Application of fuzzy analytical hierarchy process to develop walkability index: a case study of Dwarka sub city, New Delhi, India

ABSTRACT Walkability is an important aspect of the built environment, influencing the degree and intensity of walking. Very little research effort has been made in cities of developing countries like India to incorporate the user’s perspective in evolving walkability indices. This research study is an attempt to develop a walkability index from the user’s perspective in a developing environment, which shall aid the city planners in evaluating the quality of the walking environment objectively and systematically. For the development of the walkability index in the present study, empirical investigations were carried out in the Dwarka sub-city comprising street surveys incorporating pedestrian perspective and pedestrian counts. A fuzzy analytical hierarchy process with extent analysis has been performed, incorporating user ratings on critical walkability parameters to estimate the criteria weights and evolving a new path-level walkability index. It is concluded that this index exhibits a better correlation with pedestrian count when compared to the walkability index based on the existing prevalent approach adopted in the Indian context. The new walkability index will aid city planners in identifying specific pedestrian-related shortcomings as well as assist in evolving informed decision making to prioritize infrastructure investments.


Introduction
Walkability is a measure of how easy and comfortable it is to walk in a particular area.It takes into account safety, accessibility, convenience, and the overall design of the built environment.According to (Bradshaw, 1993), walkability can be defined as a foot-friendly, easy-to-use environment with level sidewalks, safe intersections, narrow streets, proper disposal facilities, proper lighting, and a total absence of obstructions, and a culture that encourages carefree walking and a built-in environment.
Walkability is particularly important in an era where congestion is a major problem caused by population growth and over-reliance on cars.Walkability can have a positive impact on the health, economy and overall liveability of an area ( (Brownson et al., 2009;Tribby et al., 2016) and Zhu and Chen, 2016).Places that are not conducive to walking are generally those with disconnected land use patterns, dead-end streets, and poor development design (Ruiz-Padillo et al., 2018).It is crucial for city planners, transportation engineers and individuals to prioritize walking and public transportation over car use.City planners around the world are working in order to promote walkability to reduce congestion and create healthier and more sustainable communities.
Many researchers have examined the walkability aspect, primarily focusing on the neighbourhood level or the macro scale, looking at factors such as urban form, density, street network patterns and land use diversity.However, these factors pose a significant challenge to be incorporated into an already-developed urban settlement.In contrast, factors related to the micro-scale, or street-level walkability, are easier to change and manage.This research attempts to understand the relative importance of such factors in arriving at a walkability index.

Literature Review
Walkability index methods are used to measure and evaluate the walkability of a particular area or a street.These methods typically consider factors such as the built environment, street network and land use in order to determine the ease and attractiveness of walking in a specific area.Walkability indexes developed in several cities rely on equal weighting, that is, all variables are given the same weight (e.g (Bradshaw, 1993).Krambeck (2006), (Walkingscore.com, 2010)).There are several different walkability index methods that have been developed and used by researchers and these are briefly described below.

Global walkability index
The 'Global Walkability Index' developed by (Krambeck, 1999) for the World Bank.This index is designed to provide a qualitative assessment of pedestrian conditions, with a particular emphasis on safety, security and convenience.It utilizes field surveys to evaluate the quality of pedestrian infrastructure across four primary domains: commercial, residential, educational and public transport terminals.Despite its qualitative methodology, the index proves effective due to its consideration of numerous crucial factors, offering valuable insights into the current state of walkability and aiding in the identification of areas requiring improvement.
• Safety and Security: i) Proportion of road accidents that resulted in pedestrian fatalities, ii) Walking path modal conflict, iii) Crossing safety, iv) Perception of security from crime, v) Quality of motorist behavior.
• Convenience and Attractiveness: i) Maintenance and cleanliness of walking paths, ii) Existence and quality of facilities for blind and disabled persons, iii) Amenities (e.g.coverage, benches, public toilets), iv) Permanent and temporary obstacles on walking paths, v) Availability of crossings along major roads; • Policy Support: i) Funding and resources devoted to pedestrian planning, ii) Presence of relevant urban design guidelines, iii) Existence and enforcement of relevant pedestrian safety laws and regulations, iv) Degree of public outreach for pedestrian and driving safety etiquette.
In this method, field surveyors ask the pedestrians to rate the selected road stretches on a scale 1 to 5 for each variable (1 being the lowest, 5 being the highest) in each of the selected areas.The average for each of the variables is translated into a rating system from 0 (lowest score) to 100 (highest score).This method identifies pedestrian preferences and analyses government policies.

