Toward Sustainable Urban Mobility: A Multidimensional Ontology-Based Framework for Assessment and Consensus Decision-Making Using DS-AHP

Abstract

Urban mobility is a critical aspect of sustainable urban development, with significant environmental, social, and economic implications. Assessing the sustainability of urban mobility systems in order to create more carbon neutral, liveable, healthier, and sustainable cities and neighborhoods for the future requires a multidimensional approach that integrates diverse factors. However, the lack of a unified assessment framework poses challenges in comparing and evaluating different urban mobility projects. This article proposes an ontology for assessing the sustainability of urban mobility systems. This ontology is based on a multidimensional approach that integrates knowledge from experts in transportation engineering, urban planning, environmental science, and social sciences to incorporate existing sustainability indicators and frameworks, as well as domain-specific knowledge. A consensus approach based on Dempster–Shäfer (DS) and Analytic Hierarchy Process (AHP) methods is proposed to account for uncertainties and to allow for the consideration of preferences and ill judgment. Through a case study in Romania, the authors demonstrated the applicability of the proposal to provide a comprehensive and flexible framework for assessing urban mobility sustainability. The proposed ontology provides a valuable tool for policymakers, urban planners, and transportation engineers to make informed decisions towards sustainable urban mobility, and the sensitivity analysis is carried out to demonstrate the robustness of the proposed framework. It has potential for iterative validation and feedback from domain experts, and can serve as a foundation for future research.

1. Introduction

For an extended period, urban mobility has been perceived as the ease of travel from origin to destination within urban areas [1]. However, with advancements in technology, the definition of urban mobility is evolving to accommodate new behaviors in the utilization of mobility services and the increasing number of stakeholders involved. According to projections from the United Nations report on urbanization prospects, it is anticipated that 66% of the world’s population will reside in urban areas by 2050, consequently doubling the demand for passenger movement [2]. This surge in urbanization poses a significant challenge for governments in facilitating mobility for both goods and people, necessitating a multidisciplinary approach in line with sustainability and climate change recommendations.

Over the years, the concept of mobility has broadened in scope with the evolution of metropolises, placing city dwellers and new technologies at the forefront of urban organization. A holistic approach to the concept of mobility, encompassing physical, social, and economic insights, has been articulated in “Mobility and urban form—theoretical issues” by [3]. This definition emphasizes a behavioral understanding of mobility, serving as a foundational premise for advocating for the role of mobility policies in shaping mobility supply to (re)model mobility behavior in a sustainable manner, necessitating a holistic and systematic approach to urban mobility planning.

Information and communication technologies are recognized by [4] as pivotal in fostering sustainable development in mobility. Similarly, Ref. [5] contend that assessing the sustainability of an urban mobility system entails considering a comprehensive set of parameters reflecting its dimensions. In this regard, sustainable urban mobility indicators as highlighted by [6] play a crucial role. Indicators are generally defined as quantitative or qualitative measurements designed to identify significant trends, highlight problems, monitor progress over time towards specific vision objectives, contribute to priority setting, and simplify complex information for both experts and the public [7].

To integrate sustainability requirements into the selection of urban mobility policies, decision-makers, considered experts in the field, must express their preferences using a decision support method [8]. While several approaches to selecting sustainable urban mobility systems exist in the literature [9,10,11], there remains a lack of common agreement or standards guiding mobility authorities in decision-making processes. Even when such indicators exist, they often suffer from redundancy, incompleteness, heterogeneity, inconsistency, or errors, leading to inappropriate and unsustainable decision-making. Moreover, this scenario often compels experts to express judgments despite lacking sufficient relevant foundations. To address these shortcomings in the planning and implementation of sustainable urban mobility systems, this paper sets out two primary objectives:

• Firstly, to propose a sustainable urban mobility ontology as a powerful tool for representing and sharing knowledge in computer sciences, resolving issues of data consistency, redundancy, and interoperability through a knowledge engineering methodology employing a holistic view of the system;
• Secondly, to define a framework for assessing the sustainability of urban mobility from a decision-making perspective, considering consensus and subjectivity in group decision-making.

The main objective is to enable decision-makers from various urban mobility-related fields to reach a consensus-based method that utilizes DS-AHP on their judgments and preferences regarding the sustainability of target policies, facilitating the selection of the most appropriate policy for a given mobility system. To validate the proposal, a realistic case study in Romania is presented, involving the selection of the best mobility policy from several alternatives for deploying eco-friendly mobility solutions that meet user requirements. The case study demonstrates the effectiveness and efficiency of the proposed approach in facilitating informed and objective decision-making in sustainable urban mobility. The authors state that the proposed ontology and sustainability assessment method are scalable, providing a significant contribution to the field of group decision-making in urban mobility. This improves the effectiveness and efficiency of decision-making processes in this field and has important implications for urban planners, policy-makers, and researchers aiming to promote sustainable mobility solutions in urban areas.

The rest of the paper is structured as follows: Section 2 presents a comprehensive literature review on sustainable urban mobility decision-making, focusing on the challenges encountered by decision-makers in this domain. Section 3 introduces the proposed approach, including the development of the sustainability ontology and DS-AHP method, and provides a detailed explanation of how it works. In Section 3.2, a realistic case study in Romania to validate the proposed approach’s effectiveness and efficiency is described, and the sensitivity analysis is carried out to demonstrate the robustness of the proposed system. Finally, the concluding section offers a summary of the proposal and highlights potential directions for future research.

2. Related Works

In this section, the main concepts of sustainable urban mobility and their challenges are first presented, followed by the different methods of its evaluation.

2.1. Sustainable Urban Mobility Challenges and Its Principal Concepts

In the literature, there are few clear definitions of sustainable urban mobility. According to Da Silva (2008), sustainable urban mobility can be defined as mobility that contributes positively to the economic and social state of a region, without compromising human health and the environment [12]. Therefore, it is mobility that (1) enables people or businesses to satisfy their accessibility and basic needs, (2) is affordable, operates efficiently, offers the possibility of choosing between several modes, and contributes to the economy and development of a region, and (3) helps limit polluting emissions by relying on a sustainable energy policy. This definition is based on studies carried out by the OECD (Organisation for Economic Co-operation and Development) and a group of specialists from the European Commission.

