User Perception-Based Optimal Route Selection for Vehicles of Disabled Persons in Urban Centers of Saudi Arabia

Abstract

People with disabilities (PWD), in their routine commutes, confront hindrances associated with road infrastructure in busy urban centers. The present study developed a user perception-based methodology to evaluate optimal routes for PWD in urban settlements in the Kingdom of Saudi Arabia (KSA). A survey captured the preferences for 105 PWD, consisting of 37 powered wheelchair users, 62 manual wheelchair users, and 6 artificial limb users. The multi-criteria decision analysis evaluated the accessibility index for PWD based on four criteria: length, number of junctions, absence of footpath, and slope. This study revealed that manual wheelchair users prefer the length criterion, powered wheelchair users emphasized the absence of footpaths, and artificial limb users were concerned about slope. The result showed that only two routes out of ten showed medium, while those remaining exhibited low accessibility. Most routes were relatively long for people with disabilities, focusing on the need for public transportation with special arrangements in most small and medium-sized cities, like the study area of Hail and Qassim province of the KSA, to reduce the distance and travel time. The proposed framework provides valuable insights to route evaluation for persons with special needs in the KSA and elsewhere.

1. Introduction

As per the World Health Organization (WHO), around 15% of the world’s population has more than one billion people who have some disability [1]. This group of individuals with disabilities possesses the fundamental right to live independently and be equal with others. This right includes equal utilization of public services and facilities and the right to decide where to live freely. Thus, it has also become necessary to make social and urban life accessible to disabled persons. Disability is a pressing social and economic issue in the KSA [2]. As of 2016, there were more than half a million people, one in every 30 people, who had some disability in the KSA [3].

According to the latest report issued by the General Authority for Statistics (KSA) in 2022, the census results indicated that the total number of individuals with mild physical difficulties or at least one disability amounted to 1,350,000 out of the total population. Mobility impairment is the most prevalent, numbering around 305,000 disabilities, constituting approximately 1% of the total population of the Kingdom. They also represent more than half (51.8%) of persons with disabilities [4]; higher rates can be anticipated with the prevalence of health issues like chronic illnesses, inactivity, traffic accidents, and others. Therefore, assessing the needs of PWD, such as providing suitable routes to their destination with mobility and ease, will enable their participation in society by completing their daily work and performing life activities to improve their quality of life with minimum difficulties [5,6].

For PWD, particularly those with mobility impairment, nearly every excursion is limited by impediments along the route. Steep slopes, absence of footpaths, narrow routes, and various others restrict their mobility and render them ineffective in their community [7,8]. Individuals are entitled to autonomous movement and the ability to utilize services available to the broader population. Nevertheless, they continue to encounter barriers to achieving accessibility [9,10]. Different and fewer route alternatives for pedestrians than other road users, such as drivers, make pedestrian route identification more complex, mainly when PWD’s specific routing needs are considered in model development [11]. Although a lot of research is concentrated on developing methods for routing pedestrians, quite a few studies take into account the specific needs of PWD, and none focus on assessing the accessibility of urban areas [12].

Although pedestrian navigation is similar to disabled persons’ vehicle navigation regarding a need for sidewalks, it is less concerned about specific sidewalk challenges because pedestrians are not as limited as wheelchair users. These navigations used in the car used time and distance as cost values, so this does not help disabled person vehicle users in their mobility. For example, wheelchair users could not efficiently manage the shortest distance and time if obstacles hindered their movement. Thus, a longer route with no barriers is better than a shorter one with obstacles hindering their movement [13]. A recently published study about routing algorithms found that the distances wheelchair users of any age have to travel are considerably longer than those of pedestrians to reach a specific destination [14].

Similarly, a study’s preliminary findings showed that manual wheelchair users travel considerably farther than powered wheelchair users or scooter users to reach the same places, traveling 35% farther than the shortest accessible route when compared between modes [15]. A significant contemporary challenge lies in accurately identifying the specific areas where cities lack sufficient accessibility and determining the nature of these limitations [16,17]. An inclusive pedestrian infrastructure can provide PWD access to social interaction, healthcare, and work opportunities [18]. City transportation planning has traditionally aimed to increase performance and efficiency [19].

Nevertheless, emerging strategies take accessibility into account as a crucial component of a sustainable planning strategy [20,21]. The emphasis has shifted from increasing traffic flow efficiency to improving people’s access to diverse locations and services through various means of transportation. Most people with mobility impairment complete their journeys by walking or wheeling, and almost all journeys start and end with these activities [22]. Many nations have implemented accessibility and antidiscrimination laws to aid in the removal of barriers. As an illustration, the Americans with Disabilities Act (ADA), enacted in 1990, mandated the accessibility of public infrastructure such as street crossings and sidewalks [23]. However, even after more than three decades, many municipalities in the world have had difficulties in fulfilling accessibility standards, resulting in several streets, sidewalks, and businesses that are still inaccessible, and an approach to removing obstacles in pedestrian infrastructure is typically absent in the majority of communities [24]. Communities face problems of inadequate infrastructure and a lack of information regarding the specific impediments that need to be rationally eliminated at their respective locations [25]. Communities frequently encounter a shortage of dependable data regarding the presence and accessibility of sidewalks and the accessibility level of sidewalks [26,27].

The term “accessibility” is commonly employed by geographers, economists, and planners. The ease of reaching a destination, based on multi-criteria, is frequently utilized to define accessibility in mobility [28]. This definition is the foundation for several statistical methods used to evaluate accessibility for pedestrian networks. Past studies have evaluated accessibility by quantifying the cost value associated with footpaths. Accessibility analysis involves the process of defining and computing accessibility measurements, as well as presenting and analyzing outcomes by considering the target group, the destinations to be reached, and the means of travel. Typically quantified in terms of cost, time, or distance, these factors can help establish an accessibility index [29]. The various factors influencing accessibility make it related to multi-criteria decision analysis (MCDA) [30]. Determining the relative weights of criteria and evaluating their significance are critical challenges in applying multi-criteria decision analysis. Given that human judgments, including preferences, are frequently imprecise and cannot be precisely quantified, using fuzzy principles in determining weights is considered significant.

Without a user perception-based route selection methodology for PWD, there is an urgent and significant need to consider the preferences and requirements of people with disabilities and evaluate the existing footpaths in urban areas in the KSA. To create a truly inclusive and accessible urban environment, it is crucial to integrate the efforts of road infrastructure designers with representatives of people with disabilities. This collaboration ensures that the design process considers the actual needs and preferences of wheelchair users, leading to spaces that are not only compliant with regulations but also practical and user-friendly for disabled individuals. The primary objectives of this study are to (i) define multi-criteria that can evaluate the preferences of PWD in selecting optimal routes, (ii) establish the relative importance of the criteria using fuzzy rank ordering, (iii) determine criteria scores using GIS and expert knowledge base, and (iv) apply MCDA to aggregate the scores for optimal route selection.

The primary contributions of this research can be summarized as follows. First, the research integrates Geographic Information Systems (GIS) with expert knowledge to assess the suitability of existing sidewalks and infrastructure [31]. This integration provides accurate and comprehensive data about areas that need improvements to facilitate mobility. Second, this study offers planners and policymakers more precise data on the obstacles faced by PWD, aiding in prioritizing infrastructure improvements and making cities more inclusive and integrated.

2. Background

Urban areas encompassing most services are places everyone visits. Despite attempts to promote sustainability and inclusivity in the planning and design of the built environment, PWD face challenges in using urban road infrastructure, restricting their capacity to actuate and engage in social interactions [13,32]. The shortest path problem was addressed in earlier research that distinguished wheelchair users’ need for others to aid in social integration. For people with mobility impairment, the shortest route is not necessarily the best option [18]. The best route prioritizes the most direct and efficient path, which may include an entry ramp or adequate drop curbs. These people need to consider certain things, like the features and characteristics of the road, to drive safely [33].

Some studies conducted on a small scale, such as within the confines of a university campus, are of limited application. Karimi et al. [34] developed a personalized accessibility map (PAM), an interactive map with accessible information and specific features that assist PWD in choosing preferred routes during navigation. PAM Pitt, the prototype, allows wheelchair users to find accessible entrances to campus buildings, determine the most efficient routes between buildings, and request personalized, accessible paths based on their needs and preferences. Using various methods and instruments and considering the particular requirements of the ADA standards, the sidewalk network database, including slope, state of the surface, length, steps, and width, in PAM-Pitt was manually collected [35]. The PAM utilizes a fuzzy logic model that Kasemsuppakorn and Karimi [16] developed to calculate the feasible routes for individuals using wheelchairs, which was tested by Kasemsuppakorn et al. [18] on participants who were wheelchair users at the University of Pittsburgh’s main campus. The evaluation results show that wheelchair users may not follow the quickest path; instead, they prefer a more accessible and comfortable approach, irrespective of the path’s length.