Ministry of Urban Development (MoUD) method
This method has been developed by Ministry of Urban Road Development (MOUD), Government of India.They especially developed this method based on the Indian conditions.According to this method, walkability index is a function of availability of footpath and pedestrian facility rating.This can be calculated using equation Walkability Index = [(W1 × Availability of footpath) + (w2 × Pedestrian Facility rating)] Where, w1 and w2 are weights (assumed 50% for both) Availability of footpath = Footpath length/Length of major roads in the city Pedestrian Facility Rating = Score estimated based on opinion on available Pedestrian facility The method considers the length of only those footpaths which are wider than 1.2 m.For finding the pedestrian facility rating, a pedestrian survey is to be carried out.To collect details related to topics covered in this survey, the following included: 1) Footpath width, 2) Footpath continuity, 3) Availability of crossings, 4) Maintenance and cleanliness, 5) Security from crime, 6) Disability infrastructure, 7) Amenities, 8) Obstructions and 9) Footpath surface

Walkscore.com method
This method calculates an area's walkability based on the distance from resident's house to nearby amenities.It is based on the following: 1) the distance to walk able locations near an address, 2) Calculating a score for each of these locations, 3) Combining these scores into one easy to read Walk Score.The Walk Score may change depending upon updation of the data sources are or improvement algorithm used is improved.Walk Score is a number between 0 and 100.

Pedestrian environment index
The pedestrian environment has been assessed in terms of two broad categories namely Pedestrian infrastructure and pedestrian route environment.The indicators for each of the two categories and the attributes representing the indicators are pedestrian infrastructure such as availability, quality, continuity, connectivity and place making.Further, each of these attributes can have measurable sub-attributes.
Weighted factor method is used to arrive at scores for each indicator of overall Pedestrian Environment Index.Each of the sub-attributes are assigned scores based on how well or poorly they meet the norms and standards on a 5-point Likert scale.
The weights are assigned to indicators based on users stated preference of criteria for walk environment based on percentage of respondents identifying a particular indicator as most important.

Clean air initiative (2011)
This method has been developed for finding the Walkability in Asian cities recommended the following attributes to be considered while survey: i) Sidewalks/footpaths cleaner and wider, ii) Low traffic volume on road, iii) Obstacle free footpaths, iv) Increased crossing points, v) Effective street lighting and vi) Easy access for disabled persons.
In addition to the above described methods, there are other methods developed for various purposes as described in Table 1.
Most of the methods reviewed were based on either quantitative or qualitative data which reflect the supply side factors or demand side factors.It is also seen that most of the methods are unable to address the users perspective on walkable environment.Further the users weightage to specific supply side factors or demand side factors are not considered in the most of the models.The present research paper intends to develop a walkability index by incorporating the user's weightages toward supply side factors and demand side factors.Pedestrian refuge on median for crossing width Pedestrian refuge height

Identification of parameters and sub parameters
From the literature review main parameters along with sub parameters of walkable levels have been identified that will be considered for the development of the walkability index from user perspective.The parameters have been classified into eight main categories as described in Table 2:

Fuzzy Extent Analysis (FEA -AHP)
The Analytic Hierarchy Process (AHP) is a multi-criteria decision-making approach and was introduced by Saaty (1977Saaty ( , 1980Saaty ( , 1983Saaty ( , 1990Saaty ( , 1994) ) (Triantaphyllou & Mann, 1995) that is used for structuring, measurement and synthesis of decisionmaking processes.It uses pairwise comparisons to establish ratios that indicate the preferences of decision-makers among different alternatives and criteria.These comparisons are recorded in a comparison matrix and used to determine the corresponding weights of the criteria and alternatives.The normalized weighted sum of the matrix helps the decision-maker to choose the best decision by providing  a weight associated with each alternative.In the literature, two different scales are used to record pairwise comparisons i.e. scale based on crisp numbers (scale of 1-9) and scale based on fuzzy numbers.Fuzzy numbers, which are part of fuzzy set theory, are sets of real numbers that have a continuous and convex membership function with a defined support range.They are used to accurately represent linguistic scales that involve vagueness and uncertainty in human thinking.Fuzzy AHP is an extension of the traditional AHP method, where human preferences are recorded as fuzzy numbers and the comparison matrix formed also consist of fuzzy numbers.This allows for more accurate representation of human decision-making processes that involve uncertainty and vagueness.Fuzzy Extent Analysis (FEA) method (Chang, 1996) is the most frequently used FAHP algorithm (Ding et al., 2008).It utilizes the concept of extent analysis combined with degree of possibility to calculate weights from fuzzy comparison matrices.
There are many different types of fuzzy numbers.However, in this paper, a triangular fuzzy number (Figure 1) used which is represented through [l m u] and membership function μM defined as follows and graphically illustrated in the Figure .Let Þ then basic fuzzy arithmetic operations are summarized as follows; Addition: Fuzzy Extent Analysis (FEA) proposed by (Chang, 1996) is one of the most popular techniques in the literature to calculate weights from fuzzy comparison matrices.Applying this theory in fuzzy comparison matrix, one can calculate the value of fuzzy synthetic extent with respect to the i th object as follows: where; In this approach, a pair wise comparison is carried out for every fuzzy weight with other fuzzy weights and the corresponding degree of possibility of being greater than other fuzzy weights is determined.The minimum of these possibilities is used as the overall score for each criterion i.That is to say by applying the comparison of the fuzzy numbers, the degree of possibility (Figure 2) is obtained for each pair wise comparison as follows: To calculate the degree of possibility for a convex fuzzy number greater than k convex fuzzy number.
Þ then weight vector is given by W I ¼ W 1 ; W 2 ; ; :W n of the fuzzy comparison matrix Ã using below equation

Adopted method
For this study, two level data collection has been done.First level data collection effort involved collecting geometric information of facility by the field surveyor while second level involved collect the ratings of sub-parameters as well as pair wise comparison of main eight parameters, which were discussed in the earlier sections.The study has been carried out in four stages are as follows: Stage 1: Data collection of geometric details of pedestrian infrastructure supply side, wherein the field surveyors have collected the data of all the identified parameters for 30 streets and compare them with the available standards in India.From the collected information the quality of walking environment has been measured which is based on the geometric attributes of pedestrian supply infrastructure.
Stage 2: During the field surveyor, 56 pedestrians have been asked to rate the qualitative parameters between 0 to 1 (0 being lowest and 1 being highest).In this stage, overall quality of walking environment has been assessed using both quantitative and qualitative data.The final score of qualitative and quantitative parameters is between 0 to 100 (0 being least and 100 being the highest).Further, the score has been divided by 10 to keep the walkability index between 0 and 10 for easy interpretation of the index.
Stage 3: While collecting the quantitative and qualitative data, 56 users were asked to do the pair wise comparison of eight main parameters to understand the user's weightage toward the eight main parameters.This pair-wise comparison helped to understand the needs of the users while choose walking as commuting mode.For this a Fuzzy synthetic Analytical Hierarchy Process method with extent analysis has been used to assess the user's weightage toward identified eight main parameters.
The walkability index from the user's perspective is expressed as below: Where, WI i = Walkability Index for a stretch i U wj = User criteria weightage to the specific main parameter j SSP j = Score of sub parameters of pedestrian facilities under specific main parameter j Stage 4: In this stage, pedestrian flow count along and across footpath data has been collected for the identified 30 paths/street segments to understand the usage level of these stretches.The usage levels were further compared with the estimated walkability index using the MoUD method and the study proposed method.This comparison helps to evaluate the both methods for the understand users in needs in Indian cities and help city planners for wise investment in promoting walking in Indian cities.

Case study area profile
Dwarka was planned as a residential township in South-West Delhi in the National Capital Territory of Delhi (India) largely to accommodate the extra population that was being attracted toward Delhi.It is near to Indira Gandhi International (IGI) Airport (about 10 kms) and serves as the administrative headquarters of South -West Delhi.It is in relatively proximity from Gurugram in Haryana, which is a major hub for large corporations in the country.Being a planned area, Dwarka Sub-City shows a highly organized spatial structure as it has been developed on the concept of sectoral development with skeleton of grid-iron structure.It shows high level of adherence to planned urbanisation.Wide roads, sectoral development, ample urban amenities, lush green landscape are some of Sub-City's characteristics.However, some sectors outside the Sub-City are urban villages which are unplanned, extremely dense and lack in basic minimum requirements for services and open spaces.