Two remarks are noteworthy: (1) urban mobility cannot be reduced to the “transport” dimension alone, and (2) sustainability must satisfy several interdependent criteria beyond the environmental factor. In fact, due to technological advancements, sustainable mobility now encompasses meeting the daily needs of users, such as commuting, accessing healthcare, and leisure activities, while considering the possibility of fulfilling these needs without traveling. According to Banister (2008), sustainable mobility aims to (1) decrease the necessity for travel, (2) encourage modal shift, (3) reduce trip length and its corresponding polluting emissions, and (4) improve the system’s efficiency [13]. Therefore, to define sustainable mobility, it is crucial to consider the diversity of characteristic elements and their interrelationships, and to identify the relevant sustainability criteria that must be met in accordance with the stakeholders’ expectations.

More recently, a study involving real cases from most cities around the world [14] has provided a classification of mobility criteria that seems aligned with the future trajectory of mobility. The proposed classification integrates the system-oriented vision advocated by Goldman and Gorham [15], considering that transportation alone cannot capture the complexity of urban mobility. Three key indices were considered:

• The maturity index, which concerns factors such as the financial attractiveness of public transportation, its share in modal distribution, the share of non-polluting modes, road density, the density of the bike lane network, urban agglomeration density, public transport frequency, and public initiatives.
• The innovation index, calculated based on criteria reflecting the penetration rate of mobility smart cards, the use of (digital) mobility platforms, bike-sharing solutions, car sharing (B2C), carpooling platforms (P2P), electronic transmission services, taxi platforms, autonomous vehicles, and other smart mobility initiatives.
• The performance index, based on (a) environmental criteria, considering carbon dioxide (CO₂) emissions, nitrogen dioxide (NO₂) concentration, particulate matter with a diameter of less than 10 micrometers (PM10) or less than 2.5 micrometers (PM2.5), (b) traffic management, including fatal accidents, congestion, etc., and (c) mode management, comprising the share of public transport, the share of non-polluting modes, the average time to commute, and the average level of motorization.

In this study, the authors then defined an overall index by subjectively assigning specific weights to each criterion, giving a total of 36 points for the criteria composing the maturity index, 24 points for the innovation index, and 40 points for the performance index. Thus, for a given city, a global mobility index out of 100 is calculated. These studies show that we need to take a holistic view of mobility if we are to achieve sustainability; other recent works refer to this issue [16,17].

A literature review on urban mobility indices [18] found that all identified indices are useful for analyzing and monitoring urban mobility and are utilized to support public policies in urban areas. In each of the studied cases, the authors choose the most feasible approach for their region and adopt different solutions according to the existing urban or regional reality. The sustainability criteria that are commonly used are classified according to the three dimensions of sustainability, i.e., economic, social, and environmental. A recent study by [14], covering most cities around the world, proposed a classification of mobility criteria in line with the future mobility trajectory, based on the system-oriented vision advocated by [15]. The study recognizes that transport alone cannot characterize the complexity of urban mobility and identifies three indicators for this purpose: (1) the maturity index based on attractiveness factors reflecting public authorities’ initiatives, (2) the innovation index computed based on intelligent mobility initiatives, and (3) the performance index based on environmental criteria.

As in the previous case, the identified criteria clearly reflect the environmental, economic, and societal dimensions found in the literature. However, both cases have a few problems. The mechanism for assigning weights and their aggregation, for the computation of the overall index, leaves little flexibility for experts to integrate their personal judgments into the assessments and reflect their preferences, uncertainties associated with them, and the specificities of the context. There are several methods available in the literature for assessing and defining sustainability indices.

2.2. Assessment of the Sustainability of Urban Mobility

The urban mobility system is complex and characterized by numerous factors that need to be considered for its assessment. It must satisfy the public and private sector decision-makers with a wide range of perspectives. However, in reality, most urban mobility decision-makers do not have complete information or the right decision rules to make the “correct" decision. Much work in the literature has focused on the question of logically assessing, presenting, and recommending the most desirable mobility system that meets the objectives and needs of different perspectives in uncertainty settings. In the assessment of sustainable mobility systems, some of the terminology used in this work needs to be introduced [19]:

• Transportation policy refers to the set of regulations, laws, and guidelines implemented by governments and transportation agencies to guide the development, operation, and maintenance of transportation systems.
• A decision is a choice made after considering several options or alternatives (policies). It involves the process of evaluating information and selecting a course of action or outcome for mobility.
• Criteria are standards, principles, or requirements used to judge, evaluate, or assess the mobility system.
• A decision-maker is a person or group of people responsible for making a choice or selecting a course of action among several mobility alternatives. Decision-makers can be individuals making personal decisions, an expert in the field, high-level executives, or government officials making decisions that may have far-reaching consequences.

According to [10,20], methods incorporating multicriteria analysis have been the most recommended and used for taking into account collective decisions and considering different evaluation and decision-making criteria in urban mobility projects in recent decades. Concerning the methods, a comparative study has been carried out by [21]. According to [10], the most commonly used methods are: Analytic Hierarchy Process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Elimination and Choice Expressing the Reality (ELECTRE), and Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE). Recent works in the literature presented in

Table 1. Synthesis of the assessment of the sustainability of an urban mobility system.

