A Rough–Fuzzy Input–Output Framework for Assessing Mobility-as-a-Service Systems: A Case Study of Chinese Cities

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Combining existing urban transportation evaluation performance assessment frameworks and MaaS-related analyses, this study develops a MaaS performance evaluation framework covering economic support, infrastructure capacity, service integration and long-term sustainability, and implements an improved rough–fuzzy BWM to derive criteria weights and a rough–fuzzy DEA to evaluate MaaS maturity under approach to handle heterogeneous data, which can be used by policymakers to benchmark MaaS maturity across cities, diagnose efficiency gaps and support policy interventions.

Abstract

Mobility-as-a-Service (MaaS) has emerged as a sustainable solution that integrates multiple transport services through digital platforms. Across different cities, MaaS development exhibits variation in terms of economic support, infrastructure capacity, service integration level, and long-term sustainability orientation. The complexity of multistakeholder interactions and functional components in MaaS ecosystems calls for a more comprehensive performance evaluation framework. To address this, this study proposes a holistic four-dimensional indicator system covering economic, infrastructure, integration and sustainability aspects. To address the hybrid uncertainties arising from the heterogeneous information aggregated by the proposed framework, encompassing both quantitative statistics and qualitative expert judgements, a novel rough–fuzzy best–worst method (BWM) and rough–fuzzy data envelopment analysis (DEA) approach is developed. The empirical application to six representative core cities in China reveals that high performance in “Integration” and “Economic” dimensions plays a pivotal role in determining overall MaaS performance, and coordinated enhancement across dimensions is also important. Comparative and sensitivity analyses validate the framework’s robustness, offering policymakers a reliable tool for benchmarking MaaS maturity.

1. Introduction

With the development of society and the continuous expansion of cities, traditional public transit services with fixed schedules and limited coverage not only lack flexibility but also cannot meet the diverse travel needs of urban and suburban residents [1,2]. The increasing car ownership has contributed to heavier traffic congestion and serious urban environmental problems such as air pollution, noise, and excessive energy consumption [3]. These challenges have reduced travel satisfaction and increased urban environmental pressures, creating an urgent demand for sustainable and resilient mobility solutions, while advances in ICT have enabled shared mobility services, including car-sharing, supported by emerging digital technologies such as blockchain [4,5,6]. However, these mobility services are typically offered by different providers through siloed platforms. Based on this, Mobility-as-a-Service (MaaS) has been proposed to integrate multiple service platforms, allowing users to complete trip planning, booking, payment, and ticketing through one specific platform [7,8]. As a multifunctional and integrated mobility paradigm for seamless, sustainable, efficient, and affordable travel, MaaS relies on the advancement of its components and coordinated collaboration of multiple stakeholders such as public authorities, operators, platform providers, and users, which is reflected in different urban contexts where MaaS systems have been gradually established [9,10,11]. These heterogeneous development patterns and the rapid evolution of MaaS highlight the need for comprehensive evaluation frameworks for improving the current performance and guiding future development. According to previous studies, a systematic assessment of an ecosystem typically comprises four stages [3,9,12,13]: (1) establishment of an evaluation indicator system, (2) collection of alternatives’ performance with respect to each indicator, (3) determination of indicators’ weights, and (4) calculation of alternatives’ priorities. To construct such an indicator system, this study adopts a multidimensional perspective that synthesizes the existing evaluation approaches.

Integration, defined as the coordination of transport modes, travel information, and service functions, has been widely recognized as a central aspect of MaaS development [9,14,15,16]. As MaaS is expected to promote low-carbon, efficient, and socially inclusive mobility, sustainability is emphasized in its evaluation [13,17,18]. Beyond integration and sustainability, previous studies have also highlighted the great influence of governance policy support, the readiness of existing public transport systems, and broader urban economic conditions on the development of MaaS [3,11,19,20]. Overall, this indicates that MaaS evaluation should incorporate a broader range of institutional, infrastructural, and socioeconomic factors, a unified and holistic framework for which is still lacking.

The assessment of MaaS performance relies on two types of indicator data: quantitative hard metrics and qualitative soft metrics. While hard metrics can be directly derived from computational models or historical datasets, soft metrics inherently depend on expert panels to provide semantic evaluations due to their non-numerical nature. This hybrid indicator composition requires evaluation frameworks capable of simultaneously accommodating measurable and descriptive information. However, converting semantic assessments into numerical representations inevitably introduces dual sources of uncertainty [21]: individual linguistic vagueness arising from cognitive ambiguity in perception and reasoning, and group-level judgment variability resulting from divergent expert backgrounds, experiences, and perspectives [22]. These dual uncertainties undermine the fidelity and robustness of non-numerical performance representation in MaaS evaluation. Fuzzy set theory models individual linguistic vagueness through membership functions but tends to compress heterogeneous expert judgements into a single representative value in group decision-making, thereby obscuring stakeholder consensus. Rough set theory addresses this limitation by modeling judgment dispersion via lower and upper approximations, preserving interpersonal variability. By integrating rough sets with fuzzy representations, the resulting rough–fuzzy framework is able to capture both individual-level linguistic vagueness and group-level judgment uncertainty in a unified manner, leading to a more robust and inclusive evaluation of MaaS performance. Existing studies have yet to establish a systematic methodology that concurrently addresses these two types of uncertainty within a hybrid indicator framework, underscoring the necessity of integrated uncertainty management in MaaS performance assessment.

After the indicator information is aggregated, MaaS maturity assessment can be regarded as a multicriteria decision-making (MCDM) problem, which typically consists of two stages: criteria weighting and alternative priority [2,23]. Among existing MCDM approaches, for criteria weighting, the best–worst method (BWM) has an advantage in maintaining high consistency outputs with fewer comparison inputs and better compatibility with uncertainty handling techniques. For alternative ranking, the Data Envelopment Analysis (DEA) proves particularly well-suited for processing multiscale data encompassing both cost and benefit indicators, enabling efficient identification of optimal solutions through frontier-based benchmarking [21]. Although the integrated BWM-DEA framework shows significant promise for evaluating MaaS under hybrid information conditions, conventional models exhibit limitations in handling heterogeneous data types and fail to address dual uncertainties during linguistic evaluations [23,24,25]. Recent studies validate rough–fuzzy set theory as an effective mechanism for capturing such hybrid uncertainties in other MCDM contexts [24,25]. Thus, synthesizing rough–fuzzy sets with BWM-DEA presents a novel pathway for simultaneously resolving hybrid information complexity and multidimensional uncertainties in MaaS assessment.

Therefore, this study establishes an indicator system that not only emphasizes integration and sustainability but also incorporates economic and infrastructural factors, providing a comprehensive basis for evaluating MaaS maturity rather than isolated performance outcomes, and for supporting its sustainable and efficient evolution. Building on this framework, a hierarchical rough–fuzzy BWM-DEA approach is proposed, integrating the strengths of rough–fuzzy numbers in representing hybrid uncertainties with the BWM’s efficiency in determining optimal weights and the DEA’s capability in assessing relative efficiency as an explicit measure of MaaS maturity across multiple criteria. This approach allows the uniform treatment of hybrid types of data, including crisp values, interval values, and linguistic assessments, producing more stable and reliable maturity evaluation results. Through this improved method, the study quantifies MaaS maturity using efficiency scores and evaluates the relative maturity levels of MaaS systems across six core cities in China’s four urban clusters, enabling a clear understanding of their developmental stages and comparative strengths.

The remainder of this paper is structured as follows. Section 2 reviews the existing literature on MaaS evaluation indicators and methodologies. Section 3 outlines the proposed indicator framework completely, including the definition and calculation of each indicator. Section 4 introduces the proposed rough–fuzzy BWM-DEA methodology. Section 5 presents a case study involving six representative cities and includes a sensitivity analysis, confirming the robustness and stability of the proposed approach. Finally, Section 6 concludes the paper with limitations and future research directions.

2. Literature Review

2.1. MaaS Evaluation

The concept of MaaS (Mobility-as-a-Service) was first proposed in Heikkilä [26]. Concurrently, the establishment of the first MaaS operator, Whim [27], marked the first attempt to operationalize the MaaS concept. Since then, numerous cities and regions have initiated MaaS deployments, providing a rich empirical basis for subsequent research and [23,28,29,30]. MaaS is regarded as a pathway toward a low-carbon, resource-efficient, and socially inclusive transportation system gradually.

Motivated by the sustainability imperatives embedded in the Sustainable Development Goals (SDGs), increasing attention has been paid to the performance of MaaS systems across different regions and cities [31], as well as the role of MaaS in shaping sustainable travel behaviour [32]. In response, several studies have examined MaaS performance through various conceptual and methodological approaches. For instance, Kamargianni and Li [16] conducted a comprehensive review of existing MaaS schemes and first proposed a three-level evaluation framework to assess MaaS platforms according to their degree of functional integration. Furthermore, Sochor and Arby [15] introduced a topological structure and enriched the extent of MaaS evaluation by incorporating diverse service functionalities and travel modes, offering a useful classification tool and strategic reference for MaaS assessment and planning. The “Levels of MaaS Integration (LMI)” taxonomy was proposed by Lyons and Hammond [14] to evaluate MaaS systems in user adoption and long-term sustainability perspectives. Most evaluations primarily concentrate on functional and service integration with limited emphasis on other perspectives. Furthermore, Jorge M. Bandeiraa [18] broadened the scope through the inclusion of coverage and sustainability dimensions. With this respect, Nikolaidou and Papadopoulos [33] proposed a standardized evaluation framework comprising four core pillars: society, users, operators, and internal operations. Moreover, Orozco-Fontalvo and Soares Lopes [2] introduced IMPReSS (Information, Multimobility, Payment, Reservation, Subscription, and Societal goals), the binary coding approach designed to capture integration levels and societal orientation of the MaaS system. Recently, Núñez and Antoniou [9] proposed an index-based framework to assess the MaaS readiness that varies across countries due to differences in infrastructure, governance, capacity, and social context. As MaaS evaluation becomes more systematized, a coherent indicator system becomes essential for guiding its assessment, as discussed in the following [3,9,12,13].

