alternatives and ranking according to compromise solution, Machine learning.

With the globalization and expansion of supply chains, the likelihood of exposure to risks and disruptions, and consequently the vulnerability, has increased, highlighting the necessity of addressing supply chain resilience [1]. Suppliers are considered the outermost boundary of a supply chain and are exposed to upstream risks and disruptions; therefore, selecting resilient suppliers is recognized as an effective approach to achieving a resilient supply chain [2].

The globalization of activities across industries has transformed sourcing and supplier selection into a global process influenced by political, legal, and cultural factors [3]. Moreover, weaknesses in transportation infrastructure, technology, and production capacity may also affect this process [4]. As supply chain structures become more complex and globalized, manufacturing firms increasingly depend on their suppliers, thereby intensifying their exposure to supply chain risks. Under such conditions, incorporating resilience into supplier selection methodologies becomes essential [5].

In risk management, suppliers represent the most common source of external risks in modern supply chains. Ensuring the continuity of supply chain flows under disruptive events is a critical concern that has drawn firms' attention toward selecting resilient suppliers [6]. Unlike the extensive body of research on traditional and green supplier selection criteria, resilience-related criteria for supplier selection have not yet been sufficiently explored [7]. Supplier selection is a critical responsibility due to its direct impact on the final product and therefore requires continuous attention [4]. This decision also lays the foundation for long-term supplier partnerships, which can contribute to a business's success or failure [8].

Suppliers play a fundamental role in achieving supply chain objectives [9]. To develop a responsive supply chain plan with respect to resilience, the procurement function must place particular emphasis on sourcing decisions. Selecting a resilient supplier is a key strategic decision in supply chain risk management [10]. A resilient supplier typically possesses high adaptability, which helps reduce vulnerability to disruptions, absorb the impacts of adverse events, and recover rapidly from disturbances, thereby ensuring an acceptable level of operational continuity following a disaster [11].

The selection of resilient suppliers is a critical decision for organizational sourcing and for achieving competitive advantage [12]. To date, limited research has addressed resilient supplier selection problems that require the simultaneous consideration of both numerical and linguistic evaluation criteria. These criteria differ fundamentally from those used in traditional supplier selection problems [13]. In logistics 4.0, given the extensive impact of sourcing decisions on supply chain resilience, efficiency, and sustainability, an appropriate decision-making framework is required. The decision-making problem involves evaluating multiple suppliers against conflicting criteria. This problem becomes more complex when decision-related information is heterogeneous, comprising qualitative information that is often imprecise or vague, as well as quantitative information that is difficult to process [14].

Traditional Multi-Criteria Decision-Making (MCDM) approaches are generally unable to effectively address the resilient supplier selection problem in logistics 4.0 due to the large volume of quantitative and qualitative data involved. The emergence of digital technologies such as machine learning, cloud computing, the Internet of Things (IoT), and blockchain has enabled managers and governments to cope with uncertainty through intelligent decision-making principles [5]. The relationship between suppliers and buyers plays a crucial role in the success of modern supply chain management and in achieving strategic objectives. Consequently, the vulnerability of suppliers at the upper tiers of the supply chain has increased with globalization. At the same time, suppliers, as a core component of supply chains, play a vital role in mitigating global risks.

Selecting resilient suppliers is therefore essential for building resilient supply chains. The present study focuses on the resilience dimension of the supplier segment, aiming to achieve a supply chain resilient to disruptions. Due to the heterogeneity of the information and components involved in supplier evaluation, a hybrid, integrated approach combining MCDM tools and machine learning techniques is adopted. Historical data from the firm's information system, along with qualitative data from decision-making experts, are used as input for this research.

This study presents a case study of the Iranian steel industry to examine supplier selection from a resilience perspective. The objective is to evaluate and cluster resilient suppliers using a combination of knowledge-driven and data-driven approaches, based on quantitative and linguistic criteria. The subsequent section reviews the literature on resilient suppliers and identifies the associated research gaps. Section 3 describes the research methodology. Section 4 presents the model implementation and data analysis, and Section 5 provides conclusions and directions for future research.