Bibliography Reference	Sustainability Assessment Method	Description
[10]	Multcriteria analysis	State of the art on multicriteria decision-making techniques in transport systems
[19]	Multcriteria analysis	Integrated approach to assessing the sustainability of a transport network under uncertainty
[20]	Multcriteria analysis	Review of the literature on multicriteria approaches for urban passenger transport systems
[22]	Multcriteria analysis	Hybrid multicriteria decision-making approach
[23]	Multcriteria analysis	Fuzzy multicriteria model for assessing the sustainability of an urban freight transport system
[24]	Multcriteria analysis	Selection of sustainable urban mobility alternatives using an integrated approach based on the fuzzy intuitionist Choquet integral
[25]	Multcriteria analysis	Algorithms applied to decision-making for the choice of sustainable transport system
[26]	Methodological framework	Methodology for assessing the sustainability of urban mobility projects
[27]	Multcriteria analysis	Assessment of sustainable urban mobility in the city of Thessaloniki
[28]	Multvariate statistical method	Uncertainty assessment of an urban mobility system
[29]	Multcriteria analysis	Highlighting the fundamental principles for the evaluation of transport projects
[30]	Multicriteria analysis	Review of the use of multicriteria decision analysis for the evaluation of transport projects
[31]	Multicriteria analysis	State-of-the-art review on multicriteria decision-making in the transport sector

clearly show the interest in multicriteria methods of analysis concerning the assessment of the sustainability of urban mobility.

The majority of the presented works (Table 1) propose multicriteria decision support methods grounded in fuzzy or integrated approaches, yet neglect to incorporate sustainability indicators. However, it is essential to consider future developments, whether technological or paradigmatic, in this context. The prevailing trend in defining sustainability is shifting beyond the integration of technologies that facilitate mobility services, adopting a more holistic perspective that encompasses human concerns, and this trajectory is expected to continue growing in response to increasingly stringent regulations and governance. As observed in the literature, methods exist to characterize the diverse range of sustainability factors, including those reflecting the new trajectory of sustainable mobility. Other methods formalize the components of the system under study, thereby better capturing their interdependencies. Nevertheless, none of these methods provides a formal framework for accommodating the specific features of the system and future developments.

2.3. Motivation and Goals

To support urban decision-makers in designing and deploying sustainable urban mobility systems that consider the requirements of all stakeholders, various approaches for choosing and evaluating criteria and for individual aggregation have been proposed in the literature. However, it would be unrealistic to adapt a method used in a specific context to another context with different specificities. Even when such indicators exist and are used in some cases, they can be incomplete, redundant, non-persistent, and erroneous. Therefore, we propose a system for implementing sustainability criteria by using an approach that helps build and evaluate them by eliciting knowledge related to them, within a framework of collective decision-making that considers the preferences of experts to reach a group consensus. The present work addresses the sustainability analysis of urban mobility from the point of view of a decision support system (DSS), aimed at providing decision-makers with a readable analysis framework.

3. Proposed Methodological Framework for Sustainability Assessment

The framework proposed in this work for the decision support system is based on a domain ontology for its evaluation. This framework takes into account the entire expression of user needs and integrates a holistic approach which now transcends the dimensions of the infrastructure to integrate the service component and the users. The knowledge for the integration of these requirements is not given; an elicitation phase is therefore envisaged to show how to exploit the repositories and standards considered with a view to developing an ontology of sustainability in order to help decision-makers in the choice of policy to deploy. An extensive multicriteria decision support approach was adopted to assess the sustainability of the urban mobility system, taking into account the following issues:

• Uncertainties linked to the subjectivity of the evaluations;
• Ambiguities relating to the incompleteness of the information to carry out the evaluation;
• Metric for aggregating individual evaluations to obtain an overall estimate;
• Consensus in a collective decision-making framework to better reflect the opinions of different experts.

The following illustration (Figure 1) summarizes the overall approach to system implementation.

3.1. Ontology Development Methodology

According to Fernandez [32], the ontology development process involves activities necessary for building ontologies. Although there is no standard methodology for creating ontologies, some of them stand out and provide the main functions of the interoperability, reusability, and integration of systems. The most popular methodologies include TOVE, METHONTOLOGY, On-To-Knowledge, AFM, OntoClean, DILIGENT, and NeOn, which have been compared in the literature [32]. In this work, we chose the METHONTOLOGY methodology [32], as it is appropriate for building an ontology domain. The METHONTOLOGY approach provides the better management of the ontology life cycle and a progressive development process with a set of activities carried out during its duration. METHONTOLOGY breaks activities down into three levels: (1) management (planning), (2) development (specification, conceptualization, formalization, integration, implementation, and maintenance), and (3) support (acquisition, documentation, and evaluation) [33,34]. The ontology proposed in this paper has been designed as follows: (1) definition of the purpose (of ontology), (2) conceptualization, (3) formalization, and (4) validation. Each step is described in the following sections (Figure 2).

Step 1.

Specification of the sustainability ontology

As mentioned previously, in this paper, the holistic analysis of the sustainability of the urban mobility system is performed with regard to the decision support. The specifications resulted of the proposed ontology are summarized in the following (Figure 3).

In the field of urban mobility, new stakeholders such as telecommunication providers, mobility service providers, and mobility infrastructure providers have emerged over the years, alongside the “historical” stakeholders like transport providers and transport infrastructure providers. These stakeholders are involved in making urban mobility systems more intelligent, providing on-demand services that are more attractive and responsive to users’ expectations [35].

Furthermore, the broader context of urban mobility supply includes meeting travel and accessibility needs, such as urban form and land use (morphology, localization of activities, intensity of land use, and related human density), the legal framework for planning, implementing, and managing mobility, and financial regulatory frameworks (e.g., taxes, fees, rates, and subsidies), among others. Therefore, experts and decision-makers from various fields related to mobility must be involved in planning mobility in a coordinated and consensus-driven framework.

Step 2.

Conceptualization of the proposed ontology

The activity of conceptualization leads to the development of a conceptual model for the ontology. This step requires defining the proposed ontology concepts, relationships, and constraints, and providing a glossary that describes all specified concepts and attributes [19,36,37]. In a broader sense, sustainability indicators are useful for monitoring and measuring the environmental status by considering a manageable number of variables or characteristics. The knowledge about sustainability presented in this paper is extracted from scientific articles, strategy papers, expert reports, which constitute the body of knowledge and interviews with experts in the field of mobility like urban planners. However, this knowledge is presented in natural language, which is not easy for a computer-based system to interpret and analyze.

