category: literaturenote citekey: chenstudyriskassessmentpedestrian2024 title: Study on the risk assessment of Pedestrian-Vehicle conflicts in channelized Right-Turn lanes based on the Hierarchical-Grey Entropy-Cloud model authors: "Chen, Ziyu; Liang, Guohua; Chen, Yixin; Yang, Xiaoyao; Liu, Yue" year: 2024 date: 2024-00-00 2024 doi: 10.1016/j.aap.2024.107664 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2024.107664" zotero_key: S9EIHVGD zotero_storage: ZZHGE8ZA collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Chen, Ziyu"

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Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

Study on the risk assessment of Pedestrian-Vehicle conflicts in channelized Right-Turn lanes based on the Hierarchical-Grey Entropy-Cloud model

Ziyu Chen , Guohua Liang * , Yixin Chen , Xiaoyao Yang , Yue Liu

College of Transportation Engineering, Chang'an University, Xi'an 710064, PR China

ARTICLE INFO

Keywords: Traffic safety Channelized right-turn lane Pedestrian-vehicle conflict Risk evaluation Hierarchical-grey entropy-cloud model

ABSTRACT

Channelized right-turn lanes (CRTLs) in urban areas have been effective in improving the efficiency of rightturning vehicles but have also presented negative impacts on pedestrian movement. Pedestrians experience confusion regarding the allocation of road space when crossing crosswalks within these areas, leading to frequent conflicts between pedestrians and motor vehicles. In this paper, considering the characteristics of pedestrianvehicle conflicts at channelized right-turn lanes as well as the ambiguity and uncertainty of the causes, a comprehensive assignment combined with a cloud model is proposed as a risk evaluation model for pedestrianvehicle conflicts. The study established a risk indicator system based on three aspects of the transportation system: pedestrians, motor vehicles, and the road environment. Combining the analytic hierarchy process (AHP), grey relational analysis (GRA), and entropy weighting method (EWM) to get the weights of indicator combinations, and then using the cloud model to realize quantitative and qualitative language transformation to complete the risk evaluation. This study employs specific road segments in Qingdao as a validation case for model analysis. The results indicate that the model's evaluation outcomes exhibited a significant level of agreement with the findings from field investigations during both peak and off-peak periods. It is demonstrated that the model has good performance for the safety assessment of pedestrian-vehicle conflicts at CRTL, and it also reflects the ability of the model to assess fuzzy randomness problems. It provides participation value for urban pedestrian-vehicle safety problems as well as applications in other fields.

1. Introduction

Channelized right-turn lanes (CRTLs) are widely used at urban intersections in right-traveling countries and regions. The design diverts right-turning traffic from same-direction vehicles in advance by installing a dedicated right-turn lane at the location of the roadway close to the intersection (van Haperen et al., 2018), so that it avoids intersection signals and drives to the target lane, in order to alleviate the congestion of right-turning vehicles and to improve the efficiency of the intersection. There are two common design forms of CTRLs, mainly the difference in the form of isolation safety islands, the first one is a physical safety island, which is isolated by curbing or physical facilities, and the other one is a safety island with ground markings or painted pavement. There are two common forms of design for channelized rightturn lanes, the main difference being the form of the isolated safety island. The first is a solid safety island, isolated by curbs or solid features. The other is a ground-marked or painted pavement safety island. It is undeniable that the effect of CTRLs' on the improvement of traffic efficiency has been verified by a large number of studies (Autey et al., 2012, Farivar et al., 2017, van Haperen et al., 2018). However, the impact of CRTLs on improving regional traffic safety remains debatable.

Currently, the assessment of safety performance for CRTLs primarily focuses on motor vehicles. For instance, Chinese scholar Guo collected the conflict probability of motor vehicles under various right-turn modes. The results show that the conflict probability of the two CRTL modes (convex channelized island and spray-painted channelized island) is at a low level, which proves that the design has a positive effect on the safety between vehicles (Guo et al., 2020). Potts compared nearly 400 traffic accident data in Toronto, including CRTLs, conventional right turn lanes, and shared right turn lanes, and found that the intersection collision probability was 70 % to 80 % higher at intersections using conventional right turn lanes compared to the other two designs (Potts et al., 2013). A study conducted in Belgium analyzed 1,295 accidents and found that intersections with CRTLs had a lower accident rate (Polders et al., 2015). The above studies do confirm the improvement of CRTLs for safety between motor vehicles. However, CRTLs are

E-mail address: lgh@chd.edu.cn (G. Liang).

^* Corresponding author.

more than just a single motor vehicle use, there are other road users as well. Improving the traffic efficiency and operation safety of motor vehicles will inevitably infringe the interests of other road users.

It has been shown that there is an impact on pedestrians with a significant increase in pedestrian-vehicle conflicts with this design (Fitzpatrick et al., 2006, Muley et al., 2017). A study of pedestrian crossing and vehicle-yielding behavior at CRTLs showed that only 15 % of vehicles yielded to pedestrians (Muley et al., 2017). Similarly, Polders' research findings indicated a decrease in overall accidents at intersections with CRTLs; however, the risk of rear-end collisions between motor vehicles significantly increased. This phenomenon is primarily attributed to conflicts between motor vehicles and pedestrians competing for the right of way. Apart from the above studies, there has been limited attention to pedestrian safety at CRTLs. What is evident is that the design of CRTLs results in pedestrians needing to cross the street a second time, and the crossing process for pedestrian changes from continuous to intermittent, increasing the risk of interacting with motor vehicles once at CRTLs. Jiang et al. (2020) used alternative safety and behavioral measures to study pedestrian safety at CRTL, and the results showed that the design of CRTL increased pedestrian risk at signalized intersections from different safety dimensions. Furthermore, unlike other locations, CRTLs are typically unsignalized, leading to chaotic and disorderly behavior of both vehicles and pedestrians. Due to the proximity of the safety island to the roadside pedestrian crosswalk, pedestrian crossing paths become more random, resulting in an enlarged potential conflict area (Chen et al., 2022a), as shown in Fig. 1. Additionally, Sheykhfard et al. (2023a) found that the probability of conflict between motor vehicles and pedestrians in this area increased significantly with the increase of vehicle traffic by collecting the driver's operation behavior through CRTL. Due to the setting of CRTL, the speed of right-turn vehicles is higher than that of traditional right-turn modes, and the speed of vehicles will change with the turning radius, which has potential risks for pedestrians. These factors contribute to the strong characteristics of randomness, ambiguity, and complexity in pedestrianvehicle conflicts at CRTL locations. In addition, pedestrians, as a vulnerable group of road users, are susceptible to influences from motor vehicles, non-motorized vehicles, etc. in their daily traffic behavior and are often at risk of injury or even death in traffic accidents (Tiwari, 2020). According to statistics, the number of road deaths has risen over the past two decades, with pedestrians accounting for more than 35 % of road deaths (World Health Organization, 2018), and the problem of pedestrian traffic safety remains serious. Furthermore, it's important to acknowledge the limitations of traditional safety evaluation methods, such as regression analysis and mathematical approaches using conflict data (Zhu et al., 2020). These methods require extensive data collection and may introduce subjectivity in factor selection and classification. Given the unique design of CRTL and traffic flow characteristics, these methods may not accurately capture the risk of pedestrian-vehicle conflict regarding factor screening, index weighting, and risk assessment. Therefore, proposing a scientific safety evaluation method for the problem of pedestrian-vehicle conflict at CRTL has become an urgent problem.

