An Expert System for Ranking and Matching Electric Vehicles to Customer Specifications and Requirements

Abstract

Electric vehicles (EVs) have become popular in the last decade because of their advantages compared to conventional vehicles. The market offers dozens of EV models in a large range of prices, performances, and specifications. This paper presents an expert system we developed to support sellers and customers in choosing an EV that matches the customers’ specifications. The system enables ranking-specific EVs according to the customers’ specifications and counting the number of mismatches. The paper analyzes a database of 53 different EVs, each with 22 different characteristics, enabling customers to choose the EV that best suits their most important specifications. Based on the customer’s requirements and the principle of fuzzy sets, the system assigns a matching value to each criterion. These matching values are the input matrix for the TOPSIS procedure that ranks all the EVs according to their matching scores for a specific customer. The applicability of the proposed method is demonstrated for one customer with specific preferred EV requirements. A Python code of this method is also available herein.

1. Introduction

Electric vehicles (EVs) have become increasingly common over the past decade because of their advantages compared to conventional vehicles [1]. Electric vehicles have made a significant breakthrough in the automotive industry, giving consumers a way to travel on the roads more confidently and providing people with opportunities to switch to more environmentally friendly ways of driving. Today’s EVs are gradually taking over more roads and replacing polluting conventional vehicles. They appear to promote the ability to store energy in clean and smart grids to reduce greenhouse gas emissions and eliminate harmful traffic loads [2]. The market offers dozens of models of electric cars with a large range of prices, performance, and other specifications. The growth rate of introducing EVs into use increased in the entire EU. In 2019, the growth rate was 48%, while in 2020, it was 86% [3]. The development of EVs is highly favored because activities related to the development of the electro-mobility sector match the need to reduce environmental pollution. Producing fully electric-powered vehicles is now a reality for major passenger vehicle manufacturers. There is a dynamic change in the percentage of production volumes relating to vehicles powered by petroleum, electricity, or hybrid combinations of the two. In 2018, the estimated number of electric cars was around 750 thousand, and the projection for 2020 was around 10 million [4]. The number of electric car models in 2023 has already exceeded 300 [5].

The variety of EVs is a challenge to anyone who wants to buy an EV that properly matches specific requirements and needs. Finding the best match is also challenging for sellers and retailers who try to help their customers purchase an EV from a given set of cars they sell. Purchasing an EV is a multicriteria decision analysis problem with many criteria, including price, energy consumption, technical specifications, and ergonomic specifications. Therefore, there is a need for a decision support system that will help buyers and sellers navigate the mission to match the customer’s requirements and the preferred car. In [6], the authors developed a forecasting model that used machine-learning methods to identify factors for predicting consumer behavior regarding willingness to purchase an EV. They found that the factors stimulating the decision to purchase an EV to the greatest extent are price, design, car class, equipment, and EV driving advantages.

This paper presents a system we developed to support sellers and customers as they work together to choose an EV that matches customers’ needs and requirements. The system enables ranking specific electric vehicles according to the customers’ needs. At the same time, it also identifies the number of instances where the customer’s requirements and the EV’s properties and specifications do not match. We analyze a real database of 53 electric cars, each with 22 different characteristics (such as price, energy consumption, and battery capacity), according to which a customer should choose an EV that best suits the needs that have been customer-defined. The system assigns a matching value to each criterion of each car according to the customer’s requirements. A value of 1 indicates a complete match of the specific vehicle’s feature with the customer’s requirement regarding that criterion; a value of 0 indicates a complete mismatch, while a matching value between 0 and 1 indicates a partial match, calculated according to the principle of fuzzy sets. A fuzzy set was defined by [7] as a class of objects with grades of membership. Such a set is represented by a membership function that assigns to each object a degree of membership in the range $\left[0,1\right]$.

The matching value matrix is the input for the Technique for Order of Preference by Similarity to the Ideal Solution (TOPSIS) procedure developed by [8]. This procedure ranks all the EVs according to their matching scores for a specific customer. The applicability of the proposed method is demonstrated for one customer with preferred EV requirements.

There is widespread (and increasing) regulation in many countries and states urging customers and producers to prefer EVs. For example, [9] mentioned that the California Air Resources Board developed the Advanced Clean Cars (ACC) program and derived a single coordinated package of requirements for model years 2015 through 2025. That assured the development of environmentally superior cars that will continue to deliver performance, utility, and safety. The Zero Emission Vehicle (ZEV) regulation acts as the technology-forcing piece of the ACC program, pushing manufacturers to produce such vehicles. Moreover, California’s governor directed the State government to help accelerate the market for ZEVs in California, setting a target of 1.5 million ZEVs by 2025. In [10,11], the authors mentioned the Paris Agreement (an international treaty signed in 2015 by 196 countries and the European Union), which aims to limit global warming by reducing the harmful effects of human-produced climate change. As the transport sector is one of the world’s largest emitters of greenhouse gases (21%), a group of governments and car manufacturers signed a declaration to transition to zero vehicle emissions by 2035 in leading countries.