A comparative analysis of the resulting concepts was conducted to gain a better understanding of the indicator selection process and to identify the most relevant ones. Generally, sustainability indicators are classified based on economic, social, and environmental factors [19]. However, new indicators are often difficult to categorize within these factors. Therefore, in order to better account for changes in urban mobility and stakeholder requirements, the indicators used in this work were grouped according to the PESTEL analysis method (Policies, Economic, Sociological, Technological, Ecological, and Legal) [38]. It is evident that there is no common agreement in the literature regarding the evaluation of sustainability indicators, which emphasizes the need for a holistic perspective. Moreover, as per [3], the assessment of urban mobility should also consider land use and specific transport-related indicators.

The main concepts associated with each of the seven key sustainability performance indicators (KPIs): political and legal (regulatory framework), economic, sociological, technological, environmental, transport, land use are summarized in the associated glossary (

Table 2. Main concepts associated.

Politic and Legal Concepts’ Glossary
Concept	Meaning/Example
Regulation	Ensuring the correct functioning (of a complex system)
Privacy	Ensuring that information is accessible only to those authorized to access it
Governance	Implementation of a set of mechanisms (rules, standards, protocols, conventions, contracts, etc.) to ensure better coordination of an organization’s stakeholders
Standardization	Making production conform to certain reference standards
Experience feedback	Information in reaction to a service, a person’s performance of a task, etc., used as a basis for improvement
Behaviors	All reactions, observable practices of a user
Economic concepts’ glossary
Energy efficiency	Minimum use of energy
Purchasing power	Capacity to buy (something)
Business opportunities	Ongoing opportunity to generate income by any representative of a network marketing company (e.g., activities generated)
Public finance	Financial affairs, money matters, fiscal matters
Dynamics	Ease of accommodation to regular changes without immediate effects on users
Social concepts’ glossary
Affordability	The state of being cheap enough for people
Traveling time	Travel time between a starting and end point
Acceptability	Admissibility, satisfactoriness
Security	The state of being free from danger or threat
Equity	Refers to a form of equality or fair treatment
Technology concepts’ glossary
IT Infrastructure	Basic physical and organizational structures and facilities needed to facilitate communication through IT
IT Applications	e.g., mobile information, reservation, or payment application
Innovative technology	All scientific, technological, organizational, financial and commercial approaches that result in the production of technologically new or improved products or processes.
Environmental concepts’ glossary
Pollution emission	e.g., air pollution, water
Traffic congestion	Traffic jam, standstill
Ecological footprint	Impact of a human or community on the environment
Energy consumption	Use of energy resources (fossil, renewable, hybrid, etc.)
Land use concepts’ glossary
Accessibility	Easy access to the different categories of existing mobility services
Activities profile	Type of system flows specific to the different categories of activities
Intensity of land-use and Human density	Land use coefficient (related to human density and density of flows, public transport demand and rentability)
Transport concepts’ glossary
Multimodality	Having or involving several modes of transport
Transport mode	A particular form of transport that is mainly distinguished by the vehicle used, and infrastructures
Infrastructure	All fixed installations that must be installed to enable the operation of transport systems
Service	All the facilities offered for the realization of urban mobility
Vehicle	Used to transport goods and people from one place to another

). The resulting KPIs of the proposed ontology is described in the following subsection.

Step 3.

Formalization of the proposed ontology

To make the model operational, a first formalization was made with the OWL standard language, chosen for its ability to represent knowledge in computers and facilitate ontology exchanges. As the reasoning process is not considered in this work, the resulting source code is not presented here, but the hierarchy of the proposed ontology is provided as suggested by [34] for the organization of criteria (Figure 4). The ontology was performed with the Protégé software 5.0.

It is interesting to note that upon analyzing the body of knowledge, it becomes apparent that any given criterion can be characterized by any of the KPIs. For example, energy consumption could be characterized by its economic, environmental, or social impact. Based on the service-oriented view adopted, we have chosen to highlight the environmental impact of energy consumption. Since the model is ontology based, such choices do not affect interoperability with another ontology based on matching concepts.

In compliance with the definition of a sustainable urban mobility system, the proposed sustainable ontology classifies sustainability indicators into Policies, Economic, Sociological, Technological, Ecological, and Legal KPIs. Additionally, to highlight the specificity of the service-oriented approach in the context of urban mobility, the indicators are not limited to the known triptych pillars (environment, economic, and social) but have integrated legal, technological, and legislative factors corresponding to the dimensions of sustainability [39]. This approach better reflects the current context and considers the new requirements of stakeholders. In fact, the sustainability indicators have been classified according to the view of an organizing mobility authority, which is the main focus of this work, leading to a sustainable framework analysis studied and suggested in the next section.

Step 4.

Implementation and maintenance of the proposed ontology

The implementation was carried out using the OWL language, which was chosen for its interoperability with other languages and its structured approach. Later, an ontological evaluation was conducted using the ontology specification document to ensure that the ontology was correctly constructed in accordance with the previously proposed architecture, meeting the ontological requirements and addressing the competency issues. Finally, a maintenance activity was performed to update and correct the ontology to reflect the new requirements.

This work facilitated decision-makers in having a shared vision and understanding the sustainable indicators for the urban mobility system. The key focus was on highlighting a service-oriented view as a KPI, based on services such as mobility, combined with the use of ICT. ICT can be instrumental in promoting collaboration and better coordination among urban mobility organizations. To validate the proposed model and analyze the feasibility of its application to a real-world problem, a theoretical framework for evaluating its ability to provide decision support to urban mobility organizing authorities by enabling them to choose the best policy based on sustainability requirements is described in the following section.

