A Dempster–Shafer Enhanced Framework for Urban Road Planning Using a Model-Based Digital Twin and MCDM Techniques

Abstract

Rapid urbanization in developing countries presents a critical challenge in the need for extensive and appropriate road expansion, which in turn contributes to traffic congestion and air pollution. Urban areas are economic engines, but their efficiency and livability rely on well-designed road networks. This study proposes a novel approach to urban road planning that leverages the power of several innovative techniques. The cornerstone of this approach is a digital twin model of the urban environment. This digital twin model facilitates the evaluation and comparison of road development proposals. To support informed decision-making, a multi-criteria decision-making (MCDM) framework is used, enabling planners to consider various factors such as traffic flow, environmental impact, and economic considerations. Spatial data and 3D visualizations are also provided to enrich the analysis. Finally, the Dempster–Shafer theory (DST) provides a robust mathematical framework to address uncertainties inherent in the weighting process. The proposed approach was applied to planning for both new road constructions and existing road expansions. By combining these elements, the model offers a sustainable and knowledge-based approach to optimize urban road planning. Results from integrating weights obtained through two weighting methods, the Analytic Hierarchy Process (AHP) and the Bayesian best–worst Method (B-BWM), showed a very high weight for the “worn-out urban texture” criterion and a meager weight for “noise pollution”. Finally, the cost path algorithm was used to evaluate the results from all three methods (AHP, B-BWM, and DST). The high degree of similarity in the results from these methods suggests a stable outcome for the proposed approach. Analysis of the study area revealed the following significant challenge for road planning: 35% of the area was deemed unsuitable, with only a tiny portion (4%) being suitable for road development based on the selected criteria. This highlights the need to explore alternative approaches or significantly adjust the current planning process.

1. Introduction

Urbanization and population growth significantly pressure urban infrastructure [1]. According to the United Nations report, more than 68% of the world’s population will live in cities by 2050 [2]. Rapid population growth often outpaces road network expansion [3], leading to a cascade of problems, including severe traffic congestion, inadequate infrastructure planning, and, ultimately, environmental degradation [4]. This compelling rationale underscores the critical importance of urban road planning, demanding immediate consideration.

Designing and managing the road network in an urban area is known as urban road planning and includes decisions about new roads, development, and the overall efficiency of the network [5]. The goals of urban road planning include improving safety, reducing traffic, reducing air pollution, and improving accessibility [5,6,7]. In addition, the significant increase in the number of vehicles is expected to increase traffic flow and further use of transportation infrastructure. Therefore, deciding to build new roads or widen existing roads can be considered to be an approach to planning and management [8]. Also, road widening enhances traffic flow and safety, so it is an effective method for dealing with the current long-term traffic challenges [9].

On the one hand, urban road planning is a complex process and a wide range of multiple and conflicting factors, such as environmental, social, and economic effects, should be considered [10]. Therefore, it is a multi-criteria decision-making (MCDM) problem [11]. On the other hand, the spatial dimension of urban road planning necessitates robust spatial analysis. Integrating geospatial information systems (GISs) with MCDM offers a powerful approach for visualizing and analyzing various factors such as traffic flow, land use, and environmental constraints [12,13]. This can help the decision-maker to have a better understanding of the prioritization between different criteria.

To help decision-makers and planners better understand the problem, a digital twin can be used [14]. Digital twins create virtual models of physical objects to simulate their behavior [14] and can be used to provide predictions for long-term planning [15].

A digital twin can be used to simulate the system’s behavior in different conditions. This allows planners to evaluate the performance of their decisions before implementing them in the real world [16]. A digital twin can be summarized in the following five dimensions: static twins, dynamic twins, operational twins, simulation twins, and predictive twins [17]. As a digital twin becomes more advanced, users can benefit from better support for decision-making and planning [18]. Therefore, by collecting data from the physical world and interpreting them in understandable terms, it is possible to make a digital twin for the existing roads and the surrounding buildings so that an estimate of the destruction of buildings and other factors involved in the planning of urban roads during road widening and construction can be made digitally that can help to provide predictions for long-term planning [18,19].

