Selection of Electric Vehicles for the Needs of Sustainable Transport under Conditions of Uncertainty—A Comparative Study on Fuzzy MCDA Methods

: All over the world, including Poland, authorities are taking steps to increase consumer interest in electric vehicles and sustainable transport as a way to reduce environmental pollution. For this reason, the electric vehicle market is dynamically and constantly developing, more and more modern vehicles are introduced to it, and purchases are often subsidized by the government. The aim of the article is to analyse the A–C segments of the Polish electric vehicle market and to recommend the most attractive vehicle from the perspective of sustainable transport. The aim of the research was achieved with the use of three multi-criteria decision aid (MCDA) methods, which deal well with the uncertainty and imprecision of data that occur in the case of many different parameters of electric vehicles. In particular, the following methods were used: the fuzzy technique for order of preference by similarity to ideal solution (TOPSIS), the fuzzy simple additive weighting (SAW) method, and the new easy approach to fuzzy preference ranking organization method for enrichment evaluation II (NEAT F-PROMETHEE II). Electric vehicle rankings obtained using each method were compared and veriﬁed by stochastic analysis. The conducted analyses and comparisons allowed us to identify the most interesting electric vehicles, which currently appear to be the Volkswagen ID.3 Pro S and Nissan LEAF e+.


Introduction
Sustainable development is a paradigm of thinking about the future in which the environmental, social and economic goals are balanced, and together they allow us to improve the quality of life [1].In turn, one of the necessary elements to achieve the goals of sustainable development is sustainable transport [2].Narrowly defined sustainable transport is transport that minimizes environmental problems and resource depletion, and understood more broadly, it should also maximize social and economic welfare [3].Electric vehicles (EVs) offer enormous potential for the development of sustainable transport due to their relatively high efficiency and potential independence from unsustainable energy sourcing [4].It is considered that EVs have even 70% lower environmental impact than diesel vehicles [5].In particular, we can distinguish battery electric vehicles (BEVs), plug-in hybrid electric vehicles (PHEVs), fuel-cell electric vehicles (FCEVs) and range-extended electric vehicles (REEVs) [6].The most widespread are BEVs and PHEVs, the market of which has been growing dynamically in recent years both in Europe [7] and all over the world [8].In 2020 alone, BEV sales in Europe increased by 106% and PHEV by 210%, year-on-year [9].It should be noted that BEVs are characterized by greater sustainability, but only when they are powered by electricity from renewable sources and managed in a sustainable manner [4].Moreover, BEVs do not allow the use of an internal combustion engine, and this possibility is abused in the case of PHEVs [6].Consequently, the market share of BEVs and the number of available models are greater than that of the PHEVs [8].
It is worth adding that along with the growth of the EVs market, the market of charging stations for such vehicles also grows dynamically, both in terms of the number of charging points and the total capacity [9].
Poland, like the entire Europe and the world, aims at the dynamic development of the EVs market in order to maintain a sustainable transport system and adjust it to the goals of the national and European climate and energy policy [10,11].It is estimated that almost 25% of greenhouse gases (GHG) in Europe are produced by the transport sector [12].Meanwhile, the objectives of the European Union (EU) climate and energy policy assume, among others, a 40% reduction in GHG emissions by 2030 (compared to 1990) [13], and in the case of Polish energy policy (PEP), it is a 30% reduction by 2030 [14].According to research, the widespread replacement of conventional cars with EVs could lead to a 36% reduction in GHG by 2050, provided of course with a high share of renewable energy in total energy production [15].Therefore, the development of the EVs market is also able to achieve the indicated energy goals almost on its own.In the case of Poland, the problem is the methods of generating electricity, because over 80% of the currently produced energy comes from burning fossil fuels [16], including 75% from coal, and 7% from natural gas and crude oil [17].As a result, the very development of EVs, without changing energy sources, will only change the place of GHG emissions [16].However, Poland plans to increase the share of renewable energy (mainly from wind farms) in energy production by 65% by 2024, which should to a large extent solve the indicated problem [17].
