
.
Step 4: The priority of each criterion is computed through reference comparisons of the best criterion against the other criteria, represented by 
. Equation (6) is utilized to calculate the priority of the best criterion over each of the criteria. Subsequently, the weight of the best criterion is determined. By substituting the weight of the best criterion into Equation (7), the weights of the remaining criteria are also derived.
|
| (6) |
|
| (7) |
Step 5: The priority of each criterion is determined through reference comparisons of each criterion against the worst criterion, expressed as 
. Equation (8) is employed to calculate the priority of each criterion over the worst criterion. Concurrently, the weight of the worst criterion is computed. By substituting the weight of the worst criterion into Equation (9), the weights of the other criteria are also calculated.
|
| (8) |
|
| (9) |
Step 6: The ultimate weights of the decision criteria are computed using Equation (10).
|
| (10) |
Step 7: The center-of-area method stands out as the most practical and direct technique for the defuzzification process, as outlined in Equation (11):
| (11) |
3.3. Ranking the end-of-life activities about safety performance using F-ARAS
ARAS, introduced by Zavadskas and Turskis [44], is grounded in the idea that understanding complex phenomena in the world can be achieved through straightforward relative comparisons. This method not only assesses the performance of alternatives but also computes the ratio of each alternative to the ideal one. In the ARAS approach, the decision team assigns relative importance to evaluation criteria and rates feasible alternatives based on numerical values. In practical scenarios, determining precise weights for criteria and alternatives can be challenging for decision-makers. To address this challenge, a fuzzy approach is employed, using fuzzy numbers instead of crisp numbers, to better adapt to real-world cases. Consequently, fuzzy logic and the ARAS technique are combined to create the F-ARAS method, enhancing the accuracy of problem formulation in real-world scenarios.
The fuzzy ARAS technique facilitates a comprehensive analysis by allowing the decision team to prioritize alternatives' preferences in the presence of vague or imprecise information. The procedural steps of the fuzzy ARAS method are outlined as follows:
Step 1: The construction of a Fuzzy Decision-Making Matrix (FDMM) involves assigning performance values (
) and attribute weights (
) as matrix entries. The selection of linguistic ratings is integral to this process. 
capturing preferences for
viable alternatives (rows) evaluated across
attributes (columns).
Step 2: Determining a hypothetical ideal value. The calculated ideal values for the criteria according to Equation (12):
| (12) |
Step 3: FDMM is normalized j according to Equation (13):
| (13) |
Step 4: Calculate the weighted normalized FDMM 
according to Equation (14):
| (14) |
Step 5: Calculate values of the optimality function, total relative importance of 
alternative according to Equation (15):
| (15) |
It’s noteworthy that the outcomes of fuzzy performance assessment for individual alternatives are expressed as fuzzy numbers 
. The center-of-area method emerges as the most practical and straightforward approach for the process of defuzzification and compute according to Equation (16):
| (16) |
Step 6: The degree of utility for an alternative is ascertained through a comparison of the analyzed variant with the ideally optimal one, 
. The equation employed to compute the utility degree 
for an alternative 
according to Equation (17):
| (17) |
Step 7: alternatives are ranked according to the value of , indicating that a higher value corresponds to increased desirability of the option.
3.4. Ranking the end-of-life activities about safety performance using F-WASPAS
MADM method, namely WASPAS, was introduced in by Zavadskas et al. [45]. This subsection extends WASPAS to the fuzzy environment. The merit of using a fuzzy approach is to assign the relative importance of attributes using fuzzy numbers instead of precise numbers. WASPAS method is still developed so that it is possible to apply this approach to solving various decision-making problems. For example an extension of the WASPAS method using fuzzy sets can be found in Turskis et al. [38]. The WSM approach calculates the total score of the alternative as a weighted sum of the criteria. The WPM approach was created to prevent alternatives that have poor attributes or criterion values. Zavadskas et al. used the multiplicative exponential weighting method (or WPM) to solve dynamically changing environment problems.
The problem solution process by applying the F-WASPAS method is shown below:
Step 1: The construction of a Fuzzy Decision-Making Matrix (FDMM) involves assigning performance values
() and attribute weights () as matrix entries. The selection of linguistic ratings is integral to this process. capturing preferences for viable alternatives (rows) evaluated across attributes (columns).
Step 2: FDMM is normalized according to Equation (18):
| (18) |
Step 3a: Calculate the weighted normalized fuzzy decision matrix 
for WSM according to Equation (19):
| (19) |
Step 3b: Calculate the weighted normalized fuzzy decision matrix 
for WPM according to Equation (20):
| (20) |
Step 4: Calculate values of the optimality function, total relative importance of alternative according to Equations (21) and (22):
| (21) |
| (22) |
It’s noteworthy that the outcomes of fuzzy performance assessment for individual alternatives are expressed as fuzzy numbers 
and 
. The center-of-area method emerges as the most practical and straightforward approach for the process of defuzzification according to Equations (23) and (24):
| (23) |
| (24) |
Step 5: The calculated value of the integrated utility function for an alternative using the F-WASPAS method can be ascertained through according to Equation (25):
| (25) |
It’s noteworthy that 
equation’s value is derived from the provided formula according to Equation (26), nevertheless, it is important to note that in the majority of research studies, this value is typically assumed to be 0.5.
| (26) |
Step 6: alternatives are ranked according to the value of K, indicating that a higher K value corresponds to increased desirability of the option.
3.5. Ranking the end-of-life activities about safety performance using hybrid MCDM approach
Extensive attention has been directed toward Multiple Criteria Decision-Making (MCDM) methods, leading to the proliferation of diverse approaches within this field. Because each MCDM method in the literature employs distinct logic to rank available options in decision problems, it is common to encounter divergent outcomes when applying multiple MCDM methods to the same problem. The ranking of options is inherently tied to the chosen approach. While instances of similar rankings across different methods for a specific problem are feasible, such occurrences are infrequent due to the limited commonality in logic among diverse methods.
In this study, we have introduced an innovative approach by amalgamating 2 established fuzzy MCDM methods based on utility functions and similarity. Following logical principles, was developed through various approaches, ultimately resulting in the creation of a novel method for ranking options. Emphasizing the importance of an effective integration method for evaluating the ultimate desirability score for each alternative, we subsequently provide a detailed elaboration on the specifics and steps of the proposed method.
Step 1: The scores assigned to the identified failure cases must be confined to the range of 0 to 1. The ranking indexes for F-ARAS and F-WASPAS are represented by and 
, respectively.
Step 2: Calculating the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) involves utilizing the following maximum (
) and minimum (
) values according to Equations (27) and (28):