The rest of the paper is structured as follows: Section 2 presents the literature review; Section 3 describes the proposed model; Section 4 presents a case study; Section 5 presents a discussion; and Section 6 presents conclusions, limitations, and future research.

2. The Literature Review

The interest in EVs in the scientific literature has increased with the popularity of EVs and the understanding that EVs are probably the next generation of vehicles. In recent years (2018–2022), the number of published papers on the “electric vehicles” topic (as counted in Google Scholar), is high, with about 40,000–60,000 publications each year. Here is an example of several papers.

In [11], the authors point out four factors for the expanded use of EVs: government policy, economic advantages, environmental considerations, and technological development. They concluded that governments should invest in developing EVs and battery technologies, provide subsidies, and develop charging infrastructure. The use cost of EVs is influenced by grid electricity price, carbon tax, and other factors. In [12], the authors presented an expert system for the decision support of an EV driver in minimizing energy consumption. Their proposed system was based on the use of multi-valued logic trees, which enabled minimizing objective functions. One of those functions was aimed at minimizing EV energy consumption at different ambient temperatures. In [13], the authors explained that the major criteria for developing electric car chassis are stiffness and strength enhancement, subject to mass reduction, cost, and time. Toward this direction, they proposed an integrated methodology for developing an electric car chassis considering the modeling and simulation concurrently.

EVs have been the subject of much research over the last few years. This selection of papers aims to highlight some of the most significant findings. In [14], the authors explored consumer intentions to adopt, buy, and use EVs by analyzing 211 peer-reviewed research articles published between 2009 and 2019. They identified four main types of influential factors: demographic, situational, contextual, and psychological. In [15], the authors focused on EV operations management based on mathematical modeling for EV charging infrastructure planning, EV charging operations, public policy, and business models. In [16], the authors evaluated the progress in EVs regarding battery technology trends and charging methods, considering various battery technologies, standards available for EV charging, power control, and battery energy management proposals. In [17], the authors analyzed the policies, strategies, and technical requirements for EV development in India and globally. The authors focused on the situation in India, highlighting the current deployment of EVs and the existing challenges and opportunities. In [18], the authors examined the developments in EV policy in China, assessing national-level policy measures and financial incentives to develop the sustainable EV industry over the past decade. They also developed a mathematical model to quantify the credit policy regime’s impact, finding a significant gap between recent EV sales and projected EV production requirements. In [19], the authors covered the development of EVs and government policies in the UK, reviewing charging equipment protocols and standards, existing EV charging facilities, and charging infrastructure circuit topologies. The authors also discussed site factors, the operation and management of charging infrastructure, and various business models. Finally, in [20], the authors proposed a multi-criteria decision-making approach to identify and classify the factors of successful EV adoption in emerging economies. They concluded that EV performance and reliability, power and charging infrastructure, and government policies were the most influential factors for EV adoption.

In [21], the authors described the characteristics and typical models of energy sources of EVs, the existing EV types, and their environmental impacts. They also investigated energy management strategies for EVs, the charging technologies, the challenges faced by EVs, and the corresponding solutions. In [1], the authors investigated the effects of an uncontrolled charging process in a low-voltage distribution grid case study and proposed a charging coordination management strategy. Their simulation results indicate that the voltages in the system’s buses and the lines’ thermal limits are major limiting factors for the integration of EVs in energy distribution networks. In [2], the authors proposed a stochastic procedure for modeling and analyzing a fleet of EVs to generate accurate charging and discharging profiles. They used a genetic algorithm to determine the optimal charging/discharging schedule for each EV in the fleet. In [22], the authors proposed a concept of multi-objective techno-economic-environmental optimization for scheduling electric vehicle charging/discharging. They optimized end-user energy cost, battery degradation, grid interaction, and CO₂ emissions in the home micro-grid context. Results from their case studies show reductions in energy cost, battery degradation, CO₂ emissions, and grid utilization. In [23], the authors stated that regular gasoline vehicles have high emission levels that contribute significantly to climate change and pollution-related health problems. EVs are a promising alternative to gasoline vehicles because they do not directly release emissions or pollutants. The authors note that the sales of EVs are affected due to a variety of limitations, such as the lack of available charging infrastructure, the long charging time, the high cost of long-range EVs, and a limited supply of affordable EVs.