3.2. Framework of the Assessment Based on the Group Consensus Approach

In order to assist decision-makers in choosing target policies for sustainability in the urban mobility system, a multicriteria decision-making approach based on group decision-making was adopted. A group decision-making problem can be defined as a decision-making problem, where a group of decision-makers express their judgments on a finite set of alternatives to reach a common solution. The decision algorithm used in this study (Figure 5) was inspired by the one proposed by [40] and based on the AHP (Analytic Hierarchy Process) method. The method was enhanced with a new step based on DS-AHP to consider uncertainty related to knowledge, such as expert opinion on the degree of plausibility or belief. This approach is particularly effective in combining different points of view by considering degrees of belief and plausibility.

The Analytic Hierarchy Process (AHP) was chosen because, in addition to the advantages shared with other methods, such as TOPSIS, ELECTRE, and PROMETHEE, it is the most widely used method as stated by [10]. AHP offers several benefits, including the use of a hierarchical structure of criteria, the possibility of scaling preferences, the ability to check the consistency of judgments, the consideration of group decisions through aggregation, and adaptability to various contexts. A comparative review of the methods is proposed in the literature [10,41,42]. In our study, we address several issues that go beyond group decision-making as proposed by [40]. Specifically, our study accounts for uncertainties caused by the subjectivity of assessments and ambiguities arising from incomplete information when making assessments aimed at achieving consensus and obtaining an overall estimate.

The consensus-building process is typically viewed as a series of transformations of the individual judgments of decision-makers into a group judgment that reaches an acceptable level of consensus [43,44]. The consensus-building process should be terminated when one of the following stopping conditions is met: (i) all members of the decision-making group have a common opinion, indicating that group consensus has been achieved, (ii) all members of the decision-making group have rejected the moderator’s recommendation, in which case the consensus-building process should be stopped, or (iii) the predefined maximum number of iterations T has been reached, where $T\ge 1$ is an integer, indicating that the consensus process has been reached.

At the end of this process based on the AHP method, the group decision is evaluated according to the DS-AHP method to refine the evaluation, considering the uncertainties and lack of knowledge of the decision-makers. The theoretical framework of the adopted method, based on the extended AHP, is presented first.

Theoretical background of the experts’ assessment

In the context of this work, each decision-maker (expert) should conduct his or her sustainability assessment, based on their own expertise and judgment on the policies provided. Moreover, the method should be able to handle multiple criteria for the same evaluation. For these reasons and more, a fuzzy approach to AHP, specifically DS/AHP [45], is adopted due to its capability to address the described issues. Later, a group consensus method is applied to determine the most suitable solution for the decision-makers while considering the sustainability requirements.

The DS/AHP is a method that combines the classical Analytic Hierarchy Process (AHP) method [46] with the theory of Dempster–Shafer [47]. It has a hierarchy structure model that is structurally similar to AHP. However, its mathematical foundation is the Dempster–Shafer theory of evidence (DST). By using DST in DS/AHP, the decision-maker (DM) can make subjective judgments on groups of Decision Alternatives (DAs) instead of individual DAs or pairwise comparisons of DAs [48]. DS/AHP is used for Multicriteria Decision Method (MCDM) issues and allows for poorly known information since a DM may not be able to provide a judgment on a given criterion. Ignorance includes incompleteness, imprecision, and uncertainty, which relate to the objective and subjective aspects of the judgment-making process [49].

The DS/AHP method produces results in the form of preference levels on groups of Decision Alternatives (DAs), known as the basic probability assignment in the Dempster–Shafer theory (DST), as well as a level of concomitant ignorance, which collectively make up a body of evidence (BOE). DS/AHP also allows for the identification of levels of belief and plausibility regarding the best DA within groups of varying sizes [50]. The following section provides a brief overview of the policy-making process used in this study, from classical AHP to DS/AHP, including the mathematical formulas employed in the analysis.

AHP method

In essence, solving an AHP-based problem involves the following steps: problem structuring, the elicitation of pairwise comparisons of criteria, the derivation of the priority vector of criteria, and the validation of results through a consistency check of judgments. In the context of group decision-making, which is the focus of this work, a specific methodology is applied to aggregate individual judgments, and the following steps are taken.

Problem structuring. An AHP model is a hierarchy of criteria with the goal of the study placed at the top level, the criteria and sub-criteria (used to choose among alternatives) in the intermediate levels, and the lowest level includes the alternatives to be evaluated. The AHP model of our work is based on the previously described ontology (Figure 6), including different policies defined as alternatives to the problem.

Elicitation of pairwise comparisons. With the hierarchy structure at hand, pairwise comparisons of criteria in a level are performed, using the immediately higher-level criteria, yielding comparison matrices in the form of Equation (1), each such matrix being of $n\ast n$ dimension (given n criteria at the level of which a pairwise matrix is performed):

$$\begin{array}{c}A=\left[\begin{array}{cccc}1& a_{12}& \dots & a_{1n}\\ \frac{1}{a_{12}}& 1& \dots & a_{2n}\\ \dots \\ \frac{1}{a_{1n}}& \frac{1}{a_{2n}}& \dots & 1\end{array}\right]\hfill \end{array}$$

(1)

Each element $a_{ij}$ represents an estimated ratio scale $w_i/w_j$ regarding the respective weights criteria i and j; it estimates whether criterion i is more important than criterion j, based on Saaty’s nine-point scale and their reciprocals: $\left\{\frac{1}{9},\frac{1}{8},\dots ,\frac{1}{2},1,2,\dots ,8,9\right\}$ [51].

Derivation of priorities vector. Given a matrix A of pairwise comparisons at a level of AHP hierarchy, the priorities vector $w={(w_1,\dots ,w_n)}^T$ for that level can be computed using one of the methods found in the literature [52]: (1) the eigenvector method, based on the mathematical formula $Aw=\lambda w$, where $\lambda$ is the eigenvalue of matrix A, (2) the geometric mean method, (3) the least squares method, and (4) the normalized columns method (the simplest to apply, particularly in a spreadsheet-based software).

