Green Supplier Evaluation in E-Commerce Systems: An Integrated Rough-Dombi BWM-TOPSIS Approach

Abstract

The rapid growth of e-commerce has created substantial environmental impacts, driving the need for advanced optimization models to enhance supply chain sustainability. As consumer preferences shift toward environmental responsibility, organizations must adopt robust quantitative methods to reduce ecological footprints while ensuring operational efficiency. This study develops a novel hybrid multi-criteria decision-making (MCDM) model to evaluate and prioritize green suppliers under uncertainty, integrating the rough-Dombi best–worst method (BWM) and an improved Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The proposed model addresses two key challenges: (1) inconsistency in expert judgments through rough set theory and Dombi aggregation operators and (2) ranking instability via an enhanced TOPSIS formulation that mitigates rank reversal. Mathematically, the rough-Dombi BWM leverages interval-valued rough numbers to model subjective expert preferences, while the Dombi operator ensures flexible and precise weight aggregation. The modified TOPSIS incorporates a dynamic distance metric to strengthen ranking robustness. A case study of five e-commerce suppliers validates the model’s effectiveness, with results identifying cost, green competitiveness, and external environmental management as the dominant evaluation dimensions. Key indicators—such as product price, pollution control, and green design—are rigorously prioritized using the proposed framework. Theoretical contributions include (1) a new rough-Dombi fusion for criteria weighting under uncertainty and (2) a stabilized TOPSIS variant with reduced sensitivity to data perturbations. Practically, the model provides e-commerce enterprises with a computationally efficient tool for sustainable supplier selection, enhancing resource allocation and green innovation. This study advances the intersection of uncertainty modeling, operational research, and sustainability analytics, offering scalable methodologies for mathematical decision-making in supply chain contexts.

1. Introduction

E-commerce enterprises (ECEs) exert significant environmental pressure due to their reliance on non-recyclable packaging, energy-intensive warehouse operations, and fossil fuel-based logistics to meet escalating consumer demands [1,2]. These challenges are exacerbated by high product return rates—often exceeding 30%—which contribute to increased packaging waste and resource depletion [3]. As online consumption continues to surge, there is growing evidence that consumers increasingly favor retailers demonstrating environmental responsibility, making sustainability not merely a market trend but an urgent requirement [4]. In this context, the selection and collaboration with suppliers by ECEs are pivotal in reducing their overall ecological footprint. Suppliers play a crucial role in fulfilling green commitments and shaping corporate social responsibility efforts across the e-commerce supply chain [5]. Engaging green suppliers can enhance waste management, reduce logistics-based emissions, and elevate brand image, particularly through collaborative endeavors with express companies and upstream manufacturers [6,7]. Consequently, the competitive advantage of online retailers increasingly depends on their supplier networks’ capacity to adopt eco-friendly practices, such as green packaging, reverse logistics, and material reuse, which not only reduce environmental impact but also enhance brand reputation and customer loyalty.

Recent research emphasizes the critical need for robust green supplier evaluation frameworks, especially for ECEs navigating complex supply chain environments. These enterprises face mounting pressure to balance sustainability goals with operational efficiency [8,9,10,11,12]. The challenges are multifaceted: ECEs must manage an extensive network of potential suppliers while confronting several key obstacles in their green initiatives. These include higher production costs for eco-friendly products, lack of standardization in green certification processes, and limited independent verification systems. The complexity is further amplified by the dynamic nature of consumer expectations and the fragmented structure of modern supply networks, making systematic supplier evaluation increasingly crucial for sustainable business operations. Notably, existing research seldom examines green supplier performance from the standpoint of ECEs; instead, most studies discuss general manufacturing or traditional enterprises. Beyond technical competencies and product quality, ECEs must also assess ecological factors to ensure that their procurement practices align with green development goals [13]. Research indicates that comprehensive supplier evaluation frameworks deliver dual benefits: they provide systematic assessment tools while enabling e-commerce enterprises to advance their environmental initiatives through strategic procurement choices [14,15,16,17].

However, significant research gaps remain in the field. Most existing studies focus on traditional manufacturing industries or general supply chain environments, failing to address the unique characteristics of e-commerce enterprises (ECEs), such as high return rates, fragmented supplier networks, and dynamic consumer demand for green packaging and sustainable logistics, which limits the applicability of traditional green supplier evaluation criteria in e-commerce contexts. Additionally, while multi-criteria decision-making (MCDM) methods are widely used in supplier evaluation, many traditional approaches (e.g., AHP and classical TOPSIS) struggle to effectively handle the uncertainty arising from subjective expert judgments. When multiple decision-makers are involved, differing backgrounds and experiences further exacerbate inconsistencies in the evaluation process. Furthermore, although the rough-Dombi method has gained attention for its ability to model and aggregate weights accurately under uncertainty, its application in green supplier evaluation remains limited. Most studies have focused on isolated decision-making scenarios or combined it with basic aggregation techniques, without fully utilizing its potential in complex e-commerce supply chains. To address these gaps, this study develops a green supplier evaluation framework based on the rough-Dombi method, specifically tailored to the needs of ECEs. By addressing the limitations of traditional methods in handling uncertainty and ensuring evaluation consistency, this study provides both a theoretical foundation for strategic procurement in ECEs and practical guidance for decision-support systems in complex supply chain management.

Supplier evaluations frequently rely on multi-criteria decision-making (MCDM) models that capture the interplay of cost, quality, service, and sustainability targets [18,19,20,21]. However, MCDM models typically rely on decision-makers’ judgments, which can lead to several issues. For instance, decision-makers often face uncertainty due to incomplete information. When multiple decision-makers are involved, their different knowledge backgrounds and experiences can lead to varying perspectives. Additionally, determining criteria weights for supplier selection using pairwise comparison methods like AHP is time-consuming and often struggles to pass consistency tests. Among various ranking methods, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a widely used approach, but traditional TOPSIS sometimes encounters rank reversal problems. Therefore, effectively addressing these aforementioned issues represents an important research gap. Accordingly, this paper aims to address four key questions:

RQ1: What are the most influential factors for ECEs when selecting green suppliers?

RQ2: In what ways can ECEs evaluate and rank potential green suppliers effectively?

RQ3: Which strategic measures should ECEs pursue to enhance their suppliers’ green performance?

RQ4: How can managers handle ambiguity arising from subjective expert judgments in multi-criteria decision-making?

Supplier evaluations frequently rely on multi-criteria decision-making (MCDM) models that capture the interplay of cost, quality, service, and sustainability targets. However, MCDM models typically depend on decision-makers’ judgments, which can lead to several issues. For instance, decision-makers often face uncertainty due to incomplete information, and when multiple experts are involved, their heterogeneous backgrounds yield divergent views. Additionally, determining criteria weights with pair-wise comparison tools such as AHP can be time-consuming and may fail the consistency test [20,21]. Among the available ranking methods, TOPSIS is widely adopted, yet traditional TOPSIS is vulnerable to rank-reversal when a dominated alternative is added or removed. Therefore, effectively addressing these shortcomings constitutes a significant research gap that motivates the hybrid rough-Dombi BWM–TOPSIS approach proposed in this study.

This study proposes a hybrid MCDM model that integrates the rough-Dombi best–worst method (rough-Dombi BWM) with the rough-TOPSIS method to evaluate green supplier (GS) performance from the perspective of ECEs. To overcome the vagueness and incompleteness often inherent in expert judgments, this study integrates rough set theory into its modeling framework. Originally introduced by Pawlak [22], rough set theory defines the uncertain boundaries of a target set using lower and upper approximations. This approach eliminates the need for predefined membership functions, offering a fully data-driven method for handling cognitive ambiguity. Compared with traditional fuzzy-set or interval number techniques, rough sets offer two salient advantages [23]. They are derived directly from the original discernibility relations and equivalence classes, which removes the need for subjective parameterization, and they express variations in expert preferences for the same criterion as interval-valued objects that can be readily handled by subsequent aggregation procedures. The rough-Dombi method effectively addresses individual and interpersonal uncertainty in decision-making, yielding more accurate and realistic outcomes [18]. The rough-Dombi method has been successfully applied to the optimal siting of public charging stations, the development of hydrogen-based alternatives for natural-gas grids, and the identification of principal barriers impeding corporate adoption of ESG practices [24,25,26]. This paper introduces the best–worst method (BWM) based on the rough-Dombi approach to determine the importance of relevant indicators influencing ECEs’ selection of green suppliers. The rough-Dombi technique is particularly effective in scenarios characterized by subjective expert judgments, limited data availability, and imprecise information, enabling more accurate and reliable decision-making outcomes [27,28]. Within the proposed rough-Dombi BWM-TOPSIS framework, experts first construct a best versus worst pairwise comparison matrix on a 1-to-9 linguistic scale. Each rating is then converted into an interval-valued rough number (IVRN); the lower and upper bounds reflect, respectively, the most pessimistic and the most optimistic perceptions of the expert group. This conversion preserves the underlying vagueness of the evaluations throughout the subsequent weight elicitation stage. The resulting IVRNs are aggregated with a Dombi geometric operator whose adjustable parameter permits flexible control of the compensation level among experts, attenuates the influence of outliers, and maintains complete traceability of the original assessments. Finally, the rough weights and the performance matrix are fed into a modified TOPSIS procedure, which enables continuous propagation of uncertainty from weight determination to the final ranking of alternatives.

