Enhancing Supply Chain Resilience Through a Fuzzy AHP and TOPSIS to Mitigate Transportation Disruption

Abstract

Supply chain resilience is a growing concern as risk becomes increasingly challenging to interpret and anticipate due to sudden global events that disrupt the core of global supply chains. This paper discusses the use of advanced technologies to enhance supply chain resilience, proposing a two-step hybrid fuzzy analytic hierarchy process (FAHP) and the technique for order of preference by similarity to ideal solution (TOPSIS) approach that evaluates a set of different supply chain KPIs or criteria that trigger possible supply chain risks, with a focus on transportation disruptions. Using FAHP, the highest potential risks from disasters are identified, and TOPSIS is used to rank alternative solutions that enhance supply chain resilience. The approach is tested on real-world applications across multiple supply chain systems involving various companies and experts to demonstrate its validity, feasibility, and applicability. Based on five criteria and six alternatives per case study, the findings showed that for manufacturing supply chains, the highest risk was attributed to travel time (46%), and the most effective solution to mitigate it was found to be strengthening highway networks (0.72). For transportation, delivery time (56%) was the primary risk, addressed by green logistics and sustainability (0.89).

1. Introduction

Recent events have shown that supply chain security is far from where it needs to be, and industrial businesses face significant threats from sudden occurrences that can lead to severe consequences. Such events do not require extensive research, as many have experienced them first-hand. A major example is the COVID-19 pandemic, which has impacted the globe, deeply affecting everyone and undoubtedly being the reason that many businesses and supply chains found themselves in critical situations, even forcing some to close their doors indefinitely due to bankruptcy [1,2]. Supply chains are prone to significant issues when sudden changes occur in their daily operations, highlighting a serious challenge since no supply chain operates smoothly all the time. This necessitates analyzing potential risks and developing solutions before unexpected disruptions affect the supply chain [3].

Building and establishing supply chain resilience is essential, as it is primarily about managing and addressing disturbances quickly and effectively, enabling the supply chain to recover rapidly from setbacks with minimal losses in goods and finances [4,5]. Based on the study by Ivanov et al. [6], supply chain disruptions are classified into three categories: production, supply, and transportation disruptions. Among these, transportation is a particularly critical and vulnerable component, as transportation disruptions such as delays, infrastructure bottlenecks, and labor shortages can ripple through the entire supply chain, causing product losses and increased costs and eventually impacting service levels and organizational performance across industries [7,8].

The focus of this study is on supply chain systems, which incorporate various technological elements throughout their processes. However, these systems heavily depend on human reasoning and expertise at the fundamental level. Suppose a problem needs to be detected before it occurs. In that case, humans who actively participate in and monitor the entire process, from raw materials to the end (customer), are better suited to provide input.

Although human expertise and reasoning are valuable, they can be subjective and inconsistent, especially under uncertainty. Fuzzy logic addresses this by mimicking human reasoning and cognition, modeling imprecise and linguistic information in a structured way and improving the reliability of expert-based decisions [9,10]. However, it achieves this in a way that decisions are not strictly binary or classified as black and white—0 or 1. Instead, considering the grey area, it focuses on interval values between 0 and 1. This approach can highlight the uncertainty that may arise from an individual human decision, making the analysis much more realistic and reliable [11].

Fuzzy logic is combined with the analytic hierarchy process (AHP) to form a fuzzy AHP model, which offers several advantages, particularly in handling subjective criteria and capturing the inherent uncertainty in decision-making. This approach models subjectivity by considering the qualitative components of decision-making using linguistic terms and fuzzy sets. Flexibility in representation expresses the degree of importance or preference in a way consistent with their subjective interpretation of the choice context. Handling uncertainty, fuzzy AHP enables decision-makers to represent uncertainty by fuzzy memberships and comparisons. Improved consistency measures: Advanced consistency measures consider the imprecise nature of assessments incorporated into fuzzy AHP. This enhances the reliability of the decision-making process by guaranteeing that subjective preferences remain consistent and logical despite uncertainty. Finally, improved decision quality results from the nuanced representation of subjective criteria, particularly where subjectivity and uncertainty are significant factors [12,13].

Fuzzy logic is integrated with the technique for order of preference by similarity to ideal solution (TOPSIS) to create a fuzzy TOPSIS model that effectively handles imprecise and uncertain information using fuzzy sets and enhances decision-making robustness. Considering the uncertain nature of the criterion values, the method is more resilient to fluctuations and errors in the data. Improved sensitivity to subjective judgments recognizes the imprecision in subjective evaluations and offers a way to take and handle such data. Accurate representation of uncertainty is helpful when making decisions based on qualitative or unclear information in real-world situations, where obtaining accurate data can be challenging [14].

This study aims to connect the industrial principle of supply chain systems with the ever-growing development of artificial intelligence, which is undoubtedly the future of humankind, to build resilience and enable risk-aware, adaptive decision-making. Despite acknowledging the disruptive nature of recent events, there remains insufficient exploration of strategies that harness advanced technologies to enhance supply chain resilience, particularly in transportation, as the world has yet to recognize that this unpredictability poses a significant danger and will eventually begin to dominate the industrial realm, causing businesses to lose control. This paper addresses this gap by investigating the application of a hybrid fuzzy AHP approach and TOPSIS in sustaining supply chain resilience against transportation disruptions. This integration could result in more accurate and better transportation disruption risk assessments, allowing stakeholders to make more informed decisions and employ proactive techniques to reduce the impact of disruptions on supply chain networks. The main contributions of this study include the development of a hybrid FAHP–fuzzy TOPSIS model tailored to transportation-related disruptions, the incorporation of expert judgment under uncertainty to enable more accurate risk prioritization, the identification of resilience-related KPIs specific to transportation and manufacturing contexts, and the provision of a scalable and flexible tool for practical risk mitigation and strategic decision support.

After that, the study has the following specific objectives:

• To identify key supply chain risks by developing a hybrid FAHP–TOPSIS framework for systematic risk evaluation and solution ranking;
• To validate the model through real-world applications across industries, particularly in transportation and manufacturing;
• To provide practical recommendations for risk mitigation;
• To ensure the model’s flexibility and scalability for various supply chain scenarios.

This study particularly focuses on transportation disruptions, given their central role in the continuity of supply chains, from raw materials to final delivery. To reflect these risks effectively, KPIs and evaluation criteria related to transportation resilience, such as delivery time and inventory level, are first identified, ensuring translatability for expert judgment. These KPIs are structured hierarchically, and their importance weights are determined using the FAHP method. Fuzzy TOPSIS is then used to evaluate and rank disruption scenarios based on their closeness to the ideal solution. This architecture equips decision-makers with actionable insights, improves readiness against transportation disruptions, and supports long-term strategic planning in uncertain operational environments. Ultimately, it contributes to the creation of more adaptive, robust, and future-proof supply chains.