2.2. MaaS Evaluation Indicator System

As discussed above, previous studies have adopted a structured, comprehensive, and multi-perspective evaluation framework to examine the dynamic, multistakeholder interactions of MaaS systems. These frameworks have proposed a wide range of indicators that support clearer assessments of MaaS developments and emerging opportunities [17]. Integration has emerged as the most widely recognized and commonly adopted prominent dimension. In parallel, sustainability has also been emphasized as a fundamental objective of MaaS. Additional perspectives have been examined across studies, typically measured through indicators such as public transport usage, vehicle ownership and usage rates, and the allocation of transport investments [3,9,12,13]. Since MaaS systems are built upon the existing urban transport system, a robust evaluation also requires attention to the underlying system conditions that influence how MaaS can be implemented and sustained in practice [30,34,35]. Although indicators used in both urban transport system assessments and MaaS evaluations have different forms, they can be summarized into two thematic dimensions: economic conditions and infrastructure readiness. Recognizing that the maturity of MaaS development is fundamentally constrained by these underlying urban capabilities, a robust evaluation must integrate both the functional performance and the foundational basis. Above all, a unified framework can be established to guide MaaS evaluation, encompassing four dimensions: economic, infrastructure, integration, and sustainability.

Existing research consistently identifies integration as a defining element of MaaS evaluation, and analyses of integration generally include three key aspects: travel mode integration, functional integration, and informational integration [15,16]. Modal integration refers to the inclusion of both public and private transport services, while functional integration means unified booking, ticketing, and payment mechanisms across different modes [14,36]. The essential aspect, informational integration, is the capability of ensuring the provision and interoperability of real-time data across platforms [37]. These components are commonly regarded as the foundational elements for assessing MaaS integration. Recent studies have further expanded the scope of this dimension to incorporate value-added service integration, such as personalization features, travel guarantees, and loyalty programs [12,33].

The economic dimension has been widely discussed in MaaS evaluation research. The financial capacity of a city plays an important role in supporting the construction and operation of MaaS, as well as the affordability of individuals, which influences service adoption and inclusiveness [2]. Economically advanced cities tend to possess greater capacity to invest in transport infrastructure, ICT systems, and platform integration technologies, which are foundational for MaaS operations [38,39]. Meanwhile, individual affordability determines the extent to which MaaS services are accessible, inclusive, and sustainable from the user perspective.

The infrastructure dimension has emerged as a critical dimension in MaaS evaluation as the implementation of the MaaS platform is a process of reallocating existing resources of the public transportation system, including infrastructure, information, and related elements, to the mobility platform [40,41]. MaaS was originally designed to increase the market share and utilization of public transport, while reducing the usage and reliance on private vehicles by offering seamless personalized mobility solutions and then reshaping user travel behavior [42]. Therefore, a robust and resilient public transportation infrastructure is critical to a MaaS platform.

Sustainability has been widely recognized as a foundational principle in MaaS research, reflecting the pursuit of balanced economic development, environmental responsibility, and social inclusion [43,44]. This principle provides clear direction and guidance for the development of urban transportation, particularly for the MaaS system [13,23]. Guided by the Sustainable Development Goals (SDGs) framework, the sustainability evaluation of a MaaS system aims to capture its ability to maintain long-term operational stability, achieve broad social acceptance, and promote environmentally friendly development [3]. Through the MaaS platform, low-carbon, integrated, and user-centered mobility services are promoted to advance the sustainability of urban transportation. At the same time, the development of urban transport in terms of policy support, technological, and so on, also plays a crucial role in the evolution of the MaaS system [45,46].

Above all, although many indicators have been identified in existing studies, their fragmented discussion underscores the need for a coherent and integrated framework for MaaS performance assessment.

2.3. MaaS Evaluation Methodology

MaaS evaluation has been examined through multiple methodological approaches in existing studies. Several studies have employed descriptive and conceptual analyses, where existing MaaS schemes are synthesized and classified according to proposed conceptual models [14,16]. Jorge M. Bandeiraa [18] proposed a framework-based scoring approach, where a fixed set of indicators is used to evaluate and compare MaaS systems through structured scoring and normalization. Questionnaire analysis and stated preference experiment are frequently employed to examine user acceptance and potential behavioral changes in response to different service attributes [47,48]. While these methods provide valuable insights, they often focus on isolated aspects and lack a unified, multidimensional evaluation framework. In contrast, MCDM methods offer a systematic and quantitative approach to integrating diverse indicators and supporting structured comparison [49]. This assessment process constitutes two core components: criteria weighting and alternative prioritization [2,23].

To determine the weights of evaluation criteria, existing studies have applied many multicriteria decision-making methods, including the Analytic Hierarchy Process (AHP) [12,50,51], Group AHP (GAHP) [52], DEMATEL [53], DEMATEL-based Analytic Network Process (DANP) [54], and the best–worst method (BWM) [46,55,56]. Among these methods, AHP and GAHP rely on a large number of pairwise comparisons, which may lead to inconsistency, especially as the number of criteria increases [23]; DEMATEL and DANP often require additional computational steps and are more suitable for structural analysis rather than direct weight derivation. BWM demonstrates distinct advantages: reduced dependency on pairwise comparison inputs, higher consistency in output results, and enhanced compatibility with uncertainty-handling techniques [57]. Therefore, BWM is adopted in this study as a reliable and transparent tool for criteria weight determination within the proposed evaluation framework.

Many methods have been employed for ranking alternatives, such as TOPSIS [58], PROMETHEE [59], gray VIKOR [54], and DEA [60,61]. Among these methods, DEA has been widely applied to assess the relative efficiency of alternatives in various fields. Unlike distance-based methods such as TOPSIS or gray VIKOR, or preference-based methods like PROMETHEE, DEA does not require the identification of an ideal solution or the specification of subjective preference functions, which will introduce arbitrariness, especially under hybrid and uncertain data conditions [21,60,62,63]. Instead, DEA compares the input–output efficiency relative to the empirically constructed efficiency frontier, making it particularly suitable for complex multicriteria performance evaluations. Therefore, this study adopts the BWM-DEA approach in weight determination and efficiency evaluation.

Traditional BWM-DEA models are unable to address hybrid data that involve both quantitative measurements and qualitative judgements [21,64]. Recent studies have introduced fuzzy set theory to process linguistic judgment data, which helps improve the capacity of the MCDM model to handle semantic vagueness [46,56,58]. However, fuzzy-based approaches typically aggregate group judgements into representative values, which may obscure inter-expert differences and introduce aggregation bias [65]. In parallel, rough set theory has been applied to preserve the dispersion of expert opinions by modeling lower and upper approximations, thereby reducing bias arising from consensus compression in group decision-making [66]. Since this study does not involve incomplete data, the gray system theory is not applicable in this context. By integrating the strengths of fuzzy set [67] and rough set [68] theories, rough–fuzzy set theory provides effective support for MCDM under hybrid conditions and has been widely adopted in related research [24,69,70]. This hybrid design jointly controls linguistic approximation bias at the individual level and aggregation bias at the group level, resulting in a more balanced representation of expert assessments and more robust MCDM outcomes under hybrid information conditions.

2.4. Research Gaps

Despite considerable progress in MaaS evaluation research, four critical gaps persist. First, recent studies adopt broader ecosystem perspectives, but much research still focuses on conceptual models with insufficient consideration of the urban transport systems that form the operational foundation of MaaS and the substantial city-development contextual differences that influence its implementation. Second, existing indicator systems are often analyzed dimension by dimension, lacking integrated tools for cross-city MaaS platform comparisons. Third, methodologies relying on single data types cannot process hybrid datasets from diverse sources required for a comprehensive MaaS assessment. Although recent studies have explored blockchain-enabled MaaS architectures to facilitate multistakeholder coordination and secure data exchange, systematic evaluation frameworks for benchmarking the performance and maturity of such systems remain absent [5,6]. Finally, city-level deployment studies are scarce, especially for Chinese urban contexts.

To bridge these gaps, this study (1) proposes a unified framework that integrates insights from existing research with the prevailing conditions of urban transport systems, allowing the evaluation framework to capture cross-city variation; (2) establishes a structured indicator system that consolidates dispersed evaluation indicators into four coherent dimensions: Economic, Infrastructure, Integration, and Sustainability; (3) develops an enhanced rough–fuzzy BWM-DEA method to handle hybrid data, heterogeneous data in both weighting and efficiency assessment; and (4) generates comparative assessments of MaaS implementation across representative Chinese cities.

3. MaaS Performance Indicator System and Calculation

Informed by the gaps identified in existing research and guided by the requirements of sustainable urban mobility, this study aims to evaluate MaaS development maturity through a unified indicator system. This system measures performance across four interconnected dimensions: Economic, Infrastructure, Integration, and Sustainability. These dimensions provide a holistic metric that captures the urban conditions supporting MaaS operations and the comprehensive level of urban MaaS maturity. Figure 1 illustrates the system-level structure of the MaaS performance evaluation framework, highlighting the interactions among key stakeholders and the four evaluation dimensions.

3.1. Economic Dimension

This dimension is assessed through three aspects: urban economic capacity, infrastructure investment efficiency, and user affordability. It reflects the economic conditions and cost structures that influence the feasibility, scalability, and sustained adoption of MaaS systems.

(1)

Urban economic capacity

From the perspective of urban economics, population size is regarded as a more representative indicator of urban scale compared to geographic area, as it indirectly reflects the diversity of transport demand and the frequency of information interaction [71,72]. In addition, the urban economic development level is measured by a composite economic development index, which is a reflection of local governments’ fiscal capacity and their ability to support service innovation, stakeholder coordination, and the advancement of smart mobility platforms [73,74].