The contributions of this study are fourfold: First, it introduces a novel multi-criteria decision-making (MCDM) framework that integrates rough-Dombi BWM with a modified TOPSIS approach, embedding the Dombi operator into rough set theory to ensure robust weight determination and ranking stability under uncertainty. Second, this study specifically tailors its evaluation criteria to address the unique operational requirements of e-commerce enterprises, filling critical gaps in existing literature by incorporating e-commerce-specific dimensions including green packaging, digital integration capabilities, and reverse logistics management—factors that are essential to sustainable e-commerce operations but underexplored in traditional supplier evaluation frameworks. Third, the practical applicability and effectiveness of the framework are validated through a real-world case study involving five suppliers from JD.com, a leading Chinese e-commerce platform, thus demonstrating its ability to address the specific challenges of green supplier evaluation in the e-commerce sector. Moreover, this study advances the application of the rough-Dombi method in decision-making under uncertainty, bridging the gap between theoretical development and practical implementation in sustainability analytics. By responding directly to the limitations of prior research, this study offers both a theoretical foundation for strategic procurement in ECEs and practical guidance for enhancing sustainable supply chain management in complex and dynamic e-commerce environments. Overall, e-commerce platform supplier evaluation confronts distinctive challenges inherent in its triadic “platform–supplier–consumer” ecosystem complexity, necessitating simultaneous accommodation of cross-category standardization imperatives, network effect dynamics, and consumer-oriented decision-making processes—characteristics fundamentally divergent from traditional manufacturing’s bilateral supply relationships and sector-specific standardization paradigms. The proposed framework systematically addresses these complexities through rough set theory’s capacity for multi-source heterogeneous information processing, Dombi operators’ capability to capture non-linear synergistic effects among suppliers, the BWM methodology’s facilitation of flexible cross-category weight calibration, and TOPSIS’s provision of transparent, interpretable interval-based evaluation outcomes. This integrated architectural design comprehensively resolves e-commerce platforms’ distinctive requirements in diversified supplier network governance, real-time data responsiveness, and consumer green cognition communication. In contrast, traditional manufacturing supplier evaluation predominantly emphasizes cost optimization and quality assurance, characterized by extended evaluation cycles and relatively diminished transparency imperatives, while lacking consideration for platform ecosystem dynamism and consumer orientation. Consequently, this research framework demonstrates unambiguous e-commerce contextual adaptability and theoretical innovation value, addressing critical gaps in existing supplier evaluation paradigms.

The remaining sections of this study are organized as follows: Section 1 reviews the relevant literature and builds an evaluation system for green supplier selection by e-commerce companies. Section 2 introduces the calculation process of the rough-Dombi best–worst method (RBWM) and rough-TOPSIS. Section 3 presents data analysis and results. Section 4 discusses the theoretical and managerial implications of this study. Section 5 explains the limitations and prospects for future research.

2. Evaluation Indicators of Green Supplier Selection for ECEs

Suppliers are pivotal nodes within the value chain of e-commerce platforms, as their performance directly correlates with the overall service quality and operational efficiency of ECEs. Compared with traditional manufacturing or brick-and-mortar retail, e-commerce platforms operate under very different conditions, so their supplier evaluation criteria must also differ. Online orders have short cycles and high return rates, which makes on-time delivery, reverse logistics service, and recyclable packaging critical. The large number of small-parcel deliveries increases packaging waste and last-mile carbon emissions, so green packaging design and cooperation with low-emission logistics providers become core indicators. Because transactions are handled digitally, real-time data integration, system compatibility, and information transparency are essential, and a supplier’s digital readiness and compliance directly affect platform reputation and user experience. Therefore, e-commerce firms must give higher priority to green packaging, digital integration, rapid response, and sustainable logistics when rating suppliers’ focus areas that clearly differ from those in traditional industries.

2.1. E-Commerce Sustainability and Green Supply Chain Management

E-commerce sustainability has experienced substantial theoretical and practical evolution, propelled by the convergence of digital transformation imperatives and environmental consciousness across global markets [29]. Contemporary scholarly investigations demonstrate that e-commerce platforms are progressively adopting comprehensive sustainability frameworks that transcend conventional environmental considerations to encompass social responsibility and economic viability within digital ecosystems [30]. Recent empirical examinations reveal that consumer environmental consciousness has intensified considerably, with over 70% of online purchasers actively pursuing environmentally responsible procurement options, thereby compelling e-commerce enterprises to integrate sustainability metrics into their fundamental operational strategies [31]. The emergence of platform-mediated green supply chain management has introduced novel complexities, as digital intermediaries must now orchestrate sustainability initiatives across heterogeneous supplier networks while maintaining operational efficiency and consumer satisfaction. Advanced technological solutions, including artificial intelligence-driven carbon footprint analytics, blockchain-enabled supply chain transparency, and Internet of Things-based real-time environmental monitoring, have fundamentally transformed how e-commerce platforms approach sustainability measurement and management [32]. Furthermore, regulatory frameworks across major markets have evolved to mandate enhanced environmental disclosure and performance standards specifically for digital commerce operations, creating both compliance pressures and competitive opportunities for sustainable differentiation.

The integration of green supply chain management principles within e-commerce contexts presents distinctive challenges that differentiate it from traditional manufacturing sustainability approaches. Recent scholarly research emphasizes that e-commerce green supply chains must address unique operational characteristics including virtual inventory management, distributed fulfillment networks, extensive packaging requirements, and complex reverse logistics systems for returns and recycling [33]. Contemporary studies underscore the critical importance of green packaging innovation, with biodegradable materials and minimal packaging designs becoming essential competitive factors rather than optional enhancements [34]. Latest empirical evidence suggests that successful e-commerce sustainability initiatives require sophisticated coordination mechanisms that align platform operators, suppliers, logistics providers, and consumers toward shared environmental objectives [35]. However, significant research lacunae persist in developing integrated evaluation frameworks that can effectively assess supplier sustainability performance within the dynamic, multi-stakeholder e-commerce environment while accommodating the rapid technological changes and evolving consumer expectations that characterize digital commerce ecosystems.

2.2. Evaluation Framework

By monitoring key environmental indicators, ECEs can engage suppliers that meet evolving eco-standards, thereby aligning with the dynamic requirements of the green economy and fostering sustainable supply chain practices. It has been suggested that environmental cost, product quality, product price, occupational health and safety, and environmental capability rank among the most pivotal criteria for sustainable supplier selection [36]. In contrast, other research classifies green supplier evaluations under two primary dimensions—green and traditional—encompassing the usage of toxic substances, resource utilization, environmental labeling, recyclable packaging, and green technology [37]. Additional studies propose as many as 25 criteria, including business policies, management plans, and reviews of new products, to thoroughly assess and enhance green supplier performance [11].

After reviewing the studies, this study develops an evaluation framework that systematically assesses green supplier selection across five dimensions: cost, green competitiveness, service level, external environmental management, and corporate social responsibility.

(1) Cost (C₁)

Product costs represent a crucial consideration for ECEs when selecting green suppliers [38], as ECEs operate with a profit motive and must factor product prices into purchasing decisions [39]. Likewise, high product quality and affordability are regarded as vital criteria in supplier selection [39]. Freight expenses inevitably arise when moving goods from suppliers to warehouses, constituting a notable portion of overall operating costs [40]. To mitigate these expenses, many ECEs adopt a zero-inventory strategy by storing goods in suppliers’ warehouses [14]. Installation, commissioning services, technical training, on-site maintenance, and related services provided by suppliers are categorized as after-sales service costs [41]. Further, communication costs incurred through ongoing collaboration between ECEs and suppliers are typically referred to as other costs [42].

(2) Green competitiveness (C₂)

With the continuous improvement of environmental protection awareness, “green” principles have become the key to the development of ECEs, and it will determine the sustainable operation of ECEs in the long term. Green design enables enterprises to reduce carbon emissions and fulfill social responsibilities, thus improving their competitiveness [43]. Green procurement is an important link for enterprises to implement green practices [44,45]. Green logistics reduces carbon emissions by improving energy efficiency, thus alleviating environmental pressure [46]. Green logistics has a significant impact on the sustainable development of enterprises [47]. With the improvement in consumers’ awareness of environmental protection, consumers are more inclined to buy environmentally friendly and recyclable packaging styles [48]. The government, the public, and enterprises all pay attention to whether suppliers use recycled materials to package products [49]. ECEs consider the materials of suppliers’ products, such as recyclability and reuse of materials when selecting suppliers [50]. Green design, green procurement, green logistics, and green express delivery are the main indicators for evaluating green supply chains [51]. In summary, green competitiveness includes green design, green logistics, green procurement, green packaging, and green reuse.

(3) Service level (C₃)

In supply chain management, service level denotes the capacity to deliver goods in accordance with ECEs’ requirements. Product prices, delivery capabilities, and service quality have been identified as fundamental criteria for assessing supplier performance [51]. The most widely adopted criteria for supplier selection include product quality, delivery capability, organizational and managerial considerations, and flexibility [52]. Timely delivery is especially recognized as a core factor for measuring supply chain performance [53]. Moreover, clear development goals and plans reflect a supplier’s management and organizational capabilities [54]. High levels of flexibility and reliability in a supplier’s operations further enhance service efficiency for ECEs [55,56]. Consequently, factors such as on-time delivery capability, product quality, organizational and managerial capacity, flexibility, and reliability are attributed to the service level dimension in this study.

(4) External environmental management (C₄)

Increased environmental awareness forces ECEs’ decision-makers to consider external environmental standards when evaluating suppliers. The inclusion of pollution control, renewable energy, waste reuse, and hazardous substance management in the supplier selection process has been confirmed as critical factors [57,58,59]. For many companies, controlling hazardous materials and disposing of hazardous waste is a priority [60,61]. Legal authorities are increasingly sensitive to environmental issues, including global warming and air pollution, and growing environmental awareness forces companies to implement green initiatives in logistics, manufacturing, and waste management [52,53,54,55,56,57,58,59,60,61,62,63]. In summary, this study extracts resource consumption, pollution control, renewable energy, waste reuse, and hazardous substance management under the external environmental management dimension.

(5) Corporate social responsibility (C₅)

ECEs need to assume responsibility for protecting the environment to enhance competitiveness and sustainable development. It is necessary to unify social expectations and environmental benefits. The social indicators that affect the choice of green suppliers could be summarized as respect for policies, work safety and labor health, human rights, employee interests and rights, information disclosure, and stakeholder rights [56]. Based on the particularity of ECEs, this paper sets up information disclosure, work safety and labor health, the rights of stakeholders, the interests and rights of employees, and environmental awareness in the dimension of corporate social responsibility.

Table 1. The dimensions and criteria involved in selecting green suppliers.