Various studies have utilized GISs for road planning. By using traffic data and noise, Ruiz-Padillo et al. [20] developed a method for prioritizing roads, and the fuzzy analytical hierarchy process (F-AHP) was used for weighting criteria. Balta and Yenil [8] employed the AHP and Delphi to determine the optimal path for green space. In this study, four aspects, including sustainability, accessibility, performance, and transportation, were considered for selecting the criteria. Sarraf and McGuire [21] presented the AHP for designed safe route planning to help users choose the most appropriate route among alternative routes. This study compared the AHP and TOPSIS methods for safe route planning. Vrtagić et al. [22] used an integrated fuzzy model to rank different road segments for traffic management. In this study, Improved Fuzzy Step-wise Weight Assessment Ratio Analysis (IMF-SWARA) and integration with measurement of alternatives and ranking according to compromise solution (MARCOS) were performed, and the results were evaluated through a sensitivity analysis. Droj et al. [23] employed mathematical models and real-time traffic data and analyzed public transportation and its impact on urban traffic using network analysis, service area analysis, and simulation methods. They also used a mathematical model to simulate the urban and rural routes. The results of this study emphasized that traffic congestion and its effects can be reduced by improving public transportation density or accessibility. Santos et al. [24] employed MCDM to consider service cost, geometry (comfort and safety), construction time and environmental factors, CO₂ emissions, GISs, and building information modelling (BIM) to enhance infrastructure investment and route planning. This study used GISs and Monte Carlo simulations to create alternatives, and the PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) method was used to prioritize routes. Additionally, BIM was used for modeling. Another approach to multi-criteria decision-making is the Dempster–Shafer theory (DST) [25]. A key advantage of the DST lies in its capacity to quantify epistemic uncertainty [26]. This framework employs a set of defined principles, most notably Dempster’s combination rule, to integrate data from multiple sources. The DST also can effectively filter out irrelevant or conflicting information [27]. The theory’s ability to combine evidence maps in a meaningful manner has led to its application across various spatial domains. Paryani et al. [28] employed frequency ratio (FR), weight of evidence (WoE) and the DST, with the aim of identifying landslide-prone areas. Then, the results of these methods were compared using multivariate logistic regression (LR) and a genetic algorithm (GA). The results of this study indicated that the GA-LR model was more accurate in predicting landslide susceptibility compared to other models. Pahlavani et al. [29] used fuzzy VIKOR and Dempster–Shafer–fuzzy AHP methods to prioritize mining areas and select the best area to reduce potential risks of mineral exploration. In a study, Nachappa et al. [25] used Analytical Network Process (ANP) and AHP methods and two machine learning models, Random Forest (RF) and Support Vector Machine (SVM), to prepare flood susceptibility maps, and they used Dempster–Shafer to optimize sensitivity maps. Then, they used the area under the receiver operating characteristic curve (AUC) to evaluate accuracy.

Digital twins have also been used in some studies. Jiang et al. [19] presented an urban road planning approach based on the digital twins, MCDM, and GISs. In this study, the AHP method was used to weight the criteria. Also, the construction of new roads and the widening of old roads have been used for urban road planning. Wang et al. [30] presented a digital twin for highway traffic that uses 3D GIS technology. The system components include a 3D GIS model of the highway, a traffic model, and a control system. This model simulated traffic behavior. Also, this system can be used to improve real-time traffic management, forecasting, and intelligent traffic infrastructure deployment. Jiang et al. [31] presented a numerical hybrid approach using online map data to investigate underpass road clearance in highway widening projects. This study focuses on the existing main road and the investigation and upgrading of underpass roads along the main road. In addition, this study used online map data to create a digital twin of existing roads, which was a cost-effective method in the initial design stage.

Despite conducting various studies in road planning using MCDM, the uncertainty in the weighting process has received less attention. Previous studies have mainly used AHP and F-AHP to model road planning, and some new weighting methods, such as the best–worst method (BWM), have yet to be considered. In addition, to model uncertainty and increase accuracy, the combination of weights obtained from different weighting methods has been given less attention. So, the fusion of weights obtained from different weighting methods can model uncertainty, increase modeling accuracy, and bring better results than using a single source of information [13,32].

Therefore, this study provides planners and decision-makers with a sustainable approach based on MCDM, digital twin, DST, and GISs for urban road planning. This approach uses digital twin technology to present the data obtained from the sensors and display the results in a digital and comprehensible model for the planners. It also considers widening old roads and constructing new roads to guide urban road planning. This study deviates from the traditional approach of finding the optimal road plan. Instead, we focus on identifying the most cost-effective path for road alignment within the “goal layer”. This goal layer represents a designated area or corridor for planned road development. By prioritizing the lowest cost position within this layer, we aim to optimize the alignment for construction efficiency while potentially achieving a satisfactory overall road plan. In addition, this study presents a hybrid approach, including the weighting methods of the AHP, the Bayesian best–worst method (B-BWM), and the Dempster–Shaffer information fusion theory to provide better results than using one MCDM method. The criteria of interest in this study are traffic congestion, worn-out urban texture, building demolition costs, air quality, and noise pollution.

2. Materials and Methods

Assigning weights to decision criteria remains a crucial yet intricate aspect of decision-making. This can be especially challenging in situations of uncertainty because it creates a vague framework for decision-making. This section discusses the theoretical foundations and methods.

2.1. Analytical Hierarchy Process (AHP)

In this study, the AHP method [33] has been used to weight the criteria. The AHP method is based on collapsing complex problems into hierarchies [34]. In the AHP method, the goal, criteria, and alternatives are arranged in a hierarchical structure, forming a three-level hierarchy. In the AHP, pairwise comparisons are conducted to evaluate the relative importance of criteria at the same level. Saaty’s scale, as shown in

Table 1. Saaty’s scale of measurement in pair-wise comparison matrices [36].

Scale	Numerical Assessment
Equal importance	1
Moderate importance	3
Strong importance	5
Very strong importance	7
Extreme importance	9
Intermediate values	2, 4, 6, 8
Values of inverse comparison	1/3, 1/5, 1/7, 1/9

, can be used to quantify these comparisons. However, it is important to note that, while the standard method does not necessitate expert opinions, incorporating them can significantly enhance the reliability of the results [35], underscoring the value of your expertise in this process.

Following the construction of the pairwise comparisons matrix (PCM), the AHP calculates the maximum eigenvalue (λmax) of the matrix (A) and its corresponding eigenvector (ω), as demonstrated in Equation (1). This step helps assess the consistency of the judgments within the PCM. The AHP then evaluates the consistency of the pairwise comparisons using the consistency index (CI) and the consistency ratio (CR), as shown in Equations (2) and (3), respectively. Here, n represents the dimension of the PCM (an n × n matrix). The random index (RI) is provided in

Table 2. Random Index [36].