According to the 'Sustainable Transport Development Strategy until 2030' in force in Poland, 600,000 BEVs [18] are to be used on Polish roads by 2030.This goal is more realistic than the previously planned 1 million EVs by 2025 [19], but still difficult to achieve.According to the latest research conducted in Poland, only 13% of respondents consider an EV as the first choice when buying a new car, including 2.7% of them claiming to buy a BEV [2].In order to encourage consumers to buy BEVs, owners have introduced privileges such as: exemption from fees in paid parking zones, free entry to clean transport zones (which currently do not exist in Poland) and the possibility of using bus lanes [18].However, these benefits are very small, considering that one of the main reasons for the low popularity of EVs in Poland is their very high price compared to conventionally powered vehicles [2,18].Therefore, several government subsidy programs for the purchase of BEVs have recently been introduced in Poland.In 2020, these were the programs 'Green car', 'Hummingbird' and 'e-Van'.In turn, in 2021, a wider program called 'My electrician' [20,21] was introduced.This program gives the opportunity to obtain government funding for the purchase of BEVs (including passenger cars and cargo cars up to 3.5 tons, mopeds, motorcycles, quads).In the case of passenger cars, a subsidy of PLN 18,750 is provided for individual users, and by declaring annual mileage over 15,000 km, a total subsidy of PLN 27,000 can be obtained.The limitation is the price of the vehicle not exceeding PLN 225,000.In addition, for large family card holders (families with at least 3 children), the subsidy is PLN 27,000 regardless of the declared annual mileage and there is no limitation related to the price of the vehicle.Such programs cause the dynamics of the development of the EVs market to increase to some extent.At the end of 2020, 18,875 EVs were on Polish roads, including 10,041 BEVs and 8834 PHEVs, while in August 2021 there were already 29,820 vehicles, including 14,256 BEVs and 15,564 PHEVs.Similarly, there are more and more charging stations, the number of which at the end of 2020 was 1.364, and in August 2021 there were already 1.631 [22].The market is also developing in terms of the range of available vehicles.In 2018, in the Polish Alternative Fuels Association catalogue presenting EVs available in Poland, there were 20 BEVs and 32 PHEVs [23], for the period 2019/2020 there were 42 BEVs and 63 PHEVs [24], and in the latest catalogue for the years 2020/2021 one can find 101 BEVs and 119 PHEVs [25].The current 'My electrician' subsidy scheme seems so attractive that it can increase the interest in BEVs, and with such a wide choice of BEVs as there is now, it is a difficult task to identify the best one.Even limited to BEVs belonging to the most popular A-C segments, there is a choice between a dozen different vehicles.Due to the fact that the purchase of an EV is several times more expensive investment than the Energies 2021, 14, 7786 3 of 25 purchase of a vehicle with an internal combustion engine [18], the decision regarding the selection of a specific BEV must be carefully considered.The choice is even more difficult as it required the analysis of many different, often imprecise and conflicting parameters of the vehicle, such as range, charging time, price, safety, etc.This is undoubtedly a multicriteria problem characterized by uncertainty.On the other hand, multi-criteria decision aid (MCDA) methods, often extended with a fuzzy set theory or stochastic analysis [26], cope with solving such problems.This is confirmed by numerous examples of the use of MCDA methods in decision-making problems related to electric vehicles, or more broadly, with sustainable transport [27].It should be noted that the solutions obtained with the use of MCDA methods should not be approached indiscriminately, because different MCDA methods may offer different solutions to the same problem [28].These differences result from: different use of criteria weights, differences in the algorithms of individual methods, the use of value scaling, the use of additional parameters influencing the obtained solution [29].Therefore, a good practice related to the use of MCDA methods is to compare the solutions obtained using different methods before issuing a recommendation.
The research presented in this article is motivated by the facts about BEVs presented above, so: All these elements make BEVs an attractive research topic of increasing practical importance and broad management and political implications.