(2)

Infrastructure in investment

Investment efficiency reflects the effectiveness of financial resources allocated to transport infrastructure projects, which are typically initiated and guided by the government and delivered or operated by relevant enterprises [75,76]. It is measured by the unit construction cost per commuter ($M{C}_{UCC}$) which represents the marginal cost ($\Delta I$) of accommodating an additional commuter ($\Delta N_C$). A lower $M{C}_{UCC}$ indicates a higher investment efficiency:

$$M{C}_{UCC}={\displaystyle \frac{\Delta I}{\Delta N_C}}$$

(1)

(3)

User cost

User cost refers to the financial and time expenditures during daily commute, typically from home to the Central Business District (CBD). It reflects the affordability and time efficiency of the MaaS system. The commuting cost ($C$) is calculated as the sum of time cost ($T_C$) and financial cost ($F_C$), following the Standard Urban Model framework [77]:

$$C=T_C+F_C$$

(2)

Time cost ($T_C$) is the product of commuting time ($t$) and the local minimum hourly wage standard ($w$):

$$T_C=t\times w$$

(3)

Financial cost ($F_C$) consists of transportation cost ($f_t$) and additional cost ($f_a$) during commuting, which includes parking fees, insurance costs, and other incidental expenditures:

$$F_C=f_t+f_a$$

(4)

$$f_t={\displaystyle \sum _{z=1}^n{s}_i}\times M_i$$

(5)

$$M_i=f(m_i,d)$$

(6)

where $s_i$ is the mode selection indicator (1 if mode $i$ is selected, 0 otherwise); $M_i$ stands for the cost associated with mode $i$, which is defined as a piecewise function of the selected transportation mode $m_i$ and the commuting distance $d$.

3.2. Infrastructure Dimension

The infrastructure dimension is designed to characterize the fundamental conditions of the urban transport system that support MaaS implementation. It provides a comprehensive assessment of transport demand, service supply, and operational efficiency, capturing both the scale and the utilization of existing transport infrastructure.

(1)

Transport demand

Transport demand is typically measured by passenger volume across various transport modes, reflecting the usage intensity of infrastructure and residents’ reliance on the urban mobility network [78]. This index is summed up by three types of passenger volumes, including the total public buses and electric buses, rail transit passenger volume, and taxi passenger volume. These three passenger volumes are calculated using the Weighted Moving Average (WMA) method, processing monthly data in 2023–2024, which assigns higher weights to more recent data so that it can capture both long-term trends and current conditions [79].

A fixed observation window of 15 months is used ($n=15$). Each time point $t$ (where $t=1$ denotes the earliest; $t=15$ denotes the most recent month) is assigned a linearly increasing weight to prioritize recency. Transport demand can be expressed by Equation (7):

$${\overline{V}}_{m_i}={\displaystyle \frac{{\displaystyle \sum _{t=1}^n{\omega }_t{V}_{m_{i}t}}}{{\displaystyle \sum _{\mathrm{t}=1}^n{\omega }_t}}}$$

(7)

where ${\overline{V}}_{{\mathrm{m}}_i}$ is the weighted monthly passenger volume for mode $i$; $V_{m_{i}t}$ represents the passenger volume for mode $i$ in month $t$; ${\omega }_{\mathrm{t}}$ is the time weighted assigned to month $t$ (${\omega }_{\mathrm{t}}=t$).

(2)

Transport demand

Transport supply represents the capability of the urban transport system to meet the needs of transport demand [80,81]. Such an index considers the operational buses’ ownership, number of bus lines, bus station coverage, car ownership, number of metro lines, transit mileage, and metro network density.

Operational bus ownership means the total number of operating public buses and electric buses. The number of bus lines reflects the total number of bus routes operating within a MaaS system. Bus station coverage reflects access to public bus services within a defined walkable distance (e.g., 500–800 m) from residential areas or key activity centers [82], selected as a more direct measure of service accessibility than mere station counts. Car ownership reflects the level of personal vehicle ownership. The number of metro lines refers to the total number of metro lines in a city. Rail transit mileage stands for the total length of rail transit lines, including subways, light rails, and other rail systems. Micromobility coverage is the spatial distribution of shared bicycle stations, reflecting the infrastructural completeness of the “first-mile” and “last-mile” segment of the urban transport system [83]. Metro network density is measured by the total length of metro lines per unit area of the city (e.g., $km/k{m}^2$), reflecting the spatial intensity and service coverage of the urban rail transit system [84]. Compared with alternatives like station density or accessibility indices, network density provides a more consistent macroscopic metric, as it relies on standardized official statistics and is less susceptible to variations in calculation methodologies or service radius definitions, which is expressed as follows:

$$D_{M{U}_j}={\displaystyle \frac{{\displaystyle \sum _{i\in U_j}{l}_i}}{A_{U_j}}}={\displaystyle \frac{L_{M{U}_j}}{A_{U_J}}}$$

(8)

where $l_j$ means the length of the metro line segment $i$ within the selected city $U_j$; $L_{M{U}_j}$ is the total length of all metro lines in the selected city $U_j$; $A_{U_j}$ is the total land area of the city $U_j$.

(3)

Transport efficiency

Transport efficiency reflects the ability of the transport system to enable urban trips with minimal travel time and disruptions [85]. In this study, transport efficiency is captured from two complementary aspects: travel time performance and transfer-related efficiency.

Travel Time Index (TTI) is adopted to assess the level of congestion across different cities. Compared to absolute delay metrics, TTI offers a standardized, dimensionless measure that eliminates biases arising from varying city sizes and road network scales, ensuring robust comparability [86]:

$$TTI={\displaystyle \frac{T_{\mathrm{peak}}}{T_{\mathrm{free}}}}$$

(9)

where $T_{\mathrm{peak}}$ is the average travel time observed during peak-hour periods (7:00–9:00 and 17:00–19:00 on workdays) compared to free-flow conditions ($T_{\mathrm{free}}$).

In addition, transfer-related efficiency is reflected by the number of transfer events experienced within a single trip. Frequent transfers are associated with additional waiting time, walking distance, and coordination costs between services, which reduce overall travel convenience [87]. This aspect is measured using Transfer Count ($TC$):

$$TC={\displaystyle \frac{P_{trip}+P_{transfer}}{P_{trip}}}$$

(10)

where $P_{trip}$ is the total number of passenger trips; $P_{transfer}$ stands for the total number of passengers who take transfers during their trips. Higher TC values indicate a greater transfer burden per trip and lower transport efficiency.

In addition, the commute time provides a direct metric of transport efficiency.

3.3. Integration Dimension

This study captures MaaS integration from five critical perspectives: construction planning, mode integration, payment integration, functionality integration, and data sharing, which collectively characterize the maturity of service integration and digital coordination in MaaS systems.

(1)

Mode integration

This index means the total number of integrated transport modes incorporated within the MaaS platform.

(2)

Functionality integration

Functionality integration means the degree to which core functions are integrated within the MaaS platform, with the topological structure shown in

Table 1. Logical structure of functionality integration.

Hierarchy	Functionality	Description
1	Data access and real-time updates	Provides information on multiple transport modes and the core function of basic data services.
2	Route planning	Offers users the travel routes and mode arrangements based on real-time travel needs and traffic data.
3	Seamless payment	Enables users to complete payments through a single interface, without switching between different applications.
4	Booking	Allows users to reserve rides through the platform, mainly for ride-hailing services, ensuring access to selected modes at specific times.
5	Package services	Combines two or more mobility services into a bundled offer that users can access through a subscription.
6	Travel-related services	Provides additional services such as car-ownership and parking services to improve convenience and efficiency.

. As a basic core function, payment integration refers to the total number of transport modes in the MaaS system that support payment through a single unified interface in the MaaS system. Both the functionality integration indicator and the construction planning indicator are evaluated using the binary chain approach proposed by [2]. This method first begins with the topological definition of the indicator’s components according to their level of integration or implementation, and then the resulting score (S) is computed as follows:

$$S={\displaystyle \sum _{i=0}^n{s}_i}\cdot 2^i$$

(11)

where $s_i\subset \{0,1\}$ represents whether the component at level $i$ is present, and $2^i$ reflets its complexity or position in the hierarchy.

(3)

Information integration

It is exploited to measure the extent of travel-related data exchange and interoperability of transport data, with the objective of supporting the functions and operational needs of the MaaS platform. In addition, the policy planning of information sharing is adopted to measure the extent of MaaS strategic policy formulation and the application scope of related projects, with a hierarchical structure shown in

Table 2. Hierarchical structure of MaaS implementation.

Hierarchy	Functionality	Description
1	MaaS development plan	A city or regional-level strategy or plan for MaaS implementation
2	Applications	Deployment of MaaS application or digital mobility platform
3	Mini program	Availability of MaaS services through third-party platforms such as WeChat
4	Implementation	Citywide deployment of the MaaS solution instead of pilot projects

.

3.4. Sustainability Dimension

The sustainability dimension evaluates the long-term viability of MaaS systems under environmental, technological, social, and institutional conditions. In this study, MaaS sustainability is assessed across four domains: green transportation, platform recognition, technology development, and policy support.

(1)

Green Transportation

From the perspective of green transportation, three indices are included for measuring green level: public transit reliance (PTR), annual per capita carbon emission (PUCE), and ownership of new energy vehicles.

PTR reflects the public’s willingness to adopt and accept public transit as a primary travel mode [48,88]. It is measured as the ratio of trips using public transit to the total number of trips:

$$PTR={\displaystyle \frac{N_{PT}}{N_{total}}}\times 100\%$$

(12)

where $N_{PT}$ is the average monthly passenger volume using public transit and $N_{total}$ means the total number of passengers across all transport modes.

Annual PUCE is the estimated amount of CO₂ emitted by an individual in a year from transport activities using public and private transport modes, measured as follows:

$$PUCE={\displaystyle \frac{{\displaystyle \sum _{i}P\times S_i\times D_i\times F_i}}{L_i\times {\eta }_i\times r_i\times c_i}}\times 365$$

(13)

where P stands for the urban population, S_i is the share rate of transport mode i, D_i represents average trip distance per trip, F_i is the average number of trips a person takes per day, L_i is the load factor, η_i is energy intensity, r_i is percentage of each energy type used by mode i, c_i is carbon content per energy unit.

Moreover, ownership of new energy vehicles refers to the total number of privately owned new energy vehicles, which reflects the level of clean energy adoption in the private vehicle sector [89,90].

(2)

Platform recognition

Platform recognition refers to the level of public satisfaction with the overall performance of the MaaS platform and is assessed through the satisfaction score of its primary interface for accessing MaaS services.

(3)

Technology development

This indicator is assessed from two aspects: technology innovation potential and smartness. Technology innovation potential is measured by the urban technological innovation ranking, which encompasses enterprise-led, government-led, and society-led innovation. Moreover, the smartness of city development is derived from the 2023 G20 Smart City Ranking, which provides a comprehensive reflection of a city’s smart development level and its readiness to support MaaS.