Tariah et al. [36] investigated the level of accessibility of mosques in Riyadh for wheelchair users. A survey was undertaken to collect viewpoints from 48 male wheelchair users (and caretakers) regarding wheelchair accessibility at commonly visited primary mosques in Riyadh’s densely populated northern and eastern regions. The majority of participants were permanent wheelchair users as a result of injuries sustained in motor vehicle accidents or strokes. Most of them visited the mosque 3–5 times daily and said that mosques were mainly inaccessible. Most participants lived within a two-kilometer radius of the mosque, and many had difficulty getting to the parking lot. The study emphasized that wheelchair users’ discontent with the accessibility of mosques may result in praying at home, aggravating their disinclination to engage in religious and social activities. Evaluating the accessibility and the broader barriers that impact mobility, such as slope, walkway existence, and junctions, can address the limitations of studies with restricted applications [36,37].

Recent developments in geospatial technology, such as wireless networks [38], GPS (Global Positioning System), GIS (Geographic Information System), and devices, could provide valuable tools for collecting, analyzing, and sharing environmental accessibility data. Wheelchair users’ mobility may be improved by using these technologies and developing services and applications specific to their needs. However, despite several attempts, the current navigation technologies are not tailored to the unique requirements of those with mobility impairments [39]. According to a recent study on the usability of geospatial mobility assistive technologies [40], information about routes is crucial for wheelchair users. Nevertheless, the existing navigation aids and internet resources sometimes lack information regarding the accessibility of sidewalks, curb cuts, and ramps. Many navigation programs, such as Google Maps, do not include data on the incline or gradient of pedestrian routes. In addition to providing information about obstacles and facilitators on sidewalks, navigation programs must also provide accurate, accessible information about specific stretches of the sidewalk to ensure safe and convenient trips [39].

The multi-criteria decision-making process is a widely used method for assessing accessibility for PWD and walkability for pedestrians. This strategy has been utilized in numerous prior studies. When employing this method, it is necessary to provide significant importance as a weight to a set of criteria. Weight elicitation is an essential step of multi-criteria decision analysis. The discussion of weights is a substantial issue in MCDM and can profoundly affect the results of multi-criteria-aiding procedures [41]. Trolese et al. [42] and Manzolli et al. [43] applied MCDA to assess the walkability of pedestrians. Trolese et al. [42] proposed a data-driven approach to compute a walkability index for streets near urban centralities. They applied it to the Milano Rogoredo railway station as a case study. The walkability index was calculated by weighted average considering several characteristics and incorporating individual judgment about a walkable environment. Manzolli et al. [43] assessed the walkability of streets in Lisbon, Portugal. This assessment involved evaluating different elements that influence the pedestrian-friendliness of a region and assigning rankings to streets based on their walkability levels. The evaluation tool chosen for this task was the outranking PROMETHEE (Preference Ranking Organization Method for Enrichment of Evaluations) method.

For people with mobility disabilities, some studies used an MCDM approach, like the analytical hierarchy process (AHP), as a model created by Kasemsuppakorn and Karimi [16] to customize routing for wheelchair users. The sidewalk parameters and user priorities were the main topics of the research. This study used traffic, distance, steps, width, slope, and surface quality as criteria. This study used three weighing methods—absolute restriction, relative restriction, and path reduction—to modify the relative weights of the various routing calculation criteria. Each of these methods was implemented in four stages: (1) sidewalk parameter weighting, (2) segment impedance value quantification, (3) wheelchair user route modeling, and (4) route selection. They employed the analytical hierarchy process AHP method based on user preferences to determine a numerical weight for each sidewalk parameter. The impedance of each segment was then measured using fuzzy logic by averaging parameter weights (e.g., user-weighted slope) and segment data values (e.g., the inclination is 2°).

Similarly, Hashemi and Karimi (2016) [13] assigned an impedance value to each segment using the AHP approach rather than fuzzy logic. They used Z-test statistics to assess how accessible the calculated routes were compared to Kasemsuppakorn and Karimi’s (2009) [16] suggestions. A different approach was followed to determine the accessibility of urban streets for disabled people [44] using an alternative technique called a point system. The study examined scientific literature and local rules to identify critical characteristics that significantly impact the Disabled Pedestrian Level of Service (DPLOS). The research identified specific measures for pedestrians with disability. The authors developed an analytical point system to quantify the DPLOS by comparing existing pedestrian infrastructure to a standard. This approach measures the pedestrian conditions of present streets by weighing the importance of several variables. A case study undertaken along Canberra Road in Sembawang, Singapore, proposed an analytical point system for assessing the DPLOS by comparing current pedestrian infrastructure to a predefined standard. However, this approach could not fully consider the distinct requirements and preferences of disabled pedestrians in different environments.

Cities face a significant issue in improving pedestrian accessibility due to a lack of trustworthy data on sidewalk accessibility [45]. There is limited knowledge regarding the specific data requirements for cities and the various perspectives and utilization of sidewalk data by different stakeholders [45]. Froehlich et al. [46] illustrate how data collection and data administration of accessibility information are two of the most significant problems confronting municipalities and parties attempting to improve municipal accessibility using remote and automated techniques [47]. Henje et al. [48] conducted a study to identify the obstacles and dangers individuals face using powered wheelchairs in traffic settings. The survey focused on analyzing the behavior and experiences of these individuals, taking into account elements related to humans, vehicles (wheelchairs), and the environment. Uneven surfaces, variations in ground level, steep gradients, interactions with other road users, and the impact of the weather were observed as barriers. Ugalde et al. [49] determined the key parameters significantly influencing the optimal route selection in the Central Business District of Baguio. After that, they introduced an innovative framework that incorporates mathematical calculations and subjective assessments into the decision-making procedure. The characteristics that affect the optimal route selection were identified after thoroughly examining the literature review. The variables included in the study were road length, road type, travel time, road slope, road width, and speed restrictions. A mathematical risk assessment was used to determine the main factors that may impact the safety of individuals with mobility impairments, and the most significant variables that influence the choice of the optimal route were evaluated. Besides these challenges, the resistance that wheelchairs face while moving is a big factor in how well wheelchair users can get around, especially on sloped or rough surfaces. A study carried out at Poznań University of Technology showed that a system that combines manual and electric power can greatly reduce this resistance and make wheelchairs move more efficiently. This can help create safer and more accessible city spaces for wheelchair users [50]. Developing a framework for assessing efficient routes for disabled persons’ vehicles in urban areas of the KSA requires considering various factors, such as the challenges faced by disabled users and the methodology for assessing the efficiency of transport services for disabled individuals.

Additionally, incorporating Geographic Information System (GIS) techniques, MCDA, and the fuzzy rank sum method can help model accessibility to relevant services, providing insights into the current situation and areas needing improvement [40]. Several studies have addressed the evaluation of urban accessibility for wheelchair users, employing various criteria and methodologies. However, applying these methodologies in the context of the KSA remains underexplored.

3. Study Area

The study sites were selected in three regions of the KSA: Riyadh, Qassim, and Hail. Each city’s urban area accommodates multiple routes and has different urban challenges. Riyadh is the capital and thus faces fast urban growth with complicated issues in terms of infrastructure and accessibility for PWD. Qassim is a big agricultural hub, which means that more services and facilities are in demand against the scale of the growing population. With its diversified topography and tourist appeal, Hail city makes enhancing smooth mobility for PWD a challenge. Such places could present wide variations in urban accessibility challenges while providing generalizable results to similar locations. This study carefully selected specific routes within each city to reflect a variety of urban environments and challenges faced by PWD. First, Riyadh, the capital of the KSA, is situated centrally, as seen in Figure 1. It is a rapidly expanding city, presenting numerous societal, economic, and ecological issues. The population growth rate of Riyadh in the year 1438 AH was 4%, significantly above the global average of 2.5%. This rapid population growth presents issues regarding adequate housing, services, facilities, and job opportunities to prevent potential urban crises [51]. This study identified three routes, which were selected in high-traffic areas that connect major medical centers, tourist sites, and transport hubs, highlighting the need for accessible infrastructure in essential and frequently used locations, with selected footpaths measuring 1850 m, 816 m, and 492 m in length.

