New Parking Lot Selection Approach Based on the Multi-Criteria Decision Making (MCDM) Methods: Health Criteria

Abstract

To find a parking space, valet parking drivers have to travel a lot, which leads to carbon dioxide (CO₂) emissions. In order to reduce these emissions, it is essential to understand a user’s needs and criteria when searching for a parking space. Several selection criteria are considered when allocating a parking space. Recent research on parking space management mentions several parameters that have an impact on the choice of a parking space: namely, the traffic situation, the availability of each parking lot in question, and the cost of parking, etc. In this article, we discuss a new criterion: the physical condition of the driver in the management of parking spaces; the identification of the driver’s bodily fragility. We also propose MCDM as a parking space allocation model that best meets the cost–benefit convention. This reflection leads us to evaluate MCDM methods in the field of intelligent parking management. Therefore, we conducted a comparison between the most recent multi-criteria decision making methods used by researchers, namely, CODA, EDAS, TOPSIS, and WASPAS. The CRITIC method was used in this paper to objectively determine the weight of each criterion. A new approach is proposed to evaluate and select the best MCDM method. Indeed, we propose a method that computes the “average inter-item correlation SW”, a combination of the “average inter-item correlation” and the SW coefficient. This approach allows us to efficiently compute the correlation between a method and the set of methods while favoring the cells with the best ranking. A case study is presented to illustrate the MCDM approach to parking space allocation and evaluation. The proposed system provides drivers with services such as intelligent parking decisions, taking into account the human aspect while reducing energy consumption, driving time, and traffic congestion caused by searching for available parking spaces.

1. Introduction

Smart parking is an integral and important part of smart city initiatives. Indeed, a vehicle faces a huge problem in finding an adequate parking space on the roads of major cities. The situation continues to worsen in major areas of large cities, especially when traveling to the hospital, work, shopping centers, etc. Nevertheless, the Internet of Things technology has enabled drivers to acquire information about parking availability and even the road conditions on the way to a parking lot. However, that panoply of information usually confuses a driver as to the most suitable parking space. Furthermore, drivers are not directed to the parking destination in an organized manner, which causes traffic congestion and unnecessary travel. This blind search for a parking space results in polluted cities and wasted valuable time and money for civilians. An intelligent parking system provides a driver with the itinerary and the information needed to reserve a parking space [1].

When searching for a parking space, several parameters contribute to the choice of the most favorable location, including the traffic situation (the distance to travel and time of arrival at the parking space), the availability of each parking space in question, the walking distance, and the cost of parking. There are many alternatives and factors that influence a parking location decision. To address this problem, we propose a new approach for smart parking management that is based on multi-criteria decision making (MCDM) methods. This new multi-criteria management system has the singularity of introducing, in addition to the usual parking choice criteria, the driver’s physical condition. In a previous work [2], we presented a parking demand management algorithm that aims to prioritize the most vulnerable drivers when allocating parking spaces. We also implemented this algorithm in a mobile application connected to external sensors via Bluetooth. Following this work, we choose to classify drivers according to their 6MWT (6 min walking test) physical ability score when processing parking requests. In fact, they are divided into two types of profiles: profiles with body fragility and profiles with no body fragility. In order to acquire the score of each driver as well as the other criteria previously mentioned, we opt for the crowdsourcing principle. It consists of gathering the necessary information by exploiting the data received from the user platform. This solution allows us to minimize the use of surveillance infrastructures (sensors, cameras, etc.) known for their exorbitant costs.

The main contribution of this work is to study for the first time the performance of multi-criteria decision making methods in the selection of the most appropriate parking location. To this end, we propose a new tool for evaluating the performance of MCDM methods that we test in this paper. This tool integrates the mean rank method and the mean inter-item correlation method along with the rank similarity coefficient. It is the average inter-item correlation by the rank similarity coefficient. This study is carried out with recent methods frequently used by researchers, namely, CODAS (combinative distance-based assessment), EDAS (evaluation based on distance from average solution), TOPSIS (technique for order preference by similarity to ideal solution), and WASPAS (weighted aggregated sum product assessment). Each of these methods is combined with the CRITIC method, criteria importance through intercriteria correlation [3], an objective technique to define the weights of the criteria in the decision making issue.

This paper is structured as follows: Section 2 describes in detail the new parking space allocation system that we propose while explaining in detail the approach to defining the physical performance of each user, predict the parking spaces that are available on the arrival at the parking lot, and, finally, explaining the multi-criteria approach in the management of smart parking lots. Section 3 presents the application and comparison of the four MCDM methods in the allocation of the best parking space. According to the findings of the case study, the function and the evaluation parameters of the MCDM methods are discussed in Section 4. A significant review of pertinent research and case studies is discussed, proposing a new method for evaluating the parameters of the MCDM methods. In the conclusion (Section 5), we provide a valuable summary of the use of multi-criteria analysis techniques in parking management decision making.