(4)

Policy support

Policy support stands for the extent of government commitment to the development and implementation of MaaS systems through strategic planning and regulatory framework [91]. Due to the heterogeneity of MaaS policy instruments and reporting practices across cities, policy support cannot be consistently quantified using a single standardized indicator. Therefore, we reviewed MaaS-related policy documents and adopted evidence-guided expert evaluation to ensure cross-city comparability.

Based on the above discussion, the complete indicator system is summarized in

Table 3. Overview of evaluation indicators with associated data characteristics and sources.

Dimension	Category	Criteria	BWM Index	DEA Index	Type	Data Resource Types
economic	Urban development level	Economic development	$D_{11}$	$C_1$	Hard	S1
		Urban scale	$D_{12}$	$C_2$	Hard	S1
	Construction cost	Construction cost	$D_{13}$	$C_3$	Hard	S1
	User cost	Commuting cost	$D_{14}$	$C_4$	Hard	S1
Infrastructure	Transport demand	Public bus and electric bus passenger volume	$D_{21}$	$C_{16}$	Hard	S1
		Rail transit passenger volume	$D_{22}$	$C_{17}$	Hard	S1
		Taxi passenger volume	$D_{23}$	$C_{18}$	Hard	S1
	Transport supply	Operating buses count	$D_{24}$	$C_{19}$	Hard	S1
		Car ownership.	$D_{25}$	$C_{20}$	Hard	S1
	Rail transit construction	Rail transit mileage	$D_{26}$	$C_{21}$	Hard	S3
		Number of metro lines	$D_{27}$	$C_{22}$	Hard	S1
		Metro network density	$D_{28}$	$C_{23}$	Hard	S1
	Urban surface public transportation construction.	Bus lines	$D_{29}$	$C_{24}$	Hard	S1
		bus station coverage	$D_{210}$	$C_5$	Soft	S3
		Traffic congestion	$D_{211}$	$C_8$	Hard	S1
	Convenience	Transit times	$D_{212}$	$C_6$	Hard	S1
		Commute time	$D_{213}$	$C_7$	Hard	S1
		Micro mobility service	$D_{214}$	$C_{25}$	Hard	S1
Integration	Platform construction progress.	MaaS platform construction plan	$D_{31}$	$C_9$	Hard	S1
	Platform construction progress.	Transport mode integration	$D_{32}$	$C_{26}$	Hard	S2
		Payment integration	$D_{33}$	$C_{27}$	Hard	S2
		Functionality integration	$D_{34}$	$C_{28}$	Hard	S2
	Data accessibility and sharing	Data sharing	$D_{35}$	$C_{10}$	Soft	S3
Sustainability	Green transportation	Public transit reliance	$D_{41}$	$C_{11}$	Hard	S1
		Annual per capita carbon emissions	$D_{42}$	$C_{12}$	Hard	S1
		New energy vehicle ownership	$D_{43}$	$C_{29}$	Hard	S1
	Platform recognition	Platform satisfaction	$D_{44}$	$C_{30}$	Hard	S4
	Technology development	Urban technology development potential	$D_{45}$	$C_{13}$	Hard	S1
		Smart city development	$D_{46}$	$C_{14}$	Hard	S1
	Policy support	Policy support	$D_{47}$	$C_{15}$	Soft	S3

. For clarity, the data resources of each indicator in Table 3 are denoted using a data source type code. S1 refers to statistical data obtained from official reports and public databases, including official statistical yearbooks, transport operation reports, and public transport databases [92,93,94,95,96,97,98,99]. Specific sources such as the National Bureau of Statistics of China, the Ministry of Transport statistical reports, and urban transport monitoring platforms are cited in the reference list [100,101,102,103]. S2 denotes platform-based indicators, constructed using a binary-chain identification process based on publicly available information. S3 represents expert evaluation informed by relevant policy documents, planning reports, and supporting materials, while allowing experts to incorporate their professional experience and judgment. S4 indicates app-based user data. Detailed data sources corresponding to each category are provided in the reference list [104,105].

4. MaaS Evaluation Methodology

Drawing on the indicator system established in Section 3, the MCDM process involves two main stages. The first stage is determining the criteria weights using the rough–fuzzy BWM, and the obtained criteria weights are applied to assess the efficiency and relative ranking of MaaS platforms using the rough–fuzzy DEA method.

The first stage relies on the decision-makers’ (DMs) judgments through linguistic terms data. In the second stage, the indicator dataset contains heterogeneous data types, including crisp data, expert-assessed linguistic-term data, and interval data. To standardize the data formats, this study adopts rough–fuzzy numbers (RFNs), which are integrated into both the BWM and DEA process [34]. This integration ultimately forms the rough–fuzzy BWM-DEA methodology used in this study.

4.1. Standardization of Hybrid Information into Rough–Fuzzy Number

Rough–Fuzzy Number (RFN) integrates fuzzy set theory and rough set theory to resolve the specific uncertainties encountered in MaaS evaluation. Expert judgements involve intrapersonal ambiguity caused by cognitive vagueness and interpersonal variability arising from group divergence. To address both, this framework employs fuzzy set theory to model linguistic vagueness into Triangular Fuzzy Numbers (TFN) and rough set theory to aggregate diverse opinions into approximation boundaries [35,55]. This synthesis standardizes data processing across both methodological stages: capturing comparison uncertainty in rough–fuzzy BWM to derive weights, and handling data imprecision in rough–fuzzy DEA to compute efficiency scores. To enable unified processing within the MCDM process, all these data types are standardized into RFNs through a series of transformation procedures, as illustrated in Figure 2.

4.2. Criteria Weights Determination Based on Hierarchical Rough–Fuzzy BWM

To determine the weights of evaluation criteria within a group of DMs, a hierarchical rough–fuzzy BWM is employed, combining the RFNs into the traditional crisp BWM. The calculation consists of six steps, shown in Figure 3.

(1)

Step 1: Establishment of evaluation criteria and hierarchical structure

Based on research and extensive investigations, including expert interviews, stakeholder consultations, and literature reviews, a structured set of evaluation criteria is developed, each of which is categorized into specific dimensions forming a two-level hierarchical structure. The full set of criteria can be represented as follows: $D=\{D_{11},D_{12},\dots ,D_{1n_1};\dots ;D_{i1},D_{i2},\dots ,D_{ij},\dots ,D_{i{n}_i};\dots ;D_{k1},D_{k2},\dots \dots D_{k{n}_k}\}$, where $D_k$ denotes the $k$-th dimension, $n_k$ is defined as the total number of sub-criteria in $D_k$ and $D_{ij}$ refers to the $j$-th criterion within the dimension $i$. The instances of criteria are presented in Table 3.

(2)

Step 2: Obtaining the best and worst criteria within and across dimensions

The decision-making group, composed of r DMs, the best (most important) criterion or dimension (B), and the worst (least important) criterion and dimension (W) at both hierarchical levels are identified. If two or more criteria (or dimensions) are selected as the best and the worst, one best and worst element can be selected randomly to execute the subsequent comparison steps.

(3)

Step 3: Constructing the group linguistic BO and OW vectors at both inter-dimensional and intra-dimensional levels

In this step, the BO (Best-to-Others) vectors and OW (Others-to-Worst) vectors are constructed at two levels. At the inter-dimensional level, DMs evaluate the relative importance of the best dimension compared to the other dimensions to form the BO vectors, and assess the importance of each dimension compared to the worst dimension to form the OW vectors:

$$B{O}_k^{\dim }=[p_{B_1}^k,p_{B_2}^k,\dots ,p_{B_i}^k,\dots p_{B_{n_{\dim }}}^k]$$

(14)

$$O{W}_k^{\dim }=[p_{{}_{1}W}^k,p_{{}_{2}W}^k,\dots ,p_{jW}^k,\dots ,p_{n_{\dim }W}^k]$$

(15)

where $p_{B_i}^k$ denotes the linguistic preference of the best dimension over dimension i, and $p_{iW}^k$ represents the preference of dimension j over the worst dimension, assessed by the k-th DM. Here, $k\in \{1,2,\dots ,r\}$, and $i\in \{1,2,\dots ,n_{\dim }\}$ where $n_{\dim }$ is the total number of dimensions.

The group BO and OW vectors from all r DMs are aggregated into metrics:

$$B{O}^{\dim }=\begin{array}{c}\\ B{O}_1\\ B{O}_2\\ ⋮\\ B{O}_r\end{array}\left[\begin{array}{cccc}{D}_1& D_2& \cdots & D_{n_{\dim }}\\ p_{B1}^1& p_{B2}^1& \cdots & p_{B{n}_{\dim }}^1\\ p_{B1}^2& p_{B2}^2& \cdots & p_{B{n}_{\dim }}^2\\ ⋮& ⋮& \ddots & ⋮\\ p_{B1}^r& p_{B2}^r& \cdots & p_{B{n}_{\dim }}^r\end{array}\right]$$

(16)

$$O{W}^{\dim }=\begin{array}{c}\\ O{W}_1\\ O{W}_2\\ ⋮\\ O{W}_r\end{array}\left[\begin{array}{cccc}{D}_1& D_2& \cdots & D_{n_{\dim }}\\ p_{1W}^1& p_{2W}^1& \cdots & p_{n_{\dim }W}^1\\ p_{1W}^2& p_{2W}^2& \cdots & p_{n_{\dim }W}^2\\ ⋮& ⋮& \ddots & ⋮\\ p_{1W}^r& p_{2W}^r& \cdots & p_{n_{\dim }W}^r\end{array}\right]$$

(17)

At the intra-dimensional level, the BO and OW vectors are constructed as follows:

$$B{O}_k^{(i)}=[p_{i{B}_1}^k,p_{i{B}_2}^k,\dots ,p_{i{B}_j}^k,\dots p_{i{B}_{n_i}}^k]$$

(18)

$$O{W}_k^{(i)}=[p_{i1W}^k,p_{i2W}^k,\dots ,p_{ijW}^k,\dots p_{i{n}_{i}W}^k]$$

(19)

Similarly, the group BO and OW vectors from all r DMs are aggregated into group-level metrics:

$$B{O}^{(i)}=\begin{array}{c}\\ B{O}_1\\ B{O}_2\\ ⋮\\ B{O}_r\end{array}\left[\begin{array}{cccc}{D}_{11}& D_{12}& \cdots & D_{1n_i}\\ p_{iB1}^1& p_{iB2}^1& \cdots & p_{iB{n}_i}^1\\ p_{iB1}^2& p_{iB2}^2& \cdots & p_{iB{n}_i}^2\\ ⋮& ⋮& \ddots & ⋮\\ p_{iB1}^r& p_{iB2}^r& \cdots & p_{iB{n}_i}^r\end{array}\right]$$

(20)

$$O{W}^{(i)}=\begin{array}{c}\\ O{W}_1\\ O{W}_2\\ ⋮\\ O{W}_r\end{array}\left[\begin{array}{cccc}{C}_1& C_2& \cdots & C_{n_i}\\ p_{i1W}^1& p_{i2W}^1& \cdots & p_{i{n}_{i}W}^1\\ p_{i1W}^2& p_{i2W}^2& \cdots & p_{i{n}_{i}W}^2\\ ⋮& ⋮& \ddots & ⋮\\ p_{i1W}^r& p_{i2W}^r& \cdots & p_{i{n}_{i}W}^r\end{array}\right]$$

(21)

where $p_{i{B}_j}^k$ is the preference of the best sub-criterion over sub-criterion j within dimension i, and $p_{ijW}^k$ is the preference of sub-criterion j over the worst sub-criterion under the same dimension. Here, $n_i$ represents the number of sub-criteria under dimension $D_i$.