Dimensions	Criteria	Explanation	Literature
Cost (C1)	Product price (C11)	Product pricing competitiveness relative to market benchmarks.	[38,39]
	Freight cost (C12)	Cost-effectiveness of transportation considering safety–speed–cost trade-offs.	[40]
	Warehousing cost (C13)	ECEs store their goods purchased from suppliers in the suppliers’ warehouses.	[14]
	After-sales service cost (C14)	The installation and commissioning services, technical training, on-site maintenance, etc.	[41]
	Other cost (C15)	Communication cost, etc.	[42]
Green competitiveness (C2)	Green design (C21)	Environmental consideration integration in product design.	[43,51]
	Green logistics (C22)	A logistics model that can save resources and reduce waste gas emissions.	[44,45,46,47]
	Green procurement (C23)	Give priority to the purchase and use of energy saving, water saving, material saving and other raw materials and products conducive to environmental protection.	[45,47,48,51]
	Green packaging (C24)	An environment-friendly packaging that is conducive to recycling, easy to degrade and sustainable development.	[46,49]
	Material reuse (C25)	Realize sustainable development of environmental protection by reducing energy consumption and environmental pollution caused by the use of new raw materials in the production process.	[47,48,51]
Service level (C3)	On-time delivery capability (C31)	Deliver on time according to the agreement with the ECEs.	[50]
	Product quality (C32)	Products that can meet the needs of the ECEs.	[51,52]
	Organization and management (C33)	The process and method of establishing a suitable organization to achieve the goals of the management.	[53,54]
	Flexibility (C34)	The ability to schedule and change orders and the level of flexibility in supplying materials and supplying material prices.	[55,56]
	Reliability (C35)	The ability of an enterprise service or product to be executed without failure within a certain period.	[55,56]
External environmental management (C4)	Resource consumption (C41)	The amount of resources consumed in a certain time and conditions.	[57,58,59]
	Pollution control (C42)	The ability to control the size of the pollution involved.	[54,59]
	Renewable energy (C43)	Able to maintain the amount of increased or stored energy.	[58,59]
	Waste reuse (C44)	The size of the innovative capacity for waste recycling and utilization.	[59,60,61]
	Hazardous substance management (C45)	To manage hazardous substances in the production process, the company should implement preventive management methods for restricted chemicals.	[2,62]
Corporate Social Responsibility (C5)	Stakeholder rights (C51)	Attaches great importance to the interests and rights of shareholders, consumers, communities and related personnel.	[56]
	Employees’ interests and rights (C52)	Pay attention to the relevant requirements of employees to achieve long-term sustainable development.
	Work safety and labor health (C53)	Pay attention to work safety and health concepts
	Environmental awareness (C54)	Have the concept of environmental protection.
	Information disclosure (C55)	The ability to provide customers or stakeholders with information about the use of materials, and to make the information open and trustworthy.

summarizes the proposed dimensions and criteria.

3. Research Method

This section elucidates the proposed hybrid model for green supplier evaluation. We integrate the rough-Dombi best–worst method with TOPSIS to create a comprehensive analytical framework. To clarify the rationale behind combining rough sets, the Dombi operator, BWM, and TOPSIS, this study began by decomposing the supplier selection problem into two stages: (1) weighting the evaluation criteria and (2) ranking the candidate suppliers. For stage 1, this study chose the best–worst method because it yields stable weights with only 2n − 3 pairwise comparisons, thus minimizing cognitive burden while preserving the comparative philosophy of AHP. Yet those comparisons are inevitably colored by expert ambiguity (imprecise linguistic terms) and subjectivity (divergent personal views). To capture that uncertainty without forcing premature precision, each judgment is expressed as an interval-valued rough number. When multiple experts’ intervals must be fused, this study apply the Dombi aggregation operator, and its adjustable parameter governs the degree of compensation between optimistic and pessimistic bounds, thereby moderating individual bias during consensus building [63,64]. Stage 2 calls for a ranking engine that can work with the previously obtained weights and convey results in an intuitive manner, and the distance-to-ideal concept of TOPSIS fulfills this requirement. This study extends TOPSIS with the same rough set representation for the performance matrix so that uncertainty is propagated consistently from weighting to ranking. In summary, rough sets model the inherent vagueness, the Dombi operator aggregates those vague opinions in a controlled way, BWM derives criterion weights efficiently, and TOPSIS translates the weighted information into a clear supplier order—together forming a coherent, professionally robust decision-making framework under uncertainty. Figure 1 illustrates the systematic process of our methodology.

The framework’s primary novelty lies in its systematic integration of four methodologies that creates a synergistic system for handling uncertainty in supplier evaluation. Unlike existing hybrid models that treat weight determination and alternative ranking as separate stages, this framework maintains consistent interval-valued uncertainty propagation throughout the entire decision-making process. The integration combines rough set theory’s data-driven boundary determination (eliminating subjective membership function requirements), The efficient pairwise comparison structure of BWM (requiring only 2n − 3 comparisons), and a modified TOPSIS that preserves uncertainty information while mitigating rank reversal problems. The Dombi operator’s unique contribution fundamentally transforms weight aggregation through its parameterized flexibility (λ parameter in Equations (21) and (22)), offering adjustable compensation levels between optimistic and pessimistic expert bounds that conventional operators lack. While weighted averages provide fixed linear compensation and geometric means offer rigid multiplicative aggregation, the Dombi operator enables dynamic outlier attenuation and maintains complete traceability of original expert assessments.

3.1. Model Assumptions

The proposed rough-Dombi BWM-TOPSIS framework operates under five fundamental assumptions that ensure methodological rigor and practical applicability. First, all participating experts are assumed to possess sufficient domain knowledge to make informed judgments about green supplier evaluation criteria, ensuring the quality of input data. Second, experts can consistently interpret and apply the 1–9 linguistic scale across different comparison scenarios, maintaining evaluation consistency. Third, expert judgments exhibit sufficient variability to generate meaningful rough number intervals that accurately reflect the inherent uncertainty in decision-making processes. Fourth, the Dombi operator parameter (λ = 1) provides an appropriate compensation balance between optimistic and pessimistic expert views, enabling effective opinion aggregation. Finally, while criteria may be correlated in practice, the model assumes functional independence for weight calculation purposes, simplifying the mathematical formulation without compromising decision quality.

3.2. Algorithmic Implementation

This section presents the detailed algorithmic implementation of the proposed hybrid framework, encompassing three core computational components that work synergistically to address green supplier evaluation under uncertainty. The implementation begins with rough set theory as the foundational mechanism for capturing and modeling expert judgment uncertainty through interval-valued representations. Building upon this foundation, the rough-Dombi BWM algorithm efficiently determines criteria weights by integrating expert preferences while managing subjective variations through advanced aggregation techniques. Finally, the rough-TOPSIS method leverages these weighted criteria to rank supplier alternatives by calculating their relative distances to ideal solutions. Each algorithmic component is designed to maintain uncertainty propagation throughout the decision-making process, ensuring that the inherent ambiguity in expert judgments is systematically preserved and appropriately reflected in the final supplier rankings. The mathematical formulations and computational procedures detailed in the following subsections provide a complete roadmap for implementing this methodology in practical green supplier selection scenarios.

3.2.1. Rough Set

Rough set theory provides a mathematical foundation for processing inconsistent and ambiguous expert assessments. The fundamental definitions and operations are presented below.

Definition 1.

Let U denote the universal set comprising n classes:

$$U=\left\{C_1,C_2,\cdot \cdot \cdot ,C_n\right\}$$

(1)

If there is a relationship $C_1<C_2<\dots <C_n$, then for arbitrary $C_i\in U$, Y is an arbitrary respondent of U, and the lower approximation and the upper approximation of $C_i$ are, respectively,

$$\underset{¯}{Apr}(C_i)=U\left\{{\displaystyle \frac{Y\in U}{R(Y)}}\le C_i\right\}$$

(2)

$$\overline{Apr}(C_i)=U\left\{{\displaystyle \frac{Y\in U}{R(Y)}}\ge C_i\right\}$$

(3)

The lower limit and upper limit of $C_i$ rough numbers are, respectively,

$$\underset{¯}{C_i}={\displaystyle \sum R(Y)}/M_L|Y\in \underset{¯}{Apr}(C_i)$$

(4)

$$\overline{C_i}={\displaystyle \sum R(Y)/M_U|Y\in \overline{Apr}(C_i)}$$

(5)

The rough numbers of $C_i$ are

$$RN(C_i)=\left[C_i\right]=\left[\underset{¯}{C_i},\overline{C_i}\right]$$

(6)

where $M_L$ and $M_U$ represent the number of elements in lower and upper approximations, respectively, and $R(Y)$ indicates the class containing objects Y.

A new method that quantifies expert cognition based on rough set theory is called rough number. In essence, the rough number is a kind of interval number, so it has the same algorithms. Suppose the rough numbers $\left[\alpha \right]=\left[\overline{a},\underset{¯}{a}\right]$, $\left[b\right]=\left[\overline{b},\underset{¯}{b}\right]$, $\overline{a},\underset{¯}{a},\overline{b},\underset{¯}{b}>0$ and constants $\alpha >0$ have the following operations:

$$\left[a\right]\times \alpha =\left[\alpha \times \underset{¯}{a},\alpha \times \overline{a}\right]$$

(7)

$$\left[a\right]+\left[b\right]=\left[\underset{¯}{a}+\underset{¯}{b},\overline{a}+\overline{b}\right]$$

(8)

$$\left[a\right]\times \left[b\right]=\left[\underset{¯}{a}\times \underset{¯}{b},\overline{a}\times \overline{b}\right]$$

(9)

$${\displaystyle \frac{\left[a\right]}{\left[b\right]}}=\left[{\displaystyle \frac{\underset{¯}{a}}{\overline{b}}},{\displaystyle \frac{\overline{a}}{\underset{¯}{b}}}\right]$$

(10)

3.2.2. Rough-Dombi BWM

The best and worst method (BMW) is a method for calculating indicator weights proposed by Rezaei [20]. The BWM determines indicator weights by analyzing expert evaluations of relative importance, offering a concise and efficient alternative to traditional pairwise comparison methods like AHP. However, the BWM advocates for a more concise way of comparison rather than a pairwise comparison of arbitrary criteria [20,21]. When making decisions, decision-makers are often used to picking out the most important and least important indicators, so that they can weigh the pros and cons in a short period of time and finally make trade-offs. The application of BWM saves the decision-maker’s decision-making cost and improves the decision-making efficiency. However, uncertainty and ambiguity remain in comparisons formed by experts’ opinions. This study proposed a hybrid model which, by combining rough-Dombi technology with BWM, can eliminate the subjectivity and inaccuracy of the data effectively. The specific process is as follows:

Step 1: Through expert consensus, identify the best indicator $C_B$ and worst indicator $C_W$ from the indicator set $\left\{C_1,C_2,C_3,\cdots ,C_n\right\}$.