The aim of this study is to propose a comprehensive safety evaluation model to effectively assess the pedestrian-vehicle conflict problem at

CRTL. And make the model as portable and generalizable as possible. With this aim, a field survey was conducted in four CRTLs, starting from the frequent pedestrian-vehicle conflicts in the region, analyzing the characteristics of motor vehicles, pedestrians, and road environment in the region, and constructing a multilevel evaluation index system for the problem of pedestrian-vehicle conflicts in CRTLs. When determining the weights of the indicators, the methods of AHP, GRA and EWM are combined. Based on the obtained weights combined with the cloud model digital features, the cloud generator is further used to complete the conversion between quantitative and qualitative language to complete the evaluation of the risk of pedestrian-vehicle conflict in the region.

This paper is structured as follows: the second part is a literature review. The third part is the methodology, which describes the construction process of the safety evaluation model. The fourth part is the case study. Finally, the fifth part is the conclusion and discussion, which summarizes the findings and discusses the limitations as well as future research directions.

2. Literature review

2.1. Factors affecting the safety of pedestrian-vehicle interaction

Pedestrian-motor vehicle interaction safety has been a key issue in the industry, and scholars in many countries and regions have conducted a large number of studies to explore the factors affecting pedestrianvehicle conflicts (accidents). In contrast to traditional road safety research based on historical accident data (Niaki et al., 2016, Wang et al., 2019), the interaction between pedestrians and motor vehicles is more random and difficult to record. With the application of traffic conflict technology, most of the research in this field has been conducted based on this technology. Sheykhfard et al. (2023b) analyzed pedestrian-vehicle conflicts across urban and non-urban areas, considering intersections with and without markings. They categorized risk levels using safety surrogate indicators and proposed strategies for avoiding pedestrian-vehicle collisions. In the study of pedestrian-vehicle conflicts at urban intersections, it was found that factors such as age, gender, distraction behavior, crossing speed, pedestrian flow, and companion crossing in pedestrian characteristics, and factors such as headway, vehicle type, and traffic flow in vehicle characteristics have different degrees of influence on the severity of conflicts (Pour et al., 2018, Liu et al., 2021, Hamilton et al., 2022, Wen et al., 2022, Mingfang et al., 2023). Pedestrians using mobile phones or listening to music while crossing the street can become distracted and disregard road information, significantly increasing the risk of pedestrian crossing (Pesic et al., 2016, Truong et al., 2022). In addition to this, spatial crossing violations (irregular use of crosswalks) generated by pedestrians due to proximity psychology, especially in areas where the length of crosswalks is small, lead to drivers being unable to estimate the location of pedestrians' presence, shortening their reaction time, and seriously jeopardizing traffic safety (Qu et al., 2017, Chen et al., 2022a). Regarding road design and environmental factors, several studies have demonstrated the influence of such factors. For example, Babic et al. (2020) reviewed and summarized about the impact of traffic signs on driver as well as road safety. Arhin et al. (2022) demonstrated the efficacy of pedestrian warning signs in enhancing pedestrian-vehicle safety. Additionally, Sheykhfard et al. (2022) found that the presence or absence of crosswalk lines significantly affects the severity of pedestrian-vehicle conflicts. These studies affirm the positive impact of traffic markings on road safety. In terms of channelization design, the turning radius of curves has a significant impact on vehicle speed. The influence of weather and visibility on traffic has also been confirmed, such as the effect of rain or snow on pedestrian trajectories (Ding, 2023) and the impact of visibility on vehicle motion states (Peng et al., 2017, Peng et al., 2018).

The research findings mentioned above regarding safety issues at Fig. 1. Pedestrian-vehicle conflict area. CRTLs provide critical reference value for the selection and evaluation of indicators in this study. In summary, considering various factors within observable and recordable conditions is crucial for studying pedestrianvehicle conflicts. It is also essential to take into account the characteristics of traffic flow and road design within the study area.

2.2. Traffic safety evaluation

Traffic safety assessment can be divided into pre-evaluation and post-evaluation. Pre-evaluation is commonly used in the road design stage to determine whether the design is reasonable, whether the design speed meets the needs of traffic scenarios, and whether there are any risks according to the corresponding specifications (Lyu et al., 2023). On the other hand, traditional post-evaluation involves the use of accident data or traffic conflict data to evaluate safety issues across different regions and time periods (Zhu et al., 2020, Cheng et al., 2021). With the technological development of computational power, real-time evaluation using trajectory data based on traffic conflict technology has also been researched (Hu et al., 2022), but this method requires strong arithmetic performance support. Due to the abstraction, randomness and uncertainty of the traffic system and safety influencing factors, the key to the evaluation of traffic conflicts is how to reflect the randomness and ambiguity of the natural language scientifically, and how to accurately convert the qualitative and quantitative language. Currently, common methods used include AHP, EWM and Fuzzy Analysis (Wang et al., 2010, Cheng et al., 2011), but none of them can take into account both fuzziness and randomness (Zhu et al., 2013). For example, AHP decomposes a complex problem into factors and forms a hierarchical structure, and determines the weights of the indicators through expert scoring, but this method is highly subjective and not easily convincing, and it is difficult to determine the weights when there are too many indicators (Ayag and Ozdemir, 2006). The EWM uses information entropy to calculate the weights of each indicator according to the degree of indicator change (Zeleny and Cochrane, 1982). Although it possesses objectivity, it lacks flexibility and cannot handle the uncertainty and fuzziness of decision problems. Since the proposal of the cloud model by Li and Liu in 2004 (Li and Liu, 2004), this method has been successfully applied in the fields of intelligent control, data mining, and network security due to its advantages in handling uncertainty and its flexibility and adaptability.