2. Literature Review

In the wake of the COVID-19 pandemic, global supply chains have encountered extraordinary and extended disruptions that exposed vulnerabilities, especially in transportation [15]. Transportation disruptions exposed the fragility of interconnected logistics systems, making them a focal point for resilience modeling [16]. These successive failures revealed the urgent need for comprehensive resilience modeling that is capable of capturing the complexity, uncertainty, and systemic nature of such threats [17].

Traditionally, two main types of risk assessment have been used: quantitative methods, which are based on statistical analysis, historical data, mathematical models, and probabilistic techniques to quantify the possibility and effects of disruption, and qualitative approaches, which involve the opinion of experts who may participate in workshops or surveys to identify and rank potential risks, in addition to tools such as risk matrices [18,19,20].

Therefore, to address these challenges, researchers and practitioners have increasingly turned to artificial intelligence (AI)-based decision support systems that can manage complexity and uncertainty more effectively than traditional methods [21]. Among these approaches, fuzzy logic has emerged as a particularly valuable tool for modeling uncertain conditions in real-world decision-making. Fuzzy logic systems use rule-based reasoning methods. Decision-making processes are built on IF–THEN rules incorporating linguistic variables and fuzzy membership functions. This method successfully captures specialist knowledge and deals with real-life situations [22].

Recent research explores the integration of AI with multi-criteria decision-making (MCDM) techniques across various domains, including emergency and supply chain management. In the context of COVID-19, hybrid models such as AHP–TOPSIS have been effectively applied to evaluate and prioritize alternatives under rapidly changing conditions. Among MCDM techniques, fuzzy AHP (FAHP) and fuzzy TOPSIS stand out for their ability to handle uncertainty and subjectivity in complex decision-making scenarios. FAHP is particularly suited to capturing imprecise expert judgments and deriving fuzzy weights for criteria, while fuzzy TOPSIS excels in ranking alternatives based on their closeness to an ideal solution [23,24].

By combining these complementary methods, researchers can support more structured, transparent, and resilient decision-making, particularly when addressing transportation disruptions in post-COVID-19 supply chain environments.

As summarized in

Table 1. Key research contributions to supply chain resilience enhancement using FAHP and TOPSIS.

Paper	Approach	Conclusion	Advantages	Shortcomings/Future Work
[25]	Integrated fuzzy AHP and TOPSIS approach.	The two-step method ranks disruption strategies Case study confirms storage capacity as the top solution	- Combines qualitative (interviews) and quantitative (MCDM) analysis - Handles uncertainty and subjectivity via fuzzy logic - Real case application increases relevance	- Complexity in fuzzy logic calculations - Requires expert input for consistency and accuracy
[26]	Hybrid fuzzy AHP–TOPSIS framework for risk assessment in GSCM.	- Framework supports stepwise implementation of green initiatives - Helps assess and reduce GSCM risks - Prioritizes solutions under uncertainty	- Handles vagueness via linguistic terms - Practical, replicable method - Supports decision-making in risk-prone GSCM	- Results may vary by industry/context - Explore fuzzy VIKOR, ELECTRE, PROMETHEE - Extend to other sectors or risk types - Include more expert opinions
[27]	Integrated FAHP–TOPSIS model for supply chain risk (automotive case study)	- Identifies key risk stages in PLC/OPC - Prioritizes strategies to reduce SC risk and improve performance	- Integrated analysis of lifecycle and operations with performance factors - Supports decision-making under uncertainty - Novel application of fuzzy multi-criteria model to both PLC and OPC risks	- Criteria focused mainly on economic risks - Narrow range of risk assessment criteria
[28]	Evaluate using multi-criteria decision-making (e.g., Fuzzy AHP–TOPSIS); test robustness via sensitivity analysis.	Environmental (green) and social aspects are key to improving supply chain performance under CSR. Certain alternatives (e.g., suppliers, technology) often have a higher impact.	Structured and adaptable framework, incorporates expert insights, supports prioritization, and better decision-making in CSR integration.	Results may be limited by scope (region, sector, number of alternatives) and depend on expert input.
[29]	Hybrid AHP–TOPSIS for supplier evaluation in Pegah Zanjan Company	Effectively identified and ranked the top suppliers based on key performance indicators (KPIs) under uncertainty	- Combines strengths of AHP (weighting) and TOPSIS (ranking) - Reduces pairwise comparison complexity - Suitable for uncertain, real-world conditions	- Relies on expert input - Limited generalizability without adaptation - Requires careful handling of fuzzy data
[30]	FAHP–TOPSIS for prioritizing resilience indicators in a combined cycle power plant	Identified key resilience factors—structural stability, management awareness, and risk acceptance—as most critical	- Structured prioritization of indicators - Combines expert input with analytical methods - Applicable to other process industries	- Relies on subjective expert input - Limited to one case study - May require recalibration for other sectors

, several studies have employed integrated FAHP–TOPSIS frameworks to enhance resilience in various supply chain domains. These publications demonstrate that combining fuzzy MCDM methods improves decision-making transparency, supports structured risk evaluation, and enhances adaptability across industries.

The recent literature shows a lack of methodologies that combine fuzzy AHP and TOPSIS in transportation disruption risk assessment. The combination of fuzzy AHP and TOPSIS can potentially improve the resilience of transportation disruption risk evaluations by simultaneously addressing uncertainty in the criteria weights and the outcome scores. By combining these two fuzzy techniques, researchers can construct stronger models that better represent the complex and unpredictable nature of transportation networks. Existing approaches are available for combined fuzzy AHP and TOPSIS; however, there are still prominent gaps in the field of supply chain regarding its broader applicability across different industries and complex multi-criteria decision-making scenarios.

While disruptions in the supply chain are a major concern for global enterprises, combining fuzzy AHP and TOPSIS to evaluate and prevent disruptions is an area of research that is not yet fully explored. Fuzzy AHP, known for its ability to handle uncertainties and imprecise input, has been used in various decision-making processes. However, its use, particularly in supply chain disruptions, is limited. There is a significant gap in understanding the hidden nature of disruptions due to a lack of studies on how fuzzy AHP can be efficiently used to analyze disruption possibilities, effects, and recovery techniques in supply chains.

Moreover, there is a limitation of resources on fuzzy TOPSIS and its application in assessing transportation disruptions within supply chains. When transportation systems are disrupted, fuzzy TOPSIS, known for its ability to rank alternatives in uncertain situations, can provide essential insights into optimal decision-making. However, the lack of studies concentrating on this integration leaves investigators uncertain about using fuzzy TOPSIS for practical disruption risk evaluation and mitigation methodologies for transportation. The limited literature on these topics highlights future research opportunities.

One of the primary challenges is the lack of real-world validation of fuzzy AHP and TOPSIS in supply chain disruptions. Determining the practical applicability, dependability, and generalizability of these fuzzy techniques in diverse and dynamic supply chain systems is complicated without comprehensive real-world validations.

Comprehensive supply chains include sophisticated networks with several interconnected elements, making it challenging to model and apply fuzzy AHP and fuzzy TOPSIS comprehensively. The absence of case studies in complete supply networks limits our understanding of how these fuzzy approaches adapt to the complexities of real-world supply chain structures and dynamics.

