Abstract
The procurement of medical equipment is a critical concern for healthcare organizations striving to deliver comprehensive patient care. Thus, the procurement process, including performance evaluation and selection of medical equipment suppliers, poses a significant challenge for healthcare organizations. The decision-making process also involves multiple decision-makers making subjective judgments about various quantitative and qualitative criteria for several alternative suppliers. This paper presents a framework for medical equipment supplier evaluation under uncertain assessment information by integrating rank order centroid (ROC) and fuzzy analytic hierarchy process (fuzzy AHP) techniques. The first stage involves identifying the key criteria influencing the performance evaluation of medical equipment suppliers for healthcare organizations. The ROC technique is used to assign weights to the important criteria, reducing uncertainty of weight assignment and subjective judgment information of the decision-makers. The fuzzy AHP method is then applied to evaluate and rank potential suppliers based on their overall performance. The approach is validated through a case study in a hospital setting, demonstrating the practical applicability of the proposed approach in a real-world scenario. Results indicate that the proposed hybrid method effectively supports group decision-making under uncertainty, providing healthcare organizations with a systematic and logical approach for selecting the most suitable medical equipment supplier. This framework enhances procurement efficiency and supports better resource allocation in healthcare.
Keywords: Supplier selection, Medical equipment procurement, Healthcare, Rank order centroid, Fuzzy AHP, Mechanical ventilator
Subject terms: Engineering, Mathematics and computing
Introduction
The medical or healthcare industry stands as one of the largest and fastest-growing and is regarded as one of the top service sectors globally, distinguished by its significant budgets, extensive workforce, broad consumer base, and essential services1–3. Its primary role is to deliver organized patient care through specialized and highly qualified medical and nursing professionals. Unlike other industries, healthcare is uniquely complex, with patient care as its foremost priority4–6. Beyond individual well-being, the healthcare sector also significantly contributes to community welfare. A well-functioning healthcare system, including medicine and medical supply, has become an increasingly important component of society and impacts the growth and development of cities7.
Medical equipment is a fundamental component of the healthcare industry, which is essential to supply and control the necessary services, such as diagnostics, treatment, or rehabilitation, for disease patients in a safe and effective way8,9. However, managing the lifecycle costs of these medical supplies and equipment poses a considerable financial challenge for healthcare organizations. These organizations must balance cost control with the imperative to maintain and improve service quality10–12. Without a systematic approach to procurement and supplier selection, healthcare delivery costs can rise disproportionately. The growing number of medical equipment providers also introduces risks of substandard quality and insufficient maintenance services13,14. Efficient procurement is therefore essential to address supply chain challenges within the healthcare system. Failures or delays in supplying quality medical equipment can disrupt hospital service delivery chains, underlining the critical importance of selecting reliable suppliers4. Recognizing this, healthcare organizations increasingly prioritize procurement strategies to enhance operational efficiency.
In the procurement process, selecting medical equipment suppliers is a complex and critical task that requires careful consideration12,15. Healthcare organizations, much like other businesses, consider various subjective and objective criteria when choosing suppliers. While cost, delivery, and quality are commonly used criteria in conventional supplier selection, the specific concerns and criteria can vary across industries16,17. The criteria for evaluating medical equipment suppliers for healthcare organizations may be different. Erginel and Gecer (2016) highlighted that healthcare organizations consider relevant service quality criteria when evaluating medical equipment suppliers18. Furthermore, while most criteria for supplier selection are traditionally considered by decision-makers (DMs) from the purchasing area, the evaluation criteria for medical equipment suppliers are possibly determined by medical professionals and specialists. The criteria may extend beyond conventional metrics to include product characteristics, warranties, and other factors critical to patient care.
According to a literature survey, numerous studies have been conducted on the selection of suppliers to address real-world issues. Due to the varying contexts of purchasing, these studies have employed a diverse range of supplier assessment criteria19. However, relatively few studies have focused specifically on how healthcare organizations select medical equipment suppliers and the key criteria they prioritize. Healthcare organizations increasingly require decision frameworks that enable efficient supplier selection processes20. Establishing such a systematic and logical selection process is vital for healthcare organizations. It is also important for medical equipment providers to understand healthcare preferences in order to strengthen their market position and continually enhance their offerings accordingly.
This study has two primary objectives. The first is to identify and prioritize the key criteria influencing the evaluation and selection of medical equipment suppliers from the perspective of healthcare organizations. The second is to propose a systematic approach to streamline the selection process. To address the first objective, ROC, a rank-based method, is employed to determine the relative weight of each criterion. This method minimizes uncertainty in weight assignment and mitigates subjective biases in decision-making. For the second objective, the study employs the fuzzy AHP method.
AHP is a widely used method for solving the supplier selection problem21,22. Its flexibility allows for both subjective and objective evaluations of qualitative and quantitative data. AHP enables problem breakdown into hierarchical levels, facilitating analysis at varying levels of detail. It also provides a means to assess the consistency of evaluations conducted by DMs23–25. However, a common criticism of AHP is its inability to address the subjectivity and uncertainty inherent in real-world scenarios, where DMs often provide imprecise or incomplete information through linguistic judgments26,27.
To address these limitations, fuzzy logic is incorporated into AHP. Fuzzy logic provides a framework for interpreting imprecise or vague assessments based on linguistic variables. The integration of fuzzy logic with AHP has been widely adopted to account for inconsistencies among DMs, offering a structured approach to deal with ambiguity, vagueness, and imprecise information regarding alternatives and criteria28–31. Moreover, this method facilitates obtaining rankings and identifying the best alternative through a straightforward mathematical approach. Hence, fuzzy AHP is selected as the foundational principle for this study.
This study demonstrates the application of fuzzy AHP in a real procurement scenario involving the selection of a mechanical ventilator supplier for a hospital in Thailand. Mechanical ventilators have gained significant prominence due to their critical role in treating severe respiratory conditions and their heightened demand during the COVID-19 pandemic. This application highlights the relevance of the proposed framework in facilitating informed purchasing decisions in the healthcare sector. To the best of the authors’ knowledge, no prior research has combined fuzzy AHP with ROC to address the supplier selection problem in the medical equipment domain, particularly concerning mechanical ventilators. This study addresses this gap by providing DMs and practitioners in the health and medical industries with insights into systematic and effective decision-support tools for evaluating and selecting medical equipment suppliers.
This paper is structured as follows: “Related work” reviews related literature, highlighting key criteria for supplier selection in healthcare. Section “Methodology” outlines the research process and provides an overview of the ROC and fuzzy AHP methods. Section “Medical equipment supplier performance evaluation criteria” identifies and prioritizes the critical criteria influencing medical equipment supplier evaluation. Subsequently, the relative weights of these criteria are determined. Section “Application for selecting a hospital medical equipment supplier” presents a real-world application of the proposed framework, including sensitivity analysis to evaluate the impact of criteria weights on decision-making. Finally, “Managerial and practical implications” and “Conclusion” provide managerial and practical implications, as well as concluding remarks.