Traffic systems are inherently uncertain, but existing evaluation methods often overlook this randomness. Therefore, this study uses the cloud model to consider various weight determination methods, aiming to minimize subjective bias and data quality issues. By adjusting the cloud model's evaluation matrix with combined weights, it improves accuracy in describing the fuzziness and randomness of traffic safety while addressing objectivity weaknesses.

3. Methodologies

The transport system is a complex system, and the decision-making

of transport participants is not the result of a single factor guide, but the behavior made under the coupling of multiple factors. In studies on traffic safety, determining the level of influence of factor indicators is the key point. This study employs an empowerment approach combining subjectivity and objectivity. The evaluation language is finally converted using a cloud model, and the evaluation method flowchart is shown in Fig. 2. This section mainly introduces the evaluation index system constructed in the study, the method for determining index weights, and the application of the cloud model.

3.1. Construct index system and AHP

This study uses the AHP for subjective weight determination (Saaty, 1986), widely utilized in transportation research, particularly in analyzing traffic accidents. AHP's ability to break down complex traffic issues into hierarchical levels enables systematic organization and summarization of various factors in pedestrian-vehicle conflict scenarios. This method facilitates understanding the relationships among these factors and allows flexible adjustment of outcomes and evaluation criteria, suiting the diverse research areas and subjects within traffic conflict studies (Gass, 2005, Kumar and Vaidya, 2006).

Based on the design characteristics of CRTLs and previous research findings, and in combination with the actual case scenarios, this study has established a two-layer evaluation index system. First layer: includes three basic traffic components − pedestrians, motor vehicles, and road environment. The second layer digs into the foundations of the first layer respectively, containing 11 indicators such as pedestrian walking speed, pedestrian flow, average vehicle speed, headway, turning radius, as shown in Fig. 3. Table 1 elucidates the details and rationale of the second-layer indicators.

Unlike single-layer indicators, this study first conducted pairwise comparisons of the first-layer indicators, namely pedestrians (*U*1), motor vehicles (*U*2), and road environment (*U*3), using paired comparison methods and a 1–9 scaling scheme to construct a judgment matrix (Saaty, 2010). The scaling method refers to Table 2. The same applies to the second tier of indicators. The results are then tested for consistency to obtain the indicator hierarchical weights, denoted as ωi.

3.2. Grey entropy weight calculation

3.2.1. Grey relativity

Grey relational analysis (GRA) is a mathematical method for quantifying the correlation between variables, originally proposed by Chinese scholar Deng Ju-Long in 1982 (Ju-Long, 1982). GRA has strong objectivity by calculating the similarity of the geometric shape of the data sequence curve to determine the degree of correlation between the indicators. Unlike traditional correlation analysis methods, GRA has no rigid requirement for the amount of data and does not require the original data to obey any statistical distribution. This advantage is consistent with the diversity of traffic conflict factors and the complexity

Fig. 2. Evaluation modeling process.

Fig. 3. Risk Evaluation Index of Vehicle − Pedestrian Conflict.

Table 1 Shows the description or reason of the secondary indicators.

Indicators	Explanation or Reason
C1: Walking speed C2: Proportion of crossings using crosswalks	Average speed of pedestrians crossing CRTL Pedestrians not using crosswalks to cross the street increases the risk of pedestrian-vehicle conflicts( Chen et al., 2022b)
C3: Proportion of use of technological devices	Behaviors such as talking on the phone and looking down at a cell phone can lead to distractions for pedestrians(Zhang et al., 2018).
C4: Proportion of crossings in groups	Differences in crossing behavior between pedestrians crossing alone and in groups(Zhang et al., 2020)
C5: Pedestrian flow	Number of pedestrians crossing CRTL per unit hour
C6: Proportion of large vehicles	Percentage of large vehicles in the total number of vehicles(Wen et al., 2022)
C7: Average vehicle speed	Average speed of vehicles approaching CRTLs
C8: Average headway	Mean headway within CRTLs(Feng and Pei, 2007)
C9: Degree of road marking integrity	The integrity of lane lines, crosswalk lines and other road markings(Li et al., 2017)
C10: Right-turn lane turning radius	The turning radius affects drivers' visibility and vehicle speed(Autey et al., 2012)
C11: Warning sign installation	The installation of warning signs and markings( Rezapour and Ksaibati, 2022)

Table 2 Intensity of Importance for Factors ((adapted from(Saaty, 1986)).

Intensity	Definition	Explanation
1	Equal importance	Two activities contribute equally to the objective.
3	Moderate importance	Experience and judgment slightly favor one activity over another.
5	Essential importance	Experience and judgment strongly favor one activity over another.
7	Demonstrated importance	An activity is strongly favored in practice.
9	Extreme importance	The evidence favoring one activity over another is of the highest possible order of affirmation.

of data types (Kuo et al., 2008). Due to traffic safety incidents being rare events, data scarcity is a common occurrence in research. The characteristic of GRA not relying on data volume is also one of the reasons for selecting it as an objective weighting method (Lu-rong, 2009).

Prior to conducting grey analysis on the system, the first step is to determine the sequence of characteristic indexes for the system, namely the sub-index sequence, is determined and dimensionlessly processed. The system feature series x is:

$$x_i = {x_i(1), ..., x_i(k), ..., x_i(n)}$$ (1)

where:xi(k) is the value of the *k*th system feature sequence.

The data sequence that reflects the behavior characteristics of the system is called the parent index sequence. The parent index sequence is expressed as:

$$y = {y(1), ..., y(k), ..., y(n)}$$ (2)

where: y(k) is the value of the parent indicator corresponding to the *k*th system feature sequence.