In current approaches, such as fuzzy AHP and TOPSIS, the limited emphasis on KPIs may lead to an incomplete understanding of the overall impact of disruptions. Without considering a practical set of KPIs, researchers may overlook possibilities to thoroughly analyze the performance of transportation systems under multiple disruptive scenarios and potentially fail to find areas for improvement.

Despite these promising efforts, the gaps can be summarized as follows:

• Lack of transportation-specific FAHP–TOPSIS applications: While Table 1 demonstrates a wide range of uses, relatively few studies focus directly on transportation disruption assessment, especially within post-COVID recovery planning.
• Limited integration with real-world KPIs: The limited emphasis on KPIs restricts the ability to evaluate the full operational impact of disruptions across multiple scenarios.
• Insufficient real-world validation: Many of the studies in Table 1 are based on case studies or expert input, with limited testing in live, dynamic supply chain environments. This raises concerns about generalizability and dependability.
• Insufficient use of AI-based decision support systems: Although fuzzy logic is a foundational component of many AI systems, few models explicitly integrate machine learning or adaptive AI to refine criteria weights or outcome scores over time.

To bridge these gaps, this study proposes an integrated FAHP–TOPSIS framework focused on transportation disruptions in supply chains. It emphasizes post-COVID recovery, includes real-world KPIs, and shows how structured decision-making can support more resilient planning. The approach also sets the stage for future integration with AI-based decision support systems.

3. Methodology

3.1. Overview of Proposed Approach: A Hybrid Fuzzy AHP and TOPSIS System for Supply Chain Resilience Enhancement

Through a combination of empirical analysis and the development of a hybrid fuzzy AHP (FAHP) and TOPSIS system, this paper endeavors to uncover how transportation logistics can be first described under an umbrella of appropriate KPIs or criteria. It will then showcase the analysis of such criteria to pinpoint high-risk points and, finally, propose strategies and solutions that leverage fuzzy logic analysis to enhance resilience. The significance of this study lies in its potential to contribute to the advancement of supply chain management practices, fostering adaptability and responsiveness in the face of uncertainties [11,31].

The two hybrid fuzzy approaches consist of two main processes. FAHP calculates the relative importance of selected criteria and sets appropriate weights [32]. The second process is TOPSIS, which compares a set of alternatives based on a pre-specified criterion. This method is used in business across various industries whenever there is a need to make an analytical decision based on collected data [33].

First, expert pairwise comparison decisions are inserted as whole-number preferences; however, they are translated into fuzzy inputs decoded into triangular fuzzy numbers. In other words, they are changed into interval forms using a linguistic terms profile. Triangular inputs are introduced into the fuzzy AHP system to establish the criteria weights, which are then used as inputs to the TOPSIS model. To initiate the TOPSIS method, alternatives must be established against specific criteria. Again, expert decisions need to be fed as input to determine the extent to which the proposed alternatives or solutions are connected or influenced by the set criteria. The result will be to rank the other options from best to worst [34,35].

This two-step hybrid approach identifies the most critical criteria based on the highest weight. As a result, it highlights the most critical point to consider when a potential risk arises, as this is where the threat to the supply chain is most likely to occur. In response, the TOPSIS method identifies possible alternatives or solutions that can be implemented either before the risk occurs or during the risk to mitigate its adverse impact significantly. The solutions are ranked, and the highest-weight criteria indicate the highest potential for problems in the supply chain. The highest alternative rank represents the best possible solution to implement before that problem occurs. Figure 1 presents a summary of the proposed methodology and the chronological steps of action.

Two real-life case studies were examined to validate this approach, each representing a distinct form of supply chain (i.e., manufacturing and transportation). For each case study, data were collected from expert managers within supply chain organizations and entered into the fuzzy AHP and TOPSIS generators, which were initialized, created, and constructed through the proposed system in this work. This system generates criteria weights based on the criteria assigned to the supply chain field and ranks the proposed alternatives.

The proposed method comprises several inputs and outputs, as demonstrated in Figure 2, which presents a block diagram of the input/output flow for this proposed methodology. The following steps briefly explain the block diagram flow to achieve the highest risk weight and the best alternative to mitigate it:

• Establish the supply chain system’s appropriate criteria or key performance indicators. This is achieved either by choosing pre-set criteria based on research or by criteria selected by the supply chain experts themselves. The chosen criteria must be well-fitted to describe the chosen process. This system works on integrating five criteria.
• Input expert preferences by comparing all five chosen criteria with one another: Which criterion is relatively more important, and by how much? On a scale of 1–9, 1 means both criteria are equally important. Values from 2 to 9 reflect the increasing importance of one criterion over the other, with 2 being the lowest meaningful difference and 9 the highest, as illustrated in

  Table 2. The AHP scale and definition [36].

  Intensity of Importance	Definition
  1	Equal importance
  3	Somewhat more important
  5	Much more important
  7	Very much more important
  9	Absolutely more important
  2, 4, 6, 8	Intermediate values

  . This step is performed by individuals well-familiarized with the chosen supply chain’s entire working system.

3.

Evaluate the state of the expert input data. To start the data fuzzification process, the data should be discrete for entry into the first generator (i.e., fuzzy linguistic terms). The values are fuzzified into triangular fuzzy numbers for each discrete data scale to be presented as fuzzy inputs.

4.

Initialize the second generator (i.e., fuzzy AHP). In this block, pairwise comparisons are carried out to generate the weights for each criterion.

5.

Establish the appropriate alternatives that present the proposed solutions for transportation disruptions in the chosen supply chain system. The experts can again select these alternatives or conduct thorough research to suggest appropriate solutions based on the selected supply chain. This system integrates six alternatives.

6.

Input expert preferences that compare the relevance of each criterion to the corresponding alternative. The expert input data should also be on a scale from 1 to 9. In the scale, values of 9 are the most relevant, and values of 1 are the lowest. In addition, it is highly recommended and more effective to use the same experts, as in step 2, to input the data for the TOPSIS analysis.

7.

Initialize the third and final generator (i.e., TOPSIS). In this block, the main aim is to use the previously calculated criterion weights in the fuzzy AHP block as inputs to establish connections between the criteria and the alternatives. Here, the objective is to find the shortest distance to the positive ideal solution and the longest to the negative ideal solution. The outcome calculates the relative closeness for the alternatives and their rankings from highest to lowest. The highest rank corresponds to the best possible solution to implement.

3.2. Establishment of Evaluation Criteria (KPIs)

The KPIs and decision criteria were chosen based on the previous work and industrial benchmarking to identify all the commonly cited performance indicators related to supply chain resilience. More importantly, the list of supply chain key experts (i.e., from the real-life case studies) were interviewed to provide their inputs and context that were utilized to validate the list of KPIs and criteria. The selection approach is an expert-driven, context-specific KPI selection that guarantees relevance and which originated from previous work and the literature and was then tuned through local domain insights. Once the list of indicators is validated, the fuzzy AHP technique is employed to organize the KPIs (criteria and sub-criteria) into the AHP tree. The most important KPIs (i.e., 5 KPIs) are then prioritized to enter the next phase of fuzzy TOPSIS, where solution strategies are selected.