2. New Approach for Smart Parking Allocation

The proposed solution is mainly based on crowdsourcing. A parking management system uses smartphones. Unlike previous approaches [4]), our approach does not require any additional infrastructure (the installation of IoT sensors), nor vehicle modification or user interaction, only the installation of a smartphone application. It can collect large amounts of data in real time via the many connected mobile devices.

As smartphones have become ubiquitous, several applications and research projects have attempted to exploit their capabilities to facilitate the parking process. In general, previous research aims to occupy the available spaces in a parking lot without paying attention to the physical coordinates of each parking space in the lot. However, we are interested in each user’s bodily frailty and the probability that a parking space is available in order to suggest more optimal proposals and allocations. This solution also aims, via crowdsourcing, to detect drivers with low physical ability compared with normal drivers through distance-based walking speed monitoring (6MWT).

The selection of a place is influenced by many factors. A parking reservation system is described as a mathematical formulation in [5]. Based on the ideas of pareto-optimality and non-dominance, a set of compromise solutions are created for each user request by maximizing the various criteria individually and concurrently. However, they contend that the ranking system ELECTRE III, a multi-criteria decision-making method, should be taken into account in order to establish the optimum compromise alternative. The system must balance driver preferences with operational restraints in order to provide online space allocation based on real-time information.

The analytic hierarchy process (AHP) was investigated as a decision-making technique by [6] with the same concept to establish the weighting of factors and choose the best parking for drivers. The design of the smartphone-based parking advice system that will be used to implement the suggested algorithm is also presented in this paper. Drivers can use a smartphone to request information from the system, such as the best parking location that the suggested algorithm recommends as well as the route to the advised parking.

According to our search, these two articles are the only ones that mention using multi-criteria decision approaches for parking assignment. These techniques are mostly utilized for spatial decision-making, such as selecting the optimum site for a parking lot that best serves community needs [7,8] and, particularly, parking lots for electric vehicle charging [9].

2.1. Identification of the Driver’s Profile

There are many studies aimed at assessing the functional performances of individuals. The research offers measures that are easy to use, administer, analyze, and interpret. The information is readily available, requires little equipment, and is feasible in most settings. Physical function is correlated with the “ability to move” and “ability to perform daily activities”, which is assessed directly by an individual’s activity, usually measured in time, number, or distance.

The 6MWT is the most widely used method for assessing endurance and the ability to walk long distances. The 6MWT was first described as a field test of ability in 1963 [10]. The 6MWT has been shown to be effective in assessing submaximal functional performance at a level similar to that required for daily physical activity. The 6MWT consists of walking as much as possible for 6 min. It is part of the adapted physical activity (APA) management protocol. The 6 Minute Walk Test has prognostic value in the initial assessment of a patient, and changes in the 6 Minute Walk Test over time also have predictive significance. The 6MWT has also been used to study the impact of wearing a face mask during SARS-CoV-2 [11]. It is incorporated into models that typically determine the next steps in patient management. A study was conducted by M. J. Oliveira et al. [12] to test the validity of the equations proposed by the different researchers. A quadratic regression analysis model proposed by [13] shows that age, gender, and BMI explain 46% of the variability in 6MWT scores. The derived Equation (1) for the 6MWT is based on this analysis, considering only anthropometric and demographic data. Distances in the 6MWT are associated with age, sex, and height, as well as with body mass index (BMI). In addition, regression equations to predict 6MWT scores for middle-aged and older adults have been calculated and improved by several investigators over time. Age, sex, BMI, and ΔHR were the most significant predictors of 6MWT scores, and the regression equations by [13] explained approximately 34% to 38% of the variance in 6MWT scores.

$$\begin{array}{cc}\begin{array}{c}6MW{D}_{pred}=890.46-(6.11·age)+(0.0345·age)+(48.87·gender)-(4.87·BMI)\\ man=1,woman=0\end{array}& \end{array}$$

(1)

Such a simple and effective method of assessing the performance level of the physical function can be easily embedded in a mobile application. This is by simply retrieving the distance travelled by a user in a 6-min walk from their smartphone and combining it with the other parameters of the regression equation. A greater distance represents a better physical fitness performance for the user. Anthropometric and demographic data are obtained through a questionnaire that riders will fill out when installing the application, while the distance covered in 6 min is retrieved via the smartphone sensor each time a user walks. The app also uses the three-axis gyroscope in order to trigger the test only when a walking activity is detected. Consequently, the application performs several walking tests for each user to measure their actual physical capacity, as shown in Figure 1.

2.2. Prediction of Parking Space Availability

A driver’s parking behavior differs depending on the type of parking lot (closed or open lot or underground parking), the time of day (work time), and the day (weekend, vacations, etc.), etc. In crowded parking lots, a driver often parks in the first free space in the belief that after 9 o’clock, all parking spaces will be occupied. This blind parking is more visible in the underground parking lots of shopping malls, because a driver has more difficulty in positioning himself and determining the parking lot that is the closest to his destination. Indeed, several factors influence the choice of parking space, which have a direct impact on the forecasting and management of available spaces.