Related work
While numerous studies address supplier selection in various industries, research specifically focusing on medical supply and equipment suppliers remains limited. Some studies, however, provide insights into healthcare supplier evaluations, highlighting diverse criteria and methodologies. Yazdani et al. (2020) examined supplier selection for a hospital in Spain, providing products such as arm slings, posture supports, orthopedic pillows, physiography devices, and specialized powders. Best worst method (BWM) and decision-making trial and evaluation laboratory (DEMATEL) were used to weigh six criteria: quality, technology utilization, flexibility, batch volume, inventory capacity, and price. Among these, price, quality, and technology emerged as top priorities7. Tavana et al. (2021) assessed medical equipment suppliers for a cardiovascular hospital in Iran, using 18 criteria. Delivery time, quality certifications, cost, redundancy, conformance to standards, and flexibility were identified as the most influential criteria12. Similarly, Liu et al. (2022) focused on emergency medical supplier selection during the COVID-19 pandemic in Wuhan. Six criteria were considered in the study: economy, robustness, supply capacity, response speed, quality, and information capability32. Salimian et al. (2022) explored supplier selection for surgery devices in a transplant center, considering 17 criteria categorized into economic, social, and environmental aspects. Quality, reliability, and pollution control emerged as the three most important criteria33. Pamucar et al. (2023) addressed supplier selection for medical face masks and face shields for a hospital in Istanbul, Turkey. Eighteen criteria were classified into technical, environmental, and social aspects, with job creation, stakeholder rights, green training, occupational health and safety systems, and pollution restrictions ranking as the most critical factors20.
Rostami et al. (2023) evaluated suppliers for oxygen concentrators for a hospital in Tehran, Iran. Here, 24 criteria were grouped into digitalization, resiliency, sustainability, and leagile (lean-agile) categories. Their findings highlighted quality, restorative capacity, market sensitivity, greenhouse gas emission, reliability, and cost as the most important criteria34. Gurmani et al. (2023) assessed suppliers for emergency medical supplies, including automatic external defibrillators, oxygen tanks, and portable suction units. Five criteria used in the evaluation include supply capacity, product cost, financial stability, product quality, and logistic speed35. Akcan and Güldeş (2019) evaluate suppliers for a public hospital in Turkey. AHP was applied to determine the weights of the selection criteria. Here, 15 criteria were categorized into five groups: logistics, quality, cost, flexibility, and reliability36. Bahadori et al. (2020) investigated suppliers for medical consumer goods in a military hospital, considering six criteria: quality, price, supplier’s background, payment terms, packaging and transporting quality, and timely delivery. The score for each criterion was obtained through a Likert scale4. Stević et al. (2020) focused on supplier selection for a private polyclinic providing eye surgical interventions in Bosnia and Herzegovina, using 21 criteria in the analysis. The five most important criteria reported in this study were quality, price, on-time delivery, reliability, and reputation37. Göncü and Çetin (2022) identified criteria considered by healthcare enterprises when selecting suppliers. The ANP method was used to weigh 17 criteria classified into six main aspects: sustainability, occupational health and safety, technical, quality, logistics, and price. Brand image, purchase cost, and health impacts emerged as significant criteria38.
Other studies focusing on the pharmaceutical industry offer additional insights. Chakraborty et al. (2023) evaluated healthcare supplier selection for pharmaceutical items, considering six criteria including price, flexibility, responsiveness, reliability, delivery performance, and quality39. Nazari-Shirkouhi et al. (2023) examined suppliers for a pharmaceutical company in Iran. Eight criteria considered in this study were delivery, quality, price, responsiveness, vulnerability, adaptive capability, risk awareness, and technology level40. Sheykhizadeh et al. (2024) selected supplier for an Iranian pharmaceutical company by considering four main criteria, including lean, agile, resilience, and green, which include eighteen supplier selection sub-criteria. The four most important criteria were surplus inventory, just-in-time delivery, lead time, and customer responsiveness41. Chakraborty et al. (2024) identified the most suitable pharmaceutical supplier in the Indian healthcare sector. The basis of five criteria consisting of cost, quality, delivery time, service, and flexibility was used in the evaluation42. These studies underscore the importance of tailoring supplier selection criteria to specific healthcare contexts and highlight the growing emphasis on applying multi-criteria decision-making (MCDM) methods in decision-making processes.
Methodology
The analysis of the importance of criteria using rank order centroid (ROC)
ROC is a technique used in MCDM to aggregate and analyze the rankings or preferences of alternatives based on various criteria43. It also serves as a ranking method for weight determination. The ROC rank-based weighting method derives numerical weights for each criterion by converting their ranking order based on importance or priority level. The method offers higher accuracy compared to other rank-based methods43. Furthermore, it boasts simplicity in understanding and application, proving effective in scenarios with multiple decision criteria. Implementation also requires minimal time since DMs only need to assess the priority of the criteria44. The weight value is calculated using the following formula.
 |
1 |
where 
is the weight of 
criterion. The weights are evenly distributed across the simplex of rank-order weight 
… 
, where 
. 
is the number of criteria, and 
is a rank position of 
criterion. Note that the criterion ranked first (
= 1) holds the highest importance. The ROC method is simple and straightforward to apply, however, the weights obtained are widely distributed45,46.
The analysis of the overall performance of suppliers using fuzzy AHP
Fuzzy AHP uses fuzzy numbers instead of exact numerical values to model and quantify the uncertainty of human preference in pairwise comparison. Assume that there are K DMs. The fuzzy rating of each DM 
(k = 1, 2, …, K) for each alternative 
(i = 1, 2, …, m) with respect to criteria 
(j = 1, 2, …, n) is presented as triangular fuzzy numbers (TFNs) 
(i = 1, 2, …, m; j = 1, 2, …, n; k = 1, 2, …, K). The mathematical concept of fuzzy AHP applied in this study is adopted from Bakır and Atalık (2021), summarized as follows47.
The first step is to construct the aggregated fuzzy pairwise comparison matrix 
for the alternatives. Let 
denote the aggregated fuzzy pairwise comparison matrix, containing all pairwise comparisons between each alternative 
with respect to each criterion 
of K DMs. 
can be defined by
 |
2 |
where 
which is TFN defined by Eq. (2). 
= 1 if 
is equal to 
, and 
if 
is not equal to 
.
Then the fuzzy score, 
, of the alternative 
against each criterion 
is calculated using the geometric mean technique, according to Eq. (3).
 |
3 |
where
and 
is geometric mean of the fuzzy comparison value of each alternative regarding each criterion. The values of 
can be calculated as
 |
4 |
where 
is the fuzzy aggregate comparison value of each pair of alternative regard to each criterion 
.
Next, the fuzzy scores of the alternatives 
, which is a fuzzy number, are defuzzified by applying the center of area (COA) method. The crisp value is computed as follows:
 |
5 |
where 
is the evaluation of alternative priority against each criterion.
The next step involves computing the priority score of alternatives. This score can be derived using the weighted sum method, which entails summing the products of each alternative’s priority evaluation, 
, against each criterion with the respective importance weights 
of the evaluation criteria. Note that the values of the criteria weights 
in this study were obtained from the ROC method. The priority score of each alternative 
is calculated as follows:
 |
6 |
In the final step, the ranking of alternatives is determined based on the priority score of each alternative. According to Eq. (6), the preferred alternative is the one with the highest score.
In the AHP method, the quality of the result hinges on the consistency of the pairwise comparison based on DM’s judgments, necessitating a consistency check. The consistency ratio (CR) gauges the consistency of judgments within each pairwise comparison matrix. CR is calculated by dividing the consistency index (CI) by the random consistency index (RI), as expressed by the following formula:
 |
7 |
represents the maximum eigenvalue, and 
denotes the dimension of the matrix. A pairwise comparison matrix’s consistency is deemed acceptable if the CR ratio is below 0.1. If the CR exceeds this value, a reassessment of the pairwise comparison matrix is necessary.
Medical equipment supplier performance evaluation criteria
Identification of criteria influencing medical equipment supplier evaluation and selection
A review of relevant studies identified 25 potential criteria that healthcare organizations may consider when evaluating the performance of medical equipment suppliers. These criteria were collated and categorized based on their explicit or underlying meanings. Table 1 lists all criteria that can be categorized into nine distinct groups.