The correlation coefficient and the degree of correlation of each indicator in the sub-series with the parent series can be calculated by the following formula:

$$\zeta{i}(k) = \frac{\underset{i}{\min} \inf |y(k) - x{i}(k)| + \underset{i}{\rho} \underset{k}{\max} |y(k) - x{i}(k)|}{|y(k) - x{i}(k)| + \underset{i}{\rho} \underset{k}{\max} |y(k) - x_{i}(k)|}{(3)}$$

where:ξi(k) is the correlation coefficient of xi to y(k) at point k,ρ is the grey discrimination coefficient, which takes the value of 0 ~ 1, and generally takes 0.5.

The correlation coefficients of each point can be brought into formula (4) to find the correlation ri between xi and y(k):

$$r{i} = \frac{1}{n} \sum{k=1}^{n} \xi_{i}(k) \tag{4}$$

3.2.2. Entropy weight method

Initially proposed by Shannon in 1948, information entropy quantifies the randomness and disorder of data, finding applications in various fields (Shannon, 1948). In multi-criteria decision analysis, Zeleny and Cochrane (1982) adapted it to develop the "entropy weight method (EWM)" for systematic weight determination. In traffic safety, EWM is used to assess indicator weights based on data entropy (Zong et al., 2019). It dynamically adjusts weights in different traffic conflict scenarios, making it suitable for this study (Wang et al., 2019, Zhang et al., 2023). The basic steps of the EWM are as follows:

⋅ Establish a numerical matrix. Assume there are n evaluation objects and m evaluation indicators. Let xij(i = 1, 2, …, m; j = 1, 2*,…, n*) denote the value of the *j*th evaluation indicator of the *i*th object, constituting the evaluation indicator value matrix Xij:

$$X{ij} = \begin{pmatrix} x{11} & \dots & x{1n} \ \vdots & \ddots & \vdots \ x{m1} & \dots & x_{mn} \end{pmatrix}$$

$$(5)$$

⋅ Data standardization. For positive indicators and negative indicators, formula (6) and formula (7) are adopted respectively for standardization to eliminate dimensional effects.

$$v{ij} = \frac{x{ij} - \min(x_j)}{\max(x_j) - \min(x_j)}$$

$$\tag{6}$$

$$v_{ij} = \frac{\max(xj) - x{ij}}{\max(x_j) - \min(x_j)}$$

$$(7)$$

⋅ Calculate the entropy value of the indicator. First, the weights of each evaluation indicator are calculated according to formula (8). The entropy values corresponding to the indicators are calculated as shown in formula (9):

$$P{ij} = \nu{ij} / \sum{i=1}^{m} \nu{ij} \tag{8}$$

$$E{j} = \frac{-1}{\ln(m)} \sum{i=1}^{m} P{ij} \ln P{ij}$$ (9)

⋅ Determine the weights. Based on the information entropy Ej in formula (9), the indicator weights *ωv*are calculated as:

$$\omega_{\nu} = \frac{1 - Ej}{\sum{j=1}^{m} 1 - E_j} \tag{10}$$

3.3. Combination weight

Objective data reflect inherent laws, yet in complex traffic systems with diverse participants and subjective decision-making biases, this paper combines AHP, GRA, and EWM weights. GRA emphasizes data correlation, suitable for uncertain data (Shemshadi et al., 2011), while EWM, based on information entropy, objectively reflects indicator differences (Kuo et al., 2008). Integrating these approaches enhances evaluation comprehensiveness and accuracy. The calculation method is as follows:

Using the weights obtained from formula (10), the grey relational coefficients are modified to obtain the grey entropy weight *ωj*of the *j*th evaluation indicator as:

$$\omega_j = \frac{\omega_v \cdot rj}{\sum{j=1}^n \omega_v \cdot r_j} \tag{11}$$

where:*ωv*is the entropy weight of the indicator, rj is the gray correlation of the indicator.

After obtaining the objective weight, we use the average weighting method to calculate the combination weight, that is, the subjective weight and the objective weight occupy the same important position in the combination weight. This method aims to reduce the bias that may exist by relying solely on subjective methods (Ishizaka and Labib, 2011), while maintaining the robustness and reliability of objective data. The flexibility of the weighting method allows recalibration based on changes in new data or expert opinions to maintain dynamic balance. The combination weight calculation method is as follows:

$$\omega = \varphi \omega_i + (1 - \varphi)\omega_j \tag{12}$$

where: φ is a constant, taken as 0.5; *ωi*is the hierarchical weight; *ωj*is the gray entropy weight.

3.4. Application of cloud model

The cloud model was first proposed in 1995 as an uncertain transformation model for dealing with the conversion between qualitative concepts and quantitative descriptions. It utilizes linguistic variables to describe the randomness and fuzziness in concepts, and uses numerical characteristics to reflect the probability distribution laws (Li and Liu, 2004). Let X be a set of numerical values, where X = {x}, and X is referred to as the domain. C represents a qualitative concept over the set

X. The membership degree μ(x) of x in C is characterized by a stable tendency of random numbers. If it satisfies:x ∼ *N Ex, En*ʹ2) , where *En*ʹ ∼ N En, He²) , and adheres to formula (13) for the membership degree of C, then the distribution of x over the domain is termed as a normal cloud, with each x being referred to as a cloud drop (x, μ(x)) (Li and Liu, 2004, Zhou et al., 2023).

$$\mu(x) = \exp\left{-\left(x - En\right)^2 / \left(2En^2\right)\right} \tag{13}$$

In the formula,μ(x) represents membership degree; x denotes the original variable;Ex stands for the expectation of x ,En^ʹ signifies entropy, and He represents hyper entropy.".

The model utilizes three numerical characteristics − expectation Ex, entropy En, and hyper entropy He − to reflect the randomness and correlation of the evaluation object. Ex represents the expected cloud drop distribution, serving as the optimal qualitative concept point. En measures the uncertainty level of the qualitative concept, with higher values indicating increased fuzziness. He quantifies uncertainty within entropy, where larger values signify greater cloud dispersion, increased randomness in membership degree, and thicker cloud density (Yang et al., 2018). The cloud model contains two types of cloud generators. The forward cloud generator (CG) achieves the conversion from qualitative to quantitative, while the reverse cloud generator (CG-1) achieves the conversion from quantitative to qualitative. The conversion mode is shown in Fig. 4.