A lot of research has been conducted on parking space management. Management systems use a sensor infrastructure to identify available parking spaces [14]. These systems provide real-time visibility of parking space occupancy. However, they do not provide any guarantee that a parking space will be available. Therefore, to predict the availability of parking spaces at some point in the future, more studies propose systems coupled with artificial-intelligence-based approaches that can create solutions, such as [15,16]. To successfully predict the availability of parking spaces, data generated by sensors and IoT devices, combined with machine/deep learning technical approaches can be very useful. It is an approach that allows us to assign each parking space a probability of availability when a driver arrives. In order to avoid expensive sensor infrastructure, crowdsourcing is a better alternative, as shown in Figure 2.

Unlike the majority of research studies that investigate parking occupancy, the requirements of the proposed system are to compute the probability of each location in order to assign the best parking space for each profile.

2.3. Multi-Criteria Allocation Problem

Many potential factors are involved in the parking selection process, making it a difficult procedure. In today’s society, people have become the most important resource of information. The parking selection process requires complex multi-criteria analyses. It includes a range of factors involving economic, social, technical, environmental, and political issues leading to conflicting objectives. Indeed, the search for a parking space must be conducted by optimizing many criteria related to a driver’s preferences or parking operations objectives. Among these criteria are the distance between the current position and the parking lot, the distance between the parking lot and the destination, the residual space resulting from parking the vehicle in a given space, the costs, and the waiting time for parking. In our case, optimizing drivers’ satisfaction as well as improving parking management requires the identification of objective criteria, as shown in Figure 3. Our system takes several aspects into account. In this intelligent parking system, we consider three main aspects:

1.

The economic aspect:

• Cost: consists of a price per hour of parking in the space.

2.

The environmental aspect:

• Pollution reduction: concerns the diminution of unnecessary travel (travel cost). Since drivers often prefer a parking space close to their current location to save time, minimizing the trip by avoiding a blind search would correspond to an optimization of this criterion.
• Environmental efficiency: allows for a better organization of parking and better use of space.
• Parking availability: unoccupied spaces for each parking area (the probability of finding a place to park at the time of arrival).

3.

The health status aspect:

• Driver’s profile: describes the detection of a user’s health profile in order to assign the best parking based on his health status.
• Walking distance: represents the walking distance between the parking area and the destination. These criteria have been carefully chosen to avoid any subjectivity that may influence the choice of the best location for a profile.

After defining the different decision criteria, determining their weights is a critical step in multi-criteria decision making. Therefore, this issue has received much attention in the literature. In general, there are two types of approaches for determining the weight of a criterion: subjective and objective approaches [17].

Subjective approaches are based on determining the weighting of criteria using information from decision-makers or experts involved in the decision process. On the other hand, objective methods remove the decision maker by determining the weights based on the criteria values of the alternatives. A decision matrix analysis, which involves comparing the values of alternatives with a collection of parameters, allows us to obtain data on the weights of the criteria.

For our solution, which is essentially based on data retrieved via the user’s smartphone and without human interaction, we have opted for objective decision-making methods, thus avoiding the subjective opinions of experts or human opinion in general.

However, as cited before, the CRITIC method [18] is the method used in this paper to identify the weight of each criterion. These weights will be used in each of the four methods: CODAS, TOPSIS, EDAS, and WASPAS.

3. Case of Study: Simulation of the Results

3.1. Formulation of Parking Space Allocation Problem

In this section, we propose a multi-criteria-based parking space allocation system as a smart parking system. It handles two types of users (vulnerable and non-vulnerable). Each user category has different weighting criteria. The ones for choosing a parking lot are divided into five standards.

• Walking distance criterion (C1): represents the walking distance between the parking space and the destination.
• Cost criterion (C2): represents the parking costs.
• Waiting criteria (C3): represents the waiting time before accessing the parking space.
• Driving distance criterion (C4): represents the distance covered by the vehicle between its current position and the parking place
• Availability criterion (C5): represents the probability concerning the availability of the location upon arrival.

Based on the predictions of the number of arrivals referring to drivers with bodily frailty and as well as the number of available spaces, we determine the threshold of the walking distance. For better system flexibility, the threshold will be variable based on an estimated number of demands and parking for the vulnerable.

3.2. Application of Multi-Criteria Decision Making Methods

3.2.1. Decision Matrix

According to our approach, parking space allocation differs according to a driver’s bodily frailty. The hypothesis stipulates that the maximum walking threshold for frail people is set at 3 min of walking or 200 m. This is a rather acceptable distance for a frail person. However, three scenarios are possible:

-

The parking spots are available regardless of the driver profile.

-

The parking spaces are not close enough for a driver with poor physical performance to walk to.

-

The parking spaces are not available for a driver with normal physical performance.

In order to handle these scenarios, we propose an expert system to follow logical reasoning, thanks to an inference engine applying pre-parameterized rules to facts to infer new information.

Figure 4 describes the logical operation of the parking space allocation according to a user’s profile by giving a logical sequence to each scenario.