Table 1.
Preliminary criteria for of medical equipment supplier selection.
| Criteria | Category |
|---|---|
| Product performance | Quality |
| Percentage of defective/rejected products | |
| Product certification | |
| Product characteristics | |
| Product cost | Cost |
| Average price increase per year | |
| Price volatility | |
| Compliance with agreements | Compliance |
| Availability of sampling | |
| Tracking of complaints | |
| Guarantee & warranty policy | Service |
| Terms of service | |
| Product training | |
| Company credibility | Reliability |
| Service history | |
| Technical support | Agility |
| Quick response | |
| Delivery schedule agreement | Delivery |
| On-time delivery | |
| Delivery condition | |
| Delivery reliability | |
| Expedited delivery capability | Lead time |
| Lead time | |
| Transportation distance | Transport |
| Shipment quantity |
To refine the criteria, experts specializing in medical equipment procurement—comprising medical scientists, registered nurses, equipment technologists, technicians, and medical technologists affiliated with various government healthcare agencies and hospitals in Thailand—rated the importance of the criteria on a five-point Likert scale (1 = not at all important; 5 = extremely important). The average score for each criterion was calculated, and those scoring above 4.20 were deemed highly important for evaluating the performance of medical equipment suppliers. These criteria were subsequently selected for inclusion in the study. Codes were then assigned to these criteria for further analysis, as shown in Table 2.
Table 2.
Final criteria for medical equipment supplier selection.
| Codes | Criteria | Average score | Remarks |
|---|---|---|---|
| C1 | Product performance | 4.83 | – |
| C2 | Product certification | 4.79 | – |
| C3 | Product characteristics | 4.58 | – |
| C4 | Product cost | 4.29 | – |
| C5 | Compliance with agreements | 4.58 | – |
| C6 | Availability of sampling | 4.45 | – |
| C7 | Tracking of complaints | 4.25 | – |
| C8 | Guarantee & warranty policy | 4.58 | – |
| C9 | Terms of service | 4.45 | – |
| C10 | Product training | 4.50 | – |
| C11 | Company credibility | 4.45 | – |
| C12 | Service history | 4.54 | – |
| C13 | Technical support | 4.58 | – |
| C14 | Quick response | 4.50 | – |
| C15 | On-time delivery | 4.50 | – |
| C16 | Delivery condition | 4.62 | – |
| C17 | Delivery reliability | 4.41 | – |
| – | Percentage of defective/rejected products | 4.08 | Deleted |
| – | Average price increase per year | 4.08 | Deleted |
| – | Price volatility | 4.08 | Deleted |
| – | Delivery schedule agreement | 4.17 | Deleted |
| – | Expedited delivery capability | 3.83 | Deleted |
| – | Lead time | 4.17 | Deleted |
| – | Transportation distance | 3.63 | Deleted |
| – | Shipment quantity | 3.67 | Deleted |
Table 2 identifies 17 important criteria influencing the evaluation and selection of medical equipment suppliers. These criteria encompass both quantitative and qualitative dimensions. Only seven categories remain in the study: quality (C1–C3), cost (C4), compliance (C5–C7), service (C8–C10), reliability (C11–C12), agility (C13–C14), and delivery (C15–C17). While some criteria related to quality, price, and delivery are commonly used in conventional supplier selection, there are additional considerations worth highlighting. Product quality naturally stands as one of the issues to be considered when choosing a medical equipment supplier. However, specific aspects in this realm include product certification, such as ISO certification, which is carried out by external certification parties to provide independent confirmation of international competence, ultimately contributing to the overall quality and reliability of the product.
Given the substantial investment often associated with medical equipment, product warranties and terms of service become important to ensure both product and service quality, including provisions for compensation if the product fails to perform as stated. Contrary to the assumption that older medical equipment requires more service and maintenance, newer models often necessitate more ongoing maintenance than their older counterparts. Criteria such as product training, technical support, and quick response pertain to support services. While the first two concern after-sales service, the latter involves both pre- and post-sales service. Guaranteed support services from a supplier are essential for seamless operation and enhanced treatment quality. This entails ensuring proper equipment functioning, prompt resolution of queries, and efficient and competent handling of repairs or replacements. Prompt communication is also necessary for any upgrades to the current system.
Last but not least, criteria related to company credibility and service history reflect the reliability and reputation of a supplier. In a crowded market of medical suppliers, distinguishing between legitimate and counterfeit suppliers can be challenging. Considering these criteria aids in evaluating whether a medical equipment supplier can be trusted. The criteria for evaluating medical equipment suppliers extend beyond product quality to encompass the services they provide. This is crucial because effective service from a supplier ensures that equipment remains in optimal working condition, which directly impacts patient diagnosis and treatment.
After identifying the key criteria, the next step involves determining the relative weights of these criteria to prioritize their importance in the supplier evaluation process.
Weight determination of evaluation criteria
The criteria listed in Table 2 differ in their relative importance when evaluating and selecting medical equipment suppliers. The ROC method, as described in Sect. 3.1, was applied to determine the importance weights of these criteria. Priority rankings for the seven main categories—quality, cost, compliance, service, reliability, agility, and delivery—were established based on expert evaluations. Specific criteria within each category were also ranked. The importance weight of each category and its associated criteria was calculated using Eq. (1). The global weights for all 17 criteria were subsequently computed by multiplying the importance weights of the categories by the relative weights of the criteria. Table 3 presents the computed weights and the rankings of each criterion.
Table 3.
Weights and rankings of evaluation criteria.
| Category | Importance weight | Criteria | Relative weight | Global weight | Global ranking |
|---|---|---|---|---|---|
| Quality | 0.37 | C1: Product performance | 0.61 | 0.2257 | 2 |
| C2: Product certification | 0.28 | 0.1036 | 3 | ||
| C3: Product characteristics | 0.11 | 0.0407 | 8 | ||
| Cost | 0.23 | C4: Product cost | 1.00 | 0.2300 | 1 |
| Compliance | 0.16 | C5: Compliance with agreements | 0.61 | 0.0976 | 4 |
| C6: Availability of sampling | 0.28 | 0.0448 | 7 | ||
| C7: Tracking of complaints | 0.11 | 0.0176 | 11 | ||
| Service | 0.11 | C8: Guarantee & warranty policy | 0.61 | 0.0671 | 5 |
| C9: Terms of service | 0.28 | 0.0308 | 9 | ||
| C10: Product training | 0.11 | 0.0121 | 14 | ||
| Reliability | 0.07 | C11: Company credibility | 0.75 | 0.0525 | 6 |
| C12: Service history | 0.25 | 0.0175 | 12 | ||
| Agility | 0.04 | C13: Technical support | 0.75 | 0.0300 | 10 |
| C14: Quick response | 0.25 | 0.0100 | 15 | ||
| Delivery | 0.02 | C15: On-time delivery | 0.61 | 0.0122 | 13 |
| C16: Delivery condition | 0.28 | 0.0056 | 16 | ||
| C17: Delivery reliability | 0.11 | 0.0022 | 17 |
Among the seven main criteria, product quality is the most important category, holding a weight of 37%, signifying its paramount importance in assessing medical equipment suppliers. In healthcare, delivering high-quality patient care ranks as a primary concern. While the expertise of medical staff is crucial, it is imperative to acknowledge that there are limitations to what can be achieved solely through human capacities. The utilization of state-of-the-art equipment assumes equal significance in ensuring optimal patient outcomes. Reliable and quality medical equipment is indispensable for accurate diagnosis and effective treatment, ensuring smooth operations and avoiding potential life-threatening situations caused by delays or equipment malfunctions. The second concern is the cost, which accounts for 23% of the weight. Cost is usually one of the top priorities in supplier selection criteria across various industries, including healthcare. Whether in public or private healthcare organizations, products must align with budget constraints. The remaining categories—compliance (16%), service (11%), reliability (7%), agility (4%), and delivery (2%)—contribute smaller weights but remain essential to supplier evaluation. Although delivery ranks lowest, it remains critical in supplier evaluations for medical supplies and equipment. Medical equipment deliveries require careful handling and often entail specific requirements.