In the context of the presented facts and new regulations on subsidies in the 'My electrician' program, practical and methodological research questions can be identified.As for the practical aspect, the article is a search for an answer to the question concerning which of the BEVs available on the Polish market is the optimal choice for sustainable transport, i.e., taking into account economic, social and environmental parameters.On the other hand, the question related to the methodology is whether different MCDA methods will give the same answer to the previous research question, and thus whether they will indicate the same BEV as optimal.Closely related to the indicated research questions is the aim of the research, which is to analyse selected BEVs available on the Polish market and recommend a vehicle that is the best from the perspective of sustainable transport.Here, the limitation was made to consumer vehicles and in particular, A-C segment vehicles are considered because they are more affordable than BEVs in the higher tier segments.The aim of the research was achieved with the use of three MCDA methods, which deal well with the imprecision of data and the uncertainty of decision parameters.The fuzzy technique for order of preference method by similarity to ideal solution (TOPSIS) [30], the fuzzy simple additive weighting (SAW) method [31] and the new easy approach to fuzzy preference ranking organization method for enrichment evaluation II (NEAT F-PROMETHEE II) [32] were used.In addition, a stochastic approach was also used to even better account for the uncertainty of preference and criteria weights.The application of the three methods indicated and the comparison of the results obtained with their help, as well as the extension of the approach to uncertainty through a stochastic approach to preferences, constitutes a scientific contribution to the article.
Section 2 provides an overview of the latest literature on the use of MCDA methods in sustainable transport problems, indicating the approaches to uncertainty used and publications where the results of different MCDA methods were compared.Section 3, broken down into subsections, provides technical details of the MCDA methods under consideration and the stochastic approach used.The results are presented in Section 4, and the article ends with the managerial and political implications set out in Section 5 and conclusions presented in Section 6.

Literature Review
The review of the use of MCDA methods in decision-making problems related to the broadly understood transport indicates that the most commonly used are deterministic methods, such as AHP, TOPSIS, PROMETHEE, etc. Fuzzy versions of individual methods are used less frequently, and methods based on the stochastic approach are almost never used [27].The situation is slightly different in the case of the latest publications strictly related to sustainable transport and EVs.In recent years, in publications on this subject, MCDA methods are used relatively often to capture uncertainty.For the most part, these approaches are based on the fuzzy set theory.Sałabun and Karczmarczyk [33] took up the problem of choosing BEVs for the needs of sustainable urban transport, using the COMET method based on the triangular fuzzy numbers (TrFNs).Ziemba [10], using the PROSA-C method, considered the selection of BEVs for local government and state administration units.In the quoted study, uncertainty was captured using stochastic analysis, namely Monte Carlo simulation.In turn, in the problem of choosing BEVs for private individuals, Ziemba [19] used the NEAT F-PROMETHEE method representing uncertain values as trapezoidal fuzzy numbers (TFNs).Biswas and Das [34] used the crisp MABAC method to build the BEVs ranking, and the criteria weights were defined by the fuzzy AHP method based on TrFNs.Babar et al. [35] used SWOT analysis and fuzzy linear programming with TrFNs to select the appropriate EV type for developing countries, in particular considering the case of Pakistan.Pamucar et al. [36] assessed alternative fuel vehicles from the perspective of sustainable transport.They used TrFNs and the fuzzy FUCOM method to determine the weights of the criteria, and the preferences were aggregated with the SVNF MARCOS method using neutrosophic fuzzy sets (NFS).Xu et al. [37] extended the ELECTRE method to include the interval type-2 fuzzy numbers (IT2FNs), and used this method to select the location for EVs charging stations.A similar decision problem related to locations for EVs charging stations was considered by Erbas et al. [38] and Ju et al. [39] Erbas et al. [38] used the fuzzy version of the AHP method to define uncertain weights of criteria in the form of TrFNs, while the preferences were aggregated using the crisp TOPSIS method, unable to capture the uncertainty.Additionally, Ju et al. [39] expressed the criteria weights in the form of TrFNs using the fuzzy AHP method, and captured the uncertainty of alternatives using picture fuzzy numbers (PFNs) in the grey relational projection.Liu and Wei [40] as well as Zhang et al. [41] took up the problem of risk for the development of EVs charging infrastructure in a public-private partnership.Liu and Wei [40] used the fuzzy TOPSIS method, and uncertain values were represented by TrFNs.In turn, Zhang et al. [41] captured uncertain values in the DEMATEL method using 2-tuple fuzzy numbers (2tFNs).Broniewicz and Ogrodnik [27] in one of their research approaches used TrFNs to represent uncertain weights in the fuzzy AHP method.The uncertainties were in no way captured in the remaining studies on: assessment of BEVs to support purchasing decisions [42], building a ranking of the best BEVs from the perspective of India [43], barriers to the use of EVs [44], fleet composition for small-scale car sharing [45] and urban public transport vehicles [46].