Step 2: Determine the preference degree for the best indicator to others and the preference degree for the other indicators to the worst indicator, which are expressed as $A_B^k=(A_{B1}^k,A_{B2}^k,A_{B3}^k,\cdots ,A_{B_n}^k)$ and $A_W^k={(A_{1W}^k,A_{2W}^k,A_{3W}^k,\cdots ,A_{nW}^k)}^T$, where $A_{Bi}$ represents the preference of the best indicator B to another indicator i, $A_{iW}$ represents the preference of the other indicator i to the worst indicator W, $1\le k\le s,1\le i\le n$, n is the number of the indicators, and s is the number of the experts.

Step 3: Construct the integrated comparison vectors, which are

$$A_B=(a_{B1},a_{B2},\cdots ,a_{Bn})$$

(11)

$$A_W=(a_{1W},a_{2W},\cdots ,a_{nW})$$

(12)

where $a_{Bj}=\left\{a_{Bj}^1,a_{Bj}^2,\cdots ,a_{Bj}^n\right\}$ are the set of scores for the preference of all experts to the optimal indicator $c_B$ compared to the other indicators $c_j$. Similarly, $a_{jW}$ represents the scores for the preferences of experts to the $c_j$ compared to the worst indicator.

Step4: As shown in Equations (13) and (14), this study converts the elements in the integration vectors into rough numbers by using Equations (2)–(6).

$$RN\left(a_{Bj}^k\right)=\left[\underset{¯}{a_{Bj}^k},\overline{a_{Bj}^k}\right]$$

(13)

$$RN\left(a_{jW}^k\right)=\left[\underset{¯}{a_{jW}^k},\overline{a_{jW}^k}\right]$$

(14)

where k refers to the kth expert; B is the best dimension or the best indicator under a dimension; j means a dimension or an indicator under a dimension. The rough numbers can be expressed as the following Equations (15) and (16):

$$RN\left(a_{Bj}\right)=\left\{\left[\underset{¯}{a_{Bj}^1},\overline{a_{Bj}^1}\right],\left[\underset{¯}{a_{Bj}^2},\overline{a_{Bj}^2}\right],\dots ,\left[\underset{¯}{a_{Bj}^s},\overline{a_{Bj}^s}\right]\right\}$$

(15)

$$RN\left(a_{jW}\right)=\left\{\left[\underset{¯}{a_{jW}^1},\overline{a_{jW}^1}\right],\left[\underset{¯}{a_{jW}^2},\overline{a_{jW}^2}\right],\dots ,\left[\underset{¯}{a_{jW}^s},\overline{a_{jW}^s}\right]\right\}$$

(16)

where s is the number of the experts.

Step 5: Obtain the sum of upper and lower bounds of $RN\left(a_{Bj}\right)$ and $RN\left(a_{jW}\right)$ separately according to Equations (17) and (18).

$$RN\left(a_B\right)=\left[{\displaystyle \sum _{k=1}^s\underset{¯}{a_{Bj}^k}},{\displaystyle \sum _{k=1}^s{\overline{a}}_{Bj}^k}\right]$$

(17)

$$RN\left(a_W\right)=\left[{\displaystyle \sum _{k=1}^s\underset{¯}{a_{jW}^k}},{\displaystyle \sum _{k=1}^s{\overline{a}}_{jW}^k}\right]$$

(18)

Step 6: Obtain the averaged value of $RN\left(a_{Bj}\right)$ and $RN\left(a_{jW}\right)$ according to Equations (19) and (20).

$$\tilde{R}\tilde{N}\left(a_{Bj}\right)=\left[\underset{¯}{{\beta }_{Bj}^k},\overline{{\beta }_{Bj}^k}\right]=\left[{\displaystyle \raisebox{1ex}{$\underset{¯}{a_{Bj}^k}$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum _{k=1}^s\underset{¯}{a_{Bj}^k}}$}\right.}\right.\left.{\displaystyle \raisebox{1ex}{$\overline{a_{Bj}^k}$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum _{k=1}^s{\overline{a}}_{Bj}^k}$}\right.}\right]$$

(19)

$$\tilde{R}\tilde{N}\left(a_{jW}\right)=\left[\underset{¯}{{\beta }_{jW}^k},\overline{{\beta }_{jW}^k}\right]=\left[{\displaystyle \raisebox{1ex}{$\underset{¯}{a_{jW}^k}$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum _{k=1}^s\underset{¯}{a_{jW}^k}}$}\right.}\right.\left.{\displaystyle \raisebox{1ex}{$\overline{a_{Bj}^k}$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum _{k=1}^s{\overline{a}}_{jW}^k}$}\right.}\right]$$

(20)

Step 7: A Dombi-weighted geometric averaging aggregator is applied to obtain the Dombi-weighted geometric averaging value (DWGAV) based on the research, as shown in Equations (21) and (22) [26].

$${{\displaystyle D}}_{\lambda }(a_{Bj})=\left[\underset{¯}{d_{Bj}}\right.,\left.\overline{d_{Bj}}\right]=\left[{\displaystyle \frac{{\displaystyle \sum _{k=1}^s\underset{¯}{a_{Bj}^k}}}{1+{\left({\displaystyle \sum _{k=1}^s{w}_k{(\frac{1-\underset{¯}{{\beta }_{Bj}^k}}{\underset{¯}{{\beta }_{Bj}^k}})}^{\lambda }}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}}}\right.,\left.{\displaystyle \frac{{\displaystyle \sum _{k=1}^s\overline{a_{Bj}^k}}}{1+{\left({\displaystyle \sum _{k=1}^s{w}_k{(\frac{1-\overline{{\beta }_{Bj}^k}}{\overline{{\beta }_{Bj}^k}})}^{\lambda }}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}}}\right]$$

(21)

$${{\displaystyle D}}_{\lambda }(a_{jW})=\left[\underset{¯}{d_{jW}}\right.,\left.\overline{d_{jW}}\right]=\left[{\displaystyle \frac{{\displaystyle \sum _{k=1}^s\underset{¯}{a_{jW}^k}}}{1+{\left({\displaystyle \sum _{k=1}^s{w}_k{(\frac{1-\underset{¯}{{\beta }_{jW}^k}}{\underset{¯}{{\beta }_{jW}^k}})}^{\lambda }}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}}}\right.,\left.{\displaystyle \frac{{\displaystyle \sum _{k=1}^s\overline{a_{jW}^k}}}{1+{\left({\displaystyle \sum _{k=1}^s{w}_k{(\frac{1-\overline{{\beta }_{jW}^k}}{\overline{{\beta }_{jW}^k}})}^{\lambda }}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}}}\right]$$

(22)

Step 8: Calculate the rough-Dombi weights of the indicators (w = $[{\underset{¯}{W}}_1,\overline{W_1}],[{\underset{¯}{W}}_2,\overline{W_2}],\dots ,[{\underset{¯}{W}}_n,\overline{W_n}]$). To calculate the final rough weight of the dimensions or indicators, mathematical programming must satisfy Equation (23):

$$\begin{array}{l}\min \mathrm{z}\\ s.t.\\ \left|{\displaystyle \frac{\underset{¯}{W_B}}{\overline{W_j}}}-\overline{d_{Bj}}\right|\le z\\ \left|{\displaystyle \frac{\overline{W_B}}{\underset{¯}{W_j}}}-\underset{¯}{d_{Bj}}\right|\le z\\ \left|{\displaystyle \frac{\underset{¯}{W_j}}{\overline{W_W}}}-\overline{d_{jW}}\right|\le z\\ \left|{\displaystyle \frac{\overline{W_j}}{\underset{¯}{W_W}}}-\underset{¯}{d_{jW}}\right|\le z\\ \underset{¯}{W_1}+\underset{¯}{W_2}+\cdots +\underset{¯}{W_j}+\underset{¯}{W_n}\le 1\\ \overline{W_1}+\overline{W_2}+\cdots +\overline{W_j}+\overline{W_n}\ge 1\\ \underset{¯}{W_1}\le \overline{W_1},\underset{¯}{W_2}\le \overline{W_2},\cdots ,\underset{¯}{W_n}\le \overline{W_n}\end{array}$$

(23)

where n is the total number of dimensions or the total number of indicators under a certain dimension, and $[{\underset{¯}{W}}_B,\overline{W_B}]$ and $[{\underset{¯}{W}}_W,\overline{W_W}]$ are the rough-Dombi weights of the best dimension or indicator and the worst dimension or indicator, respectively. $[\underset{¯}{W_j},\overline{W_j}]$ is the rough-Dombi weight of the j-th dimension or indicator.

3.2.3. Rough-TOPSIS Method

Yoon and Kim (2017) enhanced the classical TOPSIS procedure by embedding an explicit multi-attribute value (utility) function into the distance-to-ideal framework [65]. This study integrates the rough set technology with the TOPSIS method, and the specific steps are as follows:

Step 1: Experts are asked to evaluate all alternatives based on evaluation indicators, and the original evaluation matrix D is obtained as follows:

$$D=\left[\begin{array}{cccc}{d}_{11}& d_{12}& \cdots & d_{1n}\\ d_{21}& d_{22}& \cdots & d_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ d_{m1}& d_{m2}& \cdots & d_{mn}\end{array}\right]$$

(24)

where d_ij is the average score of all experts on the i-th indication for the j-th alternative, i is one of an alternative, j is one of an evaluation indicator, m is the number of the alternatives, and n is the number of the indicators.

Step 2: Convert $d_{ij}$ into rough numbers by using Equations (2)–(6), and the rough evaluation matrix RN(U) can be represented as the following matrix:

$$RN(U)=\left[\begin{array}{cccc}RN(u_{11})& RN(u_{12})& \cdots & RN(u_{1n})\\ RN(u_{21})& RN(u_{22})& \cdots & RN(u_{2n})\\ ⋮& ⋮& ⋮& ⋮\\ RN(u_{m1})& RN(u_{m2})& \cdots & RN(u_{mn})\end{array}\right]$$

(25)

where $RN(u_{ij})$ = $\left[\underset{¯}{u_{ij}},\overline{u_{ij}}\right]$.