Judgments’ consistency check. Since a “rational” decision-maker should not contradict himself, consistency indexes of judgments have been proposed in the literature to assess the quality of the assessments [52]: (1) the Saaty’s consistency index $CI$ and consistency ratio $CR$, (2) index of determinants, (3) geometric consistency index, (4) harmonic consistency index, (5) ambiguity index, etc. For our case study, Saaty’s consistency measurements have been used, based on the formula in Equation (2) [51]:

$$\begin{array}{c}CR=\frac{CI}{R{I}^n}\hfill \end{array}$$

(2)

where $CI=\frac{{\lambda }_{max}-n}{n-1}$, ${\lambda }_{max}$ is the highest eigenvalue, and $R{I}^n$ (a Random Index of size n) is a real number estimating the average $CI$ obtained from a large enough set of randomly generated matrices of size n. Random index values for each n are provided in the literature. In practice, according to [51], the judgment matrix with $CR⩽0.1$ is accepted as being consistent. The consistency check in our study uses this basic rule.

Pairwise comparisons in Group Decision. The results presented so far are based on the hypothesis that “a single DM is perfectly rational and can precisely express his preferences on all pairs” [52]. However, in real-world applications, group decisions (GD) are established by committees, or any other team of stakeholders/experts for pairwise comparisons elicitation purposes. In these contexts, aggregation methods are provided, including two main approaches: (i) aggregation of individual judgments (AIJ), made before computing the priority vectors; (ii) aggregation of individual priorities (AIP). In addition, several ways of aggregating are also identified: (1) consensus, (2) vote or compromise, (3) geometric mean of the individuals’ judgments, and (4) separate models or players. In our case study, the AIJ approach is used. The geometric mean method is used to aggregate single judgments due to its robustness.

Despite its simplicity and effectiveness as proven by its successful implementation in several real-world industrial applications, the AHP method has been criticized as stated by [53]. One criticism concerns the number of pairwise comparisons that a DM must perform before the ranking computations. In the context of assessing sustainability holistically, criteria from different domains of expertise are introduced, leading to a multidisciplinary assessment. An expert in financial issues may not be able to assess criteria concerning the introduction of ICT, which is recommended for the innovative transportation system in smart cities, while an expert in social sciences may not be able to provide judgments on economic criteria. For these reasons and those described earlier (subjectivity, incompleteness, group decision, an uncertainty), an alternative method for assessing the sustainability of transportation systems is considered: the DS/AHP method.

DS/AHP process

DS/AHP can be defined as a MCDM method inspired by the traditional AHP. Unlike the Saaty AHP, its analytical process is based, according to [45], on available measures of favorability knowledge on a group of DA, compared with the whole discernment frame $\mathsf{\Theta }$ (rather than pairwise comparisons used in classical AHP), with regard to a specific criterion. The associated framework is built on Dempster–Shafer theory, using the following concepts.

Main concepts of DST. Let $\mathsf{\Theta }=\left\{H_1,\dots ,H_n\right\}$ be a finite set of n mutually exclusive hypotheses (called discernment frame). According to Dempster–Shafer theory (DST), a basic probability assignment (bpa) is a function $m:2^{\mathsf{\Theta }}\to \left[0,1\right]$ (also called a mass function) satisfying:

$$\begin{array}{c}m\left(\mathsf{\Theta }\right)=0,and\hfill \\ \sum _{A\underset{=}{\subset }\mathsf{\Theta }}m\left(A\right)=1\hfill \end{array}$$

(3)

where $\mathsf{\Theta }$ is the empty set, and $2^{\mathsf{\Theta }}$ is the power set containing all the possible subsets of $\mathsf{\Theta }$. The probability assigned to $\mathsf{\Theta }$, $m\left(\mathsf{\Theta }\right)$, is interpreted as the degree of ignorance, and each subset $A\subseteq \mathsf{\Theta }$ such that $m\left(A\right)>0$ is called a focal element. After computations, the bpa values are the levels of exact belief in the preferences to the focal elements identified by a DM.

For the same piece of information, based on the bpa, different measures of confidence may be defined, among which are the belief (Bel) and the plausibility (Pls) functions, which are both functions defined, respectively, in Equations (4) and (5):

$$\begin{array}{c}Bel\left(A\right)=\sum _{B\underset{=}{\subset }A}m\left(B\right),\forall A\underset{=}{\subset }\mathsf{\Theta },\hfill \end{array}$$

(4)

$$\begin{array}{c}Pls\left(A\right)=\sum _{A\cap B\ne 0}m\left(B\right),\forall A\underset{=}{\subset }\mathsf{\Theta },\hfill \end{array}$$

(5)

$Bel\left(A\right)$ measures the exact support to A, i.e., the belief that hypothesis A is true, and shows how strongly the evidence supports A. $Pls\left(A\right)$ measures the possible support to A, i.e., the total amount of belief that could be potentially placed in A, and represents the extent to which we fail to disbelieve in A. Hence, $\left[Bel\left(A\right),Pls\left(A\right)\right]$ is the interval of support to and includes the lower and upper bounds of probability for the hypothesis A to be true, also interpreted by [45] as the imprecision on the “true probability” of A.

The evidence from different sources can be combined, assuming their independence, based on Dempster’s rule of combination given in Equation (6):

$$\begin{array}{c}\left[m_1⨁m_1\right]\left(C\right)=\left\{\begin{array}{cc}0,& C=0\\ \frac{{\sum }_{A\cap B\ne ⌀}{m}_1\left(A\right)m_2\left(B\right)}{1-{\sum }_{A\cap B\ne ⌀}{m}_1\left(A\right)m_2\left(B\right)}& C\ne 0\end{array}\right.\hfill \end{array}$$

(6)

where A and B are focal elements with their associated $bpa$ $m_1$ and $m_2$ (respectively) such that $Be{l}_1$ and $Be{l}_2$ are independent. It is obvious that $m_1\mathsf{\Theta }{m}_2$, a function $2^{\mathsf{\Theta }}\to \left[0,1\right]$, is also a $bpa$. This function is commutative and associative, i.e., it allows for combining more than two mass functions.