In order to evaluate the performance of our approach and these three scenarios, we used a parking network of the city of Lille, France [19]. This is an open dataset listing the city’s parking lots with their geometric coordinates. The distribution of parking spaces in the city is shown in Figure 5, illustrating the parking spots mapped in each area. We assumed that a traveler who is located at the Lille train station wants to find a parking space to go to the Akira restaurant. Considering the acceptable walking distance for parking from 500 to 550 m, i.e., up to 7 min, we delimited the parking search area to a radius of 400 m described in Figure 6. There are 44 parking lots within this area.

Within this area, we calculated the walking distance and the driving distance for each parking lot. Then, we generated with a python program random values for the waiting time and the cost as well as the probability of the availability of the location on the arrival of the driver. In this simulation, 21 parking lots were available in the traveler’s destination area.

In the first step, the parking spaces in

Table 1. Available parking space.

	C1	C2	C3	C4	C5	For Vulnerable People
A1	1	8.55	0.49	0.94	5	Yes
A2	2	5.24	0.03	0.82	6	Yes
A3	2	3.17	0.13	0.81	6	Yes
A4	3	2.30	0.36	0.96	5	Yes
A5	3	7.11	0.85	0.88	5	Yes
A6	4	9.24	0.08	0.90	5	No
A7	4	3.06	0.61	0.94	5	No
A8	4	3.63	0.64	0.90	6	No
A9	4	9.89	0.75	0.89	5	No
A10	4	3.23	0.01	0.92	6	No
A11	4	7.85	0.95	0.87	5	No
A12	4	8.98	0.54	0.92	5	No
A13	5	0.37	0.18	0.95	7	No
A14	5	3.62	0.64	0.92	7	No
A15	5	8.48	0.61	0.89	4	No
A16	6	2.53	0.74	0.94	7	No
A17	6	5.12	0.31	0.94	6	No
A18	6	0.79	0.12	0.99	4	No
A19	6	7.27	0.78	0.99	6	No
A20	6	2.09	0.70	0.96	6	No
A21	6	6.26	0.92	0.98	7	No
A22	6	2.31	0.97	0.91	5	No
A23	6	7.80	0.47	0.91	6	No
A24	7	7.89	0.79	0.96	6	No

are sorted by profile according to the reported threshold.

3.2.2. CRITIC Method

The CRITIC approach is used to decide the weights of the parameters in this section. This approach makes direct use of the decision matrix while accurately determining the relative weights of the various criteria. Directly related to the decision matrix is the weight of the attributes. It allows for the elimination of any bias toward subjective decisions made by decision-makers or pairwise comparisons, as in the case of other ponderation methods. The primary component of the methodology is the correlations between all criteria. The weights of the criteria derived from the analysis of correlation are taken into account, along with the contrast intensities between different types of criteria.

Initially, the decision matrix is normalized. The normalized decision matrix for each profile is shown in

Table 2. Normalized decision matrix for CRITIC method NVP.

	C1	C2	C3	C4	C5
A6	1.0000	0.0683	0.9271	0.7500	0.3333
A7	1.0000	0.7174	0.3750	0.4167	0.3333
A8	1.0000	0.6576	0.3438	0.7500	0.6667
A9	1.0000	0.0000	0.2292	0.8333	0.3333
A10	1.0000	0.6996	1.0000	0.5833	0.6667
A11	1.0000	0.2143	0.0208	1.0000	0.3333
A12	1.0000	0.0956	0.4479	0.5833	0.3333
A13	0.6667	1.0000	0.8229	0.3333	1.0000
A14	0.6667	0.6586	0.3438	0.5833	1.0000
A15	0.6667	0.1481	0.3750	0.8333	0.0000
A16	0.3333	0.7731	0.2396	0.4167	1.0000
A17	0.3333	0.5011	0.6875	0.4167	0.6667
A18	0.3333	0.9559	0.8854	0.0000	0.0000
A19	0.3333	0.2752	0.1979	0.0000	0.6667
A20	0.3333	0.8193	0.2813	0.2500	0.6667
A21	0.3333	0.3813	0.0521	0.0833	1.0000
A22	0.3333	0.7962	0.0000	0.6667	0.3333
A23	0.3333	0.2195	0.5208	0.6667	0.6667
A24	0.0000	0.2101	0.1875	0.2500	0.6667
std. dev.	0.3292	0.3151	0.3020	0.2829	0.3069

and

Table 3. Normalized decision matrix for CRITIC method VP.

	C1	C2	C3	C4	C5
A1	1.0000	0.0000	0.4390	0.1333	0.0000
A2	0.5000	0.5296	1.0000	0.9333	1.0000
A3	0.5000	0.8608	0.8780	1.0000	1.0000
A4	0.0000	1.0000	0.5976	0.0000	0.0000
A5	0.0000	0.2304	0.0000	0.5333	0.0000
std. dev.	0.3742	0.3744	0.3526	0.4053	0.4899

. The standard deviations are calculated for each criterion in these tables.

As a result, all entries in the decision matrix are linearly normalized in order to make the performance metrics comparable and dimensionless. When determining a criterion’s weight, it is important to take into account the symmetric linear correlation matrix.

Table 4. Correlation coefficient values of the NVP criteria.