The first route begins at King Fahd Medical City, a hospital frequently frequented by PWD and healthy individuals. This route, which connects to Prince Sultan Military Medical City, is considered relatively long for disabled people, particularly those who use wheelchairs. It is crucial to evaluate this route as it includes an intersection connecting two medical cities and is frequently used by many individuals with disabilities. The other route begins at Al-Masmak Castle, a historical site popular with tourists, and concludes at King Fahd Road Park, spanning 816 m. There is a path for pedestrians, and for people with disabilities to reach this place, they must cross two junctions. The last route starts at Prince Faisal bin Fahd Stadium and travels up to 492 m to reach the Riyadh Bus Station, known as Salah Al-Din Al-Ayoubi Station. This route only has one intersection.

The second city is Buraidah, located in the Qassim region, around 350 km north of Riyadh. In the heart of the most significant agricultural region in Saudi Arabia, Qassim’s capital, Buraydah, is the region’s commercial and administrative center. It is considered the primary food source for the KSA, with extensive agricultural areas dedicated to growing wheat, vegetables, and dates. Qassim comprises 70 districts with concentrated services, massive commerce centers, and recreational facilities. However, the fast-growing population from other cities is putting a significant strain on these services, while other towns and villages in Qassim lack adequate amenities. In 2019, the population of Buraidah city was 590,312, accounting for 51% of the total population in all cities in Qassim [52]. The urban area included around 42,000 hectares. Three chosen routes effectively characterize urban daily life, such as shopping centers, government facilities, and places frequented by PWD, like the Club for PWD. The routes were evaluated to identify key obstacles, such as junctions and footpaths, that could hinder smooth mobility, providing insights for improvements. The first route starts from a shopping center called Nakheel Plaza and reaches a government police facility. This route is 658 m long, and there is a footpath to facilitate wheelchair users’ movement. A single junction along this footpath somewhat hinders PWD’s movement. The second 1083 m long path, between the Qassim Regional Museum and the Technical College for Women, is considered relatively long for wheelchair users to move around independently. A footpath is designed for pedestrians and wheelchair users, with no intersections, ensuring uninterrupted mobility for individuals with disabilities. The last path begins at the Club for PWD in King Abdullah Sports City and extends to the Maternity and Children’s Hospital. Although this path starts from a place designated for people with disabilities, it needs to be re-evaluated, considering the frequent hesitation of PWD to use this path.

Hail City, located in the north of the KSA, is the capital and largest city of the Hail Region. Geographically, it is situated on the historic Najd plateau, which extends from Riyadh to Hail in the northern region, as in Figure 1. The population of Hail City is estimated to be 605,930 people [53]. Due to its historical places, varied terrain, and rainy weather in winter, Hail City attracts many tourists from the Gulf region [54]. This study evaluated four routes in the center of Hail City. The selected routes included connections between popular markets, historical sites, and vital public facilities. These paths represent typical routes that PWD might use regularly. It is crucial to assess and address any barriers to ensure safe and efficient travel, particularly given the city’s diverse terrain and intersections. The first starts from Barzan Market, the most popular market in the city center and a destination for most of the population, to Hail Tower, the middle of Hail City. It is in a vital area due to its proximity to all government centers and markets, as it is next to the Emirate of Hail, the court, and the second largest mosque in Hail City, the King Fahd Mosque. The length of the proposed route is 736 m. The second route is located between two ancient castles called A’arif and Alqashla. These historical places are considered a destination for most residents and visitors from outside the city. The path connecting them is 1059 m long, and the movement of PWD is somewhat challenging due to two junctions along the route. The King Fahd Mosque, the second-largest mosque in the city, is the destination of the third route, which begins in a bustling pedestrian area. It is in a vital location because of its proximity to government facilities and popular markets. Its length is 1480 m from beginning to end, and this route crosses four junctions. Footpaths only along a short route length pose a risk to PWD movement. The other route is between King Khalid Hospital and the Hail Public Library, up to 398 m long, making it suitable for a wheelchair user to cross. Two junctions cross the route, and footpaths are absent in some parts.

4. Methodology

4.1. Data Collection

The data were collected using subjective and objective methods to ensure they were void of prejudice. The objective was to gather data regarding footpath characteristics, including length, slope, number of junctions, and absence of footpath, using Google Earth Pro 7.3 and ArcGIS Pro 3.2.0. The digital elevation model calculated the slope with 12.5 m resolution using ArcGIS Pro and used the average for each route. Google Earth Pro calculated other criteria as shown in

Table 1. Salient features of the routes in the study area.

Route	Length (m)	Number of Junctions	Absence of Footpath (%)	Slope (%)
R1	1850	1	10.9	6.22
R2	816.5	2	6	7.46
R3	568	2	20.4	8.56
R4	658.2	1	13	6.63
R5	1083.5	0	10	3.95
R6	1295	2	14.5	3.79
R7	737	2	61.53	7
R8	1060	2	25.48	8.16
R9	1479	4	41.10	5.21
R10	398	2	33.32	3.88

. The survey was employed as a subjective way to inquire about participants’ preferences concerning these criteria. The survey played a crucial role in this research because, while literature reviews aid in identifying and gathering general methods and criteria, a survey can assist in evaluating and weighing these criteria. The survey also facilitated the collection of unique perspectives from stakeholders addressing accessibility-related concerns in the areas under analysis. Gaining a more comprehensive understanding of these perspectives and their congruence and divergence can provide critical insights for communities to efficiently address the lack of data and limited planning for improvements in footpath accessibility. This combination helps create a complete and accurate understanding of the challenges they encounter. This study employed Google Forms, which included a total of 20 questions. These questions encompassed demographic information, open questions, and multiple-choice questions. The criteria in the survey were assessed on a scale of 1 to 4, with 1 indicating high importance and 4 indicating low importance, to obtain the weights of the criteria using the fuzzy rank sum method. The survey was distributed to many disability support services centers and sports clubs in these three cities.

4.2. Framework of Analysis

The framework in Figure 2 incorporates users’ subjective perceptions to overcome the shortcomings of an entirely objective assessment. The proposed approach effectively includes the subjective impressions and perceptions of PWD in addition to objective parameters like length, slope, absence of a footpath, and number of junctions. This approach entailed gathering data via survey to obtain users’ subjective preferences for the chosen criteria. This technique seeks to offer a more thorough and precise evaluation of the accessibility of urban areas by integrating both objective and subjective factors.

Consequently, the obtained information was used to make informed choices regarding urban design and infrastructure to enhance the accessibility of impaired individuals. The suggested methodology compared different routes depending on multiple criteria; for instance, a footpath may be considered the best option according to one criterion but the worst option according to another criterion. The method evaluates various factors rather than just one, helping to find the best routes that are not only the shortest or fastest but also the safest and most accessible. MCDM estimated the importance weights of the criteria and determined the most appropriate routes for PWD on each route by calculating the Accessibility Index (ACI) based on PWD preferences asked about in a survey. The fuzzy-based MCDM approach effectively dealt with the vagueness of users’ opinions and the overall subjective nature of the issue. In addition, some parameters for the footpath’s accessibility for wheelchair users were also investigated.

The rationale for selecting this approach is as follows. The method accounts for important factors that significantly impact the mobility of PWD, such as the slope, the absence of footpaths, and the number of junctions, making it more suitable for identifying routes that provide easy access and navigation for them. Secondly, the method integrates objective data and user feedback, which helps create a complete and accurate understanding of the challenges they encounter. Thirdly, MCDM evaluates multiple factors, helping to find the best routes that are not only the shortest or fastest but also the safest and most accessible for PWD. The application of Geographic Information Systems (GIS) analyzes data more precisely, leading to reliable results that can improve urban planning and infrastructure design.

4.3. Fuzzy Rank Ordering Criteria Weighing Method

In typical MCDM, decision-makers (DMs) offer precise numerical values for the information and the ratings and weights of criteria are quantified using crisp numbers [55]. Fuzzy logic deals with subjective judgment, imprecise information, and ambiguous opinions in the MCDM problem. The MCDM method typically consists of four distinct stages: formulation of alternatives and selection criteria, weighting criteria, evaluation of alternatives, and final aggregation and ranking [55]. Weight elicitation is a crucial component in multi-criteria decision analysis, as it can substantially impact the outcomes of multi-criteria-aiding procedures.