Parkouhi and Ghadikolaei [4] proposed a model for resilient supplier selection in the wood and paper industry using fuzzy network analysis and the grey VIKOR method. They examined 42 criteria across four dimensions: benefits, opportunities, costs, and risks, and demonstrated that risk is the most critical factor influencing resilience. Suppliers characterized by price diversity, reduced vulnerability, high visibility, and on-time delivery were prioritized. Pramanik et al. [15] developed a quantitative approach for resilient supplier selection by integrating AHP, TOPSIS, and QFD in a fuzzy environment. This approach reduces conflicts among decision-makers and integrates general, technical, and resilience criteria. By employing quality, delivery time, production compliance, buffer capacity criteria, and fuzzy sets, the method enables more accurate judgments, reduces ambiguity, and prevents information loss. Hosseini and Khaled [9] combined the AHP approach with collective classification to identify eight elements related to suppliers' resilience capacity, including absorption, adaptation, and recovery. Using advanced data mining techniques, including binary logistic regression, classification trees, and neural networks, supplier resilience was predicted and subsequently incorporated into a hierarchical analysis to rank the top five suppliers based on general criteria such as quality, cost, responsiveness rate, and lead time. The results indicated that robustness, reliability, and rerouting capability are the most significant resilience factors. Hasan et al. [11] proposed a decision support system–based framework for ranking resilient suppliers in logistics 4.0 using heterogeneous data. This framework employed time-series and triangular fuzzy data to analyze qualitative attributes and ranked suppliers using fuzzy TOPSIS. Fallahpour et al. [16] introduced a super-hybrid fuzzy framework for selecting sustainable, resilient suppliers in the Malaysian palm oil industry. They identified 30 supplier evaluation criteria across three aspects: general, sustainability, and resilience, and designed a super-hybrid model incorporating FDEMATEL, FBWM, FANP, and FIS for weighting criteria and evaluating supplier performance. The results showed that cost, resource consumption, and agility were the most important sub-criteria, while flexibility, business insurance, and visibility were the least significant. Afrasiabi et al. [17] proposed a hybrid fuzzy MCDM model for selecting sustainable and resilient suppliers. In this approach, the weights of 16 selected criteria across economic, social, environmental, and resilience dimensions were determined using FBWM, and supplier evaluation was conducted using an integrated GRA–TOPSIS method. The results identified pollution control, environmental management systems, and risk awareness as the most important criteria in the sanitary fittings industry. Abedian et al. [18] developed a comprehensive model based on fuzzy set theory and Data Envelopment Analysis (DEA) for selecting green–resilient suppliers in electronic manufacturing systems.

In this model, 12 sub-criteria were considered for supplier evaluation. Fuzzy set theory was used to analyze supplier weights and performance, and to rank them; subsequently, DEA was applied to aggregate data and rank suppliers based on a single dummy input and three output variables. Ulutaş et al. [19] proposed a comprehensive grey MCDM model for resilient supplier selection. In this study, grey PSI (for objective criteria) and grey BWM (for subjective criteria) were used to determine the relative importance of criteria and sub-criteria. Subsequently, grey MCRAT and grey COBRA methods were applied to evaluate and rank suppliers in a textile company. The findings indicate that incorporating resilience attributes into supplier selection can improve risk management and operational resilience, ultimately enhancing competitive advantage and long-term sustainability. Davoudabadi et al. [20] introduced a model combining statistical techniques, decision-making methods, and mathematical programming to evaluate the efficiency of resilient suppliers. In the proposed model, DEA and entropy were employed to determine criterion weights. At the same time, a combination of Principal Component Analysis (PCA) and DEA was used to reduce dimensionality, address criterion correlations, and rank suppliers. One of the key advantages of this approach is the simultaneous utilization of quantitative and subjective data.

Considering the gap in the simultaneous use of MCDM approaches and machine learning, in a way that takes advantage of the knowledge and expertise of decision-makers, as well as the identification of hidden patterns in data and their analysis in the selection of resilient suppliers, the present study proposes and presents a combined knowledge-based and data-driven approach to facilitate the process of selecting resilient suppliers in an environment with heterogeneous data and information.