The solution strategies and alternatives were defined (i.e., the six solution strategies) using the fuzzy TOSIS technique by scoring alternatives vs. criteria; computing distances to ideal solutions; performing ranking; and conducting sensitivity checks. This process identified and validated the most appropriate supply chain resilience alternatives and strategies.

3.3. Expert Input and Data Collection

The data collection process consisted of interviews with 15 experts at each firm (i.e., manufacturing and transportation). All the selected experts were highly qualified persons working as managers of their departments with at least 10 years of experience in their careers. The experts were chosen for their in-depth knowledge of their core business and supply chain operations within their departments, as well as their ability to cover all necessary supply chain components in their firms. The chosen experts from both cases were classified as follows: Manufacturing case (15 experts): 4 warehousing and inventory management, 3 transportation and delivery management, 3 production and operations management, 2 sales and order management, and 3 purchasing management. Transportation case (15 experts): 4 sales and order management, 4 logistics and fleet management, 3 customer relationship management, and 4 operation and technology integration.

Fuzzy TOPSIS offers several advantages when dealing with imprecise and uncertain information: Modelling imprecise criteria: using fuzzy sets or linguistic terms, fuzzy TOPSIS allows decision-makers to model and manage imprecise criteria values. Robustness in the presence of uncertainty: the method considers the unclear nature of the criteria values; it is more resistant to fluctuations and errors in the data. Improved sensitivity to subjective judgments: the method recognizes the imprecision in subjective evaluations and offers a way to take and handle such data. Accurate representation of uncertainty is particularly helpful when making decisions based on qualitative or unclear information in real-world situations where obtaining accurate data can be challenging. The benefits of these approaches result from their ability to manage uncertain and unclear data, making them well-suited for real-life applications that include uncertainty and imprecision.

3.4. Linguistic Terms

For this proposed methodology, expert preferences for comparing criteria are collected using a 1–9 scale. The corresponding nine principal linguistic term translations, illustrated in

Table 3. Linguistic terms of the fuzzy system.

Discrete Scale	Linguistic Term	Fuzzy Triangular Scale
1	Equal	$\left[\mathrm{1,1},1\right]$
2	Weak advantage	$\left[\mathrm{1,2},3\right]$
3	Not bad	$\left[\mathrm{2,3},4\right]$
4	Preferrable	$\left[\mathrm{3,4},5\right]$
5	Good	$\left[\mathrm{4,5},6\right]$
6	Fairly good	$\left[\mathrm{5,6},7\right]$
7	Very good	$\left[\mathrm{6,7},8\right]$
8	Absolute	$\left[\mathrm{7,8},9\right]$
9	Perfect	$\left[\mathrm{8,9},10\right]$

, are applied to interpret these inputs. Data is gathered by asking experts the following two questions for each pairwise comparison:

• Which criterion is relatively more important?
• For the chosen criteria, how much is it relatively more important than the other criteria on a scale from 1 to 9?

Figure 3 captures the setup scale for collecting expert input. The two stated questions are set up as headers. Either criterion 1, criterion 2, or both are set as answers to the first question, and a scale from 2 to 9 is set as answers to the second question. However, as stated previously, the expert preferences should be given on a scale from 1 to 9. Here, a value of one is considered equal and thus automatically corresponds to the third option in question 1, as both are equal.

While the inputs are initially discrete numerical values (2–9), they are not considered fuzzy. Therefore, linguistic terms are used to translate these values into triangular fuzzy numbers. Table 3 summarizes the discrete values, corresponding linguistic terms, and their triangular fuzzy representations. Each discrete value is converted into a range in the following format:

$$\left[\left(pesimisstic value\right),\left(most-likely value\right),\left(optimisticvalue\right)\right]$$

However, the experts’ choice between the criteria that matter compared will affect how the triangular fuzzy numbers are input into the second block, as detailed in Appendix A (i.e., FAHP). There are two possible scenarios:

Scenario 1: Criterion 1 is relatively more important than criterion 2.

For this scenario, the triangular fuzzy number is translated into whole numbers, as shown in Table 3 and demonstrated in Figure 4. For example, if an expert selects criterion 1 as more important by a scale of 4, the corresponding fuzzy number is applied.

Scenario 2: Criterion 2 is relatively more important than criterion 1.

For this scenario, the triangular fuzzy number is translated as fraction numbers, where the inverse of the fuzzy triangular numbers is taken, as shown in Table 3 and Figure 5. For example, if an expert selects criterion 2 as more important by a scale of 4, the corresponding fuzzy number is applied.

3.5. Fuzzy Analytic Hierarchy Process (FAHP)

After the fuzzification process is completed, the second block is initiated. All triangular fuzzy inputs for the criteria comparisons are entered into a pairwise comparison matrix, and the weighted criteria are then generated. The primary concern is the highest weight, as it represents the criterion with the highest potential to create a high risk for the supply chain. Figure 6 showcases a summary of the inputs and outputs of the hybrid fuzzy AHP generator.

Multiple fuzzy AHP methods prioritize inputs. This proposed method uses the geometric mean method. The entire algorithm was constructed from scratch in Microsoft Excel to create two hybrid fuzzy AHP and TOPSIS generators that any supply chain expert can utilize efficiently. The fuzzy set for the proposed methodology is defined by the steps mentioned below:

Suppose X is a universe of interest and x is a particular element of X. In that case, a fuzzy set A defined on X can be represented as a collection of ordered pairs, where each pair consists of an element x and its corresponding degree of membership μ_A(x). This degree reflects the extent to which x belongs to the fuzzy set A. Formally, the fuzzy set can be written as Equation (1).

$$A=\left\{\left(x,{\mu }_A\left(x\right)\right)∣x\in X\right\}$$

(1)

Figure 7 represents the membership functions of two triangular fuzzy numbers, M₁ and M₂. Each fuzzy number is defined by three parameters: a lower limit (l), a modal (or peak) value (m), and an upper limit (u). Specifically, M₁ = (l₁, m₁, u₁) and M₂ = (l₂, m₂, u₂). At the lower and upper limits, the membership degree μ_m is 0, while at the modal value, it reaches the maximum membership degree of 1. The figure also illustrates the degree of possibility V(M₂ ≥ M₁), which expresses the extent to which fuzzy number M₂ is greater than or equal to M₁.

Step 1: Pairwise comparison matrix construction

After the fuzzy triangular number translations (i.e., linguistic terms), the first step is to create a matrix based on the experts’ preference inputs. Each element of the matrix represents the preference or importance of one element over another as input by the experts. An example of the matrix used to begin the fuzzy AHP procedure is shown in

Table 4. Sample matrix for fuzzy AHP initialization.

	C1			C2			C3			C4			C5
C1	1	1	1	6	7	8	5	6	7	8	9	10	5	6	7
C2				1	1	1	3	4	5	2	3	4	7	8	9
C3							1	1	1	1	2	3	3	4	5
C4										1	1	1	7	8	9
C5													1	1	1

.