Matrix Size	1	2	3	4	5	6	7	8	9	10
RI	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.51

and serves as a reference value for comparison. A low CR (generally less than 0.1) indicates acceptable consistency in the judgments within the PCM.

$$A\omega ={\lambda }_{max}\omega$$

(1)

$$CI={\displaystyle \frac{{\lambda }_{max}-n}{n-1}}$$

(2)

$$CR={\displaystyle \frac{CI}{RI}}$$

(3)

2.2. Bayesian Best–Worst Method (B-BWM)

The best–worst method (BWM), introduced by Rezaei [37], is a recent development in the field of MCDM. It streamlines the process of determining weights for decision-making criteria through pairwise comparisons. Unlike traditional methods, BWM compares the most important criterion (best) and the least important criterion (worst) with another criterion. This approach mitigates potential biases in traditional pairwise comparisons [37]. Although the BWM is valuable, it is restricted to scenarios with single decision-makers. It cannot effectively combine preferences from multiple people. Mohammadi and Rezaei [38] introduced the Bayesian best–worst method (B-BWM) to overcome this limitation in group decision-making. The process of B-BWM involves the following steps [38,39]:

Step 1: The first step involves defining the relevant criteria for the decision problem.

Step 2: Each decision-maker identifies the most important (best) and least important (worst) criteria. These selections for expert k are denoted as (best) and (worst), respectively.

Step 3: Experts compare the best and worst criteria to all others on a scale of 1 to 9.

Each element ${\mathrm{A}}_{\mathrm{B}\mathrm{i}}^{\mathrm{k}}$ represents the pairwise comparison between the “best” criterion and another criterion $\left({\mathrm{c}}_{\mathrm{i}}\right)$ by decision-maker $\mathrm{k}$, as shown in Equation (4).

$$A_B^k=\left(A_{B1}^k,A_{B2}^k,\dots ,A_{Bm}^k\right),k=1,2,\dots ,K$$

(4)

Each element ${\mathrm{A}}_{\mathrm{j}\mathrm{W}}^{\mathrm{k}}$ represents the pairwise comparison between another criterion (${\mathrm{c}}_{\mathrm{j}}$) and the “worst” criterion by decision-maker $\mathrm{k}$, as shown in Equation (5).

$$A_W^k=\left(A_{1W}^k,A_{2W}^k,\dots ,A_{mW}^k\right),k=1,2,\dots ,K$$

(5)

Step 4: Use the pairwise comparison vectors (${\mathrm{A}}_{\mathrm{B}}^{\mathrm{k}}$ and ${\mathrm{A}}_{\mathrm{W}}^{\mathrm{k}}$) for calculations within a probabilistic framework.

Step 5: The joint probability equation for group decision-making in this method is in the form is described as Equation (6).

$$p\left(w^{agg},w^{1:k}\left|A_B^{1:k},A_w^{1:k}\right.\right)$$

(6)

Step 6: Apply Bayes rule to the joint probability, as seen in Equation (7).

$$p\left(w^{agg},w^{1:k}\left|A_B^{1:k},A_w^{1:k}\right.\right)\propto p\left(A_B^{1:k},A_w^{1:k}\left|w^{agg},w^{1:k}\right.\right)p\left(w^{agg},w^{1:k}\right).$$

(7)

Equation (7) can be written like Equation (8).

$$p\left(A_B^{1:k}, A_w^{1:k}\left|w^{agg},w^{1:k}\right.\right)p\left(w^{agg},w^{1:k}\right)=p\left(w^{agg}\right){\prod }_{k=1}^{k}p\left(A_w^k\left|w^k\right.\right)p\left(A_B^k\left|w^k\right.\right)p\left(w^k,w^{agg}\right).$$

(8)

Step 7: The probability in Equation (8) can be calculated by specifying the probability distribution of each element of this equation. The probability distribution $\left({\mathrm{A}}_{\mathrm{w}}^{\mathrm{k}}\left|{\mathrm{w}}^{\mathrm{k}}\right.\right)$ and $\left({\mathrm{A}}_{\mathrm{B}}^{\mathrm{k}}\left|{\mathrm{w}}^{\mathrm{k}}\right.\right)$ is a polynomial distribution and is described by Equation (9).

$$\left(A_B^k\left|w^k\right.\right)~multinomial\left({\displaystyle \frac{1}{w^k}}\right);\left(A_w^k\left|w^k\right.\right)~multinomial\left(w^k\right), {\forall }_k=1,2,\dots ,k.$$

(9)

Step 8: Also, the probability distribution of ${\mathrm{w}}^{\mathrm{k}}$ over the condition of ${\mathrm{w}}^{\mathrm{a}\mathrm{g}\mathrm{g}}$ is the Dirichlet distribution, as described in Equation (10):

$$w^k\left|w^{agg}\right.~Dir\left(\gamma \times w^{agg}\right), {\forall }_k=1,2,\dots ,k.$$

(10)

where, ${\mathrm{w}}^{\mathrm{a}\mathrm{g}\mathrm{g}}$ (aggregated weights from multiple decision-makers) is the mean of the distribution and $\mathsf{\gamma }$ is a concentration parameter and is described in Equation (11).

$$w^k\left|w^{agg}\right.~Dir\left(\gamma \times w^{agg}\right), {\forall }_k=1,2,\dots ,k.$$

(11)

where a and b are the shape parameters of the gamma distribution.