The present study is a descriptive survey and was conducted at one of the steel manufacturing plants located in Yazd city. In terms of data collection, the research adopts a mixed approach combining library-based and field methods. The most important resilience criteria were extracted from the resilient supplier selection literature and subsequently localized through consultation with experts and industry specialists.

The statistical population consists of managers and experts from the company's purchasing department, and purposive sampling was employed based on individuals' expertise and familiarity with suppliers. The effective criteria were categorized into two groups: qualitative and quantitative. Qualitative (resilience-related) criteria were collected through questionnaires completed by experts, while quantitative (financial) criteria were obtained from the purchasing planning unit.

The weights for the resilience criteria were determined using Shannon entropy, and 24 main suppliers of the company were evaluated using the Measurement Alternatives and Ranking according to Compromise Solution (MARCOS) method. After incorporating suppliers' resilience scores into the financial data, dimensionality reduction was performed using PCA, followed by supplier clustering using the k-means algorithm. Finally, to validate the proposed framework, supplier rankings obtained from the MARCOS method were compared with those from the TOPSIS technique, and the Spearman rank correlation coefficient was calculated. In addition, the elbow method and silhouette index were employed to determine the optimal number of clusters. The main steps of the proposed model are described below.

The weights for the resilience criteria are calculated using Shannon entropy to reduce the influence of subjective judgments and enhance objectivity. This method is data-driven and widely applied in decision-making problems. The procedure consists of three main steps: normalization of the decision matrix, calculation of the entropy value for each criterion, and determination of the corresponding weights. Criteria with lower entropy values receive higher weights, as they provide more useful information. It should be noted that the computation of weights differs depending on whether the criteria are benefit- or cost-type [26]. After determining the resilience criteria weights using the Shannon entropy method, supplier performance is evaluated using the MARCOS technique. This method, introduced by Stević et al. [27] in 2020, identifies the best alternative by defining two reference solutions (ideal and anti-ideal) and calculating the relative position of each alternative with respect to these solutions. In this approach, ranking is performed based on the final utility function values, and the alternative with the highest value is considered the best supplier [28]. The steps of the MARCOS method are as follows.

Step 1. Using Eqs. (2) and (3), the initial decision matrix is extended and standardized by adding the anti-ideal and ideal solutions, where B denotes the set of benefit criteria. C represents the set of cost criteria.

AAI xaa1 xaa2 … xaan A1 x11 x12 … x1n A2 x21 x22 … x2n

X = … … … … . (1)

Am xm1 xm2 … xmn AI [ xai1 xai2 … xain ]

AAI = min i xij. jϵB, max i xij. jϵC. (2) AI = max i xij. jϵB, min i xij. jϵC. (3)

Step 2. The expanded initial decision matrix (X) is normalized. The elements of the normalized matrix N= [nij] (m×n) are obtained using Relations (4) and (5).

xai

nij = x . jϵC. (4)

ij

xij

nij = . jϵB. (5)

xai Step 3. The weighted matrix V= [vij] (m×n) is formed from the product of the normalized matrix N and the weight coefficients of each criterion (obtained from the Shannon entropy method), according to Eq. (6).

vij = nij × wj. (6)

Step 4. The degree of desirability of the Ki alternative relative to the anti-ideal and ideal solutions is estimated using Relations (7) and (8), where Si (i=1, 2… m) represents the sum of the elements of the weighted matrix

− Si

Ki = . (7)

Saai + Si

Ki = . (8)

Sai Step 5. The utility function of the options, the compromise of the observed option in relation to the ideal and anti-ideal solutions, is determined using Eq. (9).

K+ i + K− i f(Ki) = + − .

1 − f(Ki ) 1 − f(Ki ) (9)

1 + + + − f(Ki ) f(Ki ) The utility functions for the ideal and anti-ideal solutions are obtained by applying Relations (10) and (11).

− K+ i

f(Ki ) = + −. (10)

Ki + Ki

+ K− i

f(Ki ) = K++K−. (11)

Step 6. The alternatives (suppliers) are ranked according to the final values of their utility functions. A higher value indicates a more desirable alternative [27], [28].