Several papers dealt with EVs’ ranking and selection. For example, the authors in [24] proposed a model for selecting and ranking a group of EVs using the multi-attributive border approximation area comparison (MABAC) method. They employed the MABAC method to evaluate various technical and operational attributes, such as fuel economy, base model pricing, quick accelerating time, battery range, and top speed. In [25], the authors presented an integrated approach of AHP and MABAC methods for selecting and ranking the best EV. The AHP method is used to obtain weight coefficients of criteria, and the selection of EVs alternatives is evaluated using the MABAC method (AHP-MABAC). In [26], the authors proposed a comprehensive tool for robustness analysis based on TOPSIS, which they demonstrated on EVs. Their method releases the decision-maker from setting the criteria weighting. Their framework was then used for sensitivity analysis based on interval arithmetic and the MCDA approach. While the primary assessment gives initial recommendations, only after thorough analysis can the ranking of alternatives be reliably treated. In [27], the author developed a multi-criteria stochastic selection of EVs for sustainable development in Poland. Table 1 presents a summary of the EV literature reviews. The uniqueness of our proposed model is that it considers the customer’s requirements and wishes, with the result being a rank of candidate EVs sorted in decreasing order according to compliance with the customer’s needs.

Ranking and selecting an EV is a multi-criteria decision problem. Ranking according to several criteria (outputs and inputs) usually results in a multi-criteria decision analysis method (MCDA). The use of MCDA focuses on designing mathematical and computational tools to support the subjective evaluation of a finite number of alternatives under a finite number of performance criteria. In an MCDM problem, a variety of alternatives (in our case, EVs) is evaluated according to several criteria that characterize these alternatives; the goal is to choose the best alternative [28,29]. The use of MDCA methods is a popular tool in complex issues. These methods are applied to problems considering selecting the most satisfying choices or evaluating the quality of solutions [30]. Methods incorporating MCDA have received much attention from researchers and practitioners in evaluating, assessing, and ranking alternatives across diverse industries [31]. Numerous methods have been proposed for ranking alternatives according to multiple criteria. For example, [32,33] surveyed several MCDM and ranking methods. One of the most popular methods of MCDA is TOPSIS [8]. Over the years, it has gained many followers due to its simplicity, efficiency, and high correlation of results with other well-known multi-criteria methods. Numerous models and decision support systems have been developed based on the TOPSIS method of performance [34].

The TOPSIS method and its applications are widely used in the literature. In [35], the authors claimed that TOPSIS [8] is one of the most well-known classical MCDM approaches. The essential goal of the TOPSIS approach is that the most preferred alternative is not only the shortest distance from the positive ideal solution but also the farthest distance from the negative ideal solution [36]. For example, in [37], the authors used linguistic variables to show how energy policy goals toward sustainable development and options for renewable energy sources are linked and evaluated. In [38], the authors developed a TOPSIS-based MCDM approach for whole-building energy comparison, using a specific objective weighting procedure for cost-accuracy modification. In [39], the authors presented a concept of sustainable development of EVs in Tehran. They expended the conventional definition of sustainable development based on a philosophy of key aspects of human, nature, and systems performances. In their proposed method, the coefficient of each policy scenario was calculated utilizing fuzzy TOPSIS, and the various policies affecting the development of EVs in Tehran were ranked. Our paper used the TOPSIS model to rank EVs according to customers’ requirements.

A fuzzy set is a class of objects with a continuum of grades of membership. In [40], the authors presented the literature review of 50 years of fuzzy set theory. They found that fuzzy sets have shown great progress in every scientific research area, being found in many application areas in both theoretical and practical studies. They noted that in recent years, standard fuzzy sets have been extended to new types, and these extensions have been used in many areas such as energy, medicine, material, economics, and pharmacology sciences. In our paper, we used the fuzzy sets concept to describe the grades of matching (membership) between EV features and customer requirements.

In many decision-making applications, membership functions of fuzzy sets are based on subjective perceptions rather than on data or other objective entities involved in the given problem. The problem of assigning numbers to subjective perceptions is a matter of mathematical psychology and requires various techniques [41]. In [42], the authors assumed that membership values should be defined on an interval scale. In one of their experiments, they applied a straightforward rating procedure, presenting the subject with a random series of houses. Then, they asked the subject to indicate the membership degree to rate each one as pleasing. In our research, we also use an interval scale where the customer sets minimum and maximum values for a feature (e.g., number of seats) that fulfills specific requirements.

Table 1. Summary of the EVs literature review.