The few cited publications verified the results obtained using the basic MCDA method.Such verification consisted in solving the same decision problem using other MCDA methods.In particular, Ziemba verified the results of the PROSA-C method by solving the same decision problem using the PROMETHEE II method [10], and the results of the NEAT F-PROMETHEE method were verified using the Fuzzy TOPSIS [19].In turn, Ecer [42] compared the rankings obtained using methods (SECA, MARCOS, MAIRCA, COCOSO, ARAS and COPRAS), and then aggregated these rankings using another seven methods (EDAS, MABAC, WASPAS, CODAS, TOPSIS, Borda and Copeland) while comparing the aggregation results.Similarly, Broniewicz and Ogrodnik [27] solved the decision problem Energies 2021, 14, 7786 5 of 25 using various combinations of the REMBRANDT/AHP/Fuzzy AHP methods (criteria weighting) and VIKOR/TOPSIS/PROMETHEE methods (preference aggregation).
Table 1 shows all the latest (since 2018) applications of MCDA methods in problems related to sustainable transport.When summarizing and generalizing the conclusions from the analysis of these studies, the growing importance of nondeterministic methods should be noted.However, sometimes these approaches are used only partially, primarily to represent uncertain weights.On the other hand, rarely is a solution to a decision problem obtained by using one of the MCDA methods verified by using another method.In the context of the problem mentioned in the Introduction, consisting in the fact that different methods can give different recommendations, this is undoubtedly a significant imperfection of the cited research, and at the same time an important research gap that gives space for scientific discussion.TrFNs-triangular fuzzy numbers, S-stochastic uncertainty, TFNs-trapezoidal fuzzy numbers, NFS-neutrosophic fuzzy sets, IT2FNsinterval type-2 fuzzy numbers, PFNs-picture fuzzy numbers, 2tFNs-2-tuple fuzzy numbers, CW-criteria weighting, PA-preference aggregation, COMET-Characteristic Objects METhod, PROSA-C-PROMETHEE for sustainability assessment, PROMETHEE-preference ranking organization METHod for enrichment evaluation, NEAT F-PROMETHEE-new easy approach to fuzzy PROMETHEE, TOPSIStechnique for order of preference method by similarity to ideal solution, AHP-analytic hierarchy process, MABAC-multi-attributive border approximation area comparison, SECA-simultaneous evaluation of criteria and alternatives, MARCOS-measurement of alternatives and ranking according to compromise solution, MAIRCA-multi-attributive ideal-real comparative analysis, COCOSO-combined compromie solution, ARAS-additive ratio assessment, COPRAS-complex proportional assessment, EDAS-evaluation based on distance from average solution, WASPAS-weighted aggregated sum product assessment, CODAS-combinative distance-based assessment, FLPfuzzy linear programming, FUCOM-F-fuzzy full consistency method, SVNF MARCOS-single-valued neutrosophic fuzzy MARCOS, ELECTRE-elimination et choix traduisant la realité, PFWIG-picture fuzzy weighted interaction geometric operator, GRP-grey relational projection, DEMATEL-decision making trial and evaluation laboratory, ILP-integer linear programming, REMBRANDT-ratio estimation in magnitudes or decibells to rate alternatives which are non-dominated, VIKOR-vIsekrzterijumska optimizacija i kompromisno resenje.
Based on Table 1, it can be concluded that the TOPSIS and PROMETHEE methods are often used in the problems of sustainable transport.These methods are relatively uncomplicated in terms of computation, easy to implement and recognized in the scientific community dealing with MCDA methods.Another method of this type, even less computationally complicated, and at the same time widely known, is the SAW method.In practical decision problems and their solutions, it is important that stakeholders trust the methods used to solve the decision problems.Meanwhile, methods using a complicated calculation procedure may be treated by decision-makers as a 'black box' [47], which may result in the lack of trust of stakeholders in the recommendations obtained using such methods [48].It should be noted that the way the data are represented and the type of fuzzy set used have a large impact on the complexity of the fuzzy methods.Generally, it can be said that normal fuzzy sets (type-1) in the form of TrFNs or TFNs are much easier to use and interpret [49], and also much more explainable than other, more advanced, fuzzy set implementations [32,50].It is believed that the trapezoidal approximation is a reasonable compromise between the tendency to lose too much information and the tendency to introduce too complicated forms of approximation [51].Due to the need for trust in the obtained solutions, as well as in order to maintain the transparency of the methodology used and the explanation of the obtained results, the NEAT F-PROMETHEE, fuzzy TOPSIS and fuzzy SAW methods based on TFNs were used in this study.The main difference between the methods used is that the fuzzy SAW and fuzzy TOPSIS use the single synthesizing criterion.On the other hand, NEAT F-PROMETHEE uses an outranking relationship [52].In the fuzzy SAW and fuzzy TOPSIS methods, the only information about the preferences of the decision-maker is the weighting of the criteria.In turn, NEAT F-PROMETHEE additionally uses various functions and thresholds that provide additional information about the preferences of the decision-maker.Moreover, the fuzzy SAW and fuzzy TOPSIS methods use the same data normalization approach but differ in the further stages of the calculations.Fuzzy SAW uses the usual weighted average to aggregate the criteria, while fuzzy TOPSIS uses the positive-ideal and negative-ideal solution [53].On the other hand, NEAT F-PROMETHEE does not require data normalization, as the normalization process is built into the preference functions used.