Step 8: Finally, supply the prior distribution over ${\mathrm{w}}^{\mathrm{a}\mathrm{g}\mathrm{g}}$ using an uninformative Dirichlet distribution with the parameter $\mathsf{\alpha }=1$, as shown in Equation (12).

$$w^{agg}~Dir\left(\alpha \right)$$

(12)

Step 9: Due to the model’s lack of a closed-form solution, Markov Chain Monte Carlo techniques are necessary for posterior distribution computation. The Just Another Gibbs Sampler (JAGS), a leading probabilistic programming language, is employed to sample and calculate the posterior distribution, as defined in Equation (8). The model yields posterior weight distributions for each decision-maker and the aggregated weights (${\mathrm{w}}^{\mathrm{a}\mathrm{g}\mathrm{g}})$ [38].

2.3. Dempster–Shafer Theory (DST)

The Dempster–Shafer theory (DST), also known as the theory of belief functions, is a prominent framework for reasoning with uncertainty in artificial intelligence [40]. It emerged in the early 1980s as an extension of the Bayesian subjective probability theory [40,41]. Unlike classical probability, which assigns values to single events, the DST utilizes belief functions. These functions express degrees of belief not only in propositions but also in sets of propositions. This issue allows for modeling situations with incomplete or ambiguous evidence. The core concept of the DST is basic probability assignment (BPA). BPAs assign numerical measures of uncertainty to overlapping sets, subsets of hypotheses, events, propositions, and individual hypotheses themselves [40]. The critical components of the DST are as follows [39,41].

BPA is a function such that $\mathrm{m}:2⟶\left[\mathrm{0,1}\right]$, and it satisfies the following hypotheses:

$$\left(i\right)m\left(\varnothing \right)=0,ii)\sum _{B\subset A}m\left(x\right)=1$$

(13)

The belief function is defined as follows: $\mathrm{B}\mathrm{e}\mathrm{l}:2⟶\left[\mathrm{0,1}\right]$, so that

$$Bel\left(A\right)=\sum _{B\subset A}m\left(B\right)=1, for all A\subseteq Ѳ$$

(14)

The plausibility function is defined as follows: $\mathrm{P}\mathrm{l}:2⟶\left[\mathrm{0,1}\right]$ and

$$Pl(A)=\sum _{B\cap A\ne \varnothing }m\left(B\right)=1, for all A\subseteq Ѳ$$

(15)

The Dempster–Shafer’s theory’s ability to represent uncertainty makes it valuable in various fields like fuzzy data analysis, decision-making, modeling, and risk assessment. This study uses AHP, B-BWM, and the DST for urban road planning. The DST allows us to capture the inherent uncertainty in user judgments regarding quality parameters during road planning. Each exploration criterion acts as a “witness”, providing evidence. As mentioned earlier, the DST can combine evidence from independent sources. Dempster’s rule of combination, as seen in Equation (14), is used for this purpose. It combines two independent pieces of evidence (${\mathrm{m}}_1$ and ${\mathrm{m}}_2$) into a single mass function (${\mathrm{m}}_1⨁{\mathrm{m}}_2$). The denominator ($1-\sum _{\mathrm{B}\cap \mathrm{A}\ne \varnothing }{\mathrm{m}}_1\left(\mathrm{A}\right){\mathrm{m}}_2\left(\mathrm{B}\right)$) acts as a normalization factor, while the numerator ($\sum _{\mathrm{B}\cap \mathrm{A}=\varnothing }{\mathrm{m}}_1\left(\mathrm{A}\right){\mathrm{m}}_2\left(\mathrm{B}\right)$) reflects the degree of conflict between the evidence sources [39,40,41,42].

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

(16)

In the DST, the relationship between the criteria of belief (Bel) and plausibility (Pl) is as follows [43].

$$Bel\left(A\right)=1-Pl\left(-A\right)andPl\left(a\right)=1-Bel\left(A\right)$$

(17)

2.4. Identifying the Study’s Criteria

This study, like any experimental investigation, relies heavily on data collection. Based on data availability and previous studies, six criteria were identified as essential for urban road planning in this study. The selection criteria are as follows: land use (LU), demolition cost (DC), traffic congestion (TC), worn-out urban texture (WO), noise (N), and air pollution (AP). All data layers within the GIS environment were meticulously derived through in-depth investigations and field surveys. This section details the criteria employed in this study.

One of the important criteria for urban road planning is worn-out urban textures, which are areas with inadequate infrastructure that cause high traffic density and high accident rates (Figure 1a). These data were downloaded from the Cityfile website (https://cityfile.sellfile.ir/, accessed on 20 May 2024). Land use and traffic congestion are additional critical factors that have been incorporated into this study. The distribution of land use types (residential, industrial, agricultural, etc.) significantly influences traffic patterns and network design [5,19]. A pairwise comparison matrix, as shown in

Table 3. PCM for Land use.