Factors	Authors	Brief Description
Energy management and operation of EV	Boglou et al. (2020) [1]	Voltages in the system’s buses are major limiting factors for EVs.
	Elmehdi et al. (2020) [2]	Genetic algorithm for optimal charge scheduling of EVs.
	Das et al. (2020) [22]	Multi-objective optimization of EV for energy services.
	Gelmanova et al. (2018) [4]	A rough calculation of the energy efficiency and average cost of EV.
	Deptuła et al. (2022) [12]	An expert system to assess the energy consumption of an EV.
	Shen et al. (2019) [15]	Optimization models for EV service operations.
EVs in specific regions	Rokicki et al. (2021) [3]	Electromobility in European Union countries under COVID-19 conditions.
	Sobiech-Grabka et al. (2022) [6]	EVs purchase intention in Poland.
	Tal et al. (2020) [9]	EVs in California: policy and behavior perspectives.
	Yamamura et al. (2022) [10]	EVs in Brazil: an analysis of core green technologies.
	Razmjoo et al. (2022) [11]	The expansion of EVs in Europe.
	Ziemba (2020) [27]	Multi-criteria stochastic selection of EVs in Poland.
	Singh et al. (2021) [17]	Analysis of EV trends, development, and policies in India.
	Wu et al. (2021) [18]	A review of evolutionary policy incentives for EVs in China:
	Chen et al. (2020) [19]	a review on EV charging infrastructure development in the UK.
	Palit et al. (2022) [20]	An MCDA to classify the drivers for the adoption of EVs in emerging economies.
EVs design, battery, and technology	Tsirogiannis et al. (2019) [13]	EV chassis.
	Li et al. (2019) [21]	Key technologies for pure EVs.
	Tran et al. (2021) [23]	A review of range extenders in the battery of EVs.
	Sanguesa et al. (2021) [16]	A review of EV technologies and challenges.
	Chen et al. (2020) [19]	A review on EV charging infrastructure development in the UK.
Ranking and selecting EV	Biswas et al. (2019) [24]	Selection of EV using fuzzy AHP-MABAC.
	Więckowski et al. (2023) [26]	Sensitivity analysis in MCDA application to the selection of an EV.
	Onat et al. (2016) [35]	TOPSIS and fuzzy set for ranking alternative vehicle technologies.
	Singh et al. (2020) [14]	A review and meta-analysis of factors influencing the adoption of EVs.
Database	EV-Database [5]	EV database.
	Hadasik and Kubiczek (2021) [43]	Database of electric passenger cars with their specifications.

Table 1. Summary of the EVs literature review.

Factors	Authors	Brief Description
Energy management and operation of EV	Boglou et al. (2020) [1]	Voltages in the system’s buses are major limiting factors for EVs.
	Elmehdi et al. (2020) [2]	Genetic algorithm for optimal charge scheduling of EVs.
	Das et al. (2020) [22]	Multi-objective optimization of EV for energy services.
	Gelmanova et al. (2018) [4]	A rough calculation of the energy efficiency and average cost of EV.
	Deptuła et al. (2022) [12]	An expert system to assess the energy consumption of an EV.
	Shen et al. (2019) [15]	Optimization models for EV service operations.
EVs in specific regions	Rokicki et al. (2021) [3]	Electromobility in European Union countries under COVID-19 conditions.
	Sobiech-Grabka et al. (2022) [6]	EVs purchase intention in Poland.
	Tal et al. (2020) [9]	EVs in California: policy and behavior perspectives.
	Yamamura et al. (2022) [10]	EVs in Brazil: an analysis of core green technologies.
	Razmjoo et al. (2022) [11]	The expansion of EVs in Europe.
	Ziemba (2020) [27]	Multi-criteria stochastic selection of EVs in Poland.
	Singh et al. (2021) [17]	Analysis of EV trends, development, and policies in India.
	Wu et al. (2021) [18]	A review of evolutionary policy incentives for EVs in China:
	Chen et al. (2020) [19]	a review on EV charging infrastructure development in the UK.
	Palit et al. (2022) [20]	An MCDA to classify the drivers for the adoption of EVs in emerging economies.
EVs design, battery, and technology	Tsirogiannis et al. (2019) [13]	EV chassis.
	Li et al. (2019) [21]	Key technologies for pure EVs.
	Tran et al. (2021) [23]	A review of range extenders in the battery of EVs.
	Sanguesa et al. (2021) [16]	A review of EV technologies and challenges.
	Chen et al. (2020) [19]	A review on EV charging infrastructure development in the UK.
Ranking and selecting EV	Biswas et al. (2019) [24]	Selection of EV using fuzzy AHP-MABAC.
	Więckowski et al. (2023) [26]	Sensitivity analysis in MCDA application to the selection of an EV.
	Onat et al. (2016) [35]	TOPSIS and fuzzy set for ranking alternative vehicle technologies.
	Singh et al. (2020) [14]	A review and meta-analysis of factors influencing the adoption of EVs.
Database	EV-Database [5]	EV database.
	Hadasik and Kubiczek (2021) [43]	Database of electric passenger cars with their specifications.

3. The Proposed Model

This section will present the proposed model for ranking EVs according to customer requirements for best matching. The ranking–matching model combines the TOPSIS ranking method and fuzzy set. The proposed model objectively calculates the relative score of each candidate EV according to criteria defined by a specific customer, reflecting that customer’s wishes. According to the relative score obtained for that specific customer, the EVs are ranked, where the EV with the highest relative score is ranked first. The EV with the highest relative score is the EV that best matches the customer’s requirements. The model also counts the number of instances where each EV does not comply with the customers’ requirements.