The two rightmost columns in Table 3 provide the relative importance (global weight) and ranking of each criterion. Notably, product cost (C4) emerges as the most important criterion with a global weight of 23%, followed closely by product performance (C1) with 22.57%. These top two criteria signify significant concerns in assessing supplier performance. The next three important criteria are product certification (C2), compliance with basic agreements (C5), and guarantee & warranty policy (C8), which rank third, fourth, and fifth in importance, respectively. Conversely, delivery reliability (C17) is the least important. These weighted criteria serve as the basis for ranking supplier performance evaluations afterwards.
Application for selecting a hospital medical equipment supplier
The evaluation and selection of medical equipment suppliers are critical for ensuring quality healthcare services. This section empirically illustrates how the fuzzy AHP, as detailed in Sect. 3.2, is employed to tackle the problem of evaluating and selecting suppliers for medical equipment through group decision-making. To illustrate the decision-making process, we consider the example of a public hospital in Thailand. Most hospitals in Thailand are government-operated under the Ministry of Public Health, and adherence to healthcare standards is paramount. Any purchasing has to follow government regulations.
The hospital under consideration is a medium-sized, general-purpose public hospital in Nong Khai, northeastern Thailand, with a capacity of over 350 beds. The study focuses on selecting a supplier for medical ventilators needed to treat severely ill patients with respiratory issues. The ventilators must support volume-controlled, pressure-controlled, and non-invasive ventilation modes within a single device. Proposals were solicited from five suppliers capable of providing the required product, which adhered to the purchasing rules that require at least three suppliers to submit proposals for the procurement process. In the selection process, the performance of these five potential suppliers (A1–A5) was evaluated against 17 criteria (C1–C17), identified in Table 3, based on the insights and subjective judgments provided by three experts (D1–D3). Given the inherent uncertainty and ambiguity in human decision-making, a fuzzy environment was considered. To address this, TFNs were utilized to express linguistic values during the evaluation of supplier ratings. The methodology and outcomes of the fuzzy AHP were applied as represented below, with all calculations executed using Microsoft Excel.
In employing fuzzy AHP for assessment, linguistic variables were utilized to compare five alternative suppliers across evaluation criteria. These comparisons were made across nine basic linguistic terms, delineating a nine-level fuzzy scale as proposed by Kaganski et al. (2018), as illustrated in Table 448.
Table 4.
Linguistic scale for alternative ratings.
| Fuzzy number | Linguistic variable | Scale of fuzzy number |
|---|---|---|
|
Equally preferable | (1, 1, 1) |
|
Intermediate value between 1 and 3 | (1, 2, 3) |
|
Moderately preferable | (2, 3, 4) |
|
Intermediate value between 3 and 5 | (3, 4, 5) |
|
Strongly preferable | (4, 5, 6) |
|
Intermediate value between 5 and 7 | (5, 6, 7) |
|
Very strongly preferable | (6, 7, 8) |
|
Intermediate value between 7 and 9 | (7, 8, 9) |
|
Extremely preferable | (9, 9, 9) |
Firstly, fuzzy pairwise comparison matrices were constructed by each DM assigning a linguistic term, represented by TFN, to the pairwise comparison among all alternatives regarding each criterion. The computation of fuzzy values for the aggregated comparative judgments of the five alternative suppliers against each criterion was computed using Eq. (2). The resulting aggregated fuzzy pairwise comparison matrices are presented in Table 5.
Table 5.
Aggregated fuzzy pairwise comparison matrices.
| A1 | A2 | A3 | A4 | A5 | ||
|---|---|---|---|---|---|---|
| C1 | A1 | (1,1,1) | (6,7.667,9) | (3,5,7) | (3,5.333,8) | (4,5.667,8) |
| A2 | (0.111,0.132,0.167) | (1,1,1) | (0.167,0.4,1) | (0.125,0.548,1) | (0.25,0.389,1) | |
| A3 | (0.143,0.206,0.333) | (1,3,6) | (1,1,1) | (0.333,1.5,4) | (0.333,1.167,3) | |
| A4 | (0.125,0.198,0.333) | (1,3.333,8) | (0.25,1.111,3) | (1,1,1) | (0.125,2.381,6) | |
| A5 | (0.125,0.181,0.25) | (1,2.667,4) | (0.333,1.167,3) | (0.167,2.567,8) | (1,1,1) | |
| C2 | A1 | (1,1,1) | (6,7.333,8) | (2,4,4) | (2,4,4) | (2,4.333,4) |
| A2 | (0.111,0.137,0.143) | (1,1,1) | (0.125,0.225,0.167) | (0.125,0.325,0.167) | (0.167,0.2,0.25) | |
| A3 | (0.167,0.261,0.25) | (2,5,4) | (1,1,1) | (0.167,2.733,0.25) | (1,2,1) | |
| A4 | (0.143,0.278,0.2) | (1,4,3) | (0.167,1.844,0.25) | (1,1,1) | (0.25,2.444,0.5) | |
| A5 | (0.167,0.244,0.25) | (4,5,6) | (0.25,0.611,0.5) | (0.167,1.233,0.25) | (1,1,1) | |
| C3 | A1 | (1,1,1) | (6,8.333,8) | (2,3.667,4) | (2,5.667,4) | (2,4.333,4) |
| A2 | (0.111,0.122,0.111) | (1,1,1) | (0.125,0.181,0.167) | (0.111,0.751,0.111) | (0.125,0.181,0.167) | |
| A3 | (0.167,0.289,0.25) | (4,5.667,6) | (1,1,1) | (1,4.333,1) | (2,3,4) | |