Sample description
This study focuses on the collection of quantitative and qualitative data to evaluate walkability conditions in the Dwarka sub-city in Delhi, India.As part of the data collection, 30 different paths/street segments were chosen, each of which has a predominantly residential, commercial, terminal station, park, or public and semi-public area adjacent land use.The geometric features of the path/street segments and usage level (pedestrian volume count) were also collected.To gather qualitative data, 56 users were interviewed to rate the existing quality of the walking environment and provide on the pairwise comparisons of main parameters in order to arrive at criteria weightage for the identified parameters.A non-probability judgmental sampling technique was used in collecting the data from the target respondents.This was done in order to ascertain that the responses which are gathered are based on familiarity and the experience of using the sidewalks.Table 3 below shows the demographic details of the sample respondents covered during the survey.

Pedestrian volume characteristics
Pedestrian counts were also conducted at 30 locations in the case study area.
From the above table, it can be observed that at the Dwarka more has highest pedestrian count as it is one of the major interchange in the case area.Apart from that, Dwarka sector 9 metro station has relatively highest pedestrian count.Table 4 below shows pedestrian volume (usage levels) at identified thirty (30) locations.

Walkability index using MoUD method
As part of the data collection, side walk geometric parameters were measured at 30 locations where the pedestrian volume count data has been collected.Table 5 below shows the walkability index (based on supply parameters) at identified 30 locations.

Results and discussions
The main parameters criteria weight has been calculated using the Fuzzy AHP extent analysis.From the Table 6, it can be observed that the users weightage for the alongside facilities is 0.23, for security from crime is 0.19, for across facilities and safety from traffic is 0.16, for street amenities, streetscape, and visual quality is 0.10 and for microclimate  and land use diversity is 0.03, respectively.The results indicate that the key factors that are important to users for walking are alongside facilities, security from crime, crossing facilities and safety from traffic.
The walkability index of 30 paths/segments has been calculated using two methods namely first based on the criteria weightage as obtained using the F-AHP method.Additionally, the study also estimated the walkability index using facility supply-side parameters, as per the MoUD method.This present research paper made attempt to establish a relationship between pedestrian facility usage levels by MoUD method as well F-AHP method respectively.
The findings from the experimental data indicate that the walkability index calculated using a combination of user criteria weightage, quantitative and qualitative data have a stronger correlation with observed pedestrian count as compared to the walkability index calculated using only the quantitative data.Figures 3 & Figure 4 shows the regression analysis between the walkability indexes obtained by both methods and usage levels (pedestrian count) on the selected paths/street segments.

Conclusions
This pilot study aimed to create a composite walkability index using 47 path walkability indicators.The resulting formula allows for the calculation of a path walkability score for any street segment.From the Fuzzy AHP analysis, it has been clearly indicated that in the case study area users' needs quality of along facilities, security from crime as Delhi being highest in the crime rate in India and then crossing facilities and safety from traffic are important to use sidewalks.In this research, it has also evidently shows that the proposed walkability index holds a strong relationship with the usage (pedestrian count) levels comparing with walkability index estimated based on the supply side (measuring) parameters.The proposed walkability index in this study has potential applications for future research on travel behaviour.For instance, it can be integrated into a GIS  database at a city level to facilitate more advanced spatial analysis.The path level walkability may greatly influence the users in deciding to choose walking as commuting mode.However, as this study has a limitation in terms of generalizability, so more research needs to be undertaken in the future to verify the effect of this path/segment level walkability index from user's perspective.