Under each criterion, the cells were divided into three slots to present the fuzzy triangular numbers. The diagonal line of the matrix is represented as $\left[1,1,1\right]$, since each criterion is considered equal when compared to itself. Assuming A is the decision matrix of dimensions $5\times 5$, since this proposed methodology utilizes the capacity of a maximum of five criteria or KPIs (for further analysis, the number of criteria incorporated can be easily increased or decreased). Equation (2) presents the mathematical representation of the decision matrix considering five criteria, where each element ${ A}_{ij}$ is a fuzzy number defined by its lower, modal, and upper values $\left(l,m,u\right)$.

$$A=\left(\begin{array}{ccc}{a}_{11}& \dots & a_{15}\\ ⋮& \ddots & ⋮\\ a_{51}& \dots & a_{55}\end{array}\right)$$

(2)

After constructing the upper triangular part of the pairwise comparison matrix, the lower triangular elements must be derived to complete the matrix. This is achieved by taking the multiplicative reciprocal of the fuzzy triangular numbers in the upper triangle, as defined in Equation (3). Specifically, for each fuzzy number A_ij = (l,m,u), its reciprocal is calculated as:

$$A^{-1}={\left(l,m,u\right)}^{-1}=\left({\displaystyle \frac{1}{u}},{\displaystyle \frac{1}{m}},{\displaystyle \frac{1}{l}}\right) A_{ij}=1 for i=j$$

(3)

Each expert judgment between a pair of criteria is represented by three values: a lower bound l, a modal (most likely) value m, and an upper bound u, which collectively capture the range and central tendency of the assessment. These values are initially recorded in the upper triangle of the matrix.

The corresponding values in the lower triangle are calculated as reciprocals of those in the upper triangle. Specifically:

• The lower bound (L) of the reciprocal is the inverse of the maximum value of the three values, as in Equation (4), ensuring that the strongest original preference corresponds to the weakest in reverse:

$$L={\displaystyle \frac{1}{\mathit{max}\left(l,m,u\right)}}$$

(4)

• The modal value (M) of the reciprocal is the inverse of the median value, as in Equation (5):

$$M={\displaystyle \frac{1}{\mathit{median}\left(l,m,u\right)}}$$

(5)

The upper bound (U) of the reciprocal is the inverse of the minimum value, as in Equation (6), reflecting the highest confidence in the reversed comparison:

$$U={\displaystyle \frac{1}{\mathit{min}\left(l,m,u\right)}}$$

(6)

Step 2: Geometric mean calculation

After completing the pairwise comparisons, the next step in the fuzzy AHP process is to calculate the geometric mean of the judgments. This is important because decision-makers may sometimes provide extreme values, either very low or very high, during pairwise comparisons. Calculating the geometric means helps reduce the influence of these outliers and prevents any single extreme judgment from disproportionately affecting the results. As a result, this method provides a more balanced, objective, and mathematically sound aggregation of preferences, leading to a fair representation of the collective judgments. Equation (7) describes the mathematical representation for calculating the geometric mean (r_i). A_j = (l_j, m_j, u_j) denotes the triangular fuzzy number representing the comparison of criterion i to criterion j, where l_j, m_j, and u_j correspond to the lower, modal, and upper bounds, respectively. The operator ⊗ represents fuzzy multiplication, and n is the total number of criteria considered in the pairwise comparison.

$$\begin{array}{c}{r}_i={\left[A 1 \otimes A 2 \otimes A 3 \otimes A 4 \otimes A 5 \right] }^{{\displaystyle \frac{1}{n}}}, \mathit{\text{For}} n=5:=\\ \left(l_1,m_1,u_1\right)\otimes \left(l_2,m_2,u_2\right)\otimes \left(l_3,m_3,u_3\right)\otimes \left(l_4,m_4,u_4\right)\otimes \left(l_5,m_5,u_5\right) =\\ {\left(\left(l_1\times l_2\times l_3\times l_4\times l_5\right),\left(m_1\times m_2\times m_3\times m_4\times m_5\right),\left(u_1\times u_2\times u_3\times u_4\times u_5\right)\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}}\end{array}$$

(7)

Step 3: Fuzzy weight vector (fuzzy form) calculation

After calculating the geometric mean, the fuzzy weights (fuzzy triangular form, W_i) can be calculated using Equation (8). However, to simplify the calculation procedure, a couple of extended formulas can be applied as follows:

$$W_i\prime = r_i \otimes {\left(r_1\oplus r_2\oplus r_3 \oplus r_4 \oplus r_5 \right)}^{-1}$$

(8)

1.

The sum of the geometric means across all five criteria for the lower, modal, and upper limit, respectively, is calculated, as shown in Equations (9)–(11):

$${Geomean Sum}_{lower limit}=r_{l1}+r_{l2}+r_{l3}+r_{l4}+r_{l5}$$

(9)

$${Geomean Sum}_{modal limit}=r_{m1}+r_{m2}+r_{m3}+r_{m4}+r_{m5}$$

(10)

$${Geomean Sum}_{upper limit}=r_{u1}+r_{u2}+r_{u3}+r_{u4}+r_{u5}$$

(11)

2.

The inverse of the three triangular fuzzy limit summations is calculated. This is achieved by taking the inverse of each geometric sum across the three limits, as demonstrated in Equations (12)–(14):

$${{Geomean Sum}_{lower limit}}^{-1}={\displaystyle \frac{1}{r_{l1}+r_{l2}+r_{l3}+r_{l4}+r_{l5}}}$$

(12)

$${{Geomean Sum}_{modal limit}}^{-1}={\displaystyle \frac{1}{r_{l1}+r_{l2}+r_{l3}+r_{l4}+r_{l5}}}$$

(13)

$${{Geomean Sum}_{upper limit}}^{-1}={\displaystyle \frac{1}{r_{l1}+r_{l2}+r_{l3}+r_{l4}+r_{l5}}}$$

(14)

3.

The increasing order of the inverse geometric sums is calculated. Since in FAHP, fuzzy triangular numbers are being dealt with, it is necessary to calculate the fuzzy weights correctly by having each limit value in a single triangular fuzzy number (lower, modal, upper) correctly cross-multiplied with the corresponding inverse geometric value. To achieve this, Equations (15)–(17) need to be applied.

$$\begin{array}{c}Lower triangular limit’s increasing order=\\ min ({{{{Geomean Sum}_{lower limit}}^{-1}, Geomean Sum}_{modal limit}}^{-1},{{Geomean Sum}_{upper limit}}^{-1})\end{array}$$

(15)

$$\begin{array}{c}Modaltriangularlimit’sincreasingorder=\\ median\left({{{{Geomean Sum}_{lower limit}}^{-1},Geomean Sum}_{modal limit}}^{-1},{{Geomean Sum}_{upper limit}}^{-1}\right)\end{array}$$

(16)

$$\begin{array}{c}Upper triangular limit’s increasing order=\\ max ({{Geomean Sum}_{lower limit}}^{-1},{{Geomean Sum}_{modal limit}}^{-1},{{Geomean Sum}_{upper limit}}^{-1})\end{array}$$

(17)

4.