(4)

Step 4: Transformation of hierarchical group linguistic judgments into rough–fuzzy vectors

The group BO and OW vectors in the linguistic version can be transformed into rough–fuzzy vectors at both the inter-dimensional and intra-dimensional levels by applying the transformation procedure shown in Figure 2:

$$RF(B{O}^{\dim })={\left[RF({\widehat{p}}_{B1}),RF({\widehat{p}}_{B2}),\dots ,RF({\widehat{p}}_{B{n}_{\dim }})\right]}_{1\times n_{\dim }}$$

(22)

$$RF(O{W}^{\dim })={\left[RF({\widehat{p}}_{1W}),RF({\widehat{p}}_{2W}),\dots ,RF({\widehat{p}}_{n_{\dim }W})\right]}_{1\times n_{\dim }}$$

(23)

$$RF(B{O}^{(i)})={\left[RF({\widehat{p}}_{iB1}),RF({\widehat{p}}_{iB2}),\dots ,RF({\widehat{p}}_{iB{n}_i})\right]}_{1\times n_i}$$

(24)

$$RF(O{W}^{(i)})={\left[RF({\widehat{p}}_{i1W}),RF({\widehat{p}}_{i2W}),\dots ,RF({\widehat{p}}_{i{n}_{i}W})\right]}_{1\times n_i}$$

(25)

Moreover, the preference of a criterion or dimension compared to itself is equivalent and can be expressed as follows: $RF({\widehat{p}}_{BB})=([1,1],[1,1],[1,1])$ and $RF({\widehat{p}}_{WW})=([1,1],[1,1],[1,1])$.

(5)

Step 5: Rough–fuzzy weight calculation at both hierarchical levels

Based on the rough–fuzzy BO and OW vectors at both levels, the rough–fuzzy weight calculation follows a unified process. For the given evaluation element (either dimensions or sub-criteria), let $RF({\widehat{w}}_j)$ denote its rough–fuzzy weight. The optimal set of weights, which is defined as $RF(\widehat{W})={\left[RF({\widehat{w}}_1),\dots ,RF({\widehat{w}}_j),\dots ,RF({\widehat{w}}_n)\right]}_{1\times n}$, can then be obtained by solving the corresponding rough–fuzzy optimization model:

$$\min \underset{j}{\max }\left\{\begin{array}{l}\left|{\displaystyle \frac{RF({\widehat{w}}_B)}{RF({\widehat{w}}_j)}}-RF({\widehat{p}}_{Bj})\right|,\\ \left|{\displaystyle \frac{RF({\widehat{w}}_j)}{RF({\widehat{w}}_W)}}-RF({\widehat{p}}_{jW})\right|\end{array}\right\}$$

(26)

where each rough–fuzzy weight $RF({\widehat{w}}_j)$ is expressed as a Rough–Fuzzy Number with six boundaries, denoted as $RF({\widehat{w}}_j)=([w_j^{lL},w_j^{lU}],[w_j^{mL},w_j^{mU}],[w_j^{uL},w_j^{uU}])$, based on the formulation of RFNs e and the BWM framework. The six boundaries are required to maintain logical ordering consistency, such that the lower, modal, and upper components are properly nested. In addition, the rough–fuzzy weights are defined within the interval [0, 1] and collectively satisfy the normalization requirements of the BWM, as summarized below:

$$\left\{\begin{array}{l}{w}_j^{lL}\le w_j^{lU},w_j^{mL}\le w_j^{mU},w_j^{uL}\le w_j^{uU};\\ w_j^{lL}\le w_j^{mL}\le w_j^{uL},w_j^{lU}\le w_j^{mU}\le w_j^{uU};\\ 0\le w_j^{lL},w_j^{lU},w_j^{mL},w_j^{mU},w_j^{uL},w_j^{uU}\le 1;\\ {\displaystyle {\sum }_{j=1}^n{w}_j^{lL}}\le {\displaystyle {\sum }_{j=1}^n{w}_j^{mL}}\le 1;\\ 1\le {\displaystyle {\sum }_{j=1}^n{w}_j^{mU}}\le {\displaystyle {\sum }_{j=1}^n{w}_j^{uU}};\\ sum(RF({\widehat{w}}_j))\le sum(RF({\widehat{w}}_B));\\ sum(RF({\widehat{w}}_j))\ge sum(RF({\widehat{w}}_W)).\end{array}\right.$$

(27)

where $sum(RF({\widehat{w}}_j))=w_j^{lL}+w_j^{lU}+w_j^{mL}+w_j^{mU}+w_j^{uL}+w_j^{uU}$.

In the above constraints, n denotes the number of evaluation elements involved in the current level of weight determination. If the optimization is conducted at the inter-dimensional level, n refers to the number of dimensions. If the optimization is performed at the intra-dimensional level, n corresponds to the number of sub-criteria within the respective dimension.

As a result of the optimization model formulated the rough–fuzzy weights of the criteria and dimensions are obtained. The weight of dimensions can be defined as follows:

$$RF({\widehat{W}}^{\dim })={\left[RF({\widehat{w}}_1),RF({\widehat{w}}_2),\dots ,RF({\widehat{w}}_{n_{\dim }})\right]}_{1\times n_{\dim }}$$

(28)

For each dimension $D_i$, the local weight vector of its sub-criteria is as follows:

$$RF({\widehat{W}}^{(i)})={\left[RF({\widehat{w}}_{i1}),RF({\widehat{w}}_{i2}),\dots ,RF({\widehat{w}}_{i{n}_i})\right]}_{1\times n_i}$$

(29)

Subsequently, the crisp weights $w_j$ of all evaluation elements are derived using the deroughening and defuzzification approach of RFNs [106].

(6)

Step 6: Global weight synthesis

Through Step 5, the crisp weights for both dimensions and their respective sub-criteria are obtained. The crisp weights can be represented as follows:

$$W^{\dim }=[w_1,w_2,\dots ,w_{n_{\dim }}],{\displaystyle \sum _{i=1}^{n_{\dim }}{w}_i}=1$$

(30)

$$W^{(i)}=[w_{i1},w_{i2},\dots ,w_{i{n}_i}],{\displaystyle \sum _{k=1}^{n_i}{w}_{n_i}^{(i)}}=1$$

(31)

Based on the hierarchical structure, the global weight is formulated as follows:

$$w_{ij}^{global}=w_i\cdot w_{ij}$$

(32)

where $w_i$ denotes the crisp weight of dimension $D_i$; $w_{ij}$ represents the local crisp weight of sub-criterion $D_{ij}$ within the dimension $D_i$ and $w_{ij}^{global}$ is the global crisp weight of sub-criterion $D_{ij}$, reflecting its overall importance in the hierarchical structure. Accordingly, the complete set of global weights can be expressed as follows: $W^{global}=\{w_{11}^{global},w_{12}^{global},\dots ,w_{1_{n_1}}^{global};\dots ;w_{i1}^{global},w_{i2}^{global},\dots ,w_{ij}^{global},\dots ,w_{i{n}_i}^{global};\dots ;w_{k1}^{global},w_{k2}^{global},\dots \dots w_{k_{n_k}}^{global}\}$, where each $w_{ij}^{global}$ corresponds to the synthesized weight of sub-criterion $D_{ij}\in D$.

As a result of the hierarchical rough–fuzzy BWM, a complete set of global weights is obtained for all criteria. The final output of the rough–fuzzy BWM is denoted as follows:

$$W^{\ast }=\{(D_{ij},w_{ij}^{global})|D_{ij}\in D\}$$

(33)

4.3. MaaS Performance Evaluation Based on Rough–Fuzzy DEA

In this study, MaaS maturity is explicitly operationalized as the efficiency score derived from the rough–fuzzy DEA model. Methodologically, DEA efficiency characterizes the relative effectiveness with which a city transforms its multidimensional urban capacities into integrated MaaS outcomes, with the corresponding computational procedure illustrated in Figure 4.

(1)

Step 1: Definition of DMU and criteria types

In this step, each city or region is regarded as a DMU. The assessment of MaaS performance is based on a set of hybrid indicators comprising multiple criteria, which are classified as input and output data [62,107,108].

The input data is cost-oriented, which should be minimized to improve the relative efficiency of DMUs. In contrast, output data are benefit-oriented and should be maximized. In this study, the classification of input and output variables is established. Furthermore, ranking-based indicators are assigned to the input set to enhance the distinguishing capacity of the DEA model and to maintain an appropriate balance between input and output variables, which is necessary in DEA to avoid efficiency inflation and loss of differentiation under a limited number of DMUs. The input and output variables consist of hybrid information, combining crisp data, interval data, and linguistic term data. The crisp and interval data are referred to as hard data, as they are derived from objective measurements and statistical records. In contrast, linguistic term data are classified as soft data, used for criteria that lack concrete or readily available quantitative values. The soft data are collected through the DMs’ judgment using a predefined set of linguistic terms (e.g., Very High, High, Medium, Low, Very Low). The complete classification of input and output criteria, along with their corresponding data types, is illustrated in Figure 5 and

Table 4. The TFN scale of linguistic variable for evaluating criterion importance and HPTs performance.