| A4 | (0.125,0.206,0.167) | (0.333,4.833,1) | (0.125,0.429,0.167) | (1,1,1) | (0.25,0.944,0.5) | |
| A5 | (0.167,0.244,0.25) | (4,5.667,6) | (0.167,0.289,0.25) | (0.333,1.833,1) | (1,1,1) | |
| C4 | A1 | (1,1,1) | (2,3,4) | (9,9,9) | (4,5,6) | (4,5,6) |
| A2 | (0.25,0.333,0.5) | (1,1,1) | (9,9,9) | (4,5,6) | (6,7,8) | |
| A3 | (0.111,0.111,0.111) | (0.111,0.111,0.111) | (1,1,1) | (0.167,0.2,0.25) | (0.25,0.333,0.5) | |
| A4 | (0.167,0.2,0.25) | (0.167,0.2,0.25) | (4,5,6) | (1,1,1) | (1,2,3) | |
| A5 | (0.167,0.2,0.25) | (0.125,0.143,0.167) | (2,3,4) | (0.333,0.5,1) | (1,1,1) | |
| C5 | A1 | (1,1,1) | (4,7,6) | (4,5,6) | (2,5.667,4) | (2,4.333,4) |
| A2 | (0.111,0.151,0.111) | (1,1,1) | (0.167,0.344,0.25) | (0.125,1.131,0.167) | (0.125,0.225,0.167) | |
| A3 | (0.167,0.2,0.25) | (1,3.333,3) | (1,1,1) | (0.25,2.444,0.5) | (0.167,0.9,0.25) | |
| A4 | (0.125,0.206,0.167) | (0.25,3.778,0.5) | (0.2,1.194,0.333) | (1,1,1) | (0.125,0.798,0.167) | |
| A5 | (0.167,0.244,0.25) | (2,5,4) | (0.333,2.5,1) | (0.333,3.833,1) | (1,1,1) | |
| C6 | A1 | (1,1,1) | (6,7,8) | (2,5,4) | (4,6.333,6) | (2,4.333,4) |
| A2 | (0.125,0.143,0.167) | (1,1,1) | (0.143,0.389,0.2) | (0.25,1.778,0.5) | (0.125,0.798,0.167) | |
| A3 | (0.125,0.225,0.167) | (1,3.333,3) | (1,1,1) | (0.167,4.067,0.25) | (0.333,1.833,1) | |
| A4 | (0.125,0.162,0.167) | (0.25,1.278,0.5) | (0.125,1.781,0.167) | (1,1,1) | (0.167,1.817,0.25) | |
| A5 | (0.125,0.27,0.167) | (0.333,3.833,1) | (0.25,0.944,0.5) | (0.167,3.067,0.25) | (1,1,1) | |
| C7 | A1 | (1,1,1) | (4,7.333,6) | (2,5,4) | (4,6.333,6) | (2,5.667,4) |
| A2 | (0.111,0.145,0.111) | (1,1,1) | (0.167,0.317,0.25) | (0.2,1.167,0.333) | (0.25,0.389,0.5) | |
| A3 | (0.125,0.225,0.167) | (1,3.667,3) | (1,1,1) | (0.25,3.444,0.5) | (1,2.333,3) | |
| A4 | (0.125,0.162,0.167) | (0.25,2.778,0.5) | (0.125,1.159,0.167) | (1,1,1) | (0.167,2.4,0.25) | |
| A5 | (0.125,0.206,0.167) | (1,2.667,3) | (0.25,0.444,0.5) | (0.167,1.9,0.25) | (1,1,1) | |
| C8 | A1 | (1,1,1) | (1,1,1) | (1,2,3) | (1,1,1) | (1,1,1) |
| A2 | (1,1,1) | (1,1,1) | (1,1,1) | (1,1,1) | (1,1,1) | |
| A3 | (0.333,0.5,1) | (1,1,1) | (0.333,0.5,1) | (0.333,0.5,1) | (0.333,0.5,1) | |
| A4 | (1,1,1) | (1,1,1) | (1,2,3) | (1,1,1) | (1,1,1) | |
| A5 | (1,1,1) | (1,1,1) | (1,2,3) | (1,1,1) | (1,1,1) | |
| C9 | A1 | (1,1,1) | (6,7,8) | (2,3,4) | (4,6.333,6) | (2,4.333,4) |
| A2 | (0.125,0.143,0.167) | (1,1,1) | (0.143,0.189,0.2) | (0.2,0.917,0.333) | (0.2,0.278,0.333) | |
| A3 | (0.25,0.333,0.5) | (4,5.333,6) | (1,1,1) | (3,4.667,5) | (2,4,4) | |
| A4 | (0.125,0.162,0.167) | (0.333,2.167,1) | (0.167,0.217,0.25) | (1,1,1) | (0.125,0.27,0.167) | |
| A5 | (0.167,0.244,0.25) | (2,3.667,4) | (0.143,0.278,0.2) | (1,3.667,1) | (1,1,1) | |
| C10 | A1 | (1,1,1) | (4,6.333,6) | (2,3.333,4) | (4,6,6) | (4,6,6) |
| A2 | (0.125,0.162,0.167) | (1,1,1) | (0.167,0.261,0.25) | (0.25,1.222,0.5) | (0.333,0.5,1) | |
| A3 | (0.2,0.306,0.333) | (2,4,4) | (1,1,1) | (3,5,5) | (2,4,4) | |
| A4 | (0.125,0.17,0.167) | (0.25,2.111,0.5) | (0.125,0.214,0.167) | (1,1,1) | (0.25,0.889,0.5) | |
| A5 | (0.125,0.17,0.167) | (1,2,3) | (0.143,0.278,0.2) | (0.333,2.167,1) | (1,1,1) | |
| C11 | A1 | (1,1,1) | (6,7,8) | (2,3.667,4) | (4,6.333,6) | (2,3.667,4) |
| A2 | (0.125,0.143,0.167) | (1,1,1) | (0.125,0.181,0.167) | (0.25,0.444,0.5) | (0.167,0.317,0.25) | |
| A3 | (0.167,0.289,0.25) | (4,5.667,6) | (1,1,1) | (2,3.667,4) | (0.2,3.083,0.333) | |
| A4 | (0.125,0.162,0.167) | (1,2.333,3) | (0.167,0.289,0.25) | (1,1,1) | (0.143,1.139,0.2) | |
| A5 | (0.167,0.289,0.25) | (1,3.667,3) | (0.143,1.5,0.2) | (0.25,3.444,0.5) | (1,1,1) | |
| C12 | A1 | (1,1,1) | (9,9,9) | (4,5.667,6) | (6,7,8) | (3,5.333,5) |
| A2 | (0.111,0.111,0.111) | (1,1,1) | (0.143,0.189,0.2) | (0.143,0.25,0.2) | (0.167,0.317,0.25) | |
| A3 | (0.125,0.181,0.167) | (4,5.333,6) | (1,1,1) | (2,3,4) | (0.333,2.167,1) | |
| A4 | (0.125,0.143,0.167) | (2,4.333,4) | (0.25,0.333,0.5) | (1,1,1) | (0.125,1.381,0.167) | |
| A5 | (0.125,0.198,0.167) | (1,3.667,3) | (0.2,0.917,0.333) | (0.333,2.667,1) | (1,1,1) | |
| C13 | A1 | (1,1,1) | (5,7.667,7) | (2,5,4) | (4,5.333,6) | (2,5,4) |
| A2 | (0.111,0.134,0.111) | (1,1,1) | (0.167,0.2,0.25) | (0.2,0.278,0.333) | (0.167,0.261,0.25) | |
| A3 | (0.125,0.225,0.167) | (4,5,6) | (1,1,1) | (0.25,2.778,0.5) | (0.333,1.167,1) | |
| A4 | (0.143,0.189,0.2) | (2,3.667,4) | (0.167,1.178,0.25) | (1,1,1) | (0.2,1.194,0.333) | |
| A5 | (0.125,0.225,0.167) | (2,4,4) | (0.333,1.167,1) | (0.25,2.444,0.5) | (1,1,1) | |
| C14 | A1 | (1,1,1) | (6,7,8) | (2,4.333,4) | (2,4,4) | (2,4.667,4) |
| A2 | (0.125,0.143,0.167) | (1,1,1) | (0.143,0.222,0.2) | (0.167,0.233,0.25) | (0.143,0.389,0.2) | |
| A3 | (0.167,0.244,0.25) | (2,5,4) | (1,1,1) | (0.25,1.278,0.5) | (0.25,1.944,0.5) | |
| A4 | (0.167,0.261,0.25) | (3,4.333,5) | (0.25,1.778,0.5) | (1,1,1) | (0.333,2.167,1) | |
| A5 | (0.143,0.233,0.2) | (1,3.333,3) | (0.167,1.733,0.25) | (0.25,0.889,0.5) | (1,1,1) | |
| C15 | A1 | (1,1,1) | (4,6.333,6) | (4,7,6) | (9,9,9) | (4,5.667,6) |
| A2 | (0.125,0.162,0.167) | (1,1,1) | (0.2,2.75,0.333) | (2,4,4) | (0.25,1.444,0.5) | |
| A3 | (0.111,0.151,0.111) | (0.2,1.5,0.333) | (1,1,1) | (0.333,2.5,1) | (0.2,0.361,0.333) | |