DS/AHP main steps and their implementation

We have performed the DS/AHP process, based on the hypothesis that traditional AHP has been made, specifically for each hierarchical level of the problem, except for the last one. The aim is to find the priorities vector for each level of the hierarchy, except for the lowest one (in which policies’ judgments concerning the three policies at hand are placed). The values of these vectors are called criteria priority values (CPV) and used in the DS/AHP process as explained below (see Figure 3). The main steps (for each DM) of the concerned process are described in the following.

Step 1: Provide the sources of evidence regarding the criteria and DAs (Decision Alternatives).

For that purpose, each DM is provided with a survey. As illustrated in Figure 6, the values of CPV for our study are $P_{pol},P_{eco},P_{soc},P_{tech},P_{env},P_{trans},$ and $P_{land}$ (representing priority values of politic, economic, social, technology, environmental, transport, and land use criteria, respectively).

Step 2: Compute the normalized bpa (basic probability assignment) values of each focal element for each criterion.

Ref. [45] showed, based on an algebraic theory of eigenvalues, that the BOE (body of evidence) associated to each criterion can be computed using the following formulas:

$$\begin{array}{c}m\left(s_i\right)=\frac{a_i.\rho }{{\sum }_{k=1}^d{a}_k.\rho +\sqrt{d}},\hfill \\ m\left(\mathsf{\Theta }\right)=\frac{\sqrt{d}}{{\sum }_{k=1}^d{a}_k.\rho +\sqrt{d}}\hfill \end{array}$$

(7)

where we have the following:

• $\rho$ is the associated value in the CPV;
• $s_i$ the $i-th$ set (focal element) in the associated group of DA;
• $a_i$ the $i-th$ scale value assigned to $s_i$;
• d the number of focal elements in the associated group of DA;
• $\mathsf{\Theta }$ the frame of discernment (previously defined in the sub-section on the main concepts of DS/AHP).

To illustrate, let us consider the DM1 judgments and “environmental” criterion. Since there are two sets in the group of DA concerning the “environmental” criterion (see Figure 4), we have:

$$\begin{array}{c}\hfill m\left(\left\{Po{l}_1\right\}\right)=\frac{6.{\rho }_{env}}{10.{\rho }_{env}+\sqrt{2}},\\ \hfill m\left(\left\{Po{l}_2,Po{l}_3\right\}\right)=\frac{4.\rho }{10.{\rho }_{env}+\sqrt{2}},and\\ \hfill m\left(\mathsf{\Theta }\right)=\frac{\sqrt{2}}{10.{\rho }_{env}+\sqrt{2}}\end{array}$$

(8)

Step 3: Combine the bpa values under all criteria.

For a given DM, this step results in assessing the average belief of the choice of each policy, computed using the aggregation formula in Equation (6), assuming that the judgments of criteria are independent.

Step 4: Calculate the belief and plausibility of each subset of the discernment frame using Equations (3) and (4).

As a consequence, this step provides two indicators, allowing for analyzing the degree of confidence on the judgment of a DM on a focal element, and the extent to which they failed to disbelieve their judgment.

Step 5: Build up the uncertainty interval, $\left[Bel\left(A\right),Pls\left(A\right)\right],\forall Aϵ\mathsf{\Theta }$, based on the   previous results.

This interval, which is interpreted by [45] as the imprecision on the “true probability” of a focal element, will help in analyzing how much we can trust the judgments of the concerned DM: in other words, the shorter the interval, the more we can trust their judgments.

Step 6: Aggregate the judgments of all DMs and determine the ranking of each subset of the discernment frame.

At this stage, several ranking strategies can be adopted, e.g., human interpretation of the results followed by a subjective decision. Automation can also be performed using fuzzy rules, e.g., the evidential reasoning methods proposed in the literature.

The methods used to evaluate the preferences of the decision-makers are presented. In the following, the steps of the evaluation process of the judgment process will be described in algorithmic form. (See Algorithm 1).

Algorithm of the consensus model for group decision

The evaluation process follows two main steps: (i) the evaluation of group judgments based on the AHP method and consensus, and (ii) the refinement of the group decision using the DS-AHP method.

Algorithm 1 Group consensus algorithm

Require: Judgment preferences Ensure: Decision of group consensus      Begin     if (Consensus stop condition) (1) then           Group decision-making solution           Final decision    else           Refine decision-maker with maximum           if (Decision-maker accept) then                 Updating judgment                 Go to (1)          else                 Go to (1)          end if    end if    return Decision of group consensus.     End

Three conditions are possible for stopping the algorithm: (i) if all decision-makers reach an acceptable consensus, (ii) if all decision-makers reject the update notice, or (iii) if the maximum number of iterations has been reached. Prior to executing the algorithm, it is essential to verify the consistency of each decision-maker’s judgments (by checking the consistency of each decision-maker’s matrix) and determine the weight vector of each decision-maker (decision-makers’ weight vector).

4. Validation and Discussion

In order to validate the proposed sustainability ontology and analyze the feasibility of its application to a real problem, a case study was conducted and is briefly described below.

4.1. Context of the Case Study

The proposed case study was conducted as a part of an urban planning project in Bucharest, the capital of Romania. Urban mobility, especially public transport, plays a crucial role in the social and economic development of the city, which has a population of 2.25 million in the metropolitan area. Bucharest, being the political and administrative center of Romania, is a significant urban agglomeration that contributes to approximately $20\%$ of the country’s GDP and $10\%$ of its population. The City Council is responsible for implementing urban mobility projects and is assisted by a special organization called the Consultative Group for Mobility (CGM), established in 2013.

To create a Sustainable Urban Mobility Plan (SUMP), the CGM aims to identify all critical mobility-related issues along with the associated funding sources. To prepare the SUMP, the CGM conducted a series of observations to raise awareness about major mobility problems such as (i) inadequate connections to neighborhoods and the metropolitan area; (ii) significant imbalances in travel patterns; and (iii) efficient but non-integrated public transport systems (surface and underground). Consequently, by 2020, the CGM proposed four urban projects to the City Council, with the primary objective being to identify the priority policy among the alternatives intended to improve mobility as defined by the expertise of the CGM. The proposed policies are as follows: policy 1, the development of a pedestrian and cycle path; policy 2, the development of reserved lanes for public transport; policy 3, the development of a hub connecting modes of transport; policy 4, the development of a new surface mobility line; and policy 5, the development of a bike-sharing project.