Criterion Evaluation			MaaS Data
Linguistic Term	Abbr.	TFN	Linguistic Term	Abbr.	TFN
Equally preferred	E	(1, 1, 1)	Extremely high	EH	(1, 1, 2)
Weakly preferred	W	(0.5, 1, 1.5)	Very high	VH	(1, 2, 3)
Fairly preferred	F	(1.5, 2, 2.5)	High	H	(2, 3, 4)
Very preferred	V	(2.5, 3, 3.5)	Medium	M	(3, 4, 5)
Significantly preferred	S	(3.5, 4, 4.5)	Low	L	(4, 5, 6)
			Very low	VL	(5, 6, 6)

.

(2)

Step 2: Construction of the rough–fuzzy decision matrix

Given the heterogeneity of the input and output variables, it is necessary to transform all three data types into a unified RFN representation using the method shown in Figure 2:

$$RF(x_{ij})=([x_{ij}^{lL},x_{ij}^{lU}],[x_{ij}^{mL},x_{ij}^{mU}],[x_{ij}^{uL},x_{ij}^{uU}])$$

(34)

$$RF(y_{pj})=([y_{pj}^{lL},y_{pj}^{lU}],[y_{pj}^{mL},y_{pj}^{mU}],[y_{pj}^{uL},y_{pj}^{uU}])$$

(35)

Once all input and output variables have been transformed into RFNs, the evaluation structure can be organized into an input matrix and an output matrix accordingly. There are t decision-making units (DMUs), each assessed based on m input criteria and s output criteria. The input matrix $RF(X)$ which includes all cost-oriented indicators, is defined as follows:

$$RF(X)=\left[\begin{array}{ccccc}RF(x_{11})& \cdots & RF(x_{1j})& \cdots & RF(x_{1t})\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ RF(x_{i1})& \cdots & RF(x_{ij})& \cdots & RF(x_{it})\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ RF(x_{m1})& \cdots & RF(x_{mj})& \cdots & RF(x_{mt})\end{array}\right]\in R^{m\times t}$$

(36)

where $RF(x_{ij})$ is the rough–fuzzy value corresponding to the i-th input criterion of the j-th DMU, with $i\in \{1,2,\dots ,m\}$ and $j\in \{1,2,\dots ,t\}$. Similarly, the output matrix captures all benefit-oriented indicators and is defined as follows:

$$RF(Y)=\left[\begin{array}{ccccc}RF(y_{11})& \cdots & RF(y_{1j})& \cdots & RF(y_{1t})\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ RF(y_{p1})& \cdots & RF(y_{pj})& \cdots & RF(y_{pt})\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ RF(y_{s1})& \cdots & RF(y_{sj})& \cdots & RF(y_{st})\end{array}\right]\in R^{s\times t}$$

(37)

where $RF(y_{pj})$ represents the rough–fuzzy value of the $q$-th output criterion for the $j$-th DMU, with $p\in \{1,2,\dots ,s\}$, $j\in \{1,2,\dots ,t\}$ and the total number of evaluation criteria satisfies $n_{cri}=m+s$. Therefore, the complete rough–fuzzy decision matrix $RF(V)$ is constructed by vertically concatenating the input and output matrices:

$$RF(V)=\left[\begin{array}{c}RF(X)\\ RF(Y)\end{array}\right]\in R^{n_{cri}\times t}$$

(38)

(3)

Step 3: Establishment of index correspondence between BWM and DEA based on criterion identity

To align with the DEA framework, the criteria derived from BWM are reclassified according to their input–output role. Therefore, it is necessary to establish a mapping between the reindexed DEA criteria $C=\{C_1,C_2,\dots \dots ,C_{n_{cri}}\}$ and their corresponding BWM-derived weights $D_{ij}\in D$. Each $C_k$ corresponds to one sub-criterion $D_{ij}$. A one-to-one mapping is established between the hierarchical structure and DEA-compatible labels:

$$f:D_{ij}\to C_k;D_{ij}\in D$$

(39)

$${\displaystyle \sum _{i=1}^{n_{\dim }}{\displaystyle \sum _{j=1}^{n_i}1=}}{n}_{cri}$$

(40)

Let $W_C={[w_{C_1},w_{C2},\dots ,w_{C_{n_{cri}}}]}^{\mathrm{T}}$ denote the column vector of criterion weights ordered according to DEA-compatible indices.

$$f:D_{ij}\to C_k;D_{ij}\in D$$

(41)

$$Q{Q}^T=I$$

(42)

where the matrix Q serves as a transformation operator and $Q\in R^{n_{cri}\times n_{cri}}$.

(4)

Step 4: Construct the weighted rough–fuzzy decision matrix

Since all the elements (inputs and outputs) in the initial decision-making matrix have been converted into the RFNs forms $RF({\widehat{x}}_{ij})$ and $RF({\widehat{y}}_{qj})$. The weighted rough–fuzzy decision-making matrix is constructed by multiplying the rough–fuzzy decision matrix $RF(V)$ and the globally transformed weight vectors derived in Step 3. The weighted rough–fuzzy input $RF({\widehat{x}}_{ij}^{\ast })$ for the j-th DMU under the i-th input criterion is computed by the following:

$$\begin{array}{ll}\hfill RF({\widehat{x}}_{ij}^{\ast })& =w_{C_i}\times RF({\widehat{x}}_{ij})\hfill \\ & =\left[\left(w_{C_i}{x}_{ij}^{lL},w_{C_i}{x}_{ij}^{mL},w_{C_i}{x}_{ij}^{uL}\right),\left(w_{C_i}{x}_{ij}^{lU},w_{C_i}{x}_{ij}^{mU},w_{C_i}{x}_{ij}^{uU}\right)\right]\hfill \\ & =\left[\left(x_{ij}^{\ast lL},x_{ij}^{\ast mL},x_{ij}^{\ast uL}\right),\left(x_{ij}^{\ast lU},x_{ij}^{\ast mU},x_{ij}^{\ast uU}\right)\right]\hfill \end{array}$$

(43)

where $w_{C_i}$ is the global weight of the i-th criterion derived from the rough–fuzzy procedure. Specially, $w_{C_i}$ corresponds to the defuzzified representation of the rough–fuzzy weight $RF({\widehat{w}}_i)$, ensuring that the preference information elicited in the weighting stage is consistently embedded into the DEA evaluation. Moreover, $RF({\widehat{y}}_{pj}^{\ast })$ are calculated using the corresponding global output weights in an identical manner.

(5)

Step 5: Establish a rough–fuzzy DEA model to prioritize DUMs

According to the BCC model structure and the properties of rough–fuzzy numbers, each DMU is assessed by minimizing its rough–fuzzy efficiency score subject to RFN-based input and output constraints:

$$\begin{array}{l}\min RF({\widehat{\theta }}_o)\\ s.t.\\ \left\{\begin{array}{l}{\displaystyle \sum _{j=1}^{t}RF({\widehat{\xi }}_j)RF(x_{ij}^{\ast })}\le RF({\widehat{\theta }}_o)RF(x_{io}^{\ast }),\forall i\\ {\displaystyle \sum _{j=1}^{t}RF({\widehat{\xi }}_j)RF({\widehat{y}}_{pj}^{\ast })}\ge RF({\widehat{y}}_{po}^{\ast }),\forall p\\ {\displaystyle \sum _{j=1}^t{\xi }_j}=1,RF({\widehat{\xi }}_j)\ge 0,\\ j=1,\dots ,t.\end{array}\right.\end{array}$$

(44)

where $RF({\widehat{\theta }}_o)$ stands for the rough–fuzzy efficiency score of the DMU_o under evaluation, $RF(x_{io}^{\ast })$ and $RF(y_{po}^{\ast })$ represents the i-th rough–fuzzy input and the p-th rough–fuzzy output of DMU_o, respectively. $RF({\widehat{\xi }}_j)$ refers to the rough–fuzzy peer contribution coefficient associated with DMU_j, which characterizes its relative share in forming the convex reference combination used to evaluate DMU_o within the rough–fuzzy DEA framework and ${\xi }_j$ refers to the crisp value of $RF({\widehat{\xi }}_j)$. In order to linearize and minimize the deviation margin, the objective and first constraint can be rewritten as follows:

$$0\le RF({\widehat{\theta }}_o)RF({\widehat{x}}_{io}^{\ast })-{\displaystyle \sum _{j=1}^{t}RF({\widehat{\xi }}_j)RF({\widehat{x}}_{ij}^{\ast })}\le {\alpha }_o^{rf},\forall i$$

(45)

where ${\alpha }_o^{rf}$ is a deviation variable which is introduced to ensure the minimum value of $RF({\widehat{\theta }}_o)$. Then, the objective function $\min RF({\widehat{\theta }}_o)$ can be transformed as $\min {\alpha }_o^{rf}$.

$$\begin{array}{l}\min {\alpha }_o^{rf}\\ s.t.\\ \left\{\begin{array}{l}0\le RF({\widehat{\theta }}_o)RF({\widehat{x}}_{io}^{\ast })-{\displaystyle \sum _{j=1}^{t}RF({\widehat{\xi }}_j)RF({\widehat{x}}_{ij}^{\ast })}\le {\alpha }_o^{rf},\forall i\\ {\displaystyle \sum _{j=1}^{t}RF({\widehat{\xi }}_j)RF({\widehat{y}}_{pj}^{\ast })}\ge RF({\widehat{y}}_{po}^{\ast }),\forall p\\ {\displaystyle \sum _{j=1}^t{\xi }_j}=1,RF({\widehat{\xi }}_j)\ge 0,\\ j=1,\dots ,t.\end{array}\right.\end{array}$$

(46)

Based on the properties of RFNs and the structure of model constraints, the original nonlinear model can be rewritten in an equivalent linear form. For detailed mathematical formulation and boundary-level optimization, readers are referred to [106]. By solving this set of constraints, the optimal rough–fuzzy efficiency set of all DMUs can be defined as ${\left\{RF({\widehat{\theta }}_1),\dots ,RF({\widehat{\theta }}_j),\dots ,RF({\widehat{\theta }}_t)\right\}}_{1\times t}$. Furthermore, by applying the deroughness and defuzzification procedures to the RFNs, the crisp efficiency value ${\theta }_j$ of the j-th DMU (i.e., city or region) is obtained, allowing for the final prioritization of urban MaaS performance.