	C1	C2	C3	C4	C5
C1	1.0000	−0.2094	0.2396	0.6413	−0.2864
C2	−0.2094	1.0000	0.2239	−0.4107	0.2931
C3	0.2396	0.2239	1.0000	−0.0775	−0.1052
C4	0.6413	−0.4107	−0.0775	1.0000	−0.3084
C5	−0.2864	0.2931	−0.1052	−0.3084	1.0000

and

Table 5. Correlation coefficient values of the VP criteria.

	C1	C2	C3	C4	C5
C1	1.0000	−0.5042	0.3216	0.0791	0.2182
C2	−0.5042	1.0000	0.5382	0.1518	0.3730
C3	0.3216	0.5382	1.0000	0.4958	0.8245
C4	0.0791	0.1518	0.4958	1.0000	0.8998
C5	0.2182	0.3730	0.8245	0.8998	1.0000

display the correlation coefficients of the NVP profiling and VP profiling, respectively.

The weight objectives of each criterion are obtained by Cj, which stands for the amount of information included in the j criterion, after the correlation between the criterions is calculated. The

Table 6. Criteria weights for NVP profile.

	C1	C2	C3	C4	C5
Cj	5.7980	5.7050	5.3518	5.1359	5.6490
Wj	0.2098	0.2064	0.1936	0.1858	0.2044

and

Table 7. Criteria weights for VP profile.

	C1	C2	C3	C4	C5
Cj	1.4537	1.2883	0.6418	0.9620	0.8252
Wj	0.2811	0.2491	0.1241	0.1860	0.1596

show the results in detail.

We notice that for the VP profiles, the criterion that has the most weight is C1 (walking distance), then C2 (cost), then C5 (availability), then C3 (waiting time), and, finally, C4 (driving distance) has the lowest weight. The method has given more importance to the walking distance over the other criteria, as desired. In actuality, the threshold already controls how the values of walking distance vary, resulting in a decreased standard deviation.

Otherwise, the ranking of the weights of the criteria for the NVP profiles is as follows: C1 > C2 > C4 > C5 > C3; indeed, this weight ranking varies according to the decision matrix, which in turn varies according to the alternatives that are available at each time t. The advantage of this method is to define the weighting of the criteria in all objectivity. To avoid using the approaches twice in this simulation, we will only examine the various decision-making strategies in the situation of non-vulnerable profiles. In fact, the dispatching of parking spaces has little bearing on the techniques’ comparability.

3.2.3. CODAS Method

This method employs both the Euclidean and taxicab distances to assess the desirability of various options. Distance is desirable to the extent that its value relative to the NIS is high. The fundamental metric is the Euclidean distance between alternatives and the ideal negative answer. The taxicab distance is used as a secondary measurement to determine which alternative is preferable if the two have equal Euclidean distance values. By applying the CODAS technique to the parking spaces of the NVPs, the results presented in

Table 8. The CODAS method’s scores and rankings.

	CODAS’s Score	CODAS’s Ranking
A6	0.0000	7
A7	0.0048	4
A8	0.0438	3
A9	0.0035	5
A10	0.0981	2
A11	0.0001	6
A12	−0.0499	10
A13	0.3323	1
A14	−0.0276	8
A15	−0.3967	16
A16	−0.1228	11
A17	−0.3911	15
A18	−0.8345	19
A19	−0.3348	14
A20	−0.2811	13
A21	−0.0389	9
A22	−0.4501	17
A23	−0.2604	12
A24	−0.4635	18

were found.

3.2.4. TOPSIS Method

The evaluations of alternatives in the TOPSIS method depend on how far away they are from the ideal positive (PIS) and the ideal negative answer (NIS). PIS is a solution that maximizes profit criteria while minimizing cost criteria, whereas NIS maximizes cost criteria while minimizing profit criteria. The best option will be the one that has the shortest geometric distance from the PIS and the greatest distance from the ideal negative solution. Applying the TOPSIS method to the parking spaces of the NVPs yielded the results shown in

Table 9. The TOPSIS method’s scores and rankings.

	TOPSIS’s Score	TOPSIS’s Ranking
A6	0.5628	9
A7	0.5243	11
A8	0.5215	12
A9	0.5602	10
A10	0.5000	13
A11	0.5773	5
A12	0.5669	8
A13	0.3719	19
A14	0.4998	14
A15	0.5753	6
A16	0.4532	16
A17	0.5676	7
A18	0.4030	18
A19	0.5969	1
A20	0.4462	17
A21	0.5786	4
A22	0.4685	15
A23	0.5956	3
A24	0.5967	2

.

3.2.5. EDAS Method

The use of a median solution to evaluate the alternatives is this method’s primary characteristic. There are two types of distances in this method: the distance positive of the average (PDA) and the distance negative of the average (NDA). This technique is very useful in situations with contradictory attributes, and the best option is chosen by calculating the distance between each option and the ideal value.

Table 10. The scores and the EDAS method’s rankings.