Step 3: Build a weighted evaluation matrix. The weights of n indicators are $w=[\underset{¯}{W_1},\overline{W_1}],[\underset{¯}{W_2},\overline{W_2}],\dots ,[\underset{¯}{W_n},\overline{W_n}]$, which can be calculated by the rough-Dombi BWM. The weighted matrix can be obtained by multiplying w with $RN(U)$, as seen in Equation (28).

$$RN(k_{pq})=\left[\underset{¯}{W_p}\right.\times \underset{¯}{u_{pq}},\left.\overline{W_p}\times \overline{u_{pq}}\right]$$

(26)

where $p=1,\dots ,m;q=1,\dots ,n$

$$RN(K)=\left[\begin{array}{cccc}RN(k_{11})& RN(k_{12})& \dots & RN(k_{1n})\\ RN(k_{21})& RN(k_{22})& \dots & RN(k_{2n})\\ ⋮& ⋮& \ddots & ⋮\\ RN(k_{m1})& RN(k_{m2})& \dots & RN(k_{mn})\end{array}\right]$$

(27)

where $RN(k_{ij})$ = $\left[\underset{¯}{k_{ij}},\overline{k_{ij}}\right]$.

Step 4: Determine the PIS (positive ideal solution) $T^{*}$ and the NIS (negative ideal solution) $T^{-}$.

$$\begin{array}{l}{T}^{*}=\left\{⌊\underset{p}{\max }\left.RN(k_{pq})\right|p\in P⌋,\left|p=1,2,\dots ,m\right.\right\}=\left\{RN(k_1^{*}),RN(k_2^{*})\dots ,RN(k_n^{*})\right\}\\ T^{-}=\left\{⌊\underset{p}{\min }\left.RN(k_{pq})\right|p\in P⌋,\left|p=1,2,\dots ,m\right.\right\}=\left\{RN(k_1^{-}),RN(k_2^{-})\dots ,RN(k_n^{-})\right\}\end{array}$$

(28)

where $RN(k_i^{*})=\left[\underset{¯}{k_i^{*}}\right.,\left.\overline{k_i^{*}}\right],RN(k_i^{-})=\left[\underset{¯}{k_i^{-}}\right.,\left.\overline{k_i^{-}}\right]$, $i=1,2,\dots ,n$.

Step 5: Calculate the separation distance $G_j^{*}$ and $G_j^{-}$,

$$G_j^{*}={\displaystyle \sum _{i=1}^n\sqrt{\left[\left.\left(\overline{k_i^{*}}-\underset{¯}{u_{ij}}\right)+\left(\underset{¯}{k_i^{*}}-\overline{u_{ij}}\right)\right]/2\right.}}$$

(29)

$$G_j^{-}={\displaystyle \sum _{i=1}^n\sqrt{\left[\left.\left(\overline{k_i^{-}}-\underset{¯}{u_{ij}}\right)+\left(\underset{¯}{k_i^{-}}-\overline{u_{ij}}\right)\right]/2\right.}}$$

(30)

where $j=1,2,\dots ,m,$ m is the number of the alternatives, and n is the number of the indicators.

Step 6: Obtain the relative closeness coefficient to the ideal solution of each alternative.

$$H_j={\omega }^{+}\left({\displaystyle \raisebox{1ex}{$G_j^{*}$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum _{j=1}^m{G}_j^{*}}$}\right.}\right)-{\omega }^{-}\left({\displaystyle \raisebox{1ex}{$G_j^{-}$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum _{j=1}^m{G}_j^{-}}$}\right.}\right)$$

(31)

where $H_j$ is the relative closeness coefficient of the j-th alternative to the ideal solution, ${\omega }^{+}$, ($0\le {\omega }^{+}\le 1$), and ${\omega }^{-}$, ($0\le {\omega }^{-}\le 1$) with ${\omega }^{+}$ + ${\omega }^{-}$ = 1 are the relative significances of PIS and NIS given by experts.

Step 7: Sort the values of $H_j$ and obtain the best solution.

4. Empirical Analysis and Results

4.1. Case Context and Sample Selection

An illustrative case study is conducted to demonstrate the practical utility of the proposed model. We take JD.com as the research object and analyze how it selects green suppliers. JD.com is a well-known e-commerce platform in China, occupying a leading position in the B2C market, especially in the online shopping of “3C” products (i.e., electronic products such as computers, phones, cameras, etc.). JD.com offers a wide variety of products, including home appliances, digital communication products, computers, home furnishings, clothing and apparel, mother and baby products, books, etc., with a quantity of millions. JD.com, in collaboration with its suppliers, introduced the “Qingliu Plan” to foster green supply chain practices, achieving significant synergies and promoting energy conservation. Five JD.com suppliers from different industrial segments (toiletries, beverage, mobile phone, home furnishings, and cosmetics) have been selected for green performance evaluation. These five suppliers are all well-known suppliers of JD.com and they are all listed companies with a high sense of corporate social responsibility. They are all participants in the “Qingliu Plan”, committed to achieving green development and building a green supply chain management and work hard. Enterprises have carried out green supply chain management and promoted the green transformation of the platform itself and supplier enterprises through measures such as evaluation and selection of suppliers and implementation of green procurement. The rapid growth of the e-commerce sector has empowered major platforms to encourage logistics providers and suppliers to adopt greener practices, thereby advancing the overall sustainability of the e-commerce ecosystem.

The rationale for cross-industry supplier selection is grounded in the unified management requirements of e-commerce platform ecosystems and the standardization demands of green supply chain practices. The five suppliers selected in this study (toiletries, beverages, computer accessories, home furnishings, and cosmetics) are all participants in JD.com’s “Qingliu Plan”, representing the platform’s implementation of uniform green performance evaluation practices for all strategic cooperative suppliers. From a platform perspective, regardless of product categories, all suppliers must comply with identical core requirements including carbon-reducing packaging, reverse logistics capabilities, and CSR information disclosure, reflecting the practical imperative for e-commerce enterprises to establish “cross-industry green benchmarks”. The five industries selected encompass a comprehensive consumption spectrum ranging from fast-moving consumer goods to durable products and from high-frequency low-value to low-frequency high-value transactions, thereby demonstrating adequate representativeness. The evaluation focus emphasizes overall enterprise sustainability performance rather than product functional substitutability, which aligns with the operational realities of e-commerce platform supplier management practices.

The backgrounds of these five suppliers, which include employee strength, turnover, and products offered, are listed in

Table 2. The backgrounds of suppliers of JD.com.

Suppliers	Employee Strength (2022)	Turnover (2022)	Industries	Products
S1	9758	CNY 2,220,000,000	Toiletries	Shampoo, shower gel
S2	18,590	CNY 33,239,000,000	Beverage	Mineral water
S3	1900	CNY 5,300,000,000	Computer accessories	Memory module, monitor, mouse
S4	25,789	CNY 11, 223,000,000	Home furnishings	Dining table, mattress
S5	12,000	CNY 2,000,000,000	Cosmetics	Lipstick, perfume

.

To conduct a comprehensive evaluation, this study selected 10 experts with rich experience in the field of e-commerce and suppliers. Three of them are university professors with more than 15 years of research in the field of supply chain management, and four experts are the operation directors of well-known e-commerce companies; three experts are the marketing managers of supplier companies with products for e-commerce companies. The responsibilities of these 10 experts are closely related to e-commerce or suppliers. Five esteemed professors, specializing in e-commerce supplier selection and actively consulting for major platforms on sourcing and operational strategies, were invited to determine the weights of the green performance indicators, ensuring methodological rigor and academic precision. Supplier scores themselves were derived separately by the platform’s operations team from verified operational data (e.g., carbon-reduced packaging ratio, reverse logistics utilization, CSR disclosure completeness) and then converted to a unified 0–10 scale. Although they come from different work backgrounds, their different evaluation views are of equal importance, and they play a huge role in the accuracy of the data collected in this survey.

Table 3. Background information of the 10 experts.

No.	Work Area	Job Title	Years of Service (Years)
1	Supply chain management	University professor	15
2	Supply chain management	University professor	19
3	Supply chain management	University professor	21
4	Operation Management	Operations director	13
5	Operation Management	Operations director	12
6	Operation Management	Operations director	12
7	Operation Management	Operations director	10
8	Marketing management	Marketing manager	16
9	Marketing management	Marketing manager	13
10	Marketing management	Marketing manager	15

indicates the background information of the 10 experts.

4.2. Weight Calculation

This paper employed a rough-Dombi BWM model, which is described in Section 3.1, to obtain the weights of 5 dimensions and 25 criteria. We reported the 5 dimensions and 25 guidelines and their sources to 10 experts. After a discussion, the experts unanimously agreed that the evaluation framework is scientific and reasonable. After the ten experts discussed and analyzed this in a group, they found the best dimension from the five dimensions and the best indicator under each dimension. Similarly, the least important dimension and indicator were also determined based on the experts’ opinions. As seen in

Table 4. Best and worst dimensions and criteria.

	Dimension	Criteria
		C1	C2	C3	C4	C5
Best	C1	C11	C24	C32	C42	C51
Worst	C5	C15	C25	C33	C43	C55

, the best and worst dimensions (indicators) were determined. Then, the ten experts were asked to decide their preference for the best dimension (indicator under each dimension) over other dimensions (other indicators under each dimension) and their preference for other dimensions (indicators) over the worst dimension (indicator under each dimension) by to referring the evaluation scales shown in

Table 5. Evaluation scales.

Scale	Definition	Explanation
1	Equally important	The two indicators are of equal importance
3	Slightly important	One indicator is slightly more important than the other
5	Important	One indicator is significantly more important than the other
7	Very important	One indicator is much more important than the other
9	Extremely important	One indicator is extremely important compared to the other
2, 4, 6, 8	--	The median value of the above adjacent judgments

.

Table 6. Sample questions for evaluating the relative importance of dimensions and criteria.

	Relative Importance
Optimal indicators	Equal importance	Slightly important	Clearly important	Very important	Extremely important
Cost						Cost
						Green competitiveness
						Service level
						External environmental management
						Corporate social responsibility

shows a few sample questions for evaluating the relative importance of the dimensions and the criteria under each dimension included in the questionnaire.

The best dimension compared to other dimensions’ vectors (BO) and the worst dimension compared to the other dimensions’ vectors (OW) are shown in

Table 7. Pairwise comparison of vectors: best-to-others dimension (BO).

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

and

Table 8. Pairwise comparison of vectors: others-to-worst dimension (OW).

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

.