3.1. The Steps of the Proposed Model

The steps of the proposed model are executed as follows:

• Step 1: Define the EVs to be ranked and matched according to the availability in the market. The EVs being evaluated and ranked are significant because adding or removing an EV can change the scores of other EVs and their internal ranking. This phenomenon of rank reversal exists in many multicriteria ranking methods. A survey about rank reversal can be found in a review paper by [44];
• Step 2: Define the criteria for ranking the available EVs. Choose objective criteria whose values can be found in the EV specification sheet. Classify the criteria into three groups: $m$ criteria of inputs; $s$ criteria of outputs and criteria of personal preference;
• Step 3: Construct a matrix $P$ with the values of the criteria of each EV. The element $p_{i,j}$ of the matrix $P$ when $(i=1,\dots ,n)$; $(j=1,\dots ,m)$ is the value of the input criterion $j$ of EV $i$. When $(i=1,\dots ,n)$ and $(j=m+1,\dots ,m+s)$, $p_{i,j}$ is the value of the output criterion $j$ of EV $i$. When $(i=1,\dots ,n)$ and $(j=m+s+1,\dots ,m+s+k)$, $p_{i,j}$ is the value of the personal preference criterion $j$ of EV $i$.

The matrix P of all the criteria for all the EVs, with the element, is shown in Equation (1).

$$P=\left(\begin{array}{ccccccccc}{p}_{1,1}& \cdots & p_{1,m}& p_{1,m+1}& \cdots & p_{1,m+s,}& p_{1,m+s+1,}& \cdots & p_{1,m+s+k}\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ p_{i,1}& \cdots & p_{i,m}& p_{i,m+1}& \cdots & p_{i,m+s}& p_{i,m+s+1}& \cdots & p_{i,m+s+k}\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ p_{n,1}& \cdots & p_{n,m}& p_{n,m+1}& \cdots & p_{n,m+s}& p_{n,m+s+1}& \cdots & p_{n,m+s+k}\end{array}\right)$$

(1)

• Step 4: Find the minimum and maximum values of each criterion $j,$ which are $\left(\underset{i}{\min }\left\{p_{i,j}\right\}\right)$ and $\left(\underset{i}{\max }\left\{p_{i,j}\right\}\right).$ To each criterion $j,$ customers should set the minimum and maximum values of $\left(a_j\right)$ and $\left(b_j\right)$ respectively, between which the customers will consider their requirements fulfilled. If a customer decides that a criterion is not personally important or relevant, the matching value is set as 1;
• Step 5: Construct matrix Q, which converts the criteria values of each EV in matrix P, for one customer, to the range $\left[0,1\right]$, calculated according to the fuzzy set principle. The customer must determine his/her subjective minimum and maximum values ($\left(a_j\right)$ and $\left(b_j\right)$, respectively) for each input and output criterion. The converted values of matrix Q are calculated as follows:
• Step 5.1: In the case where the criterion is input, the value of an element $q_{i,j}$ is calculated according to Equation (2). The calculation is performed according to the fuzzy membership principle, as seen in Figure 1.

  $${}_{q_{i,j}=\{\begin{array}{cc}1,& p_{i,j}\le a_j\\ \frac{b_j-p_{i,j}}{b_j-a_j},& a_j<p_{i,j<b_j}\\ 0,& p_{i,j}\ge b_j\end{array}}$$

  (2)
• Step 5.2: In the case where the criterion is output, the value of an element $q_{i,j}$ $(i=1,\dots ,n;\hspace{0.17em}j=m+1,\dots ,m+s)$ is calculated according to Equation (3). The calculation is performed according to the fuzzy membership principle; see Figure 2.

  $${}_{q_{i,j}=\{\begin{array}{cc}0,& p_{i,j}\le a_j\\ \frac{p_{i,j-a_j}}{b_j-a_j},& a_j<p_{i,j<b_j}\\ 1,& p_{i,j}\ge b_j\end{array}}$$

  (3)
• Step 5.3: In the case where the criterion is a continuous personal preference (e.g., the car’s height), the value of an element $q_{i,j}$ is calculated according to Equation (4); see Figure 3.

  $${}_{q_{i,j}=\{\begin{array}{cc}0,& p_{i,j}\le a_j\\ 1,& a_j<p_{i,j<b_j}\\ 0,& p_{i,j}\ge b_j\end{array}}$$

  (4)

When the personal preference criterion is discrete (e.g., the number of doors), the value of an element $q_{i,j}$ is determined as follows: if a feature $j$ of car $i$ matches the customer’s requirement, then $q_{i,j}=1$. If a feature $j$ of car $i$ is unacceptable to the customer, then $q_{i,j}=0$.