Land Use	Commercial	Residential	Undeveloped	Offices	Industrial	Weights
Commercial	1.00	0.78	0.18	1.53	0.67	0.10284
Residential	1.28	1.00	0.27	1.86	1.48	0.14929
Undeveloped	5.71	3.68	1.00	6.10	5.30	0.55144
Offices	0.65	0.54	0.16	1.00	0.67	0.07854
Industrial	1.50	0.67	0.19	1.49	1.00	0.11790
Weights	0.10284	0.14929	0.55144	0.07854	0.07854	1.00

, was employed to develop the land use criteria map. This map is visually represented in Figure 1b. Similarly, areas experiencing high traffic congestion, often an indicator of high vehicular volume [19], are strategically targeted for road network development. A corresponding criteria map for traffic congestion is presented in Figure 1c. For environmental factors, two criteria are considered: air pollution and noise. These selections stem from two key considerations. First, vehicles are significant contributors to air and noise pollution in urban environments. As a result, areas with higher levels of such pollutants often indicate greater economic activity and traffic. Consequently, prioritizing road network development in these areas can be more strategic. The second rationale relates to the construction process itself. Road construction inherently generates noise and air pollution. Therefore, from an environmental standpoint, locating new roads in already polluted areas may be preferable, minimizing disruption to residents in cleaner, quieter neighborhoods [19]. For creating an air pollution criteria map, hourly air pollution data for Tehran from 21 March 2023 to 20 March 2024 were downloaded from the Tehran Air Quality Control Website (https://airnow.tehran.ir/, accessed on 20 May 2024). Daily averages were calculated for the following four time periods: morning (6:00 AM to 12:00 PM), noon (12:00 PM to 5:00 PM), evening (5:00 PM to 10:00 PM), and night (10:00 PM to 6:00 AM). Inverse Distance Weighted (IDW) interpolation was then applied to create maps for each pollutant (SO₂, NOx, NO₂, NO, O₃, PM₁₀, PM_2.5). Equal weight was assigned to each pollutant map. No priority was given to any specific pollutant. Consequently, seven pollutant maps (SO₂, NOx, NO₂, NO, O₃, PM₁₀, PM_2.5) were generated, each with a weight of 0.143. These maps were then combined using the weighted sum (WS) method to create the final air pollution map (Figure 1d). Following the approach used for air pollution, the hourly noise data were acquired from the Tehran Air Quality Control Company. The data were processed, and the IDW interpolation was used to create daily noise pollution maps for the following four time periods: morning (6:00 AM to 12:00 PM), noon (12:00 PM to 5:00 PM), evening (5:00 PM to 10:00 PM), and night (10:00 PM to 6:00 AM). The final noise map was generated by combining these individual maps for each time interval, Figure 1e.

This study incorporates building demolition cost as a crucial criterion for urban road planning. Demolition costs can significantly impact project feasibility [19]. For this purpose, land elevation was extracted from the ASTER Global Digital Elevation Model (GDEM) provided by NASA, which has a spatial resolution of 30 m. Similarly, building heights were obtained from the ALOS satellite’s Digital Surface Model (DSM), with a 30 m resolution, and building parcels were used to construct digital twins of the city. Equation (18) was likely used to calculate the building heights from the DSM and DEM.

$$Z_{building}=Z_{DSM}-Z_{DEM}$$

(18)

The building heights derived from Equation (16) are likely used to extrude building parcel data along the vertical axis (z-axis) within the digital twin. Figure 2 presents the resulting digital twin for the study area, where online rule packages have been used for the texture of the buildings. Then, Equation (19) is employed to generate a criteria map for estimating building demolition costs [5,19], as follows:

$$C_{demolition}=\mu {\displaystyle \frac{v\cdot p}{h}}$$

(19)

where v is the volume of a building’s digital twin, p is the average price of the building per square meter, and h represents the average height of each floor, assumed to be 3 m in this study. The amplification coefficient, µ, accounts for compensation related to loss of home and relocation of property owners. It was determined through field surveys and negotiations with property owners [5]. We determined the average building price within the study area by calculating the mean price of listings found on the Divar website (https://divar.ir/, accessed on 20 May 2024). Finally, the criteria map of building demolition cost is obtained, as shown in Figure 1f.

Effective road planning requires the integration of various factors, each represented as a GIS map. The critical role of standardization in ensuring these maps are informative, utilize consistent and measurable units, and facilitate their combination during the analysis process cannot be overstated [44,45]. This is achieved by converting all criteria values to a common scale (or unitless values) and applying a normalization technique, such as the Linear max min normalization method presented in Equations (20) and (21), which enhances the accuracy and reliability of the data.

$$a_{ij}={\displaystyle \frac{x_{ij}-x_{j}min}{x_{j}max-x_{j}min}}$$

(20)

$$a_{ij}={\displaystyle \frac{x_{j}max-x_{ij}}{x_{j}max-x_{j}min}}$$

(21)

where ${\mathrm{a}}_{\mathrm{i}\mathrm{j}}$ is the normalized values for ith score of the j criteria layer, ${\mathrm{x}}_{\mathrm{i}\mathrm{j}}$ is the raw value for ith score of the j criteria layer, ${\mathrm{x}}_{\mathrm{j}}\mathrm{m}\mathrm{a}\mathrm{x}$ and ${\mathrm{x}}_{\mathrm{j}}\mathrm{m}\mathrm{i}\mathrm{n}$, respectively, corresponds to the maximum and minimum score of the j criteria layer. Choosing which equation to use depends on the positive or negative effect that the factor has on urban road planning. The processed factor layers are shown in Figure 1.

Also, existing roads are another factor to consider when planning new roads. To prevent new road alignments from overlapping existing roads, existing roads should be considered as “forbidden zones”. These zones represent areas with no data values and are excluded from analysis and calculations. So, the purpose of designating existing roads as forbidden zones is to prevent the algorithm from proposing new road construction within these areas, with the algorithm still being able to identify potential widening locations along existing roads. However, simply designating intersections as forbidden zones could prevent new roads from connecting. So, road networks are depicted as polygons and the boundaries of intersections are extracted and expanded outwards by a specific value. Subsequently, the overlapping areas of roads, intersections, and the expanded zones are removed within these expanded boundaries [19]. This process effectively “cleans” the existing road network map, as shown in Figure 1g.