	EDAS’s Score	EDAS’s Ranking
A6	0.3270	10.0
A7	0.8479	6.0
A8	0.9091	4.0
A9	0.0000	18.0
A10	1.0000	2.0
A11	0.0436	17.0
A12	0.3651	13.0
A13	0.9854	1.0
A14	0.9091	5.0
A15	0.2509	16.0
A16	0.6454	8.0
A17	0.8642	7.0
A18	0.5991	3.0
A19	0.2653	15.0
A20	0.6816	9.0
A21	0.2420	14.0
A22	0.2659	12.0
A23	0.5021	11.0
A24	0.0312	19.0

includes the evaluation ratings given to each available parking space as well as the ranking of alternatives.

3.2.6. WASPAS Method

The Weighted Sum Model (WSM) and Weighted Product Model (WPM), two well-known MCDM methods, are combined in a novel way to create the WASPAS method. In contrast to WPM, which determines an alternative’s score as the result of evaluating each criterion’s scale at a power equal to the weight of the given criterion, the WSM method calculates an alternative’s overall score as a sum of the values of the criteria. In addition to using these techniques, WASPAS aims to increase the estimation accuracy by optimizing the aggregated ponderated function. Because of this, it was possible for us to determine the relative overall importance of each choice by obtaining many results based on different functional parameter modifications. The results are displayed in

Table 11. WASPAS method’s scores with the different λ values.

	Qi
	0	0.2	0.4	0.6	0.8	1
A6	0.3192	0.3689	0.4187	0.4684	0.5181	0.5678
A7	0.2684	0.3259	0.3834	0.4409	0.4984	0.5559
A8	0.2686	0.3326	0.3966	0.4606	0.5246	0.5886
A9	0.2045	0.2731	0.3418	0.4104	0.4791	0.5477
A10	0.6132	0.6461	0.6791	0.7120	0.7450	0.7779
A11	0.2058	0.2753	0.3448	0.4143	0.4838	0.5533
A12	0.2210	0.2855	0.3500	0.4145	0.4790	0.5436
A13	0.5364	0.5811	0.6257	0.6703	0.7149	0.7595
A14	0.2636	0.3253	0.3870	0.4487	0.5104	0.5720
A15	0.2003	0.2559	0.3116	0.3672	0.4228	0.4784
A16	0.2646	0.3215	0.3783	0.4352	0.4921	0.5490
A17	0.2623	0.3115	0.3607	0.4098	0.4590	0.5082
A18	0.4227	0.4447	0.4667	0.4887	0.5107	0.5327
A19	0.2021	0.2600	0.3178	0.3756	0.4335	0.4913
A20	0.2685	0.3194	0.3702	0.4210	0.4719	0.5227
A21	0.2088	0.2717	0.3347	0.3976	0.4605	0.5235
A22	0.2403	0.2919	0.3436	0.3952	0.4469	0.4985
A23	0.2232	0.2799	0.3366	0.3932	0.4499	0.5066
A24	0.1931	0.2496	0.3061	0.3626	0.4191	0.4756

below, and the rankings are shown in

Table 12. WASPAS method’s rankings with the different λ values.

	WASPAS 0 Ranking	WASPAS 0.2 Ranking	WASPAS 0.4 Ranking	WASPAS 0.6 Ranking	WASPAS 0.8 Ranking	WASPAS 1 Ranking
A6	4	4	4	4	4	5
A7	7	6	7	7	7	6
A8	5	5	5	5	3	3
A9	16	15	14	12	10	9
A10	1	1	1	1	1	1
A11	15	14	12	11	9	7
A12	13	12	11	10	11	10
A13	2	2	2	2	2	2
A14	9	7	6	6	6	4
A15	18	18	18	18	18	18
A16	8	8	8	8	8	8
A17	10	10	10	13	14	14
A18	3	3	3	3	5	11
A19	17	17	17	17	17	17
A20	6	9	9	9	12	13
A21	14	16	16	14	13	12
A22	11	11	13	15	16	16
A23	12	13	15	16	15	15
A24	19	19	19	19	19	19

.

3.2.7. Comparison of Case Study Rankings

Table 13. Comparison of the ranking results.

	C1	C2	C3	C4	C5	CODAS Ranking	TOPSIS Ranking	EDAS Ranking	WASPAS 0.0 Ranking	WASPAS 1.0 Ranking
A1	1	8.55	0.49	0.94	5	3	14	12	9	3
A2	2	5.24	0.03	0.82	6	14	11	6	5	5
A3	2	3.17	0.13	0.81	6	21	18	2	6	10
A4	3	2.3	0.36	0.96	5	6	17	4	7	6
A5	3	0.11	0.85	0.88	5	1	24	7	2	1
A6	4	9.24	0.08	0.9	5	9	8	11	8	9
A7	4	3.06	0.61	0.94	5	7	12	8	10	11
A8	4	3.63	0.64	0.9	6	17	13	9	13	17
A9	4	9.89	0.75	0.89	5	11	9	22	20	13
A10	4	3.23	0.01	0.92	6	2	16	3	1	2
A11	4	7.85	0.95	0.87	5	12	4	21	21	14
A12	4	8.98	0.54	0.92	5	8	7	17	17	12
A13	5	0.37	0.18	0.95	7	23	23	5	4	8
A14	5	3.62	0.64	0.92	7	24	15	14	16	24
A15	5	8.48	0.61	0.89	4	4	6	18	18	7
A16	6	2.53	0.74	0.94	7	22	20	15	15	23
A17	6	5.12	0.31	0.94	6	18	10	10	12	19
A18	6	0.79	0.12	0.99	4	5	22	1	3	4
A19	6	7.27	0.78	0.99	6	13	1	20	22	18
A20	6	2.09	0.7	0.96	6	15	21	13	11	16
A21	6	6.26	0.92	0.98	7	20	5	23	23	22
A22	6	2.31	0.97	0.91	5	10	19	16	14	15
A23	6	7.8	0.47	0.91	6	19	2	19	19	21
A24	7	7.89	0.79	0.96	6	16	3	24	24	20