In the final step, the fuzzy weights are computed by multiplying each component of the triangular fuzzy number, namely the lower, modal, and upper limits associated with each criterion, by the corresponding values from the ordered inverse geometric means. This element-wise multiplication preserves the fuzzy structure of the data and results in a set of fuzzy weights that reflect the relative importance of each criterion. To validate the fuzziness of the results, the aggregated modal values of the criteria can be checked; if their total exceeds one, it confirms the fuzzy nature of the weights, which may go beyond the normalized upper limit of values.

Step 4: Normalized weights: (non-fuzzy form) calculation

The proposed method adopts a hybrid multi-stage process that requires the input of normalized, non-fuzzy weights for subsequent decision-making analysis, such as integration with classical methods like TOPSIS. Therefore, the fuzzy weights must first be defuzzied and then normalized to yield crisp values. The defuzzification is typically performed by computing the average of the lower, modal, and upper limits of each triangular fuzzy number. These crisp values are then normalized to ensure their sum equals one, as shown in Equation (18).

$$W={\displaystyle \frac{W_i}{\sum _n^{i-1}{W}_i}}$$

(18)

where W_i is the defuzzied weight of the ith criterion, and n is the total number of criteria.

This normalization ensures that the resulting weights are dimensionless and sum to unity, making them suitable for input into classical multi-criteria decision-making frameworks. After normalization, the criteria can also be ranked in descending order of their importance based on the magnitude of these weights; ranks are given from largest (1) to smallest (5).

3.6. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

After the normalized criteria weights are established through the FAHP process, it can be concluded that the highest-weight criterion demonstrates the highest possible point of risk. However, finding an appropriate solution or alternative is critical to make this proposed method more effective and valuable in achieving supply chain resilience. That is why a second AI-based methodology is used (i.e., TOPSIS). The following are the steps to perform TOPSIS and their corresponding translation into the developed algorithm.

Step 1: Expert input (alternative preferences)

Expert input is entered, describing the user’s ratings from 1 to 9 in terms of the level of relation between a criterion and a matrix of alternatives. The closer the ratings are to 9, the higher the relationship between a specific criterion and a particular alternative, and vice versa. This paper has five criteria/KPIs, whose weights are transported from the fuzzy AHP analysis, and six proposed alternatives/solutions. An illustrative example of the input matrix is presented in

Table 5. Expert ratings matrix showing the relationship between criteria and alternatives.

Weight	w1	w2	w3	w4	w5
	C1	C2	C3	C4	C5
A1	3	7	7	3	4
A2	6	9	2	4	7
A3	7	8	3	9	6
A4	3	5	9	6	2
A5	5	8	4	4	9
A6	7	1	3	5	8

.

Step 2: Intermediate criteria vs. alternatives matrix for normalization

To prepare for normalization, an intermediate matrix is generated by squaring each value in the original decision matrix

X = [x_ij], where I = 1, 2…, m denotes alternatives and j = 1, 2…, n denotes criteria. For each column j, the sum of squared values is computed as per Equation (19).

$$S_j=\sum _{i=1}^m{x}_{ij}^2$$

(19)

Then, the square root of each column sum is calculated to serve as normalization denominators in the next step to let all values in each column be scaled relative to the same magnitude.

Step 3: Normalization of the matrix

The normalized matrix R [r_ij] is computed by dividing each original matrix element x_ij by the square root (S_j) of the sum of squares of its respective column as per Equation (20).

$$r_{ij}={\displaystyle \frac{x_{ij}}{\sqrt{{\sum }_{i=1}^m{x}_{ij}^2}}}={\displaystyle \frac{x_{ij}}{\sqrt{S_j}}},\hspace{1em}\mathrm{for} i=1,2,\dots ,m \mathrm{and} j=1,2,\dots ,n$$

(20)

Step 4: Weighted normalized matrix and ideal solutions

As mentioned previously, the main values required for the TOPSIS method are the positive and negative ideal solutions. To calculate them, a weighted normalized matrix is first generated V [V_ij], which is achieved by simply multiplying the normalized matrix $r_{ij}$ by the criteria weights $w_j$ obtained from the FAHP analysis. Each criterion weight is multiplied by its corresponding column, as demonstrated in Equation (21).

$$V_{ij}=w_j \times r_{ij},\hspace{1em}$$

(21)

Next, the simple maximum and minimum formulas are used to calculate the positive ideal solution A* and negative ideal solutions A⁻ for each criterion j, as shown in Equations (22) and (23).

$$A*=\mathit{max}j\left(V_{ij}\right)$$

(22)

$$A^{-}=\mathit{min}j\left(V_{ij}\right)$$

(23)

Step 5: Calculation of Euclidean distances

After establishing the positive and negative ideal solutions $A* \mathrm{and} A^{-}$, the next step is to measure the distances from each point to each ideal solution to develop the closest alternative to the positive ideal solution and the furthest alternative to the negative ideal solution. The distance from the ideal positive solution $S_i*$ and negative ideal solution $S_i^{-}$ can be calculated using Equation (24) and Equation (25), respectively.

$$S_i^{*}=\sqrt{\sum _{j=1}^m(V_{ij }-A^{*}{)}^2}$$

(24)

$$S_i^{-}=\sqrt{\sum _{j=1}^m(V_{ij }-A^{-}{)}^2}$$

(25)

Step 6: Calculation of the relative closeness to ideal solution (performance score) and ranking

The final step in TOPSIS is to calculate the relative closeness to the ideal solution, or, in other words, the performance scores. This ultimately gives the best possible solution application under the given criteria weights. Overall, the deduced best alternative (i.e., rank 1) solution is considered the optimal solution to apply to the supply chain system, aiming to severely reduce risks, particularly the highest point of risk, which concerns the criterion with the most significant weight calculated in FAHP. Equation (26) illustrates how the Euclidean distances, derived for the negative and positive ideal solutions, are used to calculate the performance scores $P_i$.

$$P_i={\displaystyle \frac{S_i^{-}}{S_i^{*}+S_i^{-}}}$$

(26)

The alternative solutions can then be ranked from best to worst based on the final calculated performance scores.

3.7. System’s Implementation on Real Case Studies

To demonstrate the implementation of the proposed approach in this work, the following sections will provide two real-life applications. The collected data of those real-life applications are based on expert opinions of managers in two known companies in Jordan (i.e., a hygienic paper manufacturer and a transportation solutions group).

4. Manufacturing Case Study

In this work, the manufacturing case is a suitable company for a real-life application, as the supply chain plays a huge role in manufacturing. Five main criteria were presented for this case so that the experts could compare and choose which criterion is relatively more important. This helps identify which criteria will cause the highest delay in the supply chain manufacturing process if any problem occurs. Furthermore, six alternatives were also presented to determine the best solution for the identified criteria.

Table 6. Manufacturing criteria.

#	CRITERIA
C1	Travel Time
C2	Inventory Level
C3	Cost of Implementing Solution
C4	Warehousing
C5	Maintenance

presents the criteria identified for the selected manufacturing company, chosen for their significance in the manufacturing field. These five criteria are evaluated using the fuzzy AHP method, with expert input used to assign their weights. Based on this analysis,

Table 7. Manufacturing alternatives.