The outcome of Step 5 is the matrix $Q_{n,m+s+k}$, where each element $0\le q_{i,j}\le 1$ is the amount that features $j$ of car $i$, fulfilling a requirement of this specific customer;

• Step 6: Choose a ranking method for evaluating and ranking the EVs according to matrix Q. We used the TOPSIS ranking method developed by [8] for order preference by similarity to an ideal solution. Our TOPSIS version, adjusted for EVs and ranked for a specific customer, works as follows:
• Step 6.1: Used the matrix Q constructed in Step 5 for the specific customer;
• Step 6.2: Evaluate the weight of each criterion, $\left(w_j\hspace{0.17em}\hspace{0.17em}j=1,\dots ,m+s+k\right).$

The weights express the customer’s preference regarding the relative importance of the criteria. The values of the weights are determined subjectively by the customer. We recommend the following weights:

• 1—Extra importance;
• 0.75—Very strong importance;
• 0.5—Strong importance;
• 0.25—Medium importance;
• 0—Not important.

If the customer feels that all the criteria have the same importance, then $w_j=1\hspace{0.17em}\hspace{0.17em}\forall j=1,\dots ,m+s+k.$;

• Step 6.3: Determine the positive and negative solutions for all the criteria according to Equation (5).

  $$\begin{array}{l}{q}_j^{+*}=\left\{\max \left(q_{i,j}\right)\right\},\hspace{0.17em}i=1,\dots n.\\ q_j^{-*}=\left\{\min \left(q_{i,j}\right)\right\},\hspace{0.17em}i=1,\dots n.\end{array}$$

  (5)
• Step 6.4: Calculate each EV’s separation measures (positive and negative) according to Equation (6).

  $$d_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^{m+s+k}{\left(w_j\left(q_j^{+*}-q_{i,j}\right)\right)}^2}},d_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^{m+s+k}{\left(w_j\left(q_j^{-*}-q_{i,j}\right)\right)}^2}},i=1,\dots ,n.$$

  (6)
• Step 6.5: Calculate the relative closeness coefficient to the ideal solution of each EV according to Equation (7).

  $$S_i=\frac{d_i^{-}}{d_i^{-}+d_i^{+}},i=1,\dots ,n.$$

  (7)

The value $S_i$ obtained by Equation (7) is the EV $j$ score for a specific customer according to that customer’s requirements and preferences;

• Step 6.6: To obtain a rank of the ESs $\left(R_i\right)$, sort the EVs according to $S_i$ in decreasing order. The most preferred EV is ranked $R_i=1$ first, and so on;
• Step 7: Calculate $I{n}_i$, the number of instances where a specific EV does not comply with the customers’ requirements. This calculation is performed by counting the number of $q_{i,j}=0$ for an EV. Let’s define

  $${\delta }_{i,j}=\{\begin{array}{cc}1& q_{i,j=0}\\ 0& q_{i,j>0}\end{array}$$

  and the non-compliance of $E{V}_i$ is calculated by using (8)

  $$N{c}_i={\displaystyle \sum _{j=1}^{m+s+k}{\delta }_{i,j}}$$

  (8)

At the end of the procedure, each EV has three values, a score $(S_i)$, a rank $\left(R_i\right)$, and a number $\left(N{c}_i\right)$, indicating the instances when the EV did not comply with customer requirements.

3.2. Summary of the Methodology

The proposed system assigns each vehicle criterion a matching value according to the customer’s requirements. A system-generated value of 1 for a specific requirement indicates complete matching of the car to the customer’s requirements for that specific characteristic. A value of 0 indicates no matching, while a value between 0 and 1 indicates partial matching, calculated according to the principle of fuzzy sets. The calculated matching values are the input matrix values for the TOPSIS procedure, which ranks the EVs according to the matching scores of a specific customer. The values of the weights are determined subjectively by the customer. If a customer decides that a criterion is not (or no longer is) important or relevant, then the matching value for such criterion is set as 1.

4. Case Study

To illustrate the proposed method, we use a dataset of 53 EVs with their specifications. The dataset was collected by [43] in Poland and is available online. Each EV in the dataset is characterized by 22 criteria that we classified into three groups, where the input group contains 3 criteria, the outputs group contains 12 criteria, and the personal preference group contains 7 criteria; see

Table 2. Criteria classification.

No.	Symbol	Criterion	Type
1	$X_1$	Minimal price (gross) [PLN]	Inputs
2	$X_2$	Acceleration 0–100 kph [s]
3	$X_3$	Mean—Energy consumption [kWh/100 km]
4	$Y_1$	Engine power [KM]	Outputs
5	$Y_2$	Maximum torque [Nm]
6	$Y_3$	Battery capacity [kWh]
7	$Y_4$	Range (WLTP) [km]
8	$Y_5$	Wheelbase [cm]
9	$Y_6$	Length [cm]
10	$Y_7$	Width [cm]
11	$Y_8$	Permissible gross weight [kg]
12	$Y_9$	Maximum load capacity [kg]
13	$Y_{10}$	Maximum speed [kph]
14	$Y_{11}$	Boot capacity (VDA) [l]
15	$Y_{12}$	Maximum DC charging power [kW]
16	$Z_1$	Type of brakes	Personal preference
17	$Z_2$	Drive type
18	$Z_3$	Height [cm]
19	$Z_4$	Minimal empty weight [kg]
20	$Z_5$	Number of seats
21	$Z_6$	Number of doors
22	$Z_7$	Tire size [in]

. This data is used to generate matrix P (Steps 1, 2, and 3).