Prioritizing suppliers based on qualitative supplier selection criteria is challenging because it requires human judgment. Such evaluations may appear vague and are often difficult to interpret [29]. Due to decision-makers' sometimes ambiguous or inadequate knowledge, machine learning approaches are employed to complement and support the decision-making process. By integrating knowledge-based and data-driven approaches, the advantages of both can be simultaneously exploited. In this study, the output of the supplier evaluation technique (the MARCOS method) enables qualitative criteria to be measured and quantified. Consequently, a column titled supplier score can be readily added to the financial data, which is inherently quantitative. Subsequently, PCA is applied to reduce the dimensionality of the data in the supplier selection process. This method facilitates decision-making by eliminating indicator correlations and identifying hidden patterns in complex datasets. Principal components are obtained as linear combinations of the original variables, and the first principal component accounts for the maximum variance in the data [13]. This approach transforms complex data into a smaller set of principal components that are more suitable for subsequent analyses. Step 1. The decision matrix is constructed according to Eq. (12), where n denotes the number of suppliers and p represents the number of criteria

X11. X12. … . X1P X21. X22. … . X2P

L = (X1. X2. … . XP) = … . (12)

[Xn1. Xn2. … . XnP] Step 2. Data normalization is performed using Relations (13) and (14) for the input and output data, respectively.

′ Li

L = . (13)

maxLi

′ minLi

L = L . (14)

Since L' is a scale-free (dimensionless) data, a different normalization procedure must be used for the inputs and outputs, as provided by L'; then, the matrix L' is used as input to continue the PCA process Eq. (15).

X11 ′ . X12 ′ . … . X1P ′ X21 ′ . X′ 22. … . X2P ′ ′ ′ ′ ′ …

L = (X1. X2. … . Xp) = … . (15)

[Xn1 ′ . Xn2 ′ . … . X′ nP] Step 3. The covariance matrix V is obtained using Eq. (16).

1 ′ ′ ′ ′

Vik = ∑(Xji − ̅ X i)(Xjk − ̅ X k). i = 1. 2. … . p. k = 1. 2. … . p. (16)

Step 4. The eigenvalues and eigenvectors of the covariance matrix are obtained from Eq. (17). λ is a set of eigenvalues.

|V − λI| = 0, VX′ = λX′. (17)

Step 5. The normalized eigenvalues are equivalent to the principal components. The maximum eigenvalue refers to the first vector and represents the first principal component. Consider the eigenvalues according to Eq. (18) and the corresponding normalized eigenvectors α1, α2, and αp.

λ1 ≥ λ2 ≥ ⋯ ≥ λP ≥ 0. (18) XPC1 α . α . … . α X′1

11 12 1P

XPC2 α21. α22. … . α2P X′2 ∙ … ∙

= … × . (19)

∙ … ∙ X [αP1. αP2. … . αPP]P×P [X′ ] [ PCP]P×1 P P×1 According to Eq. (19), Xpci (i=1, 2… p) is the i − th principal component and is the linear combination of X1', X2'… Xp' (i.e., the original normalized variables). It should be noted that each principal component is formed as a linear combination of the original data set by Eq. (20). Eqs. (21) and (22) are used to calculate the variance and covariance matrices of the variables [30].

XPCi = αi1X1 ′ + αi2X2 ′ + ⋯ + αiPXP ′ . i = 1. 2. … . p. (20) Var(XPCi) = αt iVαi. i = 1. 2. … . p. (21) Cov(XPCi. XPCk) = αt iVαk. i = 1. 2. … . p. k = 1. 2. … . p. (22)

In the final stage of the proposed framework, namely supplier clustering, the k-means algorithm was employed. This algorithm is an unsupervised learning technique that partitions and groups objects based on their characteristics. The clustering process is performed by minimizing the sum of squared distances between data points and their corresponding cluster centers. The k-means algorithm partitions a dataset containing n objects or records into k clusters (k < n), so that intra-cluster similarity is maximized and inter-cluster similarity is minimized. In other words, clustering groups data objects so that the within-cluster distances are small and the between-cluster distances are large. The similarity within each cluster is measured with respect to the mean (average) of the objects in that cluster, called the cluster center.