3.4.1. Evaluation cloud model for pedestrian-vehicle conflicts

Pedestrian-vehicle conflict assessment is a complex and uncertain process involving a variety of factors such as pedestrian behavior, vehicle speed, and road conditions. Cloud modeling can effectively deal with these uncertainties and provide a more accurate and comprehensive perspective on conflict assessment. The model construction steps are as follows:

⋅ Establish evaluation matrix. Firstly, the evaluation criteria are classified into risk levels based on quantitative data. Experts assign scores to different indicators of each sample within the corresponding intervals based on the grading results of the indicators. This method can effectively reduce subjective biases (Chen et al., 2022a). The evaluation matrix Z of m × n is obtained by scoring n evaluation indexes by m experts in the industry. Zij is the evaluation and scoring result of expert i on the *j*th index.

$$Z = \begin{pmatrix} Z{11} & \dots & Z{1n} \ \vdots & \ddots & \vdots \ Z{m1} & \dots & Z{mn} \end{pmatrix}$$

$$(14)$$

⋅ Calculate the numerical characteristics of the evaluation indicators. Indicator evaluation cloud:Cij ⁼ ( Exj,Enj,Hej ) , j = 1,2,…,n. In order to avoid the case that the hyper-entropy is an imaginary number, the MBCT-SR algorithm is used to calculate the numerical characteristics (Changlin and Guoyin, 2013):

Fig. 4. Cloud generators.

$$Ex{j} = \frac{1}{m} \sum{i=1}^{m} Z_{ij} \tag{15}$$

Randomly sample N cloud droplets Zi (i = 1, 2, …, N):

$$Zi = {Z{i1}, Z{i2}, ..., Z{im}}, \overline{Zi} = \frac{1}{r} \sum{i=1}^{m} Z_{ij}$$ (16)

$$DZ{i} = Y^{2} = \frac{1}{m-1} \sum{i=1}^{m} \left[ Z{ij} - \overline{Z{i}} \right]^{2}$$ (17)

$$Y^{2} = \left{ Y{1}^{2}, Y{2}^{2}, \dots, Y_{m}^{2}, \right} \tag{18}$$

Calculate the entropy and hyper-entropy for each indicator as follows:

$$En_{j} = \frac{1}{2}\sqrt{4(EY^{2})^{2} - 2DY^{2}}$$ (19)

$$He_j = \sqrt{EY^2 - En_i^2} \tag{20}$$

Where: Exj is the expectation of the *j*th indicator; Enj is the entropy of the *j*th indicator; Hej is the hyper-entropy of the *j*th indicator;m is the number of indicators.

⋅ Calculate the comprehensive evaluation cloud. Substituting the combined weights obtained from formula (12) into C, the comprehensive evaluation cloud is obtained:

$$C = \begin{pmatrix} \omega_1 \ \vdots \ \omega_n \end{pmatrix}^T \begin{pmatrix} Ex_1 & En_1 & He_1 \ \vdots & \vdots & \vdots \ Ex_n & En_n & He_n \end{pmatrix} = (Ex, En, He)$$ (21)

⋅ Use the CG to produce the comprehensive cloud image for the risk of pedestrian-vehicle conflicts.

3.5. Criteria for selecting experts

To minimize the biases introduced by individual cognitive perceptions of subjective methods employed in the evaluation model, the study developed selection criteria for the evaluation experts involved in AHP and cloud models: The number of experts depends on the size of the evaluation indicator system and should not be too small. However, experts must be required to have a wealth of relevant experience and professionalism to ensure a proper understanding of the evaluation indicators. Their occupations include but are not limited to professors, industry practitioners, government officials, engineers, etc., on the premise of ensuring good professional quality.

4. Case study

4.1. 1 survey location

The study site is situated in Laoshan District, Qingdao, China. This intersection is formed by the intersection of the east–west arterial road, Hong Kong East Road, and the north–south arterial road, Haier Road. Each approach is equipped with a CRTL and is labeled based on its location, as illustrated in Fig. 5. Due to the presence of numerous commercial, residential, and tourist attractions in Laoshan District, the traffic volume in the area is at a relatively high level. The study section carries the majority of the commuting, shopping, and tourist-generated traffic within the region. According to the data from the summer of 2021, the average daily traffic (ADT) on Hong Kong East Road exceeded 20,000 vehicles, while Haier Road had an ADT of approximately 15,000 vehicles. Furthermore, the immediate vicinity of the research site is characterized by substantial pedestrian traffic-generating structures, including shopping malls, office complexes, and subway stations. The pedestrian flow is adequate to accommodate the requirements of this study. Moreover, the uniform distribution of these structures across various entry points effectively mitigates the influence of environmental variances on pedestrian crossing trajectories (Yongheng et al., 2019). The CRTLs involved in this study are all physical safety islands designed with a configuration where a dedicated right-turn lane is established in the far-right lane of the road near the intersection to segregate rightturning vehicles.

4.2. Data collection

The research utilizes a 'video + artificial' approach for data collection, as depicted in Fig. 6. Road environmental factors were assessed using UAV photography and on-site surveys, while surveillance videos captured pedestrian and motor vehicle activities above CRTL lanes. Tracker software facilitated the extraction of trajectory data, ensuring accuracy through manual correction (Trocaru et al., 2019). Subsequently, motion state indicators such as speed and headway time distance were analyzed. This study defines pedestrian-vehicle conflicts using the temporal dimension indicator, Post-Encroachment Time (PET), sourced from Surrogate Safety Measures (SSM) as the conflict metric (Gettman et al., 2008). Considering relevant research and CRTL traffic characteristics, a conflict threshold of 3.5 s was established. PET values less than 3.5 s denote pedestrian-vehicle conflicts (Chen et al., 2017, Kumar et al., 2019, Wu et al., 2020, Chen et al., 2023). Additionally, pedestrian group crossing and technology device use were categorized as follows: (i) Clustered crossing occurs when over 2 pedestrians cross with a gap less than 3 body lengths, and (ii) Technology device usage encompasses activities like phone calls, music listening, and mobile phone interaction.

Fig. 7 illustrates the traffic volume of the studied road. To ensure the reliability of the research findings, this study selected two time periods

Fig. 5. Survey location.