#	ALTERNATIVES
A1	Establish fire stations
A2	Storage locations and capacities to meet post-disaster demand in different locations
A3	Aim of strengthening the highway network
A4	Extra vehicles
A5	Extra inventory in the focal company
A6	Allocating a fixed budget for emergency needs

displays six alternatives or solutions selected according to how well they address the prioritized criteria.

5. Transportation Solutions Case Study

The transportation solutions group is recognized as one of the world’s largest container transportation businesses. The company’s core business, worldwide distribution, container shipping services, and logistics and supply chain services are all part of the company.

Table 8. Transportation criteria.

#	CRITERIA
C1	Vehicle utilization
C2	Technology integration
C3	Customer service
C4	Safety and security
C5	Delivery time

presents the criteria identified for the selected transportation company, chosen for their significance in the transportation field. These five criteria are evaluated using the fuzzy AHP method, with expert input used to assign their weights. Based on this analysis,

Table 9. Transportation alternatives.

#	ALTERNATIVES
A1	Emergency Response Plans
A2	Green Logistics and Sustainability
A3	Supplier and Carrier Relationship Management
A4	Real-Time Monitoring and IoT
A5	Fleet Management Systems
A6	Route Optimization

displays six alternatives or solutions selected according to how well they address the prioritized criteria.

System Validation

To validate the proposed decision-support framework, criteria and alternatives were carefully defined for each of the two case studies, one focused on transportation and the other on manufacturing. These were selected to realistically represent real-world supply chain challenges specific to their respective sectors. The criteria were established based on the relevant literature, expert input, and industry practices, while the alternatives were drawn from practical strategies currently adopted or considered within the respective companies. During the FAHP process, the Consistency Ratio (CR), which indicates the level of consistency in the judgment, was computed for each expert’s input to ensure the logical soundness of pairwise comparisons using Equations (27) and (28) [37].

$$C.I.={\displaystyle \frac{{\lambda }_{\max }-n}{n-1}}$$

(27)

$$C.R.={\displaystyle \frac{C.I.}{R.I.}}$$

(28)

where λ_max is the maximum eigenvalue of the pairwise comparison matrix, n is the number of criteria or alternatives being compared, C.I. is the Consistency Index, and R.I. is the Random Index (the average C.I. of randomly generated matrices of the same order, depending on n, as listed in

Table 10. Thresholds of the relative errors [37].

n	1	2	3	4	5	6	7	8	9	10	11	12
R.I.	0	0	0.52	0.89	1.12	1.26	1.36	1.41	1.46	1.49	1.52	1.54

. All CR values were within acceptable thresholds, indicating consistent and reliable expert evaluations.

The results presented in this section reflect the output generated using FAHP for criteria weighting and the TOPSIS method for ranking the alternatives. To enhance transparency and traceability, a summary of the expert input data, covering both FAHP pairwise comparisons and TOPSIS preference scores, is provided in Appendix B. These input sheets represent the initial assessments from experts at both case companies and serve as the foundation for the computational analysis and resulting rankings discussed herein.

6. Results and Discussion

6.1. Manufacturing Supply Chain Case Study Results

The expert input data was entered into the FAHP and TOPSIS programs, and the corresponding matrix tables were generated accordingly. A detailed view of the generated matrix tables is provided in Appendix C.

• Outcomes of FAHP:

As demonstrated in Figure A3A,B in Appendix D, the criteria were calculated and are presented to illustrate the weight distribution among the five criteria. The highest criterion weight belongs to the first criterion, “travel time,” followed by “inventory level, “warehousing, “maintenance,” and, lastly, “cost of implementing the solution.” The travel time criterion, which take around almost half of the weights (46%), is a valid and expected outcome since the manufacturing supply chain heavily relies on the concept of time. No supply chain process can start if a delay in raw materials, equipment, goods, etc., occurs. Delays can lead to an increase in bottlenecks, which ultimately affect the company’s operational performance and speed. As a result, this may damage the company’s reputation among consumers, leading to negative consequences. For this manufacturing case, the highest potential risk lies in travel time.

The inventory level criterion follows travel time, with a weight of 27%, which is the second highest. Again, this makes sense because inventory levels and raw material stock fuel any manufacturing supply chain, since they represent a form of the final goods or are even the final products themselves.

• Outcomes of TOPSIS:

Now that the travel time criterion was marked as the highest-risk criterion, TOPSIS calculated the best possible alternative solution to be implemented. As shown in Figure A3C in Appendix D, an alternating trend curve is presented for the six proposed alternatives. The highest performance score belongs to the alternative “aim of strengthening highway network” (0.72) followed by “allocating fix budget for emergency needs” (0.70), then “extra vehicles” (0.58), “extra inventory in focal company” (0.42), “storage locations and capacities to meet post disaster demand in different locations” (0.29), and, finally, “establish fire stations” (0.24).

While the results of each case study cannot be faulted, as each case in the manufacturing supply chain industry is unique, this case study is no exception and reflects practical priorities in solution selections. This is a road transport manufacturing case study that proposes the best solution to mitigate the highest risk, namely “travel time,” by strengthening the highway network. This directly validates the approach, as the highest risk identified through the FAHP process and the best solution determined through the TOPSIS are highly matched. This confirms that the experts’ effective input reflects excellent knowledge of the company’s supply chain system.

6.2. Transportation Supply Chain Case Study Results

The expert input data was entered into the FAHP and TOPSIS programs, and the corresponding matrix tables were generated accordingly. A detailed view of the generated matrix is provided in Appendix C.

• Outcomes of FAHP:

As demonstrated in Figure A4A,B in Appendix D, the criteria weights were calculated and are presented to illustrate the distribution of weights among the five criteria. The relationship between the criteria and their weights is increasingly proportional. The highest criterion weight, unlike the manufacturing case study, belongs to the last criterion, “delivery time,” followed by “safety and security,” “customer service,” and, lastly, “technology integration” and “vehicle utilization,” which have approximately the same weight value.

Again, the delivery time criterion, which accounts for more than half of the weight (56%), is a valid and expected outcome, as in the manufacturing case study, the transportation supply chain heavily relies on the concept of time. However, in the transportation field, time is even more critical, as the primary goal of any transportation company is to move a specific product or parcel from one location to another.

The safety and security criterion follows, with a weighting of 19%, which is the second highest. Again, this is common sense because transportation services are required to maintain the safety and security of the goods that they are transporting. Otherwise, no one becomes interested in using such services if the products they ship are likely to be damaged or lost.

• Outcomes of TOPSIS:

The delivery time criterion was marked as the highest-risk criterion, and TOPSIS calculated the best possible alternative solution to be implemented. As seen in Figure A4C in Appendix D, an alternating trend curve is presented between the six proposed alternatives. The highest performance score belongs to the alternative “green logistics and sustainability” (0.89) followed by “fleet management systems” (0.36), then “emergency response plans” (0.33), “supplier and carrier relationship management” (0.32), “real time monitoring and IoT” (0.15), and, finally, “route optimization” (0.07).