5. Case Study

5.1. Case Cities

Urban clusters in China have several structural advantages that create favorable conditions for the development of MaaS, including concentrated transport infrastructure, policy coordination mechanisms, intensive inter- and intra-city travel demand, and the catalytic role of core cities in driving regional mobility innovation and resource integration in shaping coordinated regional transport development [37]. Considering these advantages, in this study, six representative Chinese cities are selected for performance evaluation: Beijing, Shanghai, Tianjin, Guangzhou, Shenzhen, and Chongqing, drawn from key national urban agglomerations including Beijing–Tianjin–Hebei (BTH), Yangtze River Delta (YRD), Pearl River Delta (PRD), and the Chengdu–Chongqing urban cluster [38,39]. As shown in Figure 6, the selected cities are located in the red-highlighted zones and serve as core cities within their respective urban clusters. In this role, they concentrate economic activities, coordinate regional transport systems, and lead the implementation of integrated smart mobility initiatives [109]. Moreover, the red-zone core cities exhibit relatively similar levels of economic capacity, transport infrastructure provision, and institutional support for digital mobility systems, which provides a consistent basis for evaluating differences in MaaS maturity and operational efficiency.

Other important urban centers located in the yellow-highlighted zones, such as Xi’an and Harbin, also play significant roles within their respective urban clusters. However, their overall urban development conditions differ more from those of the selected core cities. Including cities with markedly different baseline conditions in the same benchmarking group could obscure efficiency-related differences by introducing large structural disparities. Therefore, this study focuses on the selected red-zone cities to ensure a more coherent and interpretable efficiency comparison of MaaS maturity across cities.

5.2. Evaluation Results

In this study, the decision-making team includes a professor specializing in MaaS, three senior transportation researchers, and a government official. These experts were selected based on their professional involvement in MaaS-related research, planning, or policy implementation. Each expert has over five years of experience in their respective domains, denoted as DM1–DM5. Based on the consensus of the DMs, the best and worst criteria were selected at each level of the proposed indicator system. The resulting BO and OW vectors (Tables S1–S5 in Supplementary Material) are converted into RFNs following the rules defined in Table 4 and the procedure illustrated in Figure 2 and used as input to the hierarchical rough–fuzzy BWM model. By applying the global weights of all sub-criteria were obtained and are presented in

Table 5. Raw data of the 30 MaaS criteria for six cities.

Types	Criterion	Unit	${\mathit{A}}_1$(Beijing)	${\mathit{A}}_2$(Shanghai)	${\mathit{A}}_3$(Tianjin)	${\mathit{A}}_4$(Shenzhen)	${\mathit{A}}_5$(Guangzhou)	${\mathit{A}}_6$(Chongqing)
Input (Cost Criteria)	$C_1$	Ranking No.	2	1	6	3	4	5
	$C_2$	Ranking No.	3	2	6	5	4	1
	$C_3$	CNY	(22.9364, 46.6764)	(18.0000, 49.9800)	(16.6900, 38.0760)	(15.3200, 34.1200)	(16.16360, 41.3800)	(16.0000, 32.6200)
	$C_4$	10,000 CNY	36	26	25	15	23	20
	$C_5$	/	VL, L, M, H, H	EH, VL, VH, M, M	H, EH, L, L, VL	VH, VH, EH, EH, EH	L, M, H, VH, VH	M, H, VL, VL, L
	$C_6$	/	1.644	1.617	1.554	1.549	1.593	1.521
	$C_7$	min	47	40	39	36	38	40
	$C_8$	/	2.125	1.928	1.682	1.583	1.958	1.990
	$C_9$	Ranking No.	2	1	5	4	3	6
	$C_{10}$	/	VL, L, VL, VL, L	VH, M, H, VH, H	L, H, M, L, VL	H, VH, EH, EH, EH	M, VL, L, M, M	EH, EH, VH, H, VH
	$C_{11}$	Ranking No.	5	2	4	1	3	6
	$C_{12}$	Ton	0.45	0.31	0.35	0.33	0.32	0.40
	$C_{13}$	Ranking No.	1	3	5	2	4	6
	$C_{14}$	/	1	1	2	1	1	2
	$C_{15}$	/	VH, EH, EH, VH, EH	EH, VH, VH, H, H	L, L, VL, L, L	M, M, H, M, VH	H, H, M, EH, M	VL, VL, L, VL, VL
Output (Benefit Criteria)	$C_{16}$	10,000 Person-times Million	16,434.6917	9209.4500	4051.9083	6798.2474	9030.0452	17,089.5583
	$C_{17}$		28,903.05830	30,913.44170	4951.93330	23,614.97758	26,535.31730	11,531.06670
	$C_{18}$		6321.00	8505.00	3007.00	7362.87	9817.93	10,894.00
	$C_{19}$	veh	23,079	17,645	13,268	37,379	15,572	13,968
	$C_{20}$	10,000 veh	622.4	475.4	372.0	382.2	331.0	563.6
	$C_{21}$	km	808.5	881.9	295.0	567.8	680.1	462.7
	$C_{22}$	/	27	22	9	18	22	11
	$C_{23}$	/	4.804	5.243	4.919	5.249	4.147	4.728
	$C_{24}$	/	0.9615	0.9332	0.9000	0.9363	0.9082	0.8164
	$C_{25}$	/	0.406	0.349	0.311	0.392	0.332	0.172
	$C_{26}$	/	4	5	0	2	3	0
	$C_{27}$	/	2	7	0	2	5	0
	$C_{28}$	/	0.8425	0.9370	0.0000	0.0630	0.7790	0.0000
	$C_{29}$	1000 veh	61.70	128.80	23.20	86.00	38.00	20.00
	$C_{30}$	/	4.90	4.10	0.00	0.00	2.20	0.00

, serving as inputs for the subsequent DEA evaluation.

As shown in the Equations, the criteria are initially indexed by dimension in the BWM process and reindexed for DEA. The DEA uses these updated labels $C_k$. The hybrid indicator dataset of six selected cities is presented in Table 5. Hard criteria (i.e., $C_1$, $C_2$, $C_3$, $C_4$ $C_6–C_9$,$C_{10}–C_{14}$,$C_{16}–C_{30}$) are derived from statistical official sources. Soft criteria (i.e., $C_5$, $C_{10}$, $C_{15}$) are evaluated through DMs linguistic evaluations. These criteria are divided into input ($C_1–C_{15}$) and output ($C_{16}–C_{30}$) variables, as shown in Figure 5. Specifically, indicators expressed as rankings (e.g., $C_9$, $C_{11}$, $C_{13}$), with smaller values corresponding to higher levels of performance. On this basis, these indicators are incorporated as inputs in the DEA model, which also contributes to maintaining a balanced input–output structure given the limited number of DMUs. The original hybrid data of each MaaS alternative with respect to each criterion in Table 5 are transformed into RFNs according to the procedure in Figure 2. Following the methodology outlined in Figure 4, the rough–fuzzy DEA was applied to compute the performance scores. The final efficiency results and rankings are derived and summarized in

Table 6. Efficiency scores obtained by rough BWM-DEA, fuzzy BWM-DEA, and rough–fuzzy BWM-DEA.

	Rough BWM-DEA		Fuzzy BWM-DEA		Rough–Fuzzy BWM-DEA
	Efficiency Scores	Rank	Efficiency Scores	Rank	Efficiency Scores	Rank
Beijing	0.2352	2	0.2248	2	0.1944	4
Shanghai	0.2345	4	0.2243	3	0.1948	2
Tianjin	0.0340	5	0.0627	5	0.1936	5
Shenzhen	0.2407	1	0.2251	1	0.1953	1
Guangzhou	0.2352	4	0.2226	4	0.1947	3
Chongqing	0.0205	6	0.0405	6	0.0272	6

.

Figure 7 presents the obtained weights of each dimension, i.e., Economic, Infrastructure, Integration, and Sustainability. It can be seen that Integration emerges as the most important dimension, contributing 40.88%. This reflects that Integration plays a central role not only in the conceptualization but also in the implementation of MaaS, as it enables the consolidation of multiple transport modes and services into a unified platform. The dimensions of Economic (24.38%) and Infrastructure (23.81%) follow closely, receiving nearly equal weights. These two dimensions play fundamental roles in the implementation of MaaS and are regarded as prerequisites for achieving operational stability and scalability. Although Sustainability receives the lowest weight (10.9%), it remains a critical long-term strategic objective.

A more detailed view is provided at the level of individual criteria, as shown in Figure 8. Data sharing ($D_{35}$, 0.103) ranks first among all criteria. It is closely followed by Payment integration ($D_{33}$ 10, 0.084), Function integration ($D_{34}$, 0.083), and Mode integration ($D_{32}$, 0.084), all of which fundamentally depend on effective data sharing, underscoring the pivotal role of integration in MaaS performance. Economic-related indicators also feature prominently, with Economic development ($D_{11}$, 0.096) ranking second overall, and Construction cost ($D_{14}$, 0.069) and Commuting cost ($D_{14}$, 0.053) receiving substantial weights. These results highlight that, beyond technical integration, the macroeconomic environment and user affordability are critical enablers of MaaS adoption and scalability. Indicators within the Infrastructure and Sustainability dimensions hold comparatively lower individual weights but provide the necessary operational foundation and long-term resilience for MaaS systems.

As shown in Table 6, the efficiency score is adopted to quantify MaaS development maturity and reflect systematic differences in MaaS maturity across cities. Shenzhen achieves the highest at 0.1953, followed by Shanghai at 0.1948 and Guangzhou at 0.1947, indicating a relatively high level of MaaS maturity characterized by effective integration and coordinated resource utilization. Beijing at 0.1944 and Tianjin at 0.1936 exhibit slightly lower efficiency, suggesting that their MaaS systems are at an intermediate maturity level. In contrast, Chongqing at 0.0272 reveals a substantial maturity gap compared to the leading group. In the DEA process, as relative efficiency measures, they are highly sensitive to the performance of the leading benchmarks. The substantial gap between the leaders and Chongqing does not indicate insufficient infrastructure endowment in Chongqing, but it reflects a lower efficiency in transforming existing resources into high-weight MaaS maturity outcomes, relative to the efficiency frontier defined by Shenzhen.