Specific customer preferences regarding these criteria are presented in

Table 3. One-customer preferences.

No.	Criteria- $\mathit{j}$	Min	Max	$\left({\mathit{a}}_{\mathit{j}}\right)$	$\left({\mathit{b}}_{\mathit{j}}\right)$	${\mathit{w}}_{\mathit{j}}$
1	Minimal price (gross) [PLN]	82,050	794,000	120,000	300,000	1
2	Acceleration 0–100 kph [s]	2.5	14	5	10	0.75
3	Mean—Energy consumption [kWh/100 km]	13.1	33	15	25	0.5
4	Engine power [KM]	82	772	100	300	0
5	Maximum torque [Nm]	160	1140	300	700	0
6	Battery capacity [kWh]	17.6	100	30	60	1
7	Range (WLTP) [km]	148	652	300	450	1
8	Wheelbase [cm]	187.3	327.5	200	300	0.5
9	Length [cm]	269.5	514	350	450	0.5
10	Width [cm]	164.5	255.8	180	230	0.5
11	Permissible gross weight [kg]	1310	3500	2000	3000	0.75
12	Maximum load capacity [kg]	290	1056	400	750	0.5
13	Maximum speed [kph]	123	261	130	150	0.5
14	Boot capacity (VDA) [l]	171	900	300	600	1
15	Maximum DC charging power [kW]	22	270	60	150	1
16	Type of brakes	-	-	disc (front + rear)
17	Drive type	-	-	2WD (front); 2WD (rear)
18	Height [cm]	137.8	191	150	170	1
19	Minimal empty weight [kg]	1035	2710	1500	2000	0.5
20	Number of seats	2	8	4	5	0.75
21	Number of doors	3	5	4	5	0.25
22	Tire size [in]	14	21	16	17	0.5

. Table 3 contains minimum and maximum values per criterion over all the EVs in the dataset (for the numerical criteria). The minimum and maximum values are valid for all customers; these values aim to help customers define their preferences. The values $\left(a_j\right)$ and $\left(b_j\right)$ are the minimum and the maximum values, respectively, that are available to fulfill the customers’ requirements. For the two non-numeric criteria (type of brakes and drive type), the customer defined the preferred discrete options. Moreover, the customer defined weights $\left(w_j\right),$ that reflect their subjective preference regarding the relative importance of the criteria, according to the scale in step 6.2.

The values of matrix Q, which converts the criteria values of each EV in matrix P, for this customer, to the $\left[0,\hspace{0.17em}1\right]$ range, were calculated according to the fuzzy set principle; the Q values are displayed in Appendix A.

The TOPSIS ranking method on matrix Q, which yields the scores and ranks the EVs for this customer, is presented in

Table 4. The scores and the rank of the EVs.