While the results of each case study cannot be faulted, as each case in the transportation supply chain industry is unique, this case study is notable for its approach to calculating priorities in solution selections. This case study of sea, land, air, and logistics transportation presents a wide range of solution options, making it challenging to reflect all these environments specifically. The experts took a generalized approach in terms of concentrating on the logistics aspect that controls all forms of transport rather than directly finding a time-issue-related solution concerned with the highest risk of delivery time. This is a smart approach since achieving control over logistics means controlling all other transportation aspects.

Moreover, even though the first alternative solution is not a direct response to the highest-risk criteria, the second solution is considered a direct response. Fleet management systems are used to train and develop a well-experienced, competent workforce and a strong, durable fleet of vehicles. When the best employee meets the best vehicle, delivery times, safety, security, and other criteria with a high probability, the whole process will be contained and performed exceptionally.

The proposed approach of FAHP and TOPSIS could be effectively applied to other various regions and applications in industry, as this methodology is considered highly versatile and adaptable. This makes the proposed approach suitable for various other industries and regions. Mainly, for this approach to be effectively implemented in other sectors or regions, the following practical considerations should apply:

• The criteria and sub-criteria should be customized to align and adapt with the specific sector and regional context.
• Experts from the industrial sector should be involved in the data collection process to provide practical insights and verify and validate the decision-making process.
• A complete set of data should be collected on risk factors and other relevant criteria (e.g., logistical, operational, sales, technological, safety, warehousing, production, procurement, transportation, etc.).
• The assessment should be regularly updated to reflect changes in the supply chain environment and emerging risks.

As examples, and following these practical considerations, the FAHP and TOPSIS method could be implemented in the following sectors in different regions: In the retail industry, FAHP and TOPSIS could be adopted to improve supply chain agility and resilience, particularly in the fast fashion and perishable goods industries. Moreover, this approach could be employed in the construction sector to evaluate and provide risk mitigation in project management and materials sourcing and in the energy sector to assess the risk and the supplier performance of energy inputs and resources. In addition, the proposed FAHP and TOPSIS approach can be utilized to manage risks in the agricultural sector that are related to market fluctuations, logistics, and crop production.

7. Conclusions

As discussed in this paper, fuzzy AHP is a powerful method for organizing decision problems with various criteria. It also enables decision-makers to express their preferences more clearly and adaptively using linguistic variables. On the other hand, TOPSIS stands out for its ability to rank alternatives by considering both the positive and negative factors, providing a comprehensive evaluation method. This approach presents a balanced perspective on feasible alternatives, enhancing the decision-making process. The main conclusions that can be drawn from this study are as follows:

• The two-step hybrid system proposed, which merges the concepts of FAHP and TOPSIS, has proven to be a valuable approach due to its comprehensibility and systematic processing of expert input, including criteria and alternatives. The benefits of these approaches result from their ability to manage uncertain and unclear data, making them well-suited for real-life applications that include uncertainty and imprecision.
• The combination of fuzzy AHP and TOPSIS shows an integrated approach to decision-making, emphasizing the wide range of problems. As companies continue to face dynamic and unexpected challenges, adopting these methods proves to be a significant asset, providing decision-makers with tools capable of handling complex situations.
• The manufacturing case study showed high risk in travel time and inventory-level criteria, which is highly logical and reflective of the basic core aspects of a manufacturing supply chain. The best proposed solution was strengthening highway networks and allocating a fixed budget for emergency needs. An almost perfect match is concluded, highly validating the system’s processing and the experts’ input.
• The transportation case study showed high risk in the delivery time and safety and security criteria, with delivery time carrying the highest weight of 56% and safety and security following at 19%. Correspondingly, the best proposed alternatives identified by TOPSIS were green logistics (score 0.89), sustainability initiatives, and fleet management systems (0.36). This alignment between weighted risks and top solutions underscores the system’s strong ability to accurately identify critical risks and effective responses, reflecting the experts’ deep understanding of the supply chain.
• Supply chain resilience is constructed differently for each supply chain system due to the unique structure and components of supply chains in different industries. The main key takeaway from this work is to construct supply chain resilience by establishing the most important elements of a supply chain through criteria that need to be achieved to understand where the highest potential risk lies
• The managerial implications of the proposed FAHP and TOPSIS approach are described as follows: Supply chain managers can utilize the prioritized FAHP indicators and solution strategies to focus on critical resilience factors (i.e., responsiveness, flexibility, and readiness), and these executives can also use closeness-to-ideal scores from TOPSIS to guide investments through comparing alternatives (e.g., logistics service, digital visibility tools, and redesigning multiple sourcing). Moreover, supply chain managers can ensure that decisions are not overly dependent on subjective judgments. This is enabled through examining the robustness of rankings against small perturbations in criteria weights.

The proposed system has some shortcomings that can be described as follows. (1) One limitation of this work could be the number of criteria and alternatives. As shown and discussed in this paper, five criteria and six alternatives were used for each real-life application scenario. These numbers remained unchanged during this work because the FAHP–TOPSIS system was designed to meet five criteria and six alternatives to ease the implementation of the FAHP and TOPSIS methods. However, they can be easily adjusted depending on the company’s needs because the developed system is not limited to several criteria and alternatives, and it can be easily edited. (2) Another limitation could be the experts’ opinions. Since this paper’s methodology requires experts from companies to provide their ratings and preferences, it is essential to ensure that these people are indeed experts and fully understand the companies’ processes to ensure a correct evaluation. If companies use the system, giving incorrect evaluations from non-experts could falsely reflect the company’s supply chain process.

To overcome these shortcomings, the following future directions are recommended:

• For this proposed approach, it is recommended that the expert company set its criteria and alternatives based on realistic reflections of its supply chain systems. Moreover, careful research should be carried out to ensure the feasibility and financial availability of implementing potential alternatives or solutions.
• Validating the FAHP and TOPSIS approach and system empirically through validating the field data: This could be achieved through applying the model longitudinally to real supply chain events and comparing predicted rankings of mitigation or solution strategies to actual performance outcomes.
• Improving the proposed system by integrating it with GIS for location-specific routing decisions or machine learning to adapt criteria weights dynamically.
• The proposed model’s stability could be investigated and examined by considering a broader list of experts from diversified industries and then running multi-scenario simulations
• The experts in charge of the FAHP and TOPSIS inputs should be carefully considered and chosen by assessing supply chain experience, work experience, position in the entity, or the extent of active participation in the supply chain process. This is important, since non-expert input could lead to incorrect interpretation and results.
• Future studies could explore integrating other valuable software packages to apply the two-step hybrid approach to give proper and perhaps even broader outcomes.
• Integrating the FAHP and TOPSIS methodologies should be invested in, since it has been proven that such a combination allows for the effective identification of risks and solutions in other industrial fields.
• Hybrid fuzzy systems should be created with a broader range of criteria and alternative inputs or unlimited capacity for 100% flexibility in designing the company’s supply chain systems.