A committee composed of five experts from different fields was selected to choose the policy to be implemented. The objective was to provide decision-making support for selecting the best policy based on sustainability requirements. A survey in the form of questions related to the identified sustainability criteria for mobility was administered to the experts. The results of the evaluation using the approach presented earlier are described below.

4.2. Results

The presented project involved ranking the five proposed alternatives (policy 1, policy 2, policy 3, policy 4, and policy 5) by five decision-makers (DM1, DM2, DM3, DM4, and DM5) to determine which policy should be implemented. The evaluations of the alternatives were based on the criteria outlined in Figure 5. The algorithm proposed previously was implemented using Python with the Pandas and NumPy libraries. The application allowed for multicriteria evaluation with or without consensus.

For the sake of simplicity, the input matrices for the evaluations of the different decision-makers for each of the alternatives based on the selected criteria are provided in the appendix of this article. A partial view of the interface is shown in Figure 7 based on the Saaty scale. The individual evaluations of the alternatives and the grouped evaluations are presented based on the belief and plausibility functions (Equations (4) and (5)).

For this example, we have set the maximum number of iterations to $T=4$ and the maximum distance threshold to $0.15$. According to Beynon-Davies [54], if the highest level of consensus is desired, the threshold value should be close to $0.01$; otherwise, it should be set to $0.2$. The maximum distance measure obtained after the first iteration is $0.29$, which is greater than the threshold value of $0.15$. Therefore, the system requests the decision-makers to update their judgments. At the end of the third iteration, we obtain a maximum distance value of $0.11$, which is less than the threshold value of $0.15$. As a result, the system stops and proposes the best choices to consider.

The results of the individual assessment of the alternatives without consensus (a) and with consensus (b) are presented in Figure 8. According to the evaluation without consensus using directly the DS-AHP approach, Policy 4 is the preferred option with a score of $0.50$. It is worth noting that there is a significant difference between Policy 4 and the second-ranked option. On the other hand, the evaluation with consensus indicates that Policy 3 is the best option with a score of $0.45$.

One of the advantages of the proposed method is the possibility of having the evaluation in groups of alternatives. The implemented solution also allows to provide the evaluations in pairs of alternatives (Figure 9) without consensus (a) and with consensus (b). In the evaluation without consensus, policies 4 and 5 are the best, while in the evaluation with consensus, policies 3 and 4 are the best.

The result of this new approach is a decision support system that allows for better decision-making in order to deploy sustainable urban mobility systems that best meet the requirements of users. However, the choice of criteria and the evaluation of the decision-makers still need to be improved through fuzzy ontology and artificial intelligence decision support.

4.3. Sensitivity Analysis

Sensitivity analysis is essential to check the stability of the rankings. This analysis was carried out by modifying the criteria weights. In this analysis (Figure 10), the graph shows five scenarios (Scenario 1 to Scenario 5) representing different configurations of criterion weights. Each scenario has bars for five alternatives (mobility policies). The choice of the number of scenarios and alternatives is not guided by any specific criteria. Changing the criteria weights (scenarios) leads to significant changes in the ranking of the alternatives. This highlights the sensitivity of the DS-AHP process to these weights. Alternatives 2 and 4 consistently appear in the top two positions in all scenarios, suggesting that they may be less sensitive to changes in weights than alternatives 1 and 3. Overall, the analysis reveals that the DS-AHP process in this case is sensitive to the weights of the chosen criteria. The score (ranking in some cases) of the alternatives can vary considerably depending on the configuration of the weights.

4.4. Discussion and Future Direction

The findings presented in this paper underscore the critical importance of addressing the challenges posed by new technologies and rapid urbanization in the context of urban mobility planning. The proposed ontology of urban mobility sustainability and the accompanying decision-making approach represent significant steps towards enhancing decision-making processes in this domain. The successful application of the DS/AHP method in the case study conducted in Bucharest, Romania, highlights the potential of the proposed approach to effectively navigate complex decision-making scenarios. By providing decision-makers with a shared knowledge base and facilitating consensus-building, the ontology and decision-making process offer promising tools for addressing the multifaceted challenges of urban mobility planning.

However, it is essential to acknowledge the limitations and challenges associated with the proposed approach. One such limitation is the inherent imperfections in ontology design, including imprecisions, uncertainties, and ambiguities. While the incorporation of fuzzy concepts may mitigate some of these challenges, further research is needed to develop robust methodologies for ontology development in the context of urban mobility sustainability. Additionally, the sensitivity of the DS/AHP method to criteria weights and the number of alternatives underscores the need for the careful consideration and validation of these parameters. Future studies could explore alternative decision-making methodologies or refine existing approaches to enhance the robustness and reliability of decision-making processes.

5. Conclusions

In conclusion, this paper addresses the challenges faced by urban managers in selecting sustainable mobility systems amidst the emergence of new technologies and rapid urban population growth. The primary objectives include defining an ontology of urban mobility sustainability to enhance decision-making processes and proposing a new group consensus-based decision-making approach. The paper presents a case study conducted in Bucharest, Romania, to assess the feasibility of utilizing the proposed ontology with the DS/AHP method for selecting the best urban policy among alternatives. The analysis of results showcases the effectiveness and flexibility of the approach, particularly in accommodating subjectivity, incomplete information, and uncertainty associated with decision-making processes.

Looking ahead, future studies are encouraged to further refine and expand upon this approach. Given the inherent imperfections in ontology design, such as imprecisions, uncertainties, and ambiguities, integrating fuzzy concepts alongside precise ones could enhance the robustness of the sustainability indicators considered. Overall, this paper contributes to advancing sustainable urban mobility planning by providing practical tools and methodologies that can improve decision-making processes and promote the integration of new indicators in urban management practices.