displays the rankings of the four distance-based MDCM techniques: CODAS, TOPSIS, EDAS, and WASPAS. The rankings provided by these different methods are not identical and are even contradictory. This makes it very complex to choose the right multi-criteria method to solve the decision-making problem in parking space selection. However, in the next section, we discuss the governance of the researchers for this case and propose our own solution.

4. Synthesis

Choosing the best MCDM method has given rise to numerous works in the literature. In the transportation domain, a comparison of five MCDM methods was performed by [20] in order to choose the best alternative for a road trip that represents the least accident risk. The weighting of the decision criteria was based on the driver’s preferences. The authors realize a comparison between the methods PROMETHEE, AHP, Fuzzy AHP, TOPSIS, and Fuzzy TOPSIS. According to the authors’ analysis, PROMETHEE and AHP produce the best results. The authors suggest the AHP method because of its simplicity and robustness. This choice is justified by the width of implementation, the simplicity of calculation, and the promising results of the AHP method. Next, they evaluated AHP and the other methods using three different evaluation methods (Spearman’s rank correlation coefficient, average overlap (AO), and discounted cumulative gain (DCG)). An evaluation that solely focuses on the chosen AHP method all while neglecting evaluation of the other methods. However, this is a non-formal choice.

The paper of [21] compares four hybrid MCDM methods including the following methods: AHP and Fuzzy AHP were employed to calculate the weighting matrix, and TOPSIS and PROMETHEE were employed to rank the alternatives. The study is carried out within the framework of reducing the environmental impacts caused by construction projects and the exploitation of transport infrastructures. The results showed that the outcomes are almost identical between the four methods. The only difference is the ranking of the first two alternatives, the one bringing together TOPSIS and PROMETHEE. In order to validate the choice of the correct MCDM method to adopt, the authors used a baseline ranking (Environmental Impact Assessment Report, 2018) developed by an expert team, despite the fact that the result provided by PROMETHEE perfectly matches the reference ranking. It is therefore inconclusive, since human involvement in a decision is generally subject to subjectivity. This calls into question the reliability of choosing this method.

On the other hand, the study conducted by [22] defends the choice of the MCDM method with a more convincing analysis and arguments than the previously cited studies. This paper aims to choose the best-performing feature selection method for digitized texts among the various existing feature selection methods in the literature. The selection methods place digital texts into predefined classes based on their content (e.g., positive or negative, spam or not, one topic or another, useful or not). The ranking of the selection methods is performed beforehand in accordance with their accuracy as empirical measures of evaluation. Then, the performance of the results of the five MDCM methods (TOPSIS, VIKOR, GRA, the weighted sum method (WSM), and PROMOTHEE) are evaluated according to the accuracy ranking of the feature selection methods.

In this research, the results of MCDM methods are evaluated using Spearman’s rank correlation coefficient and the new WS rank similarity coefficient recently proposed by [23]. In statistics, Spearman’s rank correlation coefficient is a nonparametric measure between the rankings of two variables and assesses how well the relationship between two variables can be described using a monotonic function. In addition, Spearman’s rank correlation coefficient is capable of reflecting the conflicts between ranking orders. The more discordant the rankings of two variables, the smaller the Spearman’s rank correlation coefficient. The formula to compute Spearman’s rank correlation coefficient is:

$$\begin{array}{cc}{R}_s=1-\frac{6{\displaystyle \sum d_i^2}}{n(n^2-1)}& \end{array}$$

(2)

where $d_i$ is defined as the difference between the ranks $d_i=R_{x_i}-R_{y_i}$, and $n$ is the number of elements in the ranking.

Despite its wide use, the Spearman coefficient does not account for the fact that the top of the ranking is more important than the bottom; therefore, a change in the top ranks of the list has a similar weight to a change at the bottom of the list. The new ranking similarity factor is more sensitive to significant changes in ranking. The formula for calculating the WS coefficient is as follows:

$$\begin{array}{cc}WS=1-{\displaystyle \sum _{i=1}^n(2^{-R_{x_i}}.\frac{\left|R_{x_i}-R_{y_i}\right|}{\max \{\left|1-R_{x_i}\right|,\left|N-R_{x_i}\right|\}})}& \end{array}$$

(3)

where $WS$ is the value of similarity coefficient, $N$ is the length of the ranking, and $R_{x_i}$ and $R_{y_i}$ mean the place in the ranking for the ith element in ranking $x$ and ranking $y$, respectively.