The inputs of this algorithm include n, the number of objects in the dataset; k, the number of clusters; and d, the number of data dimensions. The output is a set of k clusters that minimizes the mean squared error criterion. The main steps of the algorithm include determining the number of clusters, selecting initial cluster centers, calculating distances between data points and their centers, grouping data points, and recalculating the cluster centers until convergence. Finally, the quality of the clusters is evaluated using the mean squared error criterion in Eq. (23), and the algorithm continues until changes in the clusters cease (convergence) [31], [32].

MSE = ∑ ∑(p − mi) . (23)

To assess the validity of the proposed approach, two methods were employed. First, the rankings of suppliers obtained using the TOPSIS and MARCOS techniques were compared, and the correlation between the rankings was calculated using the Spearman correlation coefficient. Second, the elbow method and silhouette index were used to determine the optimal number of clusters for the clustering algorithm.

The TOPSIS method benefits from simple computational procedures and the ability to provide a logical representation of performance, enabling the comparison and ranking of alternatives based on multiple criteria. In this method, alternatives are ranked according to their distances from the Positive Ideal Solution (PIS) and the Negative Ideal Solution (NIS). Initially, the original decision matrix is normalized and then weighted. Subsequently, the positive and NISs are determined based on the nature of the criteria (benefit or cost). In the next step, the distance of each alternative from the PIS and NIS is calculated. Finally, the closeness coefficient of each alternative to the PIS is computed, and the alternatives are ranked based on these coefficients [22]. After calculating supplier rankings using the TOPSIS method, they are compared with those obtained using the MARCOS method. The degree of agreement between the rankings is measured using the Spearman rank correlation coefficient (24). A value of ρ close to 1 indicates a high level of agreement between the two methods, whereas a value close to 0 indicates no agreement, and a value close to −1 implies a reverse ranking [33].

6 ∑ di 2

ρ = 1 − 2 . (24)

n(n − 1) To determine the appropriate number of clusters in the k-means algorithm, the elbow method and the silhouette index are employed. The elbow method minimizes the Within-Cluster Sum of Squares (WCSS) and illustrates the gradual change in WCSS through an "elbow" plot. The point at which the reduction in WCSS begins to slow down indicates the optimal number of clusters [34]. The silhouette index Eq. (25) also analyzes the distances between clusters and identifies how effectively data points are assigned within their respective clusters [32]. These two methods are used in complementary ways to determine the optimal number of clusters in supplier clustering.

p(j) − q(j)

Sj = . (25)

max (p(j). q(j))

To implement the proposed research model, a steel industry company was selected as a case study. First, scientific articles on resilience were reviewed, and resilience criteria for selecting resilient suppliers were extracted and shared with the company's experts. They selected and introduced 15 practical resilience indicators (Table 2).

RC13 Quality of products and services The ability of the provided goods to meet customer expectations.

RC14 Responsiveness speed The speed of the supplier's response to market demand.

RC15 Robustness Physical protection infrastructure and safety systems for the supplier's buildings and facilities to minimize the negative impacts of disruptions, especially during natural disasters.

In addition to resilience indicators, which overlap with conventional supplier selection criteria, financial indicators were also important in the organization under study's supplier evaluation process. Due to limited access to appropriate quantitative resilience data, financial data was used as a proxy. The 17 financial indicators provided by this company are listed in Table 3.

FC14 Current ratio Calculated as current assets divided by total short-term liabilities.

FC15 Quick ratio Inventory is subtracted from current assets and divided by short-term liabilities.

FC16 Cash ratio Calculated as the amount of cash divided by short-term liabilities.

FC17 P/E ratio Ratio of market value per share to earnings per share.

In the proposed supplier evaluation approach, the required information was collected through collaboration with the following: financial data for 24 main suppliers and 17 associated financial indicators. In addition, 15 criteria influencing supplier resilience were extracted from the existing literature, and after localization, experts were asked to evaluate suppliers based on these criteria using a Likert-scale questionnaire.

After data collection, the initial decision matrices were quantified according to the benefit or cost nature of the criteria. To aggregate the experts' judgments, the geometric mean method was used, and the results were presented as an integrated, quantified decision matrix.