Fig. 6. Data collection and analysis work.

Fig. 7. Change in daily traffic.

with high visibility. The chosen periods were the off-peak hour (7:00–8:00) and the peak hour (17:00–18:00). There are significant differences in traffic flow and conflict counts between these two time periods, which enhances the reliability of the study. A total of 2,814 motor vehicles and 2,159 pedestrians were recorded in this survey, resulting in 377 valid conflict samples, meeting the minimum sample size requirement for the study.

4.3. Determination of indicator weights

In this study, following the expert selection criteria outlined in sec tion 3.5, we invited five university faculty members with the rank of Associate Professor or higher to evaluate the indicators. Their tasks included pairwise comparisons on a 1–9 scale and scoring the cloud evaluation matrix on a hundred-mark system. The five invited experts all have more than 10 years of research experience in the field of traffic safety and traffic management. They have also been engaged in many safety evaluations and have a thorough understanding of the indicators of this study. Firstly, subjective weights were determined using the AHP. Subsequently, objective weights for each indicator were obtained through a combination of the GRA and EWM. Finally, the combined calculation of subjective and objective weights was conducted using the modification function (formula 12).

4.3.1. AHP − subjective weights

According to Table 2, the experts use the paired comparison method to compare and score the two layers of indicators of the evaluation system. By leveraging the expert scores, we have crafted an evaluation matrix and computed the weights for the primary evaluation criteria, i. e., pedestrians (U1), motor vehicles (U2), and road environment (U3), as

0.5917, 0.3332, and 0.0751, respectively, employing the matlab software. Check the table to get RI take 0.52, and calculate CR = CI/RI = 0*.*0136 < 0*.*1, the evaluation matrix meets the consistency test. Similarly, the weights of the evaluation system's second-level indicators C1 ~ C11 are calculated as shown in Table 3.

4.3.2. Gray entropy-objective weights

The GRA method first needs to determine the parent indicator series (Qishan et al., 1996), and the object of this study is the conflict between pedestrians and motor vehicles. With the widespread application of traffic conflicts in traffic safety analysis (Lyu et al., 2023), commonly used conflict research indicators can be broadly categorized into two main types: traffic conflict count (Meng et al., 2013) and traffic conflict rate (Shen and Wang, 2011, Sun et al., 2013, Jiang et al., 2019). Absolute value indicators, such as traffic conflict counts, are commonly used in large-scale, long-term traffic safety statistics for their simplicity and clarity. However, they have limitations, being static and isolated (Zhu et al., 2020), and are less suitable for this study, which focuses on a small area and a short time frame. Hence, this study employs relative value indicators (traffic conflict rate) for analysis, as this metric has the capability to mitigate potential influences of traffic volume disparities. The pedestrian-vehicle conflict rate was calculated using the pedestrian and motor vehicle traffic volume data collected and the number of conflicts determined through SSM. The pedestrian-vehicle conflict rate indicator is used as the parent indicator sequence of the GRA weights, and the second-tier indicators in the evaluation system are used as the sub-sequence data. Pedestrian-vehicle conflict rate calculation method is shown in formula (22), in which the calculation of traffic volume involves converting the flow of various right-turning vehicle types into a unified traffic equivalence coefficient and summing them up. The

Table 3 Evaluation index weight.

Index	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11
ωi	0.1173	0.2567	0.1305	0.0482	0.0389	0.0375	0.2362	0.0595	0.0076	0.0506	0.0169

collected data is used to construct an evaluation matrix, denoted as X, and the Grey Relational Degree, Entropy Weight, and Grey Entropy Weight of the evaluation indicators are computed according to formula (1) to (11). The results are presented in Table 4.

$$R_{\nu-p} = \frac{T}{\sqrt{Np \times N\nu}} \tag{22}$$

Where:Rv⁻ *^p*is the traffic conflict rate for motor vehicles and pedestrians, T is the number of traffic conflicts, Np is the number of people (persons/ h), and Nv is the number of vehicles (pcu/h).

4.3.3. Combination weight

By employing Formula (12), the combination of subjective and objective weights is achieved. Taking second-level evaluation indicators C1 to C11 as an example, the trend and size of subjective weights, objective weights and combination weights are compared, as shown in Fig. 8 and Fig. 9. Figs. 8 and 9 illustrate the significant weight distribution and trends. Comparative analysis of multiple weights reveals that most indicators exhibit consistent weight variation trends. Notably, subjective and objective weights show significant disparities for indicators C2, C4, and C7. Experts suggest that pedestrian crossing behavior (use of crosswalks) and vehicle entry speed into CRTL have a pronounced impact on pedestrian-vehicle conflicts. In the grey entropy analysis, these indicators' results indicate their presence of influence, albeit not as prominently as other indicators, while pedestrian clustering crossing behavior holds a significant position in affecting pedestrianvehicle conflicts. To address this disparity, the study combines both types of indicators to mitigate the influence stemming from differences in individual subjective perceptions and objective patterns.

4.4. Comprehensive evaluation of the risk of pedestrian-vehicle conflict

4.4.1. Conflict risk classification

According to the cloud model evaluation process, the indicator levels are divided into four intervals based on the risk of pedestrian-vehicle conflict. Level 1 corresponds to [0, 25), Level 2 to (25, 50], Level 3 to (50, 75], and Level 4 to (75, 100]. The standard digital features of cloud models for different risk levels are computed using formula (23) to (25), as shown in Table 5 (He et al., 2018).

$$Ex{v} = \frac{x{\text{max}} + x_{\text{min}}}{2} \tag{23}$$

$$En{\nu} = \frac{x{\text{max}} - x_{\text{min}}}{2\sqrt{2\ln 2}} \tag{24}$$

$$He_{\nu} = h$$ (25)

Where:*x*max, *x*min are the maximum and minimum values in the evaluation; h is the hyper-entropy value, reflecting the cohesion of the cloud droplets, which is usually taken to be one order of magnitude lower than Env, and in this paper h is taken to be 0.1.

After obtaining the digital features, the standard cloud map of

pedestrian-vehicle conflict risk level is generated by CG, as shown in Fig. 10. The normal cloud diagrams correspond to four different risk levels.