Table 14. Spearman’s rank correlation.

	CODAS	TOPSIS	EDAS	WASPAS y(0–0.6)	WASPAS y(0.8–1)
CODAS	1	−0.4	−0.3	−0.5	−0.2
TOPSIS	−0.4	1	−0.6	−0.2	−0.2
EDAS	−0.3	−0.6	1	0.6	0.3
WASPAS y(0–0.6)	−0.5	−0.2	0.6	1	0.9
WASPAS y(0.8–1)	−0.2	−0.1	0.3	0.9	1

and

Table 15. WS coefficient of rankings similarity.

	CODAS	TOPSIS	EDAS	WASPAS y(0–0.6)	WASPAS y(0.8–1)
CODAS	1	0.28385417	0.53125	0.44791667	0.37239583
TOPSIS	0.28385417	1	0.3515625	0.3671875	0.32552083
EDAS	0.53125	0.3515625	1	0.79166667	0.64583333
WASPAS y(0–0.6)	0.44791667	0.3671875	0.79166667	1	0.79166667
WASPAS y(0.8–1)	0.37239583	0.32552083	0.64583333	0.79166667	1

show the Spearman and WS correlation coefficients, respectively. This is a two-by-two evaluation that does not allow clear visibility of the correlation between one method and all the other methods. Since the correlation coefficient is not an additive value, we cannot speak of an average. The analysis of the correlation results for the Spearman coefficient shows that the WASPAS y method (0–0.6) is the method that has the most correlation and conformity with the other methods, whereas for the WS coefficient, it is more complicated to decide which method has more correlation (EDAS or WASPAS y (0–0.6)).

The most suitable method is to calculate the correlation of each method with the rest of the methods. The “average inter-item correlation” is a method that offers the possibility to calculate the correlation between the result of a method and the average of the results of all the methods (mean rank). An average inter-item correlation is a way of analyzing internal consistency reliability. In this paper, we use a new approach that we propose in this study to evaluate and select the best MCDM method. It consists of calculating “average inter-item correlation SW” using the WS coefficient. This approach will allow the calculating of the correlation (WS coefficient) between a method and the set of methods while favoring the cells with the best ranking. The results of this approach are presented in

Table 16. Average inter-item correlation SW.

	Average Inter-Item Correlation SW
CODAS	0.58541667
TOPSIS	0.52760417
EDAS	0.64635417
WASPAS y(0–0.6)	0.7296875
WASPAS y(0.8–1)	0.73802083

.

We clearly notice that the average inter-element correlation allows an easier identification of the best MCDM method to use.

The results highlight the WASPAS method as the method with the most consistency with other methods. The number of alternatives can affect the choice of the most efficient MCDM method. However, to further our study, it is imperative to evaluate these methods with different numbers of alternatives. The evaluation of the MCDM methods is performed according to four scenarios. The number of alternatives is as follows:

• Scenario No.1: 30 parking spaces with randomly managed criteria.
• Scenario No.2: 60 parking spaces with randomly managed criteria.
• Scenario No.3: 100 parking spaces with randomly managed criteria.
• Scenario No.4: 500 parking spaces with randomly managed criteria.

While testing each scenario, we noticed that the most reliable method changes as the values in the decision matrix change. However, we ran each scenario multiple times. Figure 7 below summarizes the number of times a method obtains the best score during each scenario.

According to the four scenarios, it is clear that WASPAS has carried over the large batch, although it should be noted that in this study, only WASPAS (y = 0) and WASPAS (y = 1) are applied. In addition, we observe that WASPAS 0 is more commonly obtained when the number of possibilities is less than or equal to 100, whereas in Scenario 4, the WASPAS 1 approach is more usually obtained for a larger number of 500 alternatives. This allows us to conclude that the WASPAS method generally produces the best results. It is the most reliable method in the four scenarios.

5. Conclusions

Multi-criteria decision making (MCDM) methods are very rarely evaluated, because they provide no reference for a final ranking. This study suggests a new method called mean inter-item correlation SW, which combines “mean inter-item correlation” and the SW coefficient to provide better station attribution. The experimental research shows that the WASPAS method is more precise than CODAS, TOPSIS, and EDAS. At each modification in the decision matrix, the outcomes of the comparison analysis of the four multi-criteria decision-making procedures in our case study are not the same. In the majority of cases, using the WASPAS method yields better results.

The study of our approach is limited to a case study of a single parking space allocation in the city of Lille. The results of this research must be evaluated under various cases according to several constraints. However, we chose to run several scenarios multiple times. Otherwise, this research could offer a useful framework for comparing MCDM methods prior to the decision-making process.

Future research directions include a multi-criteria analysis on fuzzy sets by expanding the number of alternatives using other fuzzy algorithms and scales, as well as other weighting methods that are becoming increasingly popular in intelligent parking management.