3. Proposed Methodology

This study aimed to develop an optimal road network for six municipalities of the Tehran metropolis. We employed a hybrid approach combining MCDM with a GIS and data fusion using the DST. The GIS facilitated spatial analysis and information visualization for informed decision-making. MCDM guided the weighting of various criteria and the creation of the final urban road planning map. The Dempster–Shafer theory addressed the uncertainty associated with the weighting process. Additionally, digital twin technology played a crucial role in modeling and optimizing the performance of the proposed urban road plan.

Figure 3 illustrates the research workflow. The initial stage involved a comprehensive review of relevant research to identify criteria for urban road planning. Subsequently, appropriate spatial data relevant to these criteria were collected and stored within a spatial database. These data were then used to create individual spatial layers for each criterion. Spatial analysis techniques within the GIS environment were then applied to refine these layers.

The weights for each decision-making criterion were calculated using the following two established methods: the AHP and the B-BWM. However, it is important to note that these methods were not used in isolation. Expert opinions from specialists in urban planning and geographic information systems played a significant role in informing this weighting process, adding a crucial human element to our methodology. The DST was employed for data fusion to account for the inherent uncertainty in the results from both weighting methods, leading to a more robust weighting scheme.

The obtained weights were used to generate urban road planning maps, which allowed us to visualize the potential alignments based on the chosen criteria. This visualization was a crucial step in our methodology, as it provided a tangible representation of our findings. We then compared the results derived from the two weighting methods to assess any potential discrepancies. Finally, an urban digital twin and the ArcGIS Version 10.8 software’s cost path algorithm was employed to evaluate and identify suitable locations for road widening and new road construction within the digital twin environment. The study ultimately analyzed six criteria within the GIS environment to generate the final urban road planning map using a weighted sum approach, providing a comprehensive and detailed plan for the region.

4. Implementation and Results

This section explains the stages of implementation and the results.

4.1. Study Area

District 6, occupying a central spot within Tehran’s core district, falls under the Tehran municipality and is located at a north latitude of 35°43′15.83″ and east longitude of 51°23′58.01″. This relatively small area (spanning 2137 hectares), encompassing just 2.3% of Tehran’s total sprawl, is divided into six blocks and 14 neighborhoods. According to the 2016 census, over 251,384 people call District 6 home [46]. Major highways like Resalat, Hemat, Chamran, Modares, and Kurdistan either weave through the district or run along its outskirts. While these highways appear to facilitate traffic flow, a crucial challenge persists in heavy congestion. The reliance on primary and secondary arterial roads throughout most of the day, especially during peak hours, exposes the limitations of the current internal highway network. This dependence contributes to the sluggish traffic movement that plagues District 6, making it one of Tehran’s most congested areas. As a result, District 6 has become a prime candidate for a case study focusing on urban road planning initiatives to alleviate traffic congestion (Figure 4).

4.2. AHP Weighting

Ten urban planning experts with specialized knowledge in urban planning, GISs, and civil engineering contributed to the pairwise comparison matrix. These experts were selected to provide a diverse range of perspectives and enhance the reliability of the results. The pairwise comparison method, a well-established technique for group decision-making, was employed to mitigate potential biases. The geometric mean of these pairwise comparisons was then calculated and integrated into the AHP model. Finally, we assessed the model’s consistency by calculating the inconsistency ratio. This ratio, thankfully, fell below the 0.1 threshold, indicating an acceptable level of consistency within the model. The pair-wise comparison matrix of criteria are presented in

Table 4. PCM for the AHP method.

Criteria	LU	DC	TC	WO	N	AP
LU	1.00	0.89	0.72	0.52	3.33	3.30
DC	1.12	1.00	1.40	0.95	4.50	3.80
TC	1.38	0.71	1.00	0.92	4.10	3.90
WO	1.94	0.05	0.09	1.00	5.10	4.90
N	0.30	0.22	0.24	0.20	1.00	0.68
AP	0.30	0.26	0.26	0.20	1.46	1.00

, and the final weights assigned to each criterion are presented in

Table 5. Final weights of criteria.

Criteria	LU	DC	TC	WO	N	AP
Weights	0.1713	0.2369	0.2153	0.2683	0.0494	0.0588

. The reassuringly low inconsistency ratio of 0.00765 further reinforces the validity of our model.

4.3. B-BWM Weighting

To initiate the B-BWM analysis, we first needed to identify the most and least critical criteria for our decision-making process. Ten experts participating in the study were tasked with selecting the best and worst criteria and then comparing these to all remaining criteria. We implemented this method using the Python programming environment.

Table 6. PCM of best criteria to other criteria.

Expert	1	2	3	4	5	6	7	8	9	10
Best Criteria	WO	TC	DC	DC	DC	WO	LU	WO	TC	TC
LU	3	3	1	6	4	3	1	4	1	7
DC	1	3	1	1	1	4	3	2	3	3
TC	2	1	7	2	2	2	5	2	1	1
WO	1	3	5	2	2	1	1	1	3	2
N	5	5	7	4	5	7	8	5	5	7
AP	5	5	7	5	4	7	7	5	5	6

shows the PCMs of the best criteria to other criteria. From the point of view of expert 5, Demolition Cost (DC) is the most important criteria (value 1 in the matrix) and, also from the observation of this expert, the DC is four times better than land use (LU) and air pollution (AP). Also,

Table 7. PCM of other criteria to worst criteria.