Determining weights involves ranking the criteria and converting the resulting ranking into numerical values. Utilizing rankings to derive weights through formulas can be more dependable than explicitly giving weights to criteria [41]. DMs typically have greater confidence in determining the ranks of specific criteria and find it easier to reach an agreement on them than randomly selecting the weights of those criteria. The most renowned and extensively utilized strategy is the rank sum weight method. PWD’s preferences alone define the criteria weights derived by the subjective weighting procedures.

Fuzzy concepts are applied in gathering weights because human judgments, including preferences, are frequently imprecise and cannot be characterized by precise numerical values. The proposed methodology extends the crisp rank ordering criteria weighting methods. The methods based on rank order techniques consider imprecise information about rank. In the Fuzzy Rank Ordering Criteria Weighing Method, the weights calculated for each criterion are represented as triangular fuzzy numbers (TFNs). The input is produced as a list of prioritized ‘n’ fuzzy-ranked criteria, with weights and ranks inversely correlated. The criteria are assigned fuzzy ranks in ascending sequence, with the most essential criterion being given rank 1 and the least essential criterion is given rank n based on these steps [41]:

Step 1. Ranking the criteria depends on their importance for each wheelchair user.

$$w_1\ge \cdots w_k\ge \cdots \ge w_n,\hspace{1em}\hspace{1em}k=\mathrm{1,2},\dots ,n$$

(1)

Step 2. Weighting the criteria from their fuzzy ranks.

Multi-criteria decision-making (MCDM) problems can be divided into two kinds. In classical MCDM problems, the information provided by the decision-makers (DMs) takes exact numerical values, and the ratings and the weights of criteria are measured in crisp numbers. In fuzzy multi-criteria decision-making (FMCDM) problems, as in our case, the ratings and the weights of criteria evaluated on incomplete information, imprecision, subjective judgment and vagueness are usually expressed by interval or triangle fuzzy numbers (three-dimensional values). The MCDM method typically consists of four distinct stages: formulation of alternatives and selection criteria, weighting criteria, evaluation of alternatives, and final aggregation and ranking [41]. Weight elicitation is a crucial component in multi-criteria decision analysis, as it can substantially impact the outcomes of multi-criteria-aiding procedures. Determining weights involves ranking the criteria and converting the resulting ranking into numerical values. Utilizing rankings to derive weights through formulas can be more dependable than explicitly giving weights to criteria [55]. Fuzzy concepts are applied in gathering weights because human judgments, including preferences, are frequently imprecise and cannot be characterized by precise numerical values. The proposed methodology extends the crisp rank ordering criteria weighting methods. The methods based on rank order techniques consider imprecise information about rank. In the Fuzzy Rank Ordering Criteria Weighing Method, the weights calculated for each criterion are represented as triangular fuzzy numbers (TFNs), as in Figure 3.

The input is produced as a list of prioritized ‘n’ fuzzy-ranked criteria, with weights and ranks inversely correlated. The criteria are assigned fuzzy ranks in ascending sequence, with the most essential criterion given rank 1 and the least essential criterion given rank n. The formula, fuzzy rank sum (FRS), deals with fuzzy weighting in the context of FMCDM problems. The weights obtained for each criterion are represented by triangular fuzzy numbers (l, m, u).

$$\begin{gathered} w_k\left(RFS\right)=\left(l,m,u\right)w_k\left(RFS\right)=\left({\displaystyle \frac{n-k+0.5}{n-k+0.5+\sum _{j=1,j\ne k}^n\left(n-j+1.5\right)}}, \\ {\displaystyle \frac{n-k+1}{\sum _{j=1}^n\left(n-j+1\right)}},{\displaystyle \frac{n-k+1.5}{n-k+1.5+\sum _{j=1,j\ne k}^n\left(n-j+0.5\right)}}\right)k=\mathrm{1,2},\dots ,n \end{gathered}$$

(2)

This formula results in weights that are not crisp values but fuzzy numbers. The three-dimensional nature of the weights comes from the fact that each weight in the fuzzy rank sum method is represented as a triangular fuzzy number, which includes three values:

The lower bound ($l$) (left end of the triangular fuzzy number):

$$l={\displaystyle \frac{n-k+0.5}{n-k+0.5+\sum _{j=1,j\ne k}^n(n-j+1.5)}}\hspace{1em}k=1,2,\dots ,n$$

The middle value ($m$) (the peak of the triangle):

$$m={\displaystyle \frac{n-k+1}{\sum _{j=1}^n(n-j+1)}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}k=1,2,\dots ,n$$

The upper bound ($u$) (right end of the triangular fuzzy number):

$$u={\displaystyle \frac{n-k+1.5}{n-k+1.5+\sum _{j=1,j\ne k}^n(n-j+0.5)}}\hspace{1em}k=\mathrm{1,2},\dots ,n$$

The FRS method provides triangle fuzzy numbers for weights, which is why the result is three-dimensional. This approach allows decision-makers to reflect the inherent vagueness and uncertainty in their judgments, which is crucial when precise information is unavailable or difficult to obtain.

4.4. Fuzzy TOPSIS

Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) was used to calculate the ACI for the selected routes. The ACI values range between 0 and 1, with 0 indicating no accessibility and 1 indicating the highest level of accessibility. Fuzzy TOPSIS is a multi-criteria decision analysis method, initially developed by Hwang and Yoon in 1981, with further developments by Yoon in 1987 and Hwang, Lai, and Liu in 1993. The method objectively and systematically evaluates alternatives on multiple criteria, relying on determining the closest distance to the fuzzy positive ideal solution (FPIS) and the furthest distance to the fuzzy negative ideal solution (FNIS) [57]. Under many conditions, crisp data are inadequate to model real-life situations, while human judgments, including preferences, are often vague and cannot be estimated with an exact numerical value. In this study the linguistic scale was used to assess the ratings and weights of the criteria. The selection of the accessibility criteria was based on several important factors directly related to the study objectives. Participants also quickly understood them and contributed to the decision-making process. The following are the steps of Fuzzy TOPSIS:

Step 1: The fuzzy normalized decision matrix of the alternatives ($\tilde{A}$) and the criteria weight matrix ($\tilde{W}$) are developed as follows:

$$A=\begin{array}{c}C\\ \tilde{W}\\ A_1\\ A_2\\ \dots \\ A_n\end{array}\left|\begin{array}{cccc}{C}_1& C_2& \dots & C_p\\ {\tilde{w}}_1& {\tilde{w}}_2& \dots & {\tilde{w}}_p\\ {\tilde{x}}_{11}& {\tilde{x}}_{12}& \dots & {\tilde{x}}_{1p}\\ {\tilde{x}}_{21}& {\tilde{x}}_{22}& \dots & {\tilde{x}}_{2p}\\ \dots & \dots & \dots & \dots \\ {\tilde{x}}_{n1}& {\tilde{x}}_{n2}& \dots & {\tilde{x}}_{np}\end{array}\right|$$

(3)

where ${\tilde{W}}_j$ is the importance weight of $j\mathrm{th}$ criteria, $C_j$($j=1,\dots ,n$) estimated by the survey’s participants using FRS’s weights and linguistic variables ${\tilde{x}}_{ij}$. These linguistic variables can be described by triangular fuzzy numbers, ${\tilde{x}}_{ij}$ = ($l_{ij},m_{ij},u_{ij}$) and ${\tilde{w}}_j$ = ($l_j,m_j,u_j$), where $l<m<u$. In mathematical terms, the fuzzy set A of a universe $X$ is defined by a membership function ${\mu }_{\tilde{A}}\left(x\right)$ such that $X$ → (0, 1), where ${\mu }_{\tilde{A}}\left(x\right)$ is the membership value of $\tilde{x}$ in $\tilde{A}$ as defined below, where $\tilde{A}$ = ($l,m,n$) is a triangle fuzzy number. Here, $x$ represents a criterion that belongs to $\tilde{X}=[x_1,x_2,...x_n]$.

$${\mu }_{\tilde{A}}\left(x\right)=\left\{\begin{array}{cc}0,& x\le l\\ {\displaystyle \frac{x-l}{m-l}},& l\le x\le m\\ {\displaystyle \frac{u-x}{u-m}},& m\le x\le u\\ 0,& d>u\end{array}\right\}\hspace{1em}i=1,2,\dots ,n$$

(4)

Step 2: The normalized fuzzy weighted decision matrix is calculated by multiplying the weights of the criteria ${\tilde{w}}_j$ by the fuzzified normalized scores ${\tilde{x}}_{ij}$ as

$$\tilde{V}={\left[{\tilde{v}}_{ij}\right]}_{n\times p}$$

(5a)

where

$$\begin{gathered} {\tilde{v}}_{ij}={\tilde{x}}_{ij}.{\tilde{w}}_j \\ {\tilde{v}}_{ij}=(l_{ij}\times l_j,m_{ij}\times m_{j,}{u}_{ij}\times u_j) \end{gathered}$$

(5b)

Step 3: The fuzzy positive ideal solution (FPIS: the best condition, $A^{+}$) and the fuzzy negative ideal solution (FNIS: the worst condition, $A^{-}$) are defined using the following equations:

$$A^{+}=\left\{{\tilde{v}}_1^{+},{\tilde{v}}_2^{+},\dots ,{\tilde{v}}_p^{+}\right\}$$

(6a)

$$A^{-}=\left\{{\tilde{v}}_1^{-},{\tilde{v}}_2^{-},\dots ,{\tilde{v}}_p^{-}\right\}$$

(6b)

where ${\tilde{v}}_j^{+}$ and ${\tilde{v}}_j^{-}$ correspond to ‘very high’ and ‘very low’ on the linguistical scale.