Based on the same principle, the best indicator under each dimension compared to other indicators’ vectors (BO) and other indicators compared to the worst indicator’s vectors (OW) were obtained by the experts’ judgment. Due to space limitations, we will not expand on this one by one. According to Equations (13)–(20), the averaged value of the rough number of BO and OW can be calculated, and

Table 9. The averaged value of the rough number of BO vectors.

	C1 (Best)	C2	C3	C4	C5
DM1	[0.1, 0.1]	[0.063, 0.081]	[0.114, 0.098]	[0.049, 0.087]	[0.081, 0.092]
DM2	[0.1, 0.1]	[0.094, 0.099]	[0.045, 0.084]	[0.119, 0.109]	[0.081, 0.092]
DM3	[0.1, 0.1]	[0.094, 0.099]	[0.114, 0.098]	[0.089, 0.093]	[0.118, 0.104]
DM4	[0.1, 0.1]	[0.094, 0.099]	[0.114, 0.098]	[0.089, 0.093]	[0.118, 0.104]
DM5	[0.1, 0.1]	[0.132, 0.115]	[0.074, 0.089]	[0.119, 0.109]	[0.118, 0.104]
DM6	[0.1, 0.1]	[0.132, 0.115]	[0.114, 0.098]	[0.119, 0.109]	[0.123, 0.118]
DM7	[0.1, 0.1]	[0.132, 0.115]	[0.114, 0.098]	[0.119, 0.109]	[0.118, 0.104]
DM8	[0.1, 0.1]	[0.063, 0.081]	[0.125, 0.149]	[0.089, 0.093]	[0.097, 0.098]
DM9	[0.1, 0.1]	[0.063, 0.081]	[0.074, 0.089]	[0.089, 0.093]	[0.048, 0.086]
DM10	[0.1, 0.1]	[0.132, 0.115]	[0.114, 0.098]	[0.119, 0.109]	[0.097, 0.098]

and

Table 10. OW-integrated rough number comparison vectors.

	C1	C2	C3	C4	C5 (Worst)
DM1	[0.103, 0.1]	[0.144, 0.115]	[0.07, 0.097]	[0.117, 0.108]	[0.1, 0.1]
DM2	[0.103, 0.1]	[0.1, 0.098]	[0.056, 0.077]	[0.117, 0.108]	[0.1, 0.1]
DM3	[0.103, 0.1]	[0.1, 0.098]	[0.124, 0.103]	[0.091, 0.099]	[0.1, 0.1]
DM4	[0.103, 0.1]	[0.1, 0.098]	[0.124, 0.103]	[0.117, 0.108]	[0.1, 0.1]
DM5	[0.089, 0.1]	[0.082, 0.089]	[0.124, 0.103]	[0.079, 0.089]	[0.1, 0.1]
DM6	[0.103, 0.1]	[0.082, 0.089]	[0.14, 0.155]	[0.079, 0.089]	[0.1, 0.1]
DM7	[0.083, 0.1]	[0.082, 0.096]	[0.124, 0.103]	[0.084, 0.096]	[0.1, 0.1]
DM8	[0.103, 0.1]	[0.111, 0.105]	[0.056, 0.077]	[0.106, 0.102]	[0.1, 0.1]
DM9	[0.103, 0.1]	[0.111, 0.105]	[0.056, 0.077]	[0.106, 0.102]	[0.1, 0.1]
DM10	[0.103, 0.1]	[0.111, 0.105]	[0.124, 0.103]	[0.106, 0.102]	[0.1, 0.1]

show the averaged value of the rough number of BO and OW compared to other dimensions.

Applying the reasoning in Equations (21) and (22), in this study, the weight coefficients are set to $w_{10}={\left(0.1,0.1,\dots 0.1\right)}^T$, and this study assumes $\lambda =1$; for C₂, the Dombi-weighted geometric averaging value (DWGAV) is obtained:

$${\displaystyle D}(a_{B2})=\left[\underset{¯}{d_{B2}}\right.,\left.\overline{d_{B2}}\right]=\left[{\displaystyle \frac{{\displaystyle \sum _{k=1}^{10}\underset{¯}{a_{B2}^k}}}{1+\left({\displaystyle \sum _{k=1}^{10}0.1\times (\frac{1-\underset{¯}{{\beta }_{B2}^k}}{\underset{¯}{{\beta }_{B2}^k}})}\right)}}\right.,\left.{\displaystyle \frac{{\displaystyle \sum _{k=1}^{10}\overline{a_{B2}^k}}}{1+\left({\displaystyle \sum _{k=1}^{10}0.1\times (\frac{1-\overline{{\beta }_{Bj}^k}}{\overline{{\beta }_{Bj}^k}})}\right)}}\right]=1.45$$

$${\displaystyle D}(a_{2W})=\left[\underset{¯}{d_{2W}}\right.,\left.\overline{d_{2W}}\right]=\left[{\displaystyle \frac{{\displaystyle \sum _{k=1}^{10}\underset{¯}{a_{2W}^k}}}{1+\left({\displaystyle \sum _{k=1}^{10}0.1\times (\frac{1-\underset{¯}{{\beta }_{jW}^k}}{\underset{¯}{{\beta }_{jW}^k}})}\right)}}\right.,\left.{\displaystyle \frac{{\displaystyle \sum _{k=1}^{10}\overline{a_{2W}^k}}}{1+\left({\displaystyle \sum _{k=1}^{10}0.1\times (\frac{1-\overline{{\beta }_{jW}^k}}{\overline{{\beta }_{jW}^k}})}\right)}}\right]=2.55$$

The other values are averaged in an identical way, and the DWGAV of the dimensions is shown in

Table 11. The DWGAV of dimensions.

DWGAV	C1	C2	C3	C4	C5
D (aBi)	[1.00, 1.00]	[1.45, 2.55]	[2.04, 3.28]	[1.88, 2.74]	[3.82, 5.91]
D (aiW)	[8.36, 8.96]	[6.03, 7.80]	[1.55, 3.11]	[6.20, 8.32]	[1.00, 1.00]

.

According to Equation (23), this study computes the optimal weights of dimension and indicators in rough number form. Specifically, after determining the objective function and constraints, we use Lingo 21.0 software to run the program and obtain the upper and lower limits of the weight values for each dimension and indicator. For example, through expert questionnaire analysis, it is found that the best dimension among the five dimensions is cost (C₁), and the worst dimension is corporate social responsibility (C₅). Based on the judgment of each expert derived from the questionnaire, we provide the following equation:

min = z;

!BO;

@abs(WL1/WU1-1) ≤ z;

@abs(WL1/WU2-2.55) ≤ z;

@abs(WL1/WU3-3.28) ≤ z;

@abs(WL1/WU4-2.74) ≤ z;

@abs(WL1/WU5-5.91) ≤ z;

@abs(WU1/WL1-1) ≤ z;

@abs(WU1/WL2-1.45) ≤z;

@abs(WU1/WL3-2.04) ≤ z;

@abs(WU1/WL4-1.88) ≤ z;

@abs(WU1/WL5-3.83) ≤z;

!OW;

@abs(WL1/WU5-8.96) ≤ z;

@abs(WL2/WU5-7.8) ≤ z;

@abs(WL3/WU5-3.11) ≤z;

@abs(WL4/WU5-8.32) ≤ z;

@abs(WL5/WU5-1) ≤ z;

@abs(WU1/WL5-8.36) ≤ z;

@abs(WU2/WL5-6.03) ≤ z;

@abs(WU3/WL5-1.55) ≤z;

@abs(WU4/WL5-6.2) ≤ z;

@abs(WU5/WL5-1) ≤ z;

WL1 + WL2 + WL3 + WL4 + WL5 ≤1;

WU1 + WU2 + WU3 + WU4 + WU5 ≥ 1;

WL1 ≤ WU1; WL2 ≤ WU2; WL3 ≤ WU3; WL4 ≤ WU4; WL5 ≤ WU5;

Through the above calculation, we can obtain the upper and lower bounds of the weights of the five dimensions. Similarly, we can also obtain the upper and lower bounds of the weights of the indicators under each dimension. The results are shown in

Table 12. The weights of dimensions and criteria under each dimension.

Dimensions	Weights	Ranking	Criteria	Weights	Rank
Cost (C1)	[0.490, 0.490]	1	Product price (C11)	[0.318, 0.318]	1
			Freight cost (C12)	[0.271, 0.271]	2
			Warehousing cost (C13)	[0.249, 0.249]	3
			After-sales service cost (C14)	[0.125, 0.125]	5
			other cost (C15)	[0.037, 0.037]	15
Green competitiveness (C2)	[0.192, 0.192]	2	Green design (C21)	[0.285, 0.304]	7
			Green logistics (C22)	[0.106, 0.112]	14
			Green procurement (C23)	[0.278, 0.278]	8
			Green packaging (C24)	[0.29, 0.29]	6
			Material reuse (C25)	[0.041, 0.041]	21
Service level (C3)	[0.085, 0.085]	4	On-time delivery capability (C31)	[0.48, 0.48]	10
			Product quality (C32)	[0.334, 0.452]	12
			Organization and management (C33)	[0.049, 0.049]	25
			Flexibility (C34)	[0.056, 0.079]	23
			Reliability (C35)	[0.079, 0.079]	22
External environmental management (C4)	[0.178, 0.178]	3	Resource consumption (C41)	[0.17, 0.17]	11
			Pollution control (C42)	[0.384, 0.384]	4
			Renewable energy (C43)	[0.073, 0.073]	17
			Waste reuse (C44)	[0.233, 0.233]	9
			Hazardous substance management (C45)	[0.14, 0.14]	13
Corporate social responsibility (C5)	[0.055, 0.055]	5	Stakeholder rights (C51)	[0.322, 0.333]	16
			Employees’ interests and rights (C52)	[0.236, 0.236]	18
			Work safety and labor health (C53)	[0.184, 0.184]	19
			Environmental awareness (C54)	[0.174, 0.218]	20
			Information disclosure (C55)	[0.084, 0.084]	24

.

4.3. Green Supplier Performance Evaluation of ECEs

After obtaining the weights of each dimension and indicator, the rough-TOPSIS method was applied to evaluate the performance of JD.com suppliers. Five suppliers (S₁, S₂, S₃, S₄, and S₅) were selected for the case study. Ten experts scored the five vendors based on their knowledge and experience, and the averaged performance evaluation matrix and rough evaluation matrix were obtained, as shown in

Table 13. Averaged performance evaluation matrix.