Expert	1	2	3	4	5	6	7	8	9	10
Worst Criteria	N	N	TC	LU	N	AP	N	AP	AP	N
LU	3	3	6	1	4	3	7	2	6	3
DC	4	3	7	4	5	4	7	3	3	4
TC	3	5	1	4	3	3	5	2	5	7
WO	6	3	3	3	5	7	8	5	3	6
N	1	1	1	2	1	1	1	1	1	1
AP	1	3	1	3	3	1	3	1	1	3

shows, the comparison of other criteria to the worst criteria. For example, from expert 5’s point of view, noise (N) is the worst criteria (acquired value of 1 in the matrix, which indicates the preference of worn-out texture (WO) five times over N). The resulting criteria weights obtained through this analysis are presented in

Table 8. Weights obtained from B-BWM.

Criteria	LU	DC	TC	WO	N	AP
Weights	0.1663	0.2210	0.1962	0.2378	0.0829	0.0958

.

4.4. Dempster–Shafer Theory

This section explores the application of the DST to integrate the weights obtained from the AHP and B-BWM analyses. The Dempster–Shafer theory of evidence (DST) was employed to combine the weights derived from the AHP and B-BWM methods. The weights generated by these two methods served as independent pieces of evidence, which were integrated using the DST combination rule to produce a reliable and consolidated set of weights. This method treats the weights derived from both approaches as mass functions. The execution steps of the DST were implemented within the Matlab environment. The resulting combined weights are presented in

Table 9. Weights obtained from the Dempster–Shafer combination rule.

Criteria	LU	DC	TC	WO	N	AP
Weights	0.1448	0.2662	0.2149	0.3245	0.0208	0.0288

. Interestingly, Figure 5 reveals that, similar to the AHP and B-BWM analyses, the DST assigns the highest weight to the “worn-out urban texture” criterion and the lowest weight to “noise pollution”.

4.5. The Overall Urban Road Planning Map

After determining the criteria weights using the AHP, B-BWM, and DST methods, we generated final urban road planning suitability maps for each approach. These maps were further classified into five suitability classes, as shown in Figure 6.

Table 10. Suitability map classes for three model.

Model	Suitability Maps for Urban Road Planning
	Very Highly Suitable	Highly Suitable	Moderately Suitable	Marginally Suitable	Not Suitable
AHP	0.866–0.949	0.793–0.866	0.695–0.793	0.595–0.695	0.531–0.595
B-BWM	0.856–0.945	0.797–0.856	0.710–0.797	0.617–0.710	0.551–0.617
DST	0.881–0.959	0.797–0.881	0.681–0.797	0.573–0.681	0.515–0.573

presents the results and classification breakdowns for all three methods.

As can be seen from

Table 11. The results of urban road planning maps.

Model		Number of Pixels
		Very Highly Suitable	Highly Suitable	Moderately Suitable	Marginally Suitable	Not Suitable
AHP	Pixel	3,047,517	9,714,527	30,910,554	24,102,535	5,861,714
	%	4.14	13.19	41.98	39.73	7.96
B-BWM	pixel	3,365,819	9,393,491	29,858,188	25,101,799	5,917,550
	%	4.57	12.76	40.55	34.09	8.04
DST	Pixel	3,055,359	9,661,331	26,668,199	8,221,990	26,029,968
	%	4.15	13.12	36.22	11.17	35.35

, the AHP method classified 4.14% of the area as entirely suitable for urban road planning while designating over 7.96% as unsuitable. The B-BWM results yielded a similar pattern, with 4.57% of the area deemed highly suitable and 8% classified as unsuitable. However, the DST integration produced distinct results compared to the other two methods. While 4.15% of the area was found to be suitable, a significantly higher portion (35.35%) was classified as unsuitable for urban road planning.

4.6. Evaluation of the Results

This study compared three methods, the DST, the AHP, and B-BWM, for urban road planning. Both methods generated detailed suitability maps that identified areas that were favorable for road development. While the overall suitability maps were similar, the AHP and B-BWM methods designated a slightly larger area as moderately suitable. This suggests that AHP and B-BWM might consider a broader range of areas for further evaluation during the planning process. Additionally, these methods agreed on a significant portion being unsuitable for road development, providing valuable information for avoiding construction in these areas.

We employed the cost path algorithm to assess the suitability maps generated from the AHP, B-BWM, and DST analyses. This algorithm evaluates the eight neighboring cells around a current cell and selects the path leading to the cell with the minimum accumulated cost [12,47,48,49,50]. The algorithm iterates until there is no connection between the source and destination [51]. The final route represents the path with the fewest cells between the two locations. The cost path algorithm employed in this study considered a combination of financial, environmental, and urban planning factors. Specifically, demolition costs, air pollution, noise levels, traffic congestion, and land use implications were incorporated into the cost assessment. Algorithm outputs indicate that road alignments parallel to existing roads suggest widening the existing roads. Conversely, alignments traversing buildings or undeveloped areas imply the necessity of constructing a new road. As shown in Figure 7 and Figure 8, three different alignments were produced by this algorithm for each method. The results indicate that both AHP and B-BWM methods yielded identical results for the road alignment, with a total length of 2661 m. This alignment allocates 1638 m for road widening and 1023 m for new road construction. The DST method produced a slightly different outcome. The proposed alignment stretches 2630 m, with 1536 m dedicated to widening and 1096 m dedicated to new road construction. Therefore, the DST method prioritizes new road construction over widening compared to the other two methods, reflected in the longer total length and smaller allocation for widening. Interestingly, both methods proposed similar total road lengths, suggesting that they can achieve comparable overall connectivity improvements. However, a crucial difference emerged in their allocation strategies. The AHP and B-BWM methods prioritized widening existing roads, potentially offering a more cost-effective solution in the short term by utilizing existing infrastructure. Conversely, the DST method favored constructing entirely new roads. This approach might be more beneficial for long-term development plans by expanding the road network and potentially improving accessibility in previously unserved areas.