Step 4: The distance $s_i^{+}$ and $s_i^{-}$ of each alternative from ${\tilde{v}}_j^{+}$ and ${\tilde{v}}_j^{-}$ can now be calculated as follows:

$$s_i^{+}=\sqrt{\sum _{j=1}^p{\left({\tilde{v}}_{ij}-{{\tilde{v}}_j}^{+}\right)}^2},\hspace{1em}\hspace{1em}i=1,2,\dots ,n$$

(7a)

$$s_i^{-}=\sqrt{\sum _{j=1}^p{\left({\tilde{v}}_{ij}-{{\tilde{v}}_j}^{-}\right)}^2},\hspace{1em}\hspace{1em}i=1,2,\dots ,n$$

(7b)

This step indicates how near or far the route is to the most and least accessible conditions.

Step 5: The relative closeness coefficient ${\tilde{C}}_i$ of each alternative is calculated as follows:

$${\tilde{C}}_i={\displaystyle \frac{s_i^{+}}{s_i^{+}+s_i^{-}}}\hspace{1em}i=1,2,\dots ,n$$

(8)

Step 6: The calculated fuzzy relative closeness coefficient ${\tilde{C}}_i$ is defuzzified by the following Equation:

$$P\left(\tilde{M}\right)=M={\displaystyle \frac{l+4m+u}{6}}$$

(9)

Step 7: Finally, the ACI for each route is calculated as follows:

$$ACI=1-M$$

(10)

As the ACI of a route approaches 1, it moves away from the FNIS $\left(A^{-}\right)$ and toward the FPIS $\left(A^{+}\right)$. Thus, a higher ACI value is the best case, so the index is referred to as a level of accessibility. The ACI will used as a cost value in calculating the cost of accessible routes for disabled persons vehicle users.

The pseudo-code of fuzzy TOPSIS algorithms is attached as Appendix A.

5. Results and Discussion

Table 2. Descriptive statistics of the data.

Sr. No	Demographic	Categories	Frequency	Percentage (%)
1	Gender	Female	54	51.5
		Male	51	48.5
2	Participation in the survey	Yes	105	93.4
		No	7	6.6
3	Age	18–24	23	21.90
		25–34	24	22.86
		35–44	28	26.67
		45–54	20	19.05
		55–64	10	9.52
4	Education	Less	20	19.05
		Secondary	40	38.10
		Diploma	5	4.76
		Bachelor	36	34.28
		Master	3	2.86
		PHD	1	0.95
5	Disabled persons’ vehicles used	Powered wheelchair	37	35.24
		Manual wheelchair	62	59.05
		Artificial limbs	6	5.71
6	Independence mobility Outside a residence	Yes	78	74.29
		No	27	25.71

shows descriptive statistics for the survey’s participants. The table shows that the participants were divided almost equally between males and females. The number of male participants was 51 (48.5%), whereas the number of female participants was 54 (51.5%). Thus, the points of view and challenges of both genders are given unprejudiced. One hundred and five participants agreed with the survey, while seven refused to participate. The high (94%) response means there was interest in sharing their challenges and difficulties.

Responses were collected across different age groups, which helps map the perspective of all age groups and the differences in their preferences. The number of participants in the 18–24 age group was 23 (21.90%); 24 participants were in the 25–34 age group (22.86%); the largest group was 35–44, with 28 participants (26.67%); the 45–54 group had 20 participants (19.05%); and the least number of participants were in the 55–64 age group, with 10 participants (9.52%).

The educational qualifications among the participants varied: the majority were secondary school graduates, 40 participants (38.10%), and holders of bachelor’s degrees, 36 participants (34.28%). Those with less than secondary education accounted for 20 participants (19.05%), diploma holders comprised 5 participants (4.76%), and there were 3 master’s degree holders and 1 PhD holder.

There were three categories of mobility devices employed by the respondents, with the highest being manual wheelchairs used by 62 participants (59.05%), followed by powered wheelchairs used by 37 participants, and, lastly, mobility via prosthetic limbs used by 6 participants.

Most respondents said “yes” to independent mobility out of residence. Overall, 78 out of 105 responded that they can navigate themselves for leisure or city life. However, 27 participants responded “no”, meaning not at all to navigate independently; this implied that there is inconsistency in the levels of mobility for people with disabilities.

The nearly equal participation of both genders across various age groups and with different mobility devices allows for recommendations to be made to improve accessibility in urban areas for people with disabilities based on this diverse sample.

The survey was distributed to the Centers for People with Disabilities in three cities, Riyadh, Qassim, and Hail, to collect data on the mobility difficulties faced by PWD and the most critical factors. At the beginning of the survey, PWD were asked if they faced challenges when using assistive devices, and the majority (80.9%) answered yes. Most reported that mobility challenges hindered their access to health services, educational institutions, workplaces, and shopping areas.

The findings direct urgent attention to improving infrastructure, enhancing accessibility, and ensuring the safety of PWD in urban environments. Initially, the importance of the criteria was determined for each participant by evaluating the criteria from 1 to 4 according to individual preferences, where the criterion with a high importance of 1 is assessed with fuzzy numbers, and the criterion with a high importance of 2 takes the fuzzy numbers, and so on. Then, using the measurements for the criteria, all the route parameters, ranging from 0 to 10, were fuzzified and normalized as shown in

Table 3. Linguistically defined fuzzy scale for the criteria.

Linguistic Scale	Fuzzified Value			Absence of Footpath (%)	Length (m)	Number of Junctions	Slope (%)
	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$
Very low (VL)	1	1	3	$>75$	$>800$	$\ge 4$	$>6$
Low (L)	1	3	5	$>50–75$	$>600–800$	$3$	$>4–6$
Medium (M)	3	5	7	$>25–50$	$>400–600$	$2$	$>2–4$
High (H)	5	7	9	$>0–25$	$>200–400$	$1$	$>0–2$
Very high (VH)	9	10	10	$0$	$0–200$	$No$	$0$

. For instance, the first route, R1, spanned 1850 m in Riyadh City and featured a single junction, a 10.9% footpath absence, and a 6.22% slope, all of which underwent fuzzification, as illustrated in

Table 4. Linguistic scale of the ratings of the routes.

City		Length	Number of Junctions	Absence of Footpath	Slope
Riyadh	R1	Very low	High	High	Very low
	R2	Very low	Medium	High	Very low
	R3	Medium	Medium	High	Very low
Qassim	R4	Low	High	High	Very low
	R5	Very low	Very High	High	Medium
	R6	Very low	Medium	High	Medium
Hail	R7	Low	Medium	Low	Very low
	R8	Very low	Medium	Medium	Very low
	R9	Very low	Very low	Medium	Low
	R10	High	Medium	Medium	Medium

and

Table 5. Routes after being fuzzified and normalized between 0 and 10.

Criteria	K	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$
Length	4	0.05	0.1	0.17
Number of junctions	1	0.32	0.4	0.5
Absence of footpath	2	0.23	0.3	0.39
Slope	3	0.14	0.20	0.28

. In R1, length and slope corresponded to very low (VL), number of junctions and absence of footpath corresponded to high (H), and so on for all routes. Table 5 presents the linguistic scale converted into triangular fuzzy numbers. For instance, the first participant rated the criteria to assess their importance as the following: length as 4, very low importance, number of junctions as 1, very high importance, absence of footpath as 2, and slope as 3. Each number has three fuzzy values (l, m, u), as shown in

Table 6. Fuzzy rank sum weights.