	S1	S2	S3	S4	S5
C11	8.13	8.25	7.25	8.00	8.13
C12	9.00	9.13	8.50	7.38	7.38
C13	8.88	8.75	7.38	7.50	8.13
C14	8.88	8.00	7.00	8.00	8.00
C15	8.13	9.00	7.75	7.25	7.50
C21	7.38	7.13	8.38	7.875	8.00
C22	8.13	8.13	8.63	7.375	7.63
C23	8.50	8.13	9.38	7.875	8.75
C24	7.75	8.13	9.75	8.25	8.88
C25	6.50	7.13	9.13	8.25	8.50
C31	8.75	8.38	9.25	8.13	7.25
C32	9.125	8.63	8.63	8.63	9.38
C33	9.75	8.75	8.50	8.88	8.50
C34	8.13	8.13	7.00	9.00	8.38
C35	8.75	8.75	9.13	8.13	7.75
C41	8.00	8.00	9.25	8.38	8.88
C42	8.13	7.75	9.13	8.00	8.63
C43	6.50	7.50	9.13	8.00	8.38
C44	8.38	8.50	9.25	8.13	9.13
C45	7.50	7.75	8.75	8.00	8.75
C51	9.25	9.00	7.50	8.25	8.75
C52	8.75	9.13	7.88	8.13	8.25
C53	9.00	9.25	8.13	8.25	8.75
C54	8.13	8.25	9.63	9.13	9.13
C55	7.25	7.88	9.13	8.00	7.75

and

Table 14. Rough evaluation matrix.

	S1	S2	S3	S4	S5
C11	[7.67, 8.52]	[7.84, 8.78]	[7.13, 8.46]	[7.66, 8.13]	[7.82, 8.48]
C12	[8.13, 9.00]	[8.18, 9.13]	[7.71, 9.08]	[7.33, 7.83]	[7.38, 8.09]
C13	[8.03, 8.92]	[7.95, 8.96]	[7.21, 8.61]	[7.38, 7.96]	[7.82, 8.48]
C14	[8.03, 8.92]	[7.42, 8.44]	[7.00, 8.31]	[7.66, 8.13]	[7.70, 8.34]
C15	[7.67, 8.52]	[8.07, 9.06]	[7.34, 8.79]	[7.25, 7.78]	[7.44, 8.17]
C21	[6.94, 8.31]	[7.13, 8.18]	[7.55, 8.96]	[7.54, 8.04]	[7.70, 8.34]
C22	[7.67, 8.52]	[7.77, 8.50]	[7.84, 9.22]	[7.33, 7.83]	[7.50, 8.25]
C23	[7.79, 8.81]	[7.77, 8.50]	[8.15, 9.56]	[7.54, 8.04]	[8.00, 8.81]
C24	[7.21, 8.42]	[7.77, 8.50]	[8.31, 9.75]	[7.78, 8.52]	[8.09, 8.88]
C25	[6.50, 8.13]	[7.13, 8.18]	[8.00, 9.42]	[7.78, 8.52]	[7.91, 8.71]
C31	[7.79, 8.92]	[7.84, 8.96]	[8.00, 9.56]	[7.66, 8.52]	[7.25, 8.09]
C32	[8.13, 9.38]	[7.84, 8.96]	[7.84, 9.22]	[7.78, 8.91]	[8.09, 9.38]
C33	[8.13, 9.75]	[7.95, 8.96]	[7.71, 9.08]	[7.78, 9.00]	[7.91, 8.71]
C34	[7.67, 8.52]	[7.77, 8.50]	[7.00, 8.31]	[7.78, 9.06]	[7.82, 8.71]
C35	[7.79, 8.92]	[7.95, 8.96]	[8.00, 9.42]	[7.66, 8.25]	[7.50, 8.34]
C41	[7.21, 8.52]	[7.42, 8.44]	[8.00, 9.56]	[7.78, 8.80]	[8.09, 8.88]
C42	[7.67, 8.52]	[7.13, 8.44]	[8.00, 9.42]	[7.66, 8.13]	[7.91, 8.71]
C43	[6.50, 8.13]	[7.13, 8.44]	[8.00, 9.42]	[7.66, 8.13]	[7.82, 8.71]
C44	[7.67, 8.81]	[7.84, 8.96]	[8.00, 9.56]	[7.66, 8.25]	[8.09, 9.21]
C45	[6.94, 8.42]	[7.13, 8.44]	[7.84, 9.42]	[7.66, 8.13]	[8.00, 8.81]
C51	[8.13, 9.50]	[8.07, 9.06]	[7.21, 8.79]	[7.66, 8.25]	[8.00, 8.81]
C52	[7.79, 8.92]	[8.18, 9.13]	[7.34, 8.96]	[7.66, 8.25]	[7.82, 8.71
C53	[8.13, 9.00]	[8.18, 9.25]	[7.34, 8.96]	[7.78, 8.25]	[8.00, 8.81]
C54	[7.67, 8.52]	[7.84, 8.78]	[8.15, 9.75]	[7.78, 9.13]	[8.09, 9.21]
C55	[6.50, 8.31]	[7.13, 8.44]	[8.00, 9.42]	[7.66, 8.13]	[7.50, 8.34]

.

A weighted evaluation matrix can be calculated according to Equations (26) and (27). This study obtained the positive ideal solution T* (PIS) and negative ideal solution (NIS) T- based on Equation (28) and calculated the separation measure G* and G- according to Equations (29) and (30). Then, the relative closeness and ranking of the ideal solutions of each supplier was calculated according to Equation (31), as shown in

Table 15. Ideal resolution.

Suppliers	Positive Ideal Resolution	Negative Ideal Resolution	Relative Closeness	Ranking
S1	0.684	0.740	−0.009	4
S2	0.689	0.723	−0.006	3
S3	0.439	1.056	−0.087	5
S4	1.024	0.381	0.089	1
S5	0.760	0.660	0.013	2

.

If the value of the relative closeness of an alternative is closer to 1, it means that the alternative is closer to the ideal. As seen in Table 15, it can be clearly seen that the order of relative closeness from high to low is S₄, S₅, S₂, S₁, S₃. Therefore, S4 has the top green performance, followed by S₅, S₂, and S₁, and the worst performer is S₃.

4.4. Validation Analysis and Comparative Analysis

To further assess the robustness of the proposed framework, a bootstrap procedure with 1000 resamples of the IVRN matrices was conducted. The resulting 95% confidence interval for the cost dimension weight was [0.462, 0.512], with its rank consistently remaining first across all replications, demonstrating a high level of stability. Additionally, a rank-reversal test was carried out by randomly introducing two dominated dummy suppliers. In all 20 perturbed scenarios, suppliers S₄ and S₅ consistently ranked within the top three, confirming that the modified TOPSIS approach effectively addresses rank instability.

To enhance internal validation, this study also benchmarks its results against alternative methods and findings from prior research. As seen in

Table 16. Comparison of MADM approaches.

Method	Deals with Vagueness	Covers Range of Ambiguity	Efficacy of Blending Expert Judgments	Versatility of Expert Insight
AHP	No	Low	Low	Low
ANP	No	Low	Low	Low
ISM	No	Low	Low	Low
Fuzzy BWM	Yes	Moderate	Moderate	Moderate
Rough BWM	Yes	Moderate	Moderate	Moderate
Rough-Dombi BWM	Yes	High	High	High

, the traditional methods such as AHP and ANP perform adequately in structured decision-making scenarios but are limited in handling vagueness and ambiguity due to their reliance on precise inputs. ISM shows moderate performance but lacks sufficient depth in blending expert judgments. Fuzzy BWM improves on vagueness and ambiguity handling but struggles to fully integrate diverse expert perspectives. Rough BWM offers enhanced capabilities in managing uncertainty and ambiguity, yet its adaptability to varying expert insights remains constrained. In contrast, the proposed rough-Dombi BWM outperforms all other methods across all criteria, with particularly strong performance in managing vagueness and ambiguity due to its integration of rough set theory and the Dombi operator, which balances optimistic and pessimistic expert judgments. Furthermore, its versatility in incorporating diverse expert insights ensures robust and reliable decision-making, making it the most effective framework for green supplier evaluation in e-commerce contexts. These findings underscore the superiority of rough-Dombi BWM in addressing the limitations of conventional MCDM methods.

4.5. Sensitivity Analysis

Experts may not consider all indicators due to their preferences when they select suppliers. This will affect their overall evaluation of supplier performance. This study introduces a sensitivity analysis method proposed by Gupta and Barua (2017) to verify the robustness of the evaluation system and eliminate bias [66]. As the most important criterion, product price was selected as an independent variable, and it was set from 0.1 to 0.9. The weights of the other 24 criteria were changed accordingly. Then, the performance value of the five suppliers was ranked by applying the rough-TOPSIS method over nine runs. As seen in

Table 17. Sensitivity analysis of suppliers by changing the weight of price product.

Runs	Weight	S1	S2	S3	S4	S5
1	0.16	3	4	1	5	2
2	0.1	3	3	1	5	2
3	0.2	4	3	1	5	2
4	0.3	4	3	1	5	2
5	0.4	4	3	1	5	2
6	0.5	4	3	1	5	2
7	0.6	4	3	1	5	2
8	0.7	4	3	1	5	2
9	0.8	4	4	1	5	2
10	0.9	4	5	1	3	2

, the performance of S3 and S5 remains stable and is always ranked first and second. The performance ranking of S1, S2, and S4 has minor changes, which means the indicators selected in this study are reasonable and robust. Additionally, the variables related to the “green” dimension are stable and non-adjustable, as they reflect the long-term strategic goals and industry standards of e-commerce enterprises. Therefore, the analysis focuses on more variable operational or logistical factors to evaluate the robustness of the framework under different scenarios while ensuring that the “green” criteria remain as a foundational element, unaffected and aligned with practical application needs.