4.4.2. Risk evaluation of pedestrian-vehicle conflicts

A total of four observation locations were selected to collect the basic data for this study. Based on the peak and off-peak periods of traffic flow, these data were divided into eight samples for evaluation. Experts assign scores to the evaluation indicators of each sample based on the risk interval values determined, and then input the scoring results into formula (15) to (20) to obtain numerical characteristics. The combination of weights obtained from the AHP, GRA, and EWM were applied to the numerical characteristics in formula (21) to obtain the comprehensive cloud numerical characteristics of the samples, as shown in Table 6. Subsequently, using MATLAB programming and a forward cloud generator, a comprehensive cloud diagram was generated, as illustrated in Fig. 11.

From the results in Table 6, we observe that in the study area, locations 1, 2, and 4 exhibit higher levels of expectation (Ex) during both peak and off-peak periods, indicating elevated pedestrian-vehicle conflict risk in these areas. Furthermore, the entropy values (En) for each location are all greater than the standard cloud entropy, suggesting a higher degree of fuzziness in pedestrian-vehicle conflict risk. This increased fuzziness could be attributed to the influence of various qualitative factors, leading to higher uncertainty, particularly at location 3. The results of the hyper-entropy (He) exceed the standard cloud hyper-entropy for all survey samples except 1-Off-peak hour and 2-Peak hour, indicating a higher level of randomness in pedestrian-vehicle conflicts. In Fig. 11, the numerical values corresponding to the central line within the cloud diagram reflect the overall level of risk (Ex). The width of the cloud diagram mirrors the stochastic nature of conflicts, denoted by the En index. Regarding hyper-entropy He, it primarily determines the thickness of the cloud diagram, representing the ambiguity surrounding conflict risk.

The comprehensive cloud diagrams for the survey area are overlaid with standard cloud diagrams on the same graph, providing a visual representation of the risk characteristics for each location, as shown in Fig. 12. In the overall comparison, the pedestrian-vehicle conflict risk in the study area falls between Level 2 and Level 3. Locations 1, 2, and 4 exhibit higher pedestrian-vehicle conflict risk during peak hours, posing a significant risk of severe conflicts and even accidents. Additionally, the cloud diagrams' half-widths indicate a high level of uncertainty regarding the occurrence of pedestrian-vehicle conflicts in the study area. High uncertainty is also a characteristic of traffic safety events (Azevedo et al., 2015). Nevertheless, on the whole, the pedestrianvehicle conflict risk in the studied locations remains manageable, emphasizing the need to strengthen relevant traffic safety preventive measures to prevent accidents.

4.5. Field validation of evaluation findings

Model evaluation results were validated against on-site negative

Table 4 Weight calculation results.

Index	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11
r	0.6209	0.6570	0.6298	0.6965	0.7825	0.5326	0.6353	0.6312	0.6373	0.6450	0.6499
ωv	0.0542	0.0518	0.0823	0.1517	0.0831	0.0882	0.0584	0.1307	0.0846	0.1304	0.0846
ωj	0.0518	0.0524	0.0798	0.1626	0.1001	0.0723	0.0571	0.1270	0.0830	0.1294	0.0846

Fig. 8. Comparison of different weights.

Fig. 9. Comparison of different weights.

Table 5 Standard Cloud Digital Features.

Risk level	Risk value range	Digital Features	Instruction
Level 1	[0, 25)	(12.5,10.62,1)	Lower risk of conflict
Level 2	(25, 50]	(37.5,10.62,1)	Low risk of conflict
Level 3	(50, 75]	(62.5,10.62,1)	Higher risk of conflict
Level 4	(75, 100]	(87.5,10.62,1)	High risk of conflict

Fig. 10. Standard cloud risk diagram.

issues and PET indicators (Table 7). The mean (M) of PET indicators reflects overall conflict severity, with smaller values indicating higher severity. Variance (S) indicates conflict severity randomness, with larger values suggesting greater randomness. Consistent trends were observed between PET sample mean and variance, and variations in risk level (Ex) and risk randomness (En) in the cloud model. Factors with higher weight

Table 6 Sample Integrated Cloud Digital Features.

Sample	Digital Features
	Ex	En	He
1-Peak hour	54.43	20.25	1.45
1-Off-peak hour	52.92	22.07	0.49
2-Peak hour	57.10	24.60	0.26
2-Off-peak hour	51.45	22.82	1.65
3-Peak hour	49.65	27.44	1.83
3-Off-peak hour	49.83	27.05	1.51
4-Peak hour	54.24	24.68	1.84
4-Off-peak hour	53.99	26.83	1.48

values, such as unregulated pedestrian-vehicle crosswalk use (C2), vehicle speed (C7), and right-turn radius (C10), were associated with negative issues in high-risk pedestrian-vehicle conflict areas during field validation.

The results strongly support the accuracy of the proposed model in weighting indicators and assessing risks. Addressing issues linked to high-weight indicators is vital for guiding local pedestrian-vehicle conflict prevention efforts and informing indicator selection in future studies.

5. Conclusion and discussion

In this study, the evaluation method of hierarchical-gray entropycloud model is proposed to address the characteristics of pedestrianvehicle conflicts at urban CRTLs as well as the complexity and stochasticity of the causes and the serious method effectiveness is analyzed in the field with cases. The main contributions of this study are: (i) The study thoroughly examines CRTL design features and pedestrian-vehicle conflict dynamics. It establishes a comprehensive evaluation index system with three primary and eleven secondary indicators. By validating the model's efficacy through comparison with field survey findings, it assesses pedestrian-vehicle conflict risk at CRTL. Additionally, it highlights the impact of proposed indicators on this risk. The safety factors integrated into the evaluation offer valuable insights for future safety inquiries and serve as a theoretical framework for enhancing pedestrianvehicle interaction safety for road managers; (ii) This paper presents a risk assessment model using the hierarchical-grey entropy-cloud model. It addresses randomness and uncertainty by outlining a process to establish an evaluation index system and calculate subjective and objective weights. This approach balances subjectivity and objectivity in weight determination. By integrating cloud modeling, it facilitates both quantitative and qualitative transformations, enabling effective risk assessment and handling of uncertainty. The model's versatility extends beyond traffic conflict assessment, offering insights for research involving subjective cognition and objective factors, such as safety evaluations of transportation infrastructure and water environments.