Rank (K)	Fuzzified Values
	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$
1	0.32	0.40	0.50
2	0.23	0.30	0.39
3	0.14	0.20	0.28
4	0.05	0.10	0.17

, using Equation (2) and then these fuzzy numbers used in the fuzzy normalized decision matrix as shown in

Table 7. The importance of the weight of the criteria for the first participant.

Route	Length			No. of Junctions			Absence of Footpath			Slope
	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$
R1	1	1	3	5	7	9	5	7	9	1	1	3
R2	1	1	3	3	5	7	5	7	9	1	1	3
R3	3	5	7	3	5	7	5	7	9	1	1	3
R4	1	1	3	5	7	9	5	7	9	1	1	3
R5	1	1	3	9	10	10	5	7	9	3	5	7
R6	1	1	3	3	5	7	5	7	9	3	5	7
R7	1	3	5	3	5	7	1	3	5	1	1	3
R8	1	1	3	3	5	7	3	5	7	1	1	3
R9	1	1	3	1	1	3	3	5	7	1	3	5
R10	5	7	9	3	5	7	3	5	7	3	5	7

.

In Step 2, the estimated weights were multiplied by the fuzzified and normalized route parameters in Table 5 to calculate the normalized fuzzy weighted decision matrix by multiplying the weights of the criteria ${\tilde{w}}_j$ by the fuzzified normalized scores ${\tilde{x}}_{ij}$ by using Equation (5b). For instance, the calculation for the first participation for route R1 is as follows:

For length:

$$\left(0.05\times 1, 0.1\times 1, 0.17\times 3\right)=\left(0.050, 0.100, 0.510\right)$$

Number of junctions:

$$\left(0.32\times 5, 0.4\times 7, 0.5\times 9\right)=(1.600, 2.800, 4.500)$$

Absence of footpath:

$$\left(0.23\times 5, 0.30\times 7, 0.39\times 9\right)=(1.150, 2.100, 3.510)$$

Slope:

$$\left(0.14\times 1, 0.20\times 1, 0.28\times 3\right)=(0.140, 0.200, 0.840)$$

All these calculations were carried out for only the first participant to obtain the weighted normalized decision matrix in

Table 8. Weighted normalized decision matrix for the first participant.

Route	Length			No of Junctions			Absence of Footpath			Slope
	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$	$\mathit{l}$	$\mathit{m}$	$\mathit{u}$
R1	0.050	0.100	0.510	1.600	2.800	4.500	1.150	2.100	3.510	0.140	0.200	0.840
R2	0.050	0.100	0.510	0.960	2.000	3.500	1.150	2.100	3.510	0.140	0.200	0.840
R3	0.150	0.500	1.190	0.960	2.000	3.500	1.150	2.100	3.510	0.140	0.200	0.840
R4	0.050	0.100	0.510	1.600	2.800	4.500	1.150	2.100	3.510	0.140	0.200	0.840
R5	0.050	0.100	0.510	2.880	4.000	5.000	1.150	2.100	3.510	0.420	1.000	1.960
R6	0.050	0.100	0.510	0.960	2.000	3.500	1.150	2.100	3.510	0.420	1.000	1.960
R7	0.050	0.300	0.850	0.960	2.000	3.500	0.230	0.900	1.950	0.140	0.200	0.840
R8	0.050	0.100	0.510	0.960	2.000	3.500	0.690	1.500	2.730	0.140	0.200	0.840
R9	0.050	0.100	0.510	0.320	0.400	1.500	0.690	1.500	2.730	0.140	0.600	1.400
R10	0.250	0.700	1.530	0.960	2.000	3.500	0.690	1.500	2.730	0.420	1.000	1.960

.

In Step 3, the fuzzy positive ideal condition (FPIC: the best condition, $A^{+}$) and the fuzzy negative ideal condition (FNIC: the worst condition, $A^{-}$) were defined by using Equations (6a) and (6b).

In Formulas (6a) and (6b), the fuzzy positive $A^{+}$ and negative $A^{-}$ ideal solutions are defined; the values are computed by multiplying the fuzzy number of weight for each criterion (${\tilde{w}}_j)$ by the fuzzy number of very high (VH) and very low (VL) ratings of the route, where VH corresponds to the fuzzy positive ideal solution (FPIS: the best condition, $A^{+}$) and VL corresponds to the fuzzy negative ideal solution (FNIS: the worst condition, $A^{-}$). The fuzzy numbers of the VH rating of the route are $(9,10,10)$ and the fuzzy numbers of VL (1, 1, 3). The weight of the criteria for the first participant, as an example, are as follows: for length (0.05, 0.10, 0.17), number of junctions (0.32, 0.40, 0.50), absence of footpath (0.23, 0.30, 0.39), and slope (0.14, 0.20, 0.28). All these fuzzy numbers are multiplied by VH and VL numbers to obtain $A^{+}$ and $A^{-}$ as in the following calculations:

$$\begin{gathered} A^{+}={\tilde{v}}_{ij}^{+}\times {\tilde{w}}_j \\ {A}^{+}=[\left(0.05\times 9,0.10\times 10,0.17\times 10\right),\left(0.32\times 9,0.40\times 10,0.50\times 10\right),\left(0.23\times 9,0.30\times 10,0.39\times 10\right), \\ \left(0.14\times 9,0.20\times 10,0.28\times 10\right)] \\ {A}^{+}=[\left(0.45,1.00,1.70\right),\left(2.88,4.00,5.00\right),\left(2.07,3.00,3.90\right),\left(1.26,2.00,2.80\right)] \end{gathered}$$

$$\begin{gathered} A^{-}={\tilde{v}}_{ij}^{-}\times {\tilde{w}}_j \\ {A}^{-}=[\left(0.05\times 1,0.10\times 1,0.17\times 3\right),\left(0.32\times 1,0.40\times 1,0.50\times 3\right), \\ \left(0.23\times 1,0.30\times 1,0.39\times 3\right),\left(0.14\times 1,0.20\times 1,0.28\times 3\right)] \\ {A}^{-}=[\left(0.05,0.10,0.51\right),\left(0.32,0.40,1.50\right),\left(0.23,0.30,1.17\right),\left(0.14,0.20,0.84\right)] \end{gathered}$$

Step 4 calculated the distance $s_i^{+}$ and $s_i^{-}$ of each alternative from ${\tilde{v}}_j^{+}$ and ${\tilde{v}}_j^{-}$ using Equations (7a) and (7b) as shown in

Table 9. Fuzzy separation measures.

Route	${\mathit{S}}_{\mathit{i}}^{+}$			${\mathit{S}}_{\mathit{i}}^{-}$			$\mathbf{(}{\mathit{S}}_{\mathit{i}}^{\mathbf{+}}\mathbf{+}{\mathit{S}}_{\mathit{i}}^{\mathbf{-}}\mathbf{)}$
R1	1.975	2.510	2.379	1.576	3.000	3.805	3.551	5.510	6.184
R2	2.439	2.977	2.768	1.121	2.408	3.078	3.559	5.385	5.846
R3	2.424	2.881	2.550	1.125	2.441	3.152	3.549	5.322	5.703
R4	1.975	2.510	2.379	1.576	3.000	3.805	3.551	5.510	6.184
R5	1.308	1.619	1.508	2.735	4.104	4.357	4.043	5.722	5.865
R6	2.323	2.573	2.127	1.155	2.538	3.276	3.479	5.111	5.403
R7	2.913	3.484	3.258	0.640	1.720	2.173	3.553	5.205	5.432
R8	2.647	3.209	2.979	0.788	2.000	2.536	3.435	5.209	5.516
R9	3.142	4.240	4.122	0.460	1.265	1.657	3.602	5.505	5.780
R10	2.517	2.709	2.086	0.860	2.236	2.954	3.377	4.945	5.041

. The values in formulas (5b) were used in (7a) and (7b).

Step 5 estimated the relative closeness coefficient ${\tilde{C}}_i$ of each alternative by Equation (8). Step 6 defuzzified the calculated fuzzy relative closeness coefficient ${\tilde{C}}_i$ by Equation (9), and Step 7 calculated the ACI for each route by Equation (10).

Table 10. The accessibility index $ACI$ for all routes.