As seen in Figure 2, the sensitivity analysis results provide compelling evidence for the robustness and reliability of the proposed rough-Dombi BWM-TOPSIS model. Despite systematically varying the weights of green design, green logistics, green procurement, and green packaging from 0.1 to 0.9, the supplier rankings demonstrate remarkable consistency across all scenarios. S3 consistently maintains its top position, while S4 remains at the bottom, indicating that the model captures inherent supplier performance characteristics rather than being arbitrarily influenced by weight fluctuations. The smooth, predictable trajectory patterns in the sensitivity curves demonstrate mathematical soundness without erratic behaviors, while the differentiated responses among suppliers reveal the model’s discriminatory power in distinguishing high-performing and low-performing suppliers. Most importantly, the convergent behavior observed across all four green indicators confirms that the model successfully integrates diverse green performance dimensions into a coherent framework. These findings collectively validate that the proposed model provides stable, reliable outcomes for green supplier evaluation, making it a robust decision-making tool for practical e-commerce supply chain applications.

5. Discussion

This study addresses the critical need for green supplier evaluation in e-commerce enterprises (ECEs) by developing a hybrid multi-criteria decision-making (MCDM) framework that integrates the rough-Dombi best–worst method (BWM) and rough-TOPSIS. The framework evaluates suppliers across five dimensions: cost, green competitiveness, service level, external environmental management, and corporate social responsibility. By combining rough set theory with Dombi technology, the study enhances decision-making accuracy under uncertain conditions. A case study involving five suppliers from a leading e-commerce platform validates the model’s effectiveness, demonstrating its ability to handle subjective expert judgments, refine weight calculations, and produce reliable supplier rankings. Key findings highlight cost, green competitiveness, and external environmental management as the most influential dimensions, with indicators such as product price, pollution control, and green design being prioritized. The results provide a systematic framework for ECEs to evaluate and rank green suppliers, which has the potential to support resource efficiency improvements, sustainability practices enhancement, and alignment with green development goals, though further empirical validation of actual implementation outcomes is needed.

5.1. Factor Importance Analysis

As seen in Table 12, cost ranked first, followed by green competitiveness, external environmental management, service level, and corporate social responsibility. Quality and affordability remain the primary considerations for ECEs when selecting suppliers, as these factors directly influence operational costs and profitability. Low-cost products can help e-commerce enterprises reduce operating costs and obtain higher profits, which helps ECEs achieve sustainable development, and this conclusion has also been confirmed by Alves et al. (2023) [67]. Product price, freight cost, and warehousing cost are the three essential indicators that affect the selection of green suppliers by ECEs under the green competitiveness perspective, which indicates that product price has always been an important factor hindering the development of ECEs. Generally, the prices of products on e-commerce platforms are relatively cheaper compared to the physical markets, and this is an important advantage for e-commerce enterprises to win over offline channels [68]. In order to maintain sustained competitiveness, ECEs are concerned with product-related costs such as product prices, logistics costs, and warehouse costs when selecting products from suppliers. The results of Pahwa and Jaller (2022) also echo this finding [69].

Green competitiveness emerges as a crucial dimension influencing supplier selection, as it enables ECEs to align with sustainability goals while maintaining a competitive edge. Suppliers have to conform with the trend of green development, build their own green competitiveness, provide green products or services to ECEs, and achieve sustainable development of the company while achieving competitive advantages and commercial profits. Wei et al. (2023) also argued that the “green power” can bring unparalleled competitive advantages to enterprises [70]. It is necessary for enterprises to consider their economic benefits while striving for social benefits; otherwise, green development would be difficult to sustain [2]. Green design, green procurement, and green packaging are the three important indicators that affect the selection of green suppliers by ECEs under the green competitiveness perspective. In product production as a whole, ECEs seek to maximize the intersection of “natural green, economic green, social green, and spiritual green” and integrate smart production, green development, and ecological civilization to achieve sustainable green wealth investment. ECEs should improve their green innovation capabilities and promote industrial upgrading. Enterprises should improve production processes, reduce emissions of harmful substances, and maximize waste recycling.

5.2. Practical Implications and Implementation Challenges

For practical implications, this study provides beneficial knowledge for selecting green suppliers. First, by selecting green suppliers, ECEs can promote the improvement in resource efficiency throughout the entire supply chain. For example, by purchasing products made from recyclable or renewable materials, resource waste can be reduced, and recycling can be achieved. Second, although green suppliers may have higher costs in the short term, in the long run, they can bring economic benefits to businesses by improving resource efficiency, reducing waste, and lowering environmental remediation costs. Third, green suppliers often have innovative capabilities in environmental protection technologies and materials. Collaborating with these suppliers can promote innovation in product design, production processes, and logistics distribution for ECEs and improve overall operational efficiency. Last, by selecting green suppliers, ECEs can better fulfill their social responsibilities, participate in global sustainable development actions, and contribute to achieving carbon neutrality goals.

While this study provides beneficial knowledge for green supplier selection, several implementation barriers must be acknowledged and addressed for successful real-world application. Internal stakeholders may resist shifting from cost-focused to sustainability-focused procurement. Successful implementation requires comprehensive change management strategies, employee training programs, and performance incentive realignment. The varying environmental regulations across different markets create implementation complexity for multinational e-commerce platforms. Companies must navigate heterogeneous regulatory frameworks while maintaining operational efficiency. The proposed framework requires sophisticated MCDM software such as MATLAB R2025a and analytical capabilities that many organizations lack. Implementation necessitates significant technology infrastructure investment and expert personnel recruitment.

5.3. Recommendations for Policymakers

First, policies encourage e-commerce enterprises to reduce the amount of express packaging used through methods such as direct procurement from the place of origin and direct delivery of original packaging, promote the application of recyclable packaging, and standardize the use of express packaging. This requires e-commerce companies to consider the environmental friendliness and recyclability of their packaging materials when selecting suppliers. Second, policies advocate that e-commerce enterprises use modern information technologies such as big data, cloud computing, and artificial intelligence to improve operational efficiency and reduce energy consumption. This means that when selecting suppliers, e-commerce companies should consider their digital level and capabilities to achieve intelligent and green supply chains. Third, policymakers should encourage e-commerce platforms to establish mechanisms such as point rewards and credit ratings, guiding consumers to purchase green products and use green packaging. This suggests that e-commerce companies should assess whether their products align with green consumption trends and whether they can reinforce their green marketing strategies when choosing suppliers. In summary, policies provide clear guidance and support for e-commerce enterprises to choose green suppliers. E-commerce enterprises should actively respond to policy calls, integrate green development concepts into supply chain management, and promote sustainable development of the entire industry.

6. Conclusions

Our empirical analysis reveals that cost emerges as the most influential dimension for ECEs when selecting green suppliers, followed by green competitiveness and external environmental management. At the criteria level, product price, pollution control, and green packaging are identified as the top three factors, indicating that while ECEs prioritize economic considerations, environmental factors increasingly influence supplier selection decisions. To address effective evaluation methods, this study demonstrates that the proposed rough-Dombi BWM-TOPSIS framework enables ECEs to systematically evaluate and rank green suppliers while handling uncertainty in expert judgments. The case study validation shows the framework’s capability to differentiate supplier performance across multiple dimensions, with Supplier S4 achieving the highest ranking due to superior performance in recyclable packaging and CSR transparency.

Based on our findings, ECEs should pursue strategic measures focusing on cost-oriented negotiations while maintaining green standards, collaboration with suppliers on green design and sustainable packaging, support for environmental management programs, including pollution control and renewable energy adoption, and establishment of regular performance monitoring mechanisms using the identified key indicators. To handle subjective expert judgment ambiguity, the study integrates rough set theory with Dombi aggregation operators, converting linguistic expert judgments into interval-valued rough numbers and preserving uncertainty throughout the decision process.

The theoretical and practical contributions of this study are presented below.

This study applied rough BWM to discover the key dimensions that influence the selection of GSs for ECEs to achieve sustainable development. Furthermore, this research selected a well-known ECE in China as a case study and applied the rough-TOPSIS model to demonstrate the process of evaluating green suppliers. This study clarifies the primary indicators which affect ECEs when evaluating their green suppliers, addressing existing gaps in electronic commerce research. The major theoretical contributions include the following:

(1) A comprehensive green supplier selection evaluation framework tailored to ECEs is introduced. This paper constructed an evaluation framework by considering five dimensions, which included cost, green competitiveness, service level, external environmental management, and corporate social responsibility. The proposed framework helps drive the green transformation of supply chains, enhance merchants’ environmental awareness and practices, and promote the supply and consumption of low-carbon and eco-friendly products.

(2) Rough set theory is combined with Dombi technology and BWM to ensure thorough evaluation in small amounts of data. In addition, by incorporating rough set theory, the consistency of multi expert judgments is enhanced. Dombi technology integrates expert information precisely to reduce uncertainty, while the BWM model is widely accepted for its simplicity and logic, effectively reducing bias in expert preferences. Their combination offers an accurate and flexible multi-criteria decision-making framework, enhancing consistency and reliability in assessments.

(3) This case study demonstrates the effectiveness and feasibility of the adopted rough-Dombi BWM model. This case study not only demonstrates the effectiveness of the employed rough-Dombi Bidirectional Mapping (BWM) model in addressing specific issues but also highlights its feasibility in practical applications. By comparing it with traditional methods, the model shows its advantages in dealing with complex datasets, especially when information is incomplete or uncertainty is present. The results indicate that the rough-Dombi BWM model can provide more accurate predictions and decision support, offering valuable insights for research and practice in related fields.

The application of mixed models also has certain limitations. Although rough numbers were used to reduce the subjective bias of experts, they cannot absolutely represent the consensus of stakeholders. The follow-up management of green suppliers on e-commerce platforms, such as whether to set up a corresponding incentive and restraint system, still needs to be further studied. More experts and scholars will help improve the selection and evaluation index system of green suppliers on e-commerce platforms and help e-commerce platforms meet challenges and seize opportunities. The comparative dimensions of this study focus on cross-category green performance evaluation, aligning with the platform-level goal of selecting “full-ecology green benchmarks”. While the unified evaluation framework possesses managerial utility, significant disparities exist across industries regarding environmental impact characteristics, green standard priorities, and sustainable development pathways, which this study has not adequately addressed in terms of their influence on evaluation outcomes, nor has it incorporated industry-specific environmental impact weight adjustment mechanisms. Furthermore, the selection of only one supplier per industry may inadequately represent the overall green performance levels within each respective sector and fails to account for the diversity of factors such as supplier scale and developmental stages. However, if the decision scenario involves traditional single-category procurement, it is recommended that researchers first use this framework to complete preliminary ranking within the category and then conduct a second-layer cross-category comparison as needed.