| A4 | (0.111,0.111,0.111) | (0.143,0.278,0.2) | (0.167,0.9,0.25) | (1,1,1) | (0.167,0.289,0.25) | |
| A5 | (0.125,0.181,0.167) | (0.333,1.333,1) | (1,3,3) | (2,3.667,4) | (1,1,1) | |
| C16 | A1 | (1,1,1) | (6,7,8) | (2,3.667,4) | (4,6.333,6) | (2,4.333,4) |
| A2 | (0.125,0.143,0.167) | (1,1,1) | (0.167,0.217,0.25) | (0.167,0.4,0.25) | (0.143,0.306,0.2) | |
| A3 | (0.167,0.289,0.25) | (3,4.667,5) | (1,1,1) | (2,4,4) | (0.333,1.667,1) | |
| A4 | (0.125,0.162,0.167) | (1,3,3) | (0.167,0.261,0.25) | (1,1,1) | (0.2,1.194,0.333) | |
| A5 | (0.125,0.27,0.167) | (1,4,3) | (0.2,1.417,0.333) | (0.25,2.444,0.5) | (1,1,1) | |
| C17 | A1 | (1,1,1) | (5,6.667,7) | (2,3.667,4) | (2,4.333,4) | (2,3,4) |
| A2 | (0.125,0.151,0.167) | (1,1,1) | (0.167,0.261,0.25) | (0.2,0.333,0.333) | (0.2,0.278,0.333) | |
| A3 | (0.167,0.289,0.25) | (2,4,4) | (1,1,1) | (0.333,2.167,1) | (0.25,0.944,0.5) | |
| A4 | (0.167,0.244,0.25) | (1,3.333,3) | (0.25,0.889,0.5) | (1,1,1) | (0.2,0.361,0.333) | |
| A5 | (0.25,0.333,0.5) | (2,3.667,4) | (0.333,1.833,1) | (1,3,3) | (1,1,1) | |
Next, the geometric mean of the fuzzy comparison value (
), fuzzy score (
), and crisp value (
) for each alternative concerning each criterion were computed following Eqs. (4), (3), and (5), respectively. The results are presented in Table 6.
Table 6.
Geometric means (
), fuzzy scores (
), and evaluation of alternative priority (
) of alternatives with respect to criterion C1–C17.
| A1 | A2 | A3 | A4 | A5 | ||
|---|---|---|---|---|---|---|
| C1 |
|
(1.762,1.899,2.012) | (1.106,1.198,1.33) | (1.229,1.47,1.703) | (1.201,1.517,1.789) | (1.213,1.5,1.747) |
|
(0.205,0.25,0.309) | (0.129,0.158,0.204) | (0.143,0.194,0.262) | (0.14,0.2,0.275) | (0.141,0.198,0.268) | |
|
0.255 | 0.164 | 0.200 | 0.205 | 0.202 | |
| C2 |
|
(1.67,1.833,1.838) | (1.088,1.135,1.115) | (1.341,1.615,1.454) | (1.207,1.571,1.377) | (1.411,1.519,1.516) |
|
(0.229,0.239,0.274) | (0.149,0.148,0.166) | (0.184,0.211,0.216) | (0.165,0.205,0.205) | (0.193,0.198,0.226) | |
|
0.247 | 0.154 | 0.204 | 0.192 | 0.206 | |
| C3 |
|
(1.67,1.872,1.838) | (1.08,1.175,1.092) | (1.522,1.702,1.651) | (1.129,1.493,1.232) | (1.415,1.553,1.534) |
|
(0.227,0.24,0.27) | (0.147,0.151,0.16) | (0.207,0.218,0.242) | (0.154,0.192,0.181) | (0.193,0.199,0.225) | |
|
0.246 | 0.153 | 0.223 | 0.175 | 0.206 | |
| C4 |
|
(1.821,1.872,1.919) | (1.825,1.861,1.896) | (1.104,1.119,1.145) | (1.447,1.531,1.6) | (1.294,1.371,1.45) |
|
(0.227,0.241,0.256) | (0.228,0.24,0.253) | (0.138,0.144,0.153) | (0.181,0.197,0.214) | (0.162,0.177,0.194) | |
|
0.242 | 0.240 | 0.145 | 0.197 | 0.177 | |
| C5 |
|
(1.67,1.872,1.838) | (1.088,1.233,1.111) | (1.209,1.511,1.38) | (1.112,1.475,1.167) | (1.308,1.659,1.486) |
|
(0.239,0.242,0.288) | (0.156,0.159,0.174) | (0.173,0.195,0.216) | (0.159,0.19,0.183) | (0.187,0.214,0.233) | |
|
0.256 | 0.163 | 0.195 | 0.177 | 0.211 | |
| C6 |
|
(1.719,1.883,1.872) | (1.104,1.327,1.153) | (1.213,1.599,1.402) | (1.108,1.433,1.158) | (1.134,1.556,1.239) |
|
(0.252,0.241,0.298) | (0.162,0.17,0.184) | (0.178,0.205,0.223) | (0.162,0.184,0.184) | (0.166,0.2,0.197) | |
|
0.264 | 0.172 | 0.202 | 0.177 | 0.188 | |
| C7 |
|
(1.67,1.909,1.838) | (1.116,1.247,1.17) | (1.275,1.606,1.503) | (1.108,1.496,1.158) | (1.205,1.441,1.375) |
|
(0.237,0.248,0.288) | (0.158,0.162,0.184) | (0.181,0.209,0.236) | (0.157,0.194,0.182) | (0.171,0.187,0.216) | |
|
0.258 | 0.168 | 0.208 | 0.178 | 0.191 | |
| C8 |
|
(1.38,1.431,1.476) | (1.38,1.38,1.38) | (1.185,1.246,1.38) | (1.38,1.431,1.476) | (1.38,1.431,1.476) |
|
(0.192,0.207,0.22) | (0.192,0.199,0.206) | (0.165,0.18,0.206) | (0.192,0.207,0.22) | (0.192,0.207,0.22) | |
|
0.206 | 0.199 | 0.184 | 0.206 | 0.206 | |
| C9 |
|
(1.719,1.85,1.872) | (1.108,1.204,1.152) | (1.593,1.726,1.752) | (1.118,1.307,1.209) | (1.339,1.547,1.452) |
|
(0.231,0.242,0.272) | (0.149,0.158,0.168) | (0.214,0.226,0.255) | (0.15,0.171,0.176) | (0.18,0.203,0.211) | |
|
0.249 | 0.158 | 0.232 | 0.166 | 0.198 | |
| C10 |
|
(1.719,1.867,1.872) | (1.134,1.258,1.239) | (1.523,1.703,1.703) | (1.118,1.344,1.185) | (1.211,1.412,1.399) |
|
(0.232,0.246,0.279) | (0.153,0.166,0.185) | (0.206,0.225,0.254) | (0.151,0.177,0.177) | (0.164,0.186,0.209) | |
|
0.253 | 0.168 | 0.228 | 0.168 | 0.186 | |
| C11 |
|
(1.719,1.85,1.872) | (1.108,1.158,1.158) | (1.491,1.688,1.632) | (1.195,1.375,1.358) | (1.207,1.582,1.377) |
|
(0.232,0.242,0.279) | (0.15,0.151,0.172) | (0.202,0.221,0.243) | (0.162,0.18,0.202) | (0.163,0.207,0.205) | |
|
0.251 | 0.158 | 0.222 | 0.181 | 0.192 | |
| C12 |
|
(1.872,1.947,1.961) | (1.094,1.133,1.12) | (1.495,1.635,1.648) | (1.285,1.484,1.423) | (1.216,1.532,1.406) |
|
(0.248,0.252,0.282) | (0.145,0.147,0.161) | (0.198,0.211,0.237) | (0.17,0.192,0.204) | (0.161,0.198,0.202) | |
|
0.260 | 0.151 | 0.215 | 0.189 | 0.187 | |
| C13 |
|
(1.695,1.888,1.856) | (1.105,1.134,1.142) | (1.417,1.59,1.54) | (1.285,1.485,1.42) | (1.3,1.546,1.461) |
|
(0.228,0.247,0.273) | (0.149,0.148,0.168) | (0.191,0.208,0.226) | (0.173,0.194,0.209) | (0.175,0.202,0.215) | |
|
0.249 | 0.155 | 0.208 | 0.192 | 0.197 | |
| C14 |
|
(1.67,1.838,1.838) | (1.096,1.147,1.127) | (1.297,1.568,1.443) | (1.366,1.57,1.506) | (1.207,1.484,1.377) |