Route	${\stackrel{\mathbf{~}}{\mathit{C}}}_{\mathit{i}}$			$\mathbf{Crisp}\mathbf{Score}\mathbf{(}\mathit{M}$)	$\mathit{A}\mathit{C}\mathit{I}$
R1	0.556	0.456	0.385	0.460	0.540
R2	0.685	0.553	0.473	0.562	0.438
R3	0.683	0.541	0.4472	0.549	0.451
R4	0.556	0.456	0.385	0.460	0.540
R5	0.324	0.283	0.257	0.285	0.715
R6	0.668	0.503	0.394	0.513	0.487
R7	0.820	0.669	0.600	0.683	0.317
R8	0.771	0.616	0.540	0.629	0.371
R9	0.872	0.770	0.713	0.778	0.222
R10	0.745	0.548	0.414	0.558	0.442

presents the estimated ACI values for all routes.

All these steps were repeated for all participants because each participant gives a different importance to the others based on their preferences. In the same way, the average accessibility index ACI for all participants with disabilities, manual wheelchair users, powered wheelchair users, and artificial limbs users was calculated (

Table 11. Average accessibility index ACI for all participations.

Route	All Participants	Manual Wheelchair	Powered Wheelchair	Artificial Limbs
R1	0.35	0.34	0.37	0.31
R2	0.31	0.30	0.33	0.29
R3	0.40	0.40	0.42	0.36
R4	0.35	0.34	0.37	0.31
R5	0.47	0.45	0.49	0.45
R6	0.39	0.39	0.40	0.40
R7	0.21	0.21	0.22	0.18
R8	0.24	0.23	0.26	0.22
R9	0.22	0.21	0.22	0.22
R10	0.50	0.51	0.50	0.50

).

Figure 4 shows the average accessibility index for all participants, with R10 having the highest ACI value of 0.50 and R7 having the lowest value of 0.21. The accessibility level includes five categories: very low accessibility, low accessibility, medium accessibility, high accessibility, and very high accessibility. Consequently, as shown in Figure 3, all routes have medium and low accessibility. The R10, which has medium accessibility, measures 398 m in length and has a high linguistic rating. It has a medium rating in some junctions with 2, a footpath absence rate of 33.32%, and a slope of 3.88%, as shown in Table 4.

In contrast, the 737 m long R7, the least accessible route, has a low level of accessibility and is considered the worst among all routes. The medium number of junctions (two), 61.53% footpath absence, and very steep slope (7%) resulted in an overall low rating. When comparing R10 with the rest, it is the shortest length, and the other criteria received a medium linguistic rating—the second-best route after R10 was R5 due to its very high rating in the absence of junctions. The absence of a footpath received a high rating, while the slope received a medium rating, similar to that of R10. However, the route’s length, 1083.5 m, received a very low rating, being considered relatively long for PWD, with an average accessibility index of 0.47. It had a medium level of accessibility similar to R10, as the evaluation of the criteria for them was close, and some criteria ratings were rated better in R5, but the evaluation of the length was very low. When participants were asked in the survey about the maximum distance they can travel independently, their responses were as follows: 35% of respondents can travel less than 100 m independently; 31% can travel between 100 and 300 m; 18% can travel more than 700 m; 10% can travel between 300 and 500 m; and 6% can travel between 500 and 700 m, as in the pie chart that is shown in Figure 5.

As previously mentioned, the length criterion alone cannot determine whether a route suits PWD. For instance, when considering that the R7 length was 737 m, with a low rating, and comparing it to R1, which is 1850 m long with a ‘very low’ length rating and is considered very long for PWD, and the average accessibility index for R1 was 0.35, higher than R7 (0.21). These results agree with the findings of previous studies [13,14,15,18] that the length and time criteria alone are insufficient indicators. Figure 4 clearly shows two routes (R5 and R10) with a ‘medium’ level of accessibility. The common features include a rating of ‘medium’ to ‘very high’ for the number of junctions and ‘medium’ to ‘high’ for the absence of a footpath, while the other criteria vary. The length rating was high in R10 and very low in R5, while the slope rating was medium in R5 and R10. The criteria that contributed to these routes having a medium level of accessibility include the number of junctions and the absence of footpaths. The presence of footpaths provides them with safe mobility for moving efficiently and safely away from the dangers of walking out of a footpath, such as entering a road. The presence of junctions in routes reduces connectivity; routes such as R5 and R3, rated highly, provide better connectivity. Lower ratings suggest many junctions, which might complicate navigation.

All other routes had a low level of accessibility, with their length ratings ranging from very low to low. Slopes were mostly ‘very low’ to ‘low’, where they were very steep, which can significantly reduce accessibility for individuals with mobility impairments, except for R6, which was medium, while other criteria were varied. The second worst route was R9, which had ‘very low’ ratings for the number of junctions and length; this route had many long junctions, limiting its usability and accessibility.

When taking a comprehensive view of all routes, the best route does not exceed the medium accessibility index of 0.50 and less, meaning that all routes lie below the medium level, as there are only two routes at the medium level. These findings suggest a deficiency in accessibility for PWD, a finding supported by both the results and the survey responses.

The participants, who included users of manual wheelchairs, powered wheelchairs, and artificial limbs, rated the criteria from 1 (high importance) to 4 (low importance). The average importance was calculated so that each participant could comprehend and recognize the significance of the criteria. If the average value approaches 1, it indicates the high importance of this criterion. Figure 6 illustrates this, with manual wheelchair users expressing the significance of the following criteria: length, slope, absence of a footpath, and number of junctions in that order. For powered wheelchair users, from the most important to the least important, there was the absence of a footpath, length, slopes, and junctions. Slope, length, absence of footpath, and number of junctions were the ranking criteria for the importance of artificial limb users. It is essential to consider these factors when making improvements to urban routes. While length is critical for manual wheelchair users, in powered wheelchairs, the absence of a footpath was the most critical, and the slope was the most essential criterion for artificial limbs.

For further details, Figure 7 displays the average accessibility index for various disabled persons’ vehicles, which closely aligns with the overall average for all participants. There is a slight preference for powered wheelchair users, as they often require less effort than other vehicles. The critical reason is that the most essential criterion for this category was the absence of footpaths, as shown in Figure 5, and most routes received high ratings. Consequently, three routes achieved ‘medium’ ratings, and only one route had a low rating for this criterion. Footpaths significantly boosted the ACI, facilitating more effortless mobility, preventing potential collisions and accidents, and guaranteeing direct and safe access to services and public facilities. As for artificial limbs, users received the lowest ratings based on their most important criterion: slope. Most routes had steep slopes and received ‘very low’ ratings, except for three, which received a ‘medium’ rating.

The importance of the criteria for various disabled persons’ vehicles used by males and females is evident in Figure 8 and Figure 9. Both male and female artificial limb users agree that slope is their most important criterion. However, the least essential criterion differs: for females, it was the number of junctions, while for males, both the number of junctions and the absence of footpath criteria were the least important. For powered wheelchairs used by females, the ranking of the most to least important criteria was absence of footpath, length, slope, and number of junctions. For males, it was the length, slope, absence of footpath, and the number of junctions. Males consider the number of junctions to be the least important of all the criteria. For manual wheelchair users, length was considered the most important for both males and females. For females, the absence of a footpath was also considered of high importance, similar to length, while the number of junctions was the least important for both genders. Figure 8 shows that length was the most critical criterion for males using powered and manual wheelchairs, while the number of junctions was the least important. For females, the absence of a footpath was highlighted as the most important, as shown in Figure 9, for both powered and manual wheelchair users, while the number of junctions was the least important by all female disabled persons’ vehicle users.

Considering the accessibility level of different vehicles for males and females, there is a clear difference between the artificial limbs used by males and females, as illustrated in Figure 8. R10 had the highest level of accessibility for all males and females, but there was a difference in the least accessible route. The least accessible route for males was R9, with a very low level of accessibility of 0.19, because the two most important criteria for males were the slope and then the length, and this route was relatively long, about 1479 m, with a very low rating. It had a slope of 5.21%, rated low, while the absence of a footpath and the number of junctions were equally important. For females, R7 was the lowest-rated one, and when looking at the importance of the criteria, the slope and the absence of a footpath were the most important for them. These two criteria received the lowest rating; the route was very steep at 7% with a very low rating, and the absence of a footpath was high at 61.53% with a low rating. It is clear from Figure 10 that the accessibility for females in most routes is higher than that for males, but in R5 and R7, there was a change. In R5, the slope criterion rating increased to medium, and the number of junctions increased to very high. The absence of footpaths remained at the same high rating, and length received a very low rating, as in R1 and R2, thus increasing accessibility for males. As for R7, the rating of the two most essential criteria for females, slope and absence of footpath, decreased, and slope decreased from medium in R6 to very low and absence of footpath decreased from high in R6 to low.