To determine the weights of the selected resilience indicators, the Shannon entropy technique was applied. In this process, the integrated quantified decision matrix was first normalized, and then the entropy value of each indicator was calculated. Subsequently, the degree of divergence for each indicator was determined, and its normalized weights were obtained. The resulting values are presented in Table 4, which illustrates the weight of each indicator.

Based on these results, the resilience indicator weights were used to calculate the suppliers' scores and rankings in the next step. Among these indicators, the criteria of product and service quality, reliability, agility, responsiveness, and on-time delivery were found to be the most important, respectively, compared with the other criteria.

Subsequently, the novel MARCOS technique was employed to evaluate the performance and rank the suppliers. The first step of the MARCOS method is to construct the extended initial decision matrix. As previously stated, after quantifying the decision matrices, the decision-makers' evaluations were aggregated using the geometric mean. The extended initial decision matrix was then formed by adding two rows, namely AAI and AI, which represent the anti-ideal solution and the ideal solution, respectively, to the aggregated quantitative decision matrix.

In this study, all resilience criteria are of a benefit-type nature. Therefore, the AAI (anti-ideal solution) and AI (ideal solution) rows reflect the minimum and maximum values, respectively (based on Eqs. (2) and (3)). In the next step, the extended initial decision matrix is normalized. Depending on the criterion type (cost or benefit), either a maximization or a minimization function is applied. Given the benefit-type nature of the criteria, a simple linear normalization was used.

Subsequently, the weighted normalized matrix was obtained by multiplying the importance weights of each criterion, derived from the Shannon entropy technique, by the elements of the normalized matrix. The sum of the elements in each row of the weighted normalized matrix was then calculated, followed by the computation of the degrees of desirability. Afterward, the utility functions corresponding to the ideal and anti-ideal solutions were determined. Finally, the suppliers' scores were obtained by calculating the final utility function based on Eq. (9), and their rankings were determined accordingly. The results of the MARCOS method are presented in Table 5.

According to the results, supplier S24 achieved a score of 0.73 and ranked first among the 24 suppliers. Subsequently, suppliers S23, S18, S10, and S1 ranked second to fifth with scores of 0.65, 0.62, 0.59, and 0.58, respectively. In addition, supplier S17, with a score of 0.27, ranked last. Suppliers S13 and S21 simultaneously obtained the 22nd rank.

To integrate heterogeneous information, the proposed framework creates a unified dataset by adding suppliers' resilience scores (calculated using the MARCOS method based on expert judgments) to the financial data, thereby combining data-driven and knowledge-driven information. This dataset consists of 18 indicators (17 financial indicators and one indicator, the supplier score, representing supplier resilience). It uses data from 24 suppliers of the case study company for machine learning analyses and resilient supplier selection. Before implementing the PCA method, five assumptions must be examined to ensure the validity of the results. These assumptions include: measurement of variables at a continuous level, the existence of linear relationships among variables, sampling adequacy, sufficient correlation among variables, and the absence of significant outliers. After verifying these assumptions and confirming that none were violated, the PCA was applied to the dataset using SPSS. Subsequently, the results and outputs obtained from the PCA model were interpreted.

Table 6 presents the initial and extracted communalities of each variable with respect to the extracted components. The Initial values represent the initial communalities (before extraction) and indicate the total variance of each variable that the components can explain. Therefore, this value is initially equal to 1 for all variables. The Extraction column reports the communalities after principal component extraction. The closer these values are to 1, the better the extracted components explain the original variables.

The results indicate that all variables in the dataset of this study are suitable for explaining variance after factor extraction. The lowest communality value is for variable FC16; however, since it exceeds the 0.5 threshold, there is no need to remove this variable or re-estimate the model.

In the total variance explained table (Table 7), initially, several components equal to the number of variables in the original dataset (18 criteria) are extracted. The initial eigenvalues for each component are reported in the second column. Components with eigenvalues greater than one represent genuine principal components. According to this table, of the 18 variables, four principal components have eigenvalues greater than 1. These components account for 31.65%, 24.43%, 15.69%, and 9.60% of the total variance, respectively, which together explain 81.37% of the total variance.