This study utilizes 3D visualization to present its findings. Figure 9 illustrates the buildings slated for relocation (orange) and demolition (red) as a result of the proposed road alignment. The new road alignment necessitates widening, necessitating the relocation of adjacent structures. Additionally, the proposed road alignment requires the demolition of certain buildings to accommodate the new infrastructure. The associated demolition costs are presented in Figure 10.

5. Discussion

Section 4 presented the results of road planning using three weighting methods: the Analytical Hierarchy Process (AHP), the Bayesian best–worst method (B-BWM), and the Dempster–Shafer theory (DST). Interestingly, AHP and B-BWM yielded nearly identical results. These methods identified over 4% of the area as being suitable for urban road development (widening or new construction) and over 7% as being unsuitable. The DST, however, produced distinct results. While 4.15% of the area was deemed suitable, a significantly higher portion (35.35%) was classified as unsuitable. This issue suggests that the DST amplified the weights of criteria already highly weighted in AHP and B-BWM (high mass functions) while diminishing the weights of those with lower weightings (low mass functions). The DST exhibited a similar effect for criteria with weights clustered around a central value, proportionally increasing or decreasing their weights. However, for criteria with significantly different weights, the DST caused substantial increases for some criteria while significantly decreasing others.

Examining the results from a road widening/construction perspective, the implications are significant. The Dempster–Shafer method favored new road construction over widening compared to AHP and B-BWM, suggesting a potential bias toward minimizing costs. This finding, combined with the more conservative results yielded by the combined weighting approach employed in the DST, could have a substantial impact on project costs. The Dempster–Shafer theory’s prioritization of criteria with high weights in AHP and B-BWM, such as worn-out urban textures, traffic congestion, and demolition cost, over environmental factors clearly indicates the influence of uncertainty modeling within the DST.

Traditionally, road planning involved developing separate alignments based on individual factors like environment, engineering, and traffic flow. Past studies then compared these alignments, often favoring economic considerations. Their weighting systems assigned the highest importance to economic factors, while environmental factors received the least weight. Our research yielded similar results, with economic factors again receiving the most emphasis and environmental factors receiving the least.

However, this study takes a more nuanced approach by employing multiple methods (the AHP, B-BWM, and the DST) for generating road alignments. This allows for a more comprehensive evaluation by considering different perspectives on suitability for road development. Previous studies have explored hybrid MCDM-GIS approaches for road planning by utilizing digital twins, but these methods still needed to address the use of novel weighting methods and integration theories to model uncertainty. This study proposes a DT-MCDM-DST-GIS approach to bridge this urban road planning research gap.

6. Conclusions and Future Work

This study introduces a novel method for urban road planning that combines a GIS, the AHP, B-BWM, the DST, and digital twin. This hybrid approach assists decision-makers and planners by identifying and evaluating alignments for road widening or new construction. Notably, this study leverages digital twins to represent sensor data and results within a comprehensive and comprehensible digital model, addressing previous studies’ gaps.

Employing MCDM methods (AHP and B-BWM), we identified critical criteria and indicators influencing urban road planning. The DST was then used to model uncertainty during weighting while the GIS facilitated spatial analysis. Economic, social, environmental, and engineering factors were all considered within the multi-criteria decision-making framework to ensure a comprehensive evaluation.

The high similarity between the results obtained using the proposed methods suggests a stable outcome for this approach. We applied this framework to plan for new road construction and the expansion of existing roads. Six criteria were chosen based on the research background and data availability, guiding the selection of suitable areas for road construction and widening.

This study also breaks new ground by incorporating B-BWM and the DST to model uncertainty within the weighting method, an aspect neglected in previous research. By identifying the most suitable locations for road widening and new construction, this study paves the way for further investigation in this field.

This study has some limitations that offer opportunities for future research. First, the decision-making process (MCDM) considered only six factors. Urban road planning is complex and requires a more thorough evaluation with additional factors. Second, this study used a basic, static digital twin model. Future research could greatly benefit from using real-time data, LiDAR (Light Detection and Ranging) data, and aerial photographs to create a more dynamic and informative digital twin. This would allow for a more accurate representation of the current state of the urban environment and facilitate the evaluation of how different road development scenarios might impact the city over time. Third, to address the limitations inherent in solely relying on expert opinions for weight assignment, future research should explore alternative methodologies. Incorporating quantitative approaches, such as statistical analysis of historical data or preference elicitation techniques, could provide a more objective foundation for determining criterion weights. Additionally, investigating the application of machine learning algorithms to learn weightings from large datasets of decision-making problems presents a promising avenue for further research. By combining expert knowledge with these quantitative methods, a more robust and reliable weight assignment process can be developed. While the current study effectively utilized expert opinions, MCDM methods, and the Dempster–Shafer theory, the proposed framework offers potential for broader application in future research.