EV	Car Full Name	Make	Score	Rank	Non-Compliance
Car1	Audi e-tron 55 quattro	Audi	0.6330	7	4
Car2	Audi e-tron 50 quattro	Audi	0.5963	18	4
Car3	Audi e-tron S quattro	Audi	0.6028	14	5
Car4	Audi e-tron Sportback 50 quattro	Audi	0.5959	19	4
Car5	Audi e-tron Sportback 55 quattro	Audi	0.6399	5	4
Car6	Audi e-tron Sportback S quattro	Audi	0.6046	13	5
Car7	BMW i3	BMW	0.5136	44	7
Car8	BMW i3s	BMW	0.5136	43	7
Car9	BMW iX3	BMW	0.6140	10	2
Car10	Citroën ë-C4	Citroën	0.6013	15	3
Car11	DS DS3 Crossback e-tense	DS	0.5933	22	2
Car12	Honda e	Honda	0.5183	42	5
Car13	Honda e Advance	Honda	0.5212	41	5
Car14	Hyundai Ioniq electric	Hyundai	0.5289	40	3
Car15	Hyundai Kona electric 39.2 kWh	Hyundai	0.5566	36	2
Car16	Hyundai Kona electric 64 kWh	Hyundai	0.6784	2	1
Car17	Jaguar I-Pace	Jaguar	0.6269	9	4
Car18	Kia e-Niro 39.2 kWh	Kia	0.5682	33	1
Car19	Kia e-Niro 64 kWh	Kia	0.6974	1	0
Car20	Kia e-Soul 39.2 kWh	Kia	0.5579	35	3
Car21	Kia e-Soul 64 kWh	Kia	0.6782	3	2
Car22	Mazda MX-30	Mazda	0.4784	47	5
Car23	Mercedes-Benz EQC	Mercedes-Benz	0.5948	21	4
Car24	Mini Cooper SE	Mini	0.4610	48	10
Car25	Nissan Leaf	Nissan	0.5616	34	4
Car26	Nissan Leaf e+	Nissan	0.6626	4	1
Car27	Opel Corsa-e	Opel	0.5535	38	6
Car28	Opel Mokka-e	Opel	0.5737	30	2
Car29	Peugeot e-208	Peugeot	0.5544	37	5
Car30	Peugeot e-2008	Peugeot	0.5981	17	2
Car31	Porsche Taycan 4S (Performance)	Porsche	0.6053	12	5
Car32	Porsche Taycan 4S (Performance Plus)	Porsche	0.6065	11	5
Car33	Porsche Taycan Turbo	Porsche	0.5933	23	5
Car34	Porsche Taycan Turbo S	Porsche	0.5833	28	6
Car35	Renault Zoe R110	Renault	0.5049	45	6
Car36	Renault Zoe R135	Renault	0.5909	24	4
Car37	Skoda Citigo-e iV	Skoda	0.3937	51	14
Car38	Smart fortwo EQ	Smart	0.2955	53	18
Car39	Smart forfour EQ	Smart	0.4155	50	14
Car40	Tesla Model 3 Standard Range Plus	Tesla	0.5854	27	2
Car41	Tesla Model 3 Long Range	Tesla	0.5954	20	3
Car42	Tesla Model 3 Performance	Tesla	0.5891	25	3
Car43	Tesla Model S Long Range Plus	Tesla	0.5857	26	4
Car44	Tesla Model S Performance	Tesla	0.5826	29	5
Car45	Tesla Model X Long Range Plus	Tesla	0.5697	31	6
Car46	Tesla Model X Performance	Tesla	0.5697	31	6
Car47	Volkswagen e-up!	Volkswagen	0.3891	52	14
Car48	Volkswagen ID.3 Pro Performance	Volkswagen	0.6286	8	2
Car49	Volkswagen ID.3 Pro S	Volkswagen	0.6005	16	2
Car50	Volkswagen ID.4 1st	Volkswagen	0.6356	6	3
Car51	Citroën ë-Spacetourer (M)	Citroën	0.4834	46	7
Car52	Mercedes-Benz EQV (long)	Mercedes-Benz	0.5433	39	7
Car53	Nissan e-NV200 evalia	Nissan	0.4494	49	9

. Table 4 also includes the number of instances of non-compliance between the customer requirements and the features of each EV (non-compliance is defined here as a zero score in matrix Q).

The correlation coefficient between the TOPSIS scores and the number of instances of non-compliance is −0.8833. The EV at the top of the list (Car19, Kia e-Niro 64 kWh) had zero non-compliance instances.

The top-ranked car is Car19, Kia e-Niro 64 kWh. The second-ranked car is the Hyundai Kona electric 64 kWh, with one non-compliance instance (the width criterion is 180 cm vs. 180.5 of the Kia e-Niro). This analysis demonstrates that the second-ranked car would be eliminated in regular filtering. Still, in our proposed method, this car is presented to the customer as an option that should be considered.

5. Discussion

EVs have become popular during the last decade because of their advantages compared to conventional vehicles. The market offers many EV models with various prices, performances, and other features. In this paper, we developed a system to support sellers and customers in choosing an EV that matches the requirements of each customer. The system ranks EVs according to customer requirements and counts the instances when the vehicle’s characteristics are inconsistent with those requirements. The paper presents a case study with 22 different characteristics (such as price, energy consumption, and battery capacity). Based on the values of those characteristics, the system we developed can enable a customer to choose a car (from the set of 53 available EVs in the market) that best matches the customer’s pre-defined requirements. The proposed method may also be useful in other applications, such as energy system selection or car battery selection. The great advantage of our proposed method is the ease and simplicity of its use. Excel users can easily reproduce the method step-by-step and get the same results presented in our case study. Software developers can use the Python code (in Appendix B) and implement the function to automate the proposed method.

6. Conclusions, Limitations, and Future Research

The scientific literature has proposed different methods for ranking alternatives in general, including EVs. The uniqueness of our method is the full ranking of the offered EVS, according to the requirements and the preferences of a specific customer and his/her subjective weight of each criterion. Regular filtering methods screen out EVs, so even if an EV slightly exceeds one criterion (for example, a slight deviation in price), it is removed. Our method may rank such EVs as candidates for purchase while drawing the customer’s attention to the number of deviations. That enables the customer to make a better decision.

Limitations of the study: One limitation is that ranking by the TOPSIS method may cause a rank reversal, so an addition or omission of a criterion or EVs may change the internal rank. We also assumed a linear relationship between the matched values and the customer requirements in the fuzzy sets. From a technical point of view, it is easy to set a nonlinear relation, but the problem is extracting the subjective relations from the customer.

Future research: Conduct an expanded survey of many more customers to evaluate common subjective weights for the criteria and the subjective matching relation between matched values and customer requirements in the fuzzy sets and then implement these as default values.