• Does not present 0 ••Fully
Present and does not meet the standard then 0.5 Present and meets the standard, continuous throughout the street -1.0 Side walk surface quality, material • Cracked, uneven and broken • Uneven but firm and free from cracks • even, firm, free from cracks and well-drained Continuous of side walk • Discontinuous footpath.Covers <80% of street • Covers 80-100% of stretch • Continuous footpath covering >100% of street Drains • Fully open drains along >80% of footpath.• open drains along up to 20% of footpath • on residential streets, 4 on commercial streets, visible and clear spacing between bollards • <0.6 m | 0.6-1.2m| 1.2 m for wheelchair distance of stop line from crossing • <1m | 1-2 m | 2m, clearly visible

••••••
at all due to obstructions • crossing obstructed, slightly difficult to access • Crossing is accessible even to PWD.Clear height of 2.1m.Braille signboards should be located between 1.4-1.6mhigh PWD dedicated amenities -Guiding tiles width • Present on <80% of stretch • Present on 80-99% of stretch • Present on 100% of stretch.PWD dedicated amenities -Distance from kerb edge • <400 mm away from kerb edge • 400-600 mm away from kerb edge • laid 600mm away from the edge of footpath kerb edge, compound wall Warning tiles • Not present at all important locations • Only one set of warning tiles provided • Beginning and end of the ramps and stairs, property entrances, intersections and pedestrian crossings.Amenities -benches • Benches unusable and not present at regular intervals • Benches present but at irregular intervals • Benches present at regular intervals, easily accessible even to pwd.Too fast, not ideal for crossing the street.• Slight discomfort in crossing the street due to speed of vehicles • Can comfortably cross the street due to appropriate speed of vehicles Distance of Traffic calming elements from crossing • 9m high.(Outer edge) should be located 0.25m away from the footpath kerb edge.CCTV coverage present, but irregular, or not clearly visible.50%• Good CCTV coverage throughout the public areas of the street.Clearly visible.Extremely hot, no measures taken to reduce this effect.•Shade, landscaping etc. reduce heat island effect•Enough shade, landscaping, etc. to minimize heat island effect.Water ways/fountains/ sprinklers installed for cooling effect.Pit size equal to circumference of tree.•< 1.8m x 1.8m or <.25mx2.6 m on narrow streets.•1.8 m x 1.8 m area without concrete.Narrow footpaths 1.25 m x 2.6 m.Tree pit grating•Broken, causes walking path conflict, dangerous.•Uneven/holes too big/different level from footpath.•Present, same level as footpath, flat, even and firm.Covers the whole pit.Cleanliness • Not clean.Bad odor.Visible litter.Not pedestrian friendly.On over 75% of street stretch • Litter present on parts of the stretch (Less than 25%) • Area clean and well maintained no littler, no bad odor.Moderately active frontage, at least in certain parts of the street • Active & lively frontage, interesting to walk Street art/installations/etc.• No street art/installations • Small artistic elements present on street.• Street art present, interesting to walk.Compliments and enhances the street characteristics Land use diversity Mix of activities/uses of land • entropy index value >0.50 • entropy index value 0.5 to 0.7 • entropy index value above 0.7 Source: collated from various sources by the authors.

Figure 1 .
Figure 1.Membership function of triangular fuzzy Number.
Figure 3. Relationship WI based MoUD method and pedestrian count.

Figure 4 .
Figure 4. Relationship between proposed WI and pedestrian count.

Pedestrian Environment Review (PER) method (Transport for London), it
World Bank provides a qualitative analysis of the walking conditions including safety, security and convenience of the pedestrian environment.It consists of a field walkability survey to assess pedestrian infrastructure in four areas: commercial, residential, educational and public transport terminals.
assesses the walkability of an area based on factors such as street design, pedestrian facilities, and land use.It has been widely used in the United Kingdom.(5) Walkability Index for the United States (WIUS), it was developed by United States Environmental Protection Agency (EPA, 2021) and uses GIS data to analyze the walkability of an area based on factors such as population density, street connectivity and land use.It has been used in the United States.(6) Street Smart Walk Score: (Frank et al., 2021) it uses machine learning algorithm to analyse the walkability of an area based on factors such as street design, land use, and sidewalk quality.It has been applied in various countries like the U.S.A., Canada and Australia.(7) Neighbourhood Environment Walkability Survey (NEWS): it was developed by Saelens et al. and covers eight main walkability dimensions: residential density, land use mix, land use mix access, street connectivity, infrastructure for walking, traffic safety, security from crime and aesthetics.

Table 1 .
Methods of walkability index and its purposes.
Source: The Global Walkability Index by World Bank, 1999.

Table 2 .
Main parameters and sub parameters of walkability assessing levels.

Table 4 .
Location wise pedestrian counts in peak hour.

Table 6 .
Criteria weightage using fuzzy AHP using extent analysis.