In other vehicles, powered wheelchairs used by male users, the highest accessible route was R10 with a score of 0.51, as shown in Figure 11, and the lowest route was R9 with 0.21, as was the case for male users of artificial limbs. The two most important criteria for them did not differ from those for male users of artificial limbs, as the first most important criterion was the length and the second was slope. The absence of a footpath was next and the last one was the number of junctions. The two most important criteria, length and slope, were rated very low and low, respectively, in this route, and in the highest-rated accessible route, the length rating was high, and the rest were medium. As for females, R5 was the most accessible route, with a score of 0.50. The most important criteria for them were as follows: absence of footpath, followed by length, slope, and number of junctions. The most important criterion, the absence of a footpath, was rated high, while the other criteria, such as the number of junctions, were rated very high; the slope was rated as medium and the length was rated very low. R7 was the least accessible, with a score of 0.22, indicating a low level of accessibility. The evaluation of the most important criteria illustrated that the absence of footpath and length were low, while the slope and number of junctions ranged from medium to very low. The accessibility results for manual wheelchairs used by males and females were close and similar to those for all participants.

For a high level of accessibility, the weaknesses in the ten routes must be considered and improved. The slope criterion evaluations in Table 4 reveal a common denominator among the routes, with most slopes receiving ratings ranging from very low to medium. The slope criterion is considered the least evaluated compared to other criteria, and there is an urgent need to improve it based on survey responses and route evaluations. R5 rates the best route at 3.79%, while R8 rates the worst route at 8.16%, which is considered highly steep. ADA requirements stipulate that the slope of footpaths must not exceed 5% to provide easy movement without excessive effort so as not to cause fatigue and reduce dependability. Figure 12 illustrates the five cases of slopes identified [58]. The first case, which is absolutely the best, is for the footpath’s surface to be flat. The second case, where the slope is less than 4%, is suitable and manageable for mobility. In the third scenario, a slope of 5% is deemed acceptable. However, if the slope reaches 8%, individuals with disabilities will require assistance to overcome it, and the most dangerous scenario is if it exceeds 12%.

The improvement target for this criterion is for all routes to be at an acceptable and best level so that the slopes are 5% or less, as shown in Figure 13, where it appears that there are only three routes at the required level below the improvement target limit, which are R5, R6, and R10, and others that exceed the improvement target limit need improvement.

Other criteria, such as length, the most critical criterion for manual wheelchair users, were extended for all routes except for R10, which was 398 m with a high rating, and R3, which was 568 m with a medium rating. According to the survey, the remaining routes received low to ‘very low’ ratings. Figure 5 illustrates that the majority (35%) of respondents cannot move more than 100 m, and 31% cannot travel distances greater than 300 m. The percentages were lower for longer distances. Absent, or recently started, public transport in most of Hail and Qassim cities can reduce the fixed distance between an origin and a destination, reducing the distance PWD must travel. As for the absence percentage of footpaths, route R7 was higher than half (61.53%) of their total length, whereas no footpath was available, and other routes had lower percentages. The goal is to provide dedicated paths, especially in urban areas, to ensure safety and ease of access.

An increased absence percentage of paths forces PWD and other pedestrians to walk on the streets, exposing them to traffic accidents and injuries. This risk is higher for wheelchair users, adding to their daily challenges and limiting their independence and ability to participate in social life and community activities [59,60]. The absence of footpaths also means that wheelchair users must deal with uneven surfaces, steep slopes, and other physical barriers that can make travel uncomfortable and dangerous [61]. The more junctions there are, the higher the chance of accidents is, especially if there are no traffic signals or safe pedestrian crossings. Navigating through many intersections can be exhausting for PWD, especially if the footpath is not well prepared or the traffic signals do not give them enough time to cross, which increases the time and effort required to reach their destination. If the junctions are not equipped with special pedestrian crossings or curb ramps, they significantly hinder their movement. Participants indicated that there were not enough ramps and many were steep, especially at junctions.

In responses to the survey, the majority of participants reported that they experience difficulties when moving alone. When asked whether they face challenges when moving to urban areas, 80.95% answered in the affirmative, enumerating their problems. Their answers reveal their challenges when moving—first, dangerous and unsafe conditions. Many participants reported feeling unsafe due to the lack of respect for pedestrian crossings and the presence of reckless drivers, which creates a hazardous environment. Many participants highlighted the absence or inappropriate presence of slopes in various areas, which restricts their access and makes mobility difficult. A near-unanimous agreement on this issue was also visible in the examined footpaths, as illustrated in Figure 13. Many participants reported that the roads and footpaths are uneven, contain obstacles such as barriers or poles, and do not have adequate signage. Potholes and steep slopes exacerbate the problem. Public places such as shops, restaurants, parks, and markets often inadequately accommodate PWD. Facilities such as ramps, accessible bathrooms, and proper seating are frequently missing.

The lack of appropriate signs and signals to assist PWD and others is a recurring problem that makes navigation difficult and increases the risk of accidents. One of the most critical points mentioned is the lack of awareness and community support. There is a need for more awareness and understanding within society about the challenges they face. Increased awareness can lead to better support and facilities. Overall, 73.33% of respondents said ‘no’ when asked if they thought traffic light intersections were suitable for crossing, with the most common response being that there were not enough ramps or that the ones they did have were far away. There are no accessible routes for individuals with disabilities to navigate. Most responses indicated that the road’s surface is poor, filled with potholes, and elevated—disrespect for pedestrian crossings by vehicle drivers and fear of traffic violation regulations were also included. It is very important to foucs on safety issues for PWD, which goes beyond just making things accessible. Problems like missing ramps, poorly maintained sidewalks, and unclear pedestrian signals make it more likely for accidents and injuries to happen. These dangers not only make it harder for people to move around but also cause stress and make them less confident about getting around. Addressing these safety issues requires a better plan that includes improving design standards, raising awareness in the community, and enforcing traffic rules more strictly [62,63,64,65]. This will help create safer and more inclusive spaces for everyone.

6. Conclusions

This study indicates significant mobility challenges faced by people with disabilities in the Riyadh, Qassim, and Hail provinces of the KSA. This study found that 80% of the available routes had a significant lack of accessibility, while the remaining 20% showed a ‘medium’ level of accessibility. Slope and travel distance (length of the route) were the most important criteria based on the preferences of 105 participants. The preference evaluation survey yielded a very high (94%) response, showing the high concern of disabled people about their daily movements. The assessment process revealed significant neglect of the slope criterion in 80% of routes with slopes greater than 5%, exceeding the acceptable limit specified by ADA. The remaining 20% had a suitable slope ranging from 3.79% to 3.95%. These issues need urgent attention to improve infrastructure, enhance accessibility, and ensure the safety of PWD in urban environments.

Except in a few cities, public transport projects can reduce the travel time and distance for PWD in the towns and cities of Hail and Qassim. The number of junctions and the absence of footpaths were also identified as essential criteria by the participants for most routes studied. This study also explored the impact of the type of mobility aid (powered wheelchair, manual wheelchair, and artificial limb) the users have on their preferences. Length was the most crucial criterion for manual wheelchair users, the absence of a footpath was the most important for powered wheelchair users, and slope was critical for users of artificial limbs. Although the comparison of accessibility for each disabled person’s vehicle found no significant difference from the overall average obtained from all participants, powered wheelchair users had a slight advantage due to the higher evaluation for the absence of a footpath, which emerged as their most critical criterion.

Additionally, providing public transport to reduce the distance traveled is crucial, as the majority (35%) reported being unable to travel more than 100 m, and a smaller percentage (31%) reported being unable to exceed 300 m. Reducing vehicle–pedestrian interactions, especially for PWD, is also essential. Routes with several junctions pose a significant threat to PWD. The majority of participants (73.33%) indicated that city intersections are unsuitable for several reasons mentioned in the survey, mainly due to the lack of ramps in many places, their steepness, distance from the junctions, poor road surface conditions, and fear of traffic violations and disrespect for pedestrian crossings by drivers.

Due to the limited research regarding accessibility for PWD in urban areas of Saudi Arabia, it is recommended that future research expand the scope of this study to include other cities and regions. Additionally, different criteria and their impact on the level of accessibility should be examined, such as surface quality, street lighting, pedestrian congestion, and more. Including other PWD categories, such as those with hearing and visual impairments, will improve the functionality of the proposed framework to provide an inclusive urban environment for everyone.