Based on the analysis of publications on the selection and evaluation of BEVs presented in Table 1, the criteria used to evaluate such vehicles were identified.These criteria are presented in Table 2. Table 2 shows that for the BEVs' assessment, first of all criteria describing the technical parameters of the vehicle are used.In addition, there is an economic criterion describing the price of a vehicle, social criteria related to safety, or criteria more related to the environment, such as energy consumption.It should be noted that in this study the criteria were used for which at least two references were indicated in Table 2 as use cases.

Research Procedure
The study consisted in solving the decision problem related to the construction of the EV ranking.The A-C segment vehicles available on the Polish market were taken into account.For the most part, these were vehicles meeting the price criterion required to obtain funding under the 'My electrician' program.For each of the vehicles, information about its parameters was obtained, some of the parameters were crisp data, and parameters with uncertain values were presented in the form of TFNs.Individual vehicle data were obtained from the Electric Vehicle Database [54] and Euro NCAP [55].Thus, a performance model F = C(A) was defined which included a set of alternatives A = a, b, . . ., m (which were considered EVs) and a set of criteria C = {c 1 , c 2 , . . . ,c n } (which were played by vehicle parameters).In addition, preference directions, weights, scales, preference functions and thresholds were established for each of the criteria, thus defining the preference model P(C).The alternatives performance model and the preference model provided input to the three fuzzy MCDA methods included in the reference methods collection.These methods were: fuzzy SAW [31], fuzzy TOPSIS [30] and NEAT F-PROMETHEE II [56].The decision Energies 2021, 14, 7786 8 of 25 problem was solved using each of the reference methods, resulting in three rankings of alternatives.Moreover, for each of the methods, a robustness analysis of the solution was performed depending on the value of the preference model.The last stage of the research was to compare the results obtained with the use of individual reference methods.The course of the research procedure is presented in Figure 1.
were played by vehicle parameters).In addition, preference directions, weights, scales, preference functions and thresholds were established for each of the criteria, thus defining the preference model () .The alternatives performance model and the preference model provided input to the three fuzzy MCDA methods included in the reference methods collection.These methods were: fuzzy SAW [31], fuzzy TOPSIS [30] and NEAT F-PROMETHEE II [56].The decision problem was solved using each of the reference methods, resulting in three rankings of alternatives.Moreover, for each of the methods, a robustness analysis of the solution was performed depending on the value of the preference model.The last stage of the research was to compare the results obtained with the use of individual reference methods.The course of the research procedure is presented in Figure 1.