The empirical results indicate that differences in MaaS maturity across cities are primarily driven by their ability to translate foundational urban conditions into integrated MaaS service outcomes. Cities such as Shenzhen, Shanghai, and Guangzhou exhibit relatively high levels of MaaS maturity, as they combine strong economic foundations with advanced integration capabilities. In these cities, digital integration, data sharing, and unified payment mechanisms enable the effective organization of multimodal services, while sustainability-related factors, including green travel behavior, user acceptance, technological readiness, and policy support, provide a stable basis for continuous MaaS operation.

By contrast, Beijing and Tianjin demonstrate a different maturity pattern. Although both cities possess strong infrastructural foundations, their MaaS maturity remains constrained by relatively weaker integration performance. In addition, the insufficient coordination between integration progress and sustainability-related aspects, such as platform recognition and policy alignment, further limits the consolidation of MaaS maturity. This suggests that infrastructure-oriented advantages alone are insufficient to achieve higher MaaS maturity without synchronized advancement in service integration, digital coordination, and sustainability support.

Chongqing represents an earlier stage of MaaS maturity. Despite having relatively strong physical infrastructure and certain service provisions, its overall maturity level is restricted by weaker performance in high-weight economic and integration dimensions. At the same time, limited outcomes in sustainability-related indicators, including green transport adoption and institutional support, constrain the stable operation and long-term viability of MaaS services. This indicates that existing urban conditions have not yet been effectively transformed into integrated, affordable, and sustainable MaaS services.

Overall, the results highlight that MaaS maturity is not determined by the absolute scale of urban resources, but by the efficiency with which economic, infrastructural, integration, and sustainability-related capacities are jointly transformed into integrated MaaS service outcomes. While integration and economic dimensions play a dominant role in shaping current maturity levels, sustainability serves as a critical supporting dimension that ensures the stability, social acceptance, and long-term operability of MaaS systems. Therefore, enhancing MaaS maturity requires prioritizing improvements in high-weight integration and economic dimensions, together with continuous reinforcement of sustainability-oriented practices to support resilient and low-carbon MaaS development.

5.3. Comparison and Sensitivity Analysis

To demonstrate the advantages of the proposed rough–fuzzy BWM-DEA, comparisons are conducted from two perspectives in this study. The first comparison focuses on fuzzy BWM, rough BWM, and rough–fuzzy BWM, using the same group linguistic judgment for assessing criteria weights. The second comparison is conducted using rough DEA, fuzzy DEA, and rough–fuzzy DEA under two types of weight distributions. To address uncertainty in expert judgment, three methods are commonly applied: fuzzy numbers to model vagueness in expert preferences, rough numbers to capture boundary imprecision, and rough–fuzzy numbers that combine both.

Firstly, as shown in Figure 9, compared with the rough BWM and fuzzy BWM, the proposed rough–fuzzy BWM provides a more balanced and inclusive weight distribution. Both fuzzy BWM and rough BWM tend to underestimate the weights of non-dominant criteria, as further confirmed in Figure 10a. For instance, according to the results of these three approaches, $C_1$, $C_{10}$,$C_{26}$, $C_{27}$ and $C_{28}$ are the highest important criteria, whereas $C_{24}$, $C_{29}$ are the lowest. In contrast to fuzzy BWM and rough BWM, the rough–fuzzy BWM approach shows less disparity between the highest and lowest importance. Furthermore, Figure 10b shows that, unlike the fuzzy BWM and rough BWM curves, which present more pronounced fluctuation, such as $C_{10}$, $C_{26}$ and $C_{28}$, rough–fuzzy BWM produces a smoother curve. It validates its advantage in capturing hybrid uncertainty while generating balanced weights that preserve the essential information of the evaluation.

Secondly, the rough–fuzzy DEA demonstrates greater robustness and stability under varying weight distributions compared to the rough DEA and fuzzy DEA, as shown in Figure 11. The Standard Sensitivity Index (SSI) is employed to measure the sensitivity of results to input weight variations by capturing changes in efficiency scores and rankings with 31 cases. Case 1 assigns equal weights (0.0333) to all criteria, while Cases 2–31 assign a dominant weight (0.35) to one criterion and equal weights (0.0224) to the remaining 29 criteria. As shown in Figure 11a, the SSI values of the rough DEA and fuzzy DEA are significantly higher than the rough–fuzzy DEA, especially in Tianjin and Chongqing, where the SSI values surpass 0.2, indicating strong sensitivity to weight variation. In contrast, rough–fuzzy DEA has the lower SSI values and maintains remarkable stability across all cities. Figure 11b shows that the rough–fuzzy DEA is slightly higher than the rough DEA and fuzzy DEA in the ranking-based SSI, indicating that small changes in priority values can lead to ranking adjustment. Moreover, rough–fuzzy DEA exhibits lower variability compared to the rough DEA and fuzzy DEA, except for Chongqing, whose efficiency scores are significantly lower than those of other cities, resulting in a stable ranking at the sixth position across all weight conditions. Therefore, rough–fuzzy DEA better supports decision-making by delivering more stable results under uncertainty.

Rough–fuzzy BWM improves the robustness and balance of weight allocation, while rough–fuzzy DEA enhances the stability of evaluation results. The proposed rough–fuzzy BWM-DEA approach thus offers a more comprehensive and reliable framework for performance assessment under hybrid uncertainty. As shown in Table 6, while all three methods consistently identify Shenzhen and Chongqing as the best and worst performers, rough–fuzzy BWM-DEA demonstrates notably different efficiency scores compared to the other two methods.

6. Conclusions

This study proposes a holistic evaluation framework for assessing MaaS maturity across cities, where maturity is understood as the system-level effectiveness of transforming urban conditions into integrated MaaS services. The proposed rough–fuzzy BWM-DEA framework effectively integrates qualitative and quantitative indicators, accommodating hybrid data types and addressing uncertainty in expert judgments. The empirical application to six selected cities identifies Shenzhen as the leader, followed by Shanghai, Guangzhou, Beijing, Tianjin, and Chongqing. High performance in Integration and Economic dimensions is strongly associated with better performance scores, confirming their central role in MaaS development. These findings provide valuable insights for policymakers and urban planners in formulating targeted strategies to enhance MaaS systems.

This research constructs a multidimensional indicator system with thirty criteria spanning four key domains: economic foundations, infrastructure readiness, integration capabilities, and sustainability metrics. This comprehensive structure enables holistic assessment of Mobility-as-a-Service (MaaS) system performance. To process heterogeneous evaluation data, an integrated rough–fuzzy BWM-DEA methodology is proposed, synergizing three analytical strengths: (1) uncertainty modeling by using rough set theory and fuzzy logic to jointly capture hybrid uncertainties in linguistic and numerical data; (2) weight optimization by applying BWM to efficiently derive criterion weights with minimal pairwise comparisons; and (3) efficiency benchmarking with exploiting DEA for evaluating relative efficiency across multidimensional criteria. This advanced framework uniformly processes exact numerical data, range-based inputs, and qualitative evaluations, enhancing result stability and precision compared to conventional deterministic approaches.

This study provides valuable guidance for policy recommendations specific to each city’s inherent conditions, supporting more effective and sustainable MaaS planning and implementation across China’s leading urban clusters. The comprehensive comparisons among the selected six cities provide further insights into relative strengths and weaknesses among cities, supporting more targeted and differentiated recommendations for improving MaaS planning and implementation in each urban cluster.

Based on the global weight analysis derived from the hierarchical rough–fuzzy BWM process and validated through DEA benchmarking and sensitivity analysis, integration-related criteria consistently exhibit a prominent contribution to MaaS performance. This finding highlights the importance of effective coordination mechanisms among multiple transport services and stakeholders. In this context, recent studies have explored the use of emerging digital technologies, such as blockchain, as supporting tools to facilitate trusted data sharing, inter-organizational coordination, and integrated payment processes within MaaS ecosystems. While such technologies fall beyond the methodological scope of the present evaluation framework, they reflect an important application trend that may further reinforce integration-related performance in future MaaS implementations. Accordingly, strengthening integration capabilities, together with sustained economic support and balanced infrastructural and sustainability development, remains central to advancing resilient and mature MaaS systems [5,6,40]. Moreover, economic strength is also crucial for supporting necessary infrastructure and service upgrades. Additionally, balanced development of infrastructure capabilities and continuous sustainability efforts are essential to achieve resilient, efficient, and user-centered MaaS systems. Cities should not only focus on strengthening unique integration aspects of MaaS but also on building a solid economic foundation, improving supporting infrastructure, and embedding sustainability principles into long-term mobility planning.

Above all, this study demonstrates several strengths. It establishes a comprehensive indicator system that integrates both quantitative and qualitative factors and proposes an advanced rough–fuzzy hierarchical BWM-DEA approach. This method effectively captures hybrid uncertainties and provides robust and nuanced evaluation results across cities.

Furthermore, future research would focus on both methodological improvements and broader applications. First, expanding the set of expert-based qualitative indicators could strengthen the credibility and richness of evaluation results. Second, future investigations could expand the geographical scope of application by incorporating additional cities, such as Xi’an and Harbin, as well as international metropolises like Singapore and Paris. For efficiency-based evaluation, more meaningful comparisons can be achieved when cities with broadly comparable overall conditions are benchmarked within the same analytical group. Applying the proposed framework to different urban contexts under this comparability principle would help further validate its robustness and general applicability in assessing MaaS maturity. Third, extending the evaluation to a longitudinal analysis is crucial. As MaaS systems mature, future studies could track performance evolution over time and integrate broader influencing factors, such as the advancement of ICT infrastructure capabilities (e.g., 5G networks and IoT sensor coverage) and macro-policy dynamics. Since this research includes relatively few expert-evaluated qualitative indicators in the input and output data, the potential of the method to reveal more significant differences under conditions of complex and mixed uncertainty remains to be fully demonstrated. Ultimately, the findings and approach of this study provide a foundation for improved strategic planning, policymaking, and sustainable MaaS system development across diverse urban contexts. Such an integrated evaluation approach not only facilitates the coordinated advancement of MaaS systems but also strengthens their environmental pressure and long-term urban sustainability goals.