|
(0.229,0.242,0.277) | (0.15,0.151,0.17) | (0.178,0.206,0.217) | (0.187,0.206,0.227) | (0.166,0.195,0.208) | |
|
0.249 | 0.157 | 0.200 | 0.207 | 0.189 | |
| C15 |
|
(1.856,1.961,1.947) | (1.29,1.564,1.431) | (1.13,1.407,1.227) | (1.097,1.209,1.126) | (1.348,1.558,1.558) |
|
(0.255,0.255,0.29) | (0.177,0.203,0.213) | (0.155,0.183,0.182) | (0.15,0.157,0.168) | (0.185,0.202,0.232) | |
|
0.266 | 0.198 | 0.173 | 0.158 | 0.206 | |
| C16 |
|
(1.719,1.861,1.872) | (1.099,1.156,1.133) | (1.454,1.633,1.623) | (1.2,1.412,1.366) | (1.208,1.556,1.38) |
|
(0.233,0.244,0.28) | (0.149,0.152,0.17) | (0.197,0.214,0.243) | (0.163,0.185,0.204) | (0.164,0.204,0.207) | |
|
0.253 | 0.157 | 0.218 | 0.184 | 0.192 | |
| C17 |
|
(1.644,1.796,1.821) | (1.111,1.151,1.158) | (1.303,1.531,1.465) | (1.212,1.423,1.384) | (1.356,1.58,1.569) |
|
(0.222,0.24,0.275) | (0.15,0.154,0.175) | (0.176,0.205,0.221) | (0.164,0.19,0.209) | (0.183,0.211,0.237) | |
|
0.246 | 0.160 | 0.201 | 0.188 | 0.210 | |
The priority scores, representing the global performance of each alternative supplier, were derived by multiplying the evaluation of each alternative priority against every criterion with the importance weight of each criterion. These products were then summed over all criteria, as per Eq. (6). In this study, weights 
were acquired from the ROC method, as illustrated in Table 3. The outcomes of the priority scores for all alternative suppliers are shown in Table 7.
Table 7.
The priority score of each alternative 
.
| A1 | A2 | A3 | A4 | A5 | |
|---|---|---|---|---|---|
| C1 | 0.058 | 0.037 | 0.045 | 0.046 | 0.046 |
| C2 | 0.026 | 0.016 | 0.021 | 0.020 | 0.021 |
| C3 | 0.010 | 0.006 | 0.009 | 0.007 | 0.008 |
| C4 | 0.056 | 0.055 | 0.033 | 0.045 | 0.041 |
| C5 | 0.025 | 0.016 | 0.019 | 0.017 | 0.021 |
| C6 | 0.012 | 0.008 | 0.009 | 0.008 | 0.008 |
| C7 | 0.005 | 0.003 | 0.004 | 0.003 | 0.003 |
| C8 | 0.014 | 0.013 | 0.012 | 0.014 | 0.014 |
| C9 | 0.008 | 0.005 | 0.007 | 0.005 | 0.006 |
| C10 | 0.003 | 0.002 | 0.003 | 0.002 | 0.002 |
| C11 | 0.013 | 0.008 | 0.012 | 0.010 | 0.010 |
| C12 | 0.005 | 0.003 | 0.004 | 0.003 | 0.003 |
| C13 | 0.007 | 0.005 | 0.006 | 0.006 | 0.006 |
| C14 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 |
| C15 | 0.003 | 0.002 | 0.002 | 0.002 | 0.003 |
| C16 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
| C17 | 0.001 | 0.000 | 0.000 | 0.000 | 0.000 |
| Sum | 0.248 | 0.182 | 0.190 | 0.192 | 0.196 |
Based on priority scores, the ranking order obtained is A1 > A5 > A4 > A3 > A2. Supplier A1 emerged as the top supplier with the highest score (0.248). However, it is worth noting that while supplier A1 was superior in this case study, obtaining agreement from multiple DMs can be challenging. A systematic MCDM approach can support decision-making, especially when multiple criteria are considered by multiple DMs. By following a proposed practical methodological framework, a group of DMs could reach a consensus on the best solution to a problem involving a finite number of alternative suppliers.
A sensitivity analysis was conducted to verify the stability of the rankings. This analysis involves deliberately adjusting weight values to observe slight variations and their impacts on the final rankings. Given that quality is the most critical factor among all the main criteria, the sensitivity analysis varies the weight assigned to the quality criterion from 0.1 to 0.9. The corresponding weights of other criteria are adjusted accordingly across ten different scenarios, as detailed in Table 8. Once the weights for all the main criteria have been determined, the corresponding global weights for sub-criteria are computed for each individual case. Observing any alterations in the order of importance for both the main criteria and sub-criteria, the suppliers are ranked using fuzzy AHP for each of the ten scenarios. The resulting rankings from the sensitivity analysis are compared in Table 9 to evaluate any variations.
Table 8.
Variation in weight values for all mail criteria when varying the weight value of quality criteria from 0.1 to 0.9.
| Criteria | Values of importance weights for medical equipment supplier selection criteria | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Importance weights | Case 1 (0.1) |
Case 2 (0.2) |
Case 3 (0.3) |
Case 4 (0.4) |
Case 5 (0.5) |
Case 6 (0.6) |
Case 7 (0.7) |
Case 8 (0.8) |
Case 9 (0.9) |
|
| Quality | 0.37 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
| Cost | 0.23 | 0.3286 | 0.2920 | 0.2556 | 0.2190 | 0.1825 | 0.1460 | 0.1095 | 0.0730 | 0.0365 |
| Compliance | 0.16 | 0.2286 | 0.2032 | 0.1778 | 0.1524 | 0.1270 | 0.1016 | 0.0762 | 0.0508 | 0.0254 |
| Service | 0.11 | 0.1571 | 0.1397 | 0.1222 | 0.1048 | 0.0873 | 0.0698 | 0.0524 | 0.0349 | 0.0175 |
| Reliability | 0.07 | 0.1000 | 0.0889 | 0.0778 | 0.0667 | 0.0556 | 0.0445 | 0.0334 | 0.0223 | 0.0111 |
| Agility | 0.04 | 0.0571 | 0.0508 | 0.0444 | 0.0381 | 0.0317 | 0.0254 | 0.0190 | 0.0127 | 0.0063 |
| Delivery | 0.02 | 0.0286 | 0.0254 | 0.0222 | 0.0190 | 0.0159 | 0.0127 | 0.0095 | 0.0063 | 0.0032 |
| 1.00 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
Table 9.