Fig. 11. Comprehensive cloud map of investigation site.

Fig. 12. Cloud map comparison.

In selecting evaluation indicators, this study considered CRTL design characteristics and traffic flow disparities. It included unconventional metrics like the Proportion of Crossings using Crosswalks (C2), supported by prior research (Chen et al., 2022a). Objective analyses revealed discrepancies between subjective perceptions and actual outcomes, with pedestrian spatial violations being less prominent than expected. Conversely, group crossings (C4) emerged as noteworthy, possibly due to pedestrian clustering and prolonged right-of-way occupation (Li et al., 2019). Secondly, the objective weight calculation overlooks interrelationships and interactive effects among factors, diminishing weight reliability. Hence, this study integrates multiple weight calculation methods. It's noteworthy that pedestrian crossing speed and average headway are significant factors in pedestrian-vehicle conflict studies (Pour et al., 2018, Wen et al., 2022, Mingfang et al., 2023). However, in this study's weight results, they are not prominent, mainly due to location differences. Traditional evaluation focuses on crosswalks at entry points and unsignalized sections, where pedestrians cross longer distances, directly influencing drivers' judgments. Conversely, at CRTLs, crosswalks are shorter, minimizing the impact of pedestrian speed on crossing time. Pedestrians assess drivers' willingness to yield primarily based on vehicle entry speed.

The combined assessment findings indicate consistent overall risk levels across different times at each research site. However, variations exist in both the numerical attributes of the cloud model and PET variance. Peak periods are consistently associated with increased pedestrian and vehicular traffic, resulting in shorter vehicle headways and elevated risks of pedestrian-vehicle conflicts (Kumar et al., 2019). This discrepancy is evident in Ex, where peak-hour values consistently surpass those of off-peak hours, signaling higher risk levels, except for minor deviations at Location 3. Traffic flow directly influences pedestrian crossing behavior, leading to chaotic patterns, irregular crosswalk usage, and heightened smartphone engagement, impacting pedestrian safety (Thompson et al., 2013). Lower traffic volumes at Location 3 result in higher headways and speeds. Varied pedestrian perceptions of safe gaps (Yannis et al., 2013) contribute to encounters ranging from close calls with vehicles to safer interactions, increasing entropy and PET variance, thus making conflict severity more unpredictable. Pedestrian and vehicle arrivals follow a random Poisson distribution,

Table 7 Validation analysis of evaluation results.

| Site | Period | Risk | Negative issue | Instruction | PET | | | | | |------|--------------------------|----------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------|------|------|--|--|--| | | | level | | | M | S | | | | | 1 | Peak
hour | Level 3 | ①② | Higher risk of
conflict | 2.28 | 0.27 | | | | | | Off-peak
hour | Level 3 | ③④⑤⑥(②) | Higher risk of
conflict | 2.42 | 0.24 | | | | | 2 | Peak
hour | Level 3 | ⑦⑧⑩ | Higher risk of
conflict | 2.05 | 0.41 | | | | | | Off-peak
hour | Level 3 | ④⑥⑨(⑦) | Higher risk of
conflict | 2.55 | 0.43 | | | | | 3 | Peak
hour | Level 2 | No obvious
issues | Low risk of
conflict | 2.52 | 0.88 | | | | | | Off-peak
hour | Level 2 | No obvious
issues | Low risk of
conflict | 2.44 | 0.81 | | | | | 4 | Peak
hour | Level 3 | ③⑤⑩ | Higher risk of
conflict | 2.24 | 0.72 | | | | | | Off-peak
hour | Level 3 | ③④⑤⑩ | Higher risk of
conflict | 2.48 | 0.77 | | | | | | Negative issue
number | compromised; | ① Pedestrians crossing the street in groups is evident, with
crowds forcing motor vehicles to stop frequently;
② Lack of traffic warning signs;
③ Unregulated pedestrian use of crosswalks is rampant;
④ Higher pedestrian crossing speeds;
⑤ Higher vehicle approach speeds;
⑥ Higher proportion of large and medium-sized vehicles;
⑦ Curves have a small turning radius and driver sight distance is | | | | | | | | | | ⑧ Smaller average headway; | | | | | | | |

contributing to the stochastic nature of interactions. Despite increasing traffic flow, conflict rates may not rise proportionally, elucidating disparities in He index magnitude between peak and off-peak hours across samples.

flow;

streets.

⑨ The diminished awareness of vehicles preemptively reducing speed to yield to pedestrians has resulted in disordered traffic

⑩ Pedestrians prominently use technology while crossing

Compared to conventional approaches like AHP and GRA, the hierarchical-grey entropy-cloud risk assessment model proposed here breaks down complex issues into factors during indicator system setup, facilitating the analysis of potential impact indicators within each factor. Integration of AHP, GRA, and EWM results in indicator weight determination mitigates subjectivity and objectivity imbalances. Leveraging the strengths of GRA and EWM while addressing their weaknesses reduces the influence of objective data on weight determination. Evaluation results rely on cloud modeling, which quantifies risk uncertainty, surpassing limitations of traditional evaluations. Further enhancement in evaluation accuracy is achieved through combination weight adjustment.

Admittedly, this study has some limitations. First, the study was limited to a two-hour sample from four CRTLs at one intersection due to data constraints. While the collected data met statistical requirements, expanding the temporal scope and diversifying locations could enhance reliability. Incorporating factors like weather and architectural surroundings would enrich the assessment's robustness. In addition, the intrinsic factors of traffic participants, such as psychological factors, individual differences, and the mechanism of pedestrian-vehicle conflict, deserve further research in the future.

Declaration of Generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used ChatGPT and Grammarly in order to improve readability of some sentences. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

CRediT authorship contribution statement

Ziyu Chen: Conceptualization, Formal analysis, Investigation, Methodology, Software, Writing – original draft. Guohua Liang: Conceptualization, Funding acquisition, Resources, Supervision, Writing – review & editing. Yixin Chen: Supervision, Writing – review & editing. Xiaoyao Yang: Data curation, Writing – original draft. Yue Liu: Software, Validation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgments

This study was funded by the National Natural Science Foundation of China (NSFC) (Grant No. 52172338) and the Key Research and Development Program in Shaanxi Province (Grant No. 2024GX-YBXM-131).

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