The scree plot (Fig. 1) confirms the findings obtained from the total variance explained table (Table 7). As shown in the figure, only the eigenvalues of the four components lie above the red line (greater than one). The sharp decline between the first and fourth components indicates the importance of these four components in explaining the total variance of the data. In contrast, the remaining components show no significant decrease in eigenvalues, suggesting they cannot adequately represent the overall data variability. Table 8 presents the unrotated component (factor) matrix, which indicates the degree of correlation between each variable and the extracted components (with eigenvalues greater than one). The rotated component matrix (Table 9) shows the correlations between the rotated components and the observed variables. In the first component, variable FC3, with a correlation of 0.916, was identified as the most influential. Similarly, in the second, third, and fourth components, variables FC7, FC17, and FC12 exhibited the highest correlations and impacts, with values of 0.905, 0.773, and 0.885, respectively. It should be noted that in this table, only factor loadings greater than 0.5 are reported.

The component transformation matrix (Table 10) shows the degree of correlation between the four extracted components before and after the cycle.

After applying PCA to identify latent patterns and reduce data dimensionality, the k-means clustering method was employed to group suppliers into core, backup, and alternative suppliers. To determine the appropriate number of clusters, k was varied from 2 to 8, and the corresponding outputs were collected. The results indicated that the changes in the total within-cluster distances for k values between 2 and 5 were significantly greater than those observed for k values between 5 and 8 (Table 11). Therefore, k = 5 was examined in greater detail. Optimal k-means clustering is achieved when the variability resulting from changes in the number of clusters (k) is minimized.

Table 12 shows the initial centers of these five clusters in four dimensions (due to the presence of four variables).

The algorithm is repeated until the final cluster centers are reached (convergence). In the last iteration of the algorithm, the cluster centers are shown in Table 13.

The distances between the centers of the final clusters in the last iteration are as shown in Table 14.

In the Analysis Of Variance (ANOVA) test, by examining the significance level (sig.) of the variables, the results in Table 15 show that for all variables, the sig. value is less than 0.001. Therefore, the assumption of cluster homogeneity is rejected, and the five clusters are significantly different from one another. The F tests should be used only for descriptive purposes, as the clusters have been chosen to maximize differences among cases within clusters. The observed significance levels are not corrected for this and thus cannot be interpreted as tests of the hypothesis that the cluster means are equal.

Table 16 shows the number of suppliers belonging to the five designated clusters. Cluster 1 has eight suppliers, and clusters 2 to 5 have one, eight, three, and four suppliers, respectively. Table 17 also shows the cluster number of each supplier.

To validate a portion of the proposed framework, the supplier rankings from the Marcus and TOPSIS methods were compared, and the Spearman correlation coefficient was calculated. Table 18 shows the scores and rankings of suppliers in the TOPSIS technique. The correlation coefficient between the supplier rankings obtained using the mentioned method was 0.87, indicating a strong relationship between the results of these two MCDM techniques.

Also, an elbow diagram was drawn to determine the appropriate number of clusters for values between 2 and 10. The diagram in Fig. 2 indicates that 5 clusters are the optimal number.

The profile index output for the number of clusters between 2 and 6 showed that the number of clusters was 5 (Table 19). Although none of the cluster numbers approached 1, this result is still acceptable and consistent with the elbow diagram. Due to the nature of the data and the proximity of the clusters, the profile index value is not close to one. Finally, the appropriate number of clusters for the supplier's dataset would be five.

This study evaluated suppliers' resilience under critical conditions and proposed a systematic framework to facilitate decision-making. Using MCDM techniques such as Shannon entropy and MARCOS, the resilience of suppliers was assessed. Then, the suppliers' resilience scores were combined with financial data, reduced in dimensionality using PCA, and the suppliers were subsequently clustered using the k-means algorithm. Ultimately, 24 suppliers were allocated into five clusters. The model's results were validated by comparing the MARCOS and TOPSIS methods and by calculating the Spearman correlation coefficient (0.87). By leveraging the strengths of both data-driven and knowledge-driven methods, this framework can serve as an integrated decision-support system for supplier evaluation and other strategic organizational decisions. It is recommended that future research consider environmental and sustainability factors in supplier selection, the use of big data, and the application of the model in sensitive industries requiring high resilience.

This research received no specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

All data are included in the text.

The authors declare no conflict of interest.