Ranking of suppliers by sensitivity analysis when the weight of quality criteria varies from 0.1 to 0.9.
| Supplier | Rank | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Normal case | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 | Case 7 | Case 8 | Case 9 | |
| A1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| A2 | 5 | 3 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| A3 | 4 | 5 | 5 | 4 | 4 | 4 | 4 | 3 | 3 | 3 |
| A4 | 3 | 4 | 3 | 3 | 3 | 3 | 3 | 4 | 4 | 4 |
| A5 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
Minor variations were observed in the rankings of other suppliers across different criteria preferences. Notably, supplier A1 consistently retained the top rank across all scenarios, underscoring its robustness as the most suitable choice, while supplier A5 consistently occupied the lowest rank in all ten successive trials. The sensitivity analysis validated the stability of the results, ensuring the robustness of the methodology.
Managerial and practical implications
This study aims to achieve two main objectives, each carrying significant implications for DMs in the healthcare industry, particularly regarding the evaluation and selection of medical equipment suppliers. The first objective is to compile a comprehensive list of key criteria that influence the performance evaluation of medical equipment suppliers within healthcare organizations. The second is to propose a decision support model to facilitate the assessment and selection process for these suppliers.
The study meticulously identifies and measures the importance of various criteria relevant to evaluating and selecting medical equipment suppliers. The formulation of a comprehensive list of significant criteria serves to enhance DMs’ understanding of the concept underlying the procurement process for medical equipment. This framework not only aids in evaluating supplier performance but also lays a foundation that facilitates the enhancement of suppliers’ performance, which leads to improvements in goods and services from the suppliers. The study revealed that several criteria, including both tangible and intangible ones, are required for assessing supplier performance. Furthermore, the findings demonstrate that quality is the most critical aspect, followed by cost, compliance, service, reliability, agility, and delivery. Typically, DMs rely on intuition to prioritize these criteria. However, employing scientific approaches to assign importance weights to different criteria enables more precise guidance, allowing DMs to focus on key selection criteria beneficial to their organization. For suppliers, these weighted criteria provide actionable insights to refine their products and services, ensuring they align with the needs and expectations of healthcare organizations.
The study demonstrates the practical application of the fuzzy AHP method in supporting the procurement process for medical devices in public hospitals. A real-world case study involving the procurement of mechanical ventilators illustrates the systematic approach. Five suppliers were evaluated based on seven main criteria and 17 sub-criteria. The fuzzy AHP framework facilitated the ranking of these suppliers, enabling the selection of the most suitable one. The case study provides valuable insights for both research and practice. It assists healthcare organizations in establishing systematic supplier selection processes, which could increase procurement efficiency. Such an approach facilitates improved decision-making and enhances overall operational effectiveness within healthcare settings. This systematic approach also helps DMs reduce procurement risks by conducting comprehensive evaluations of each supplier based on qualitative and quantitative criteria, allowing for the possibility of procurement from multiple suppliers. By adopting such an approach, DMs can enhance their decision-making processes and minimize potential risks associated with purchasing activities. Moreover, supplier assessments promote transparency and accountability, thereby reinforcing trust, integrity, and openness within the procurement process. Furthermore, evaluation results serve as a benchmarking mechanism for suppliers to measure their performance against the criteria employed in the supplier selection process, subsequently fostering improvements in their overall performance. This feedback enables suppliers to identify areas for improvement, align their operations with the expectations of healthcare organizations, and strive for continuous improvement in delivering high-quality products and services.
In terms of methodology, the fuzzy AHP proves effective in facilitating group decision-making, especially in environments characterized by uncertainty, ambiguity, and vagueness inherent in DM judgments. While the method requires extensive data for pairwise comparisons, it incorporates consistency checks to ensure the reliability of evaluations. Given the critical role of medical equipment in patient safety and healthcare outcomes, coupled with the substantial costs associated with such equipment and services from suppliers, it is essential to conduct a thorough and systematic evaluation process before making final purchasing decisions. Therefore, healthcare organizations must adopt strategic procurement practices to ensure seamless delivery of quality care while effectively managing costs. Applying the fuzzy-based approach with AHP requires additional computational steps compared to classical AHP, including the use of triangular fuzzy numbers and defuzzification, which can increase processing time and complexity. However, advancements in decision-support tools and spreadsheet-based implementations, such as Microsoft Excel and MATLAB, have mitigated these challenges. These modern software solutions enable efficient computation without requiring extensive computing resources, making the approach feasible even in resource-constrained healthcare settings.
Conclusion
Selecting the right medical equipment supplier is essential for the performance and efficiency of healthcare organizations. While supplier selection challenges have been widely studied, the specific context of hospital medical equipment procurement has received limited attention. Moreover, few studies have thoroughly examined the specific criteria used to assess medical equipment suppliers. Given the complexities of healthcare-related decisions—where both quantitative data and human judgment play pivotal roles—this paper addresses a significant gap in the literature.
This study presents a comprehensive decision support system designed to evaluate and select medical equipment suppliers under uncertainty. By combining the ROC and fuzzy AHP methods, the proposed framework identifies key criteria and supports DMs in managing the complexities of supplier evaluation. The hybrid approach accommodates the uncertainty and vagueness inherent in subjective judgments, enabling healthcare organizations to systematically assess supplier performance and rank alternatives based on diverse criteria. The implications of selecting an appropriate medical equipment supplier extend far beyond procurement. Effective supplier selection facilitates precise diagnoses and treatment, ensures the availability of reliable medical equipment, and significantly improves operational efficiency in delivering high-quality healthcare services.
The proposed MCDM methods offer a valuable guideline for addressing a variety of selection problems related to medical equipment. While numerous MCDM methods are available in the literature, no single approach is universally optimal. Each method has unique strengths and limitations, making the choice of an appropriate tool depend on the specific circumstances and complexities of the problem being addressed. Practitioners should select a decision-making method that aligns with their organization’s goals, resources, and problem context. The adaptability of the proposed framework ensures its applicability across different healthcare procurement scenarios, providing a robust foundation for informed and effective decision-making.
Despite its advantages, this study acknowledges certain limitations. The ROC-fuzzy AHP framework was applied without direct comparison to other MCDM techniques, such as BWM, FUCOM, SWARA, and PIPRECIA. While the selected methodology effectively addresses uncertainty and group decision-making challenges, alternative methods may provide different insights, particularly regarding weight sensitivity and ranking stability. Future research could expand on this study by conducting a comparative analysis of multiple MCDM techniques within the medical equipment procurement domain. Such an extension would provide deeper insights into the strengths and weaknesses of various approaches, potentially leading to hybrid models that further enhance decision accuracy and robustness. Additionally, while this study provides a systematic evaluation framework validated within a single healthcare institution, broader validation across multiple institutions would further strengthen the generalizability of the proposed approach. Future studies should incorporate DMs from various healthcare institutions to conduct comparative analyses and assess the model’s effectiveness across different organizational settings. This expanded validation would provide a more comprehensive understanding of the framework’s applicability and adaptability in diverse procurement environments.
Acknowledgements
This work was supported by Research of Khon Kaen University.
Author contributions
All authors contributed to the study’s conception and design.
Data availability
The datasets used and/or analyzed during the study available from the corresponding author on reasonable request.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets used and/or analyzed during the study available from the corresponding author on reasonable request.