Basic Assumptions
All reference methods used were based on fuzzy sets and allowed to represent uncertainty using TFNs.TFN a = (a 1 , a 2 , a 3 , a 4 ) is described by the membership function µ a (x) ∈ [0, 1], according to the Formula (1) [30]: On two TFNs a = (a 1 , a 2 , a 3 , a 4 ), b = (b 1 , b 2 , b 3 , b 4 ) one can perform mathematical operations described by Formulas (2)-( 8) [31]: a r = (a 1 , a 2 , a 3 , a 4 ) r = (a 1 /r, a 2 /r, a 3 /r, a 4 /r) (7) r a = r (a 1 , a 2 , a 3 , a 4 ) ∼ = (r/a 4 , r/a 3 , r/a 2 , r/a 1 ) In order to maintain the consistency of the weights used in the considered MCDA methods, the same linguistic scale was used for each method, taken directly from the fuzzy TOPSIS and NEAT F-PROMETHEE methods.The linguistic values used and the corresponding TFNs are presented in Table 3 [30,32].Robustness analysis performed for each reference method was based on stochastic simulations [57].For each of the fuzzy MCDA methods applied, L = 10,000 Monte Carlo trials were carried out, thanks to which the obtained results are characterized by a precision level of 1% while maintaining a confidence level of 95% [19].In each l-th trial, for each MCDA method, random values of the criteria weights were generated in accordance with the Formula (9): where w j l denotes the weight of the j-th criterion in the l-th trial, defined as TFN, to which corresponds a specific linguistic value LV x ; x l j is the j-th independent random variable (j = 1, 2, . . ., n) drawn in the l-th trial (l = 1, 2, . . ., L), and in practice x l j describes the index of the weight used for the j-th criterion in the l-th trial; i.i.d.means independent and identically distributed; U{1, 7} denotes a discrete uniform distribution when randomizing a number from 1 to 7, and the drawn number is the index of the linguistic value LV x from the sequence of these values.
For the NEAT F-PROMETHEE II method, apart from the criteria weights, other elements of the preference model, i.e., preference functions and thresholds, had to be generated.Preference functions were generated according to the Formula (10): where f k l j denotes the preference function for the j-th criterion in the l-th trial; k l j is the j-th independent random variable (j = 1, 2, . . ., n) drawn in the l-th trial (l = 1, 2, . . ., L), and in practice k l j describes the index of preference function used for the j-th criterion in the l-th trial; U{1, 6} denotes discrete uniform distribution when randomizing a number from 1 to 6, and the drawn number is the index of the preference function f k from the sequence of these functions.
To generate thresholds, the sample standard deviation was computed for all criteria treating each TFN as four distinct values, according to the Formula (11): where m is the number of alternatives; y ijt is the t-th TFN element describing the j-th criterion of the i-th alternative; y j is the mean of all y ijt values for the j-th criterion.Standard deviation was the basis for determining the thresholds, based on Formulas ( 12)-( 14): p l j i.i.d.∼ U 0.75σ j , 2.5σ j (13) s l j i.i.d.∼ U 0.2σ j , 0.6σ j (14) where q, p, and s are successively the indifference, preference and Gaussian thresholds; U(x, y) stands for continuous uniform distribution in the given range.After L trials, the rank acceptability indices are estimated according to the Formula (15) [58]: where B ir is the number of trials, in which the i-th alternative achieved the r-th position in the ranking.Rank acceptability indices indicate the estimated probability of achieving a specific position in the ranking of alternatives, provided that the preference model is defined in accordance with the assumptions made.The high b r i alternatives for the best ranks are the most valuable, and the least interesting are those with high acceptability for the worst ranks.

NEAT F-PROMETHEE II
In the first step of the NEAT F-PROMETHEE II method [32], the fuzzy deviation d is determined for a pair of alternatives according to the Formula ( 16): where c j ( a) denotes the fuzzy value of the alternative a on the j-th criterion.The second step consists in determining the degrees of preference using the selected preference function f k belonging to the sequence F = { f 1 , . . . ,f 6 }, according to the Formula (17): Depending on the selected preference function, the following thresholds can be used: indifference (q j ), preference (p j ) or Gaussian (s j ).The preference functions are described by the Formulas ( 18)-( 23):

•
The level criterion (f 4 ): • The V-shaped criterion with an area of indifferenc (f 5 ): • The Gaussian criterion (f 6 ): The NEAT F-PROMETHEE II method performs approximation error correction during mapping.The correction is described by the Formula (24): It should be noted that the u, v coefficients depend on the applied preference function: The next step is to determine the aggregate preference indices according to the Formula (25): where w j is defuzzified and normalized (∑ n j=1 w j = 1) weight of the j-th criterion; n is the number of criteria.
Then, the positive and negative outranking flows should be calculated, and on their basis net outranking flows are calculated, according to the Formulas ( 26) and ( 27): Both the criteria weights and the values φ net ( a) during the calculation procedure are defuzzified using the centroid method, according to the Formula (28) [59]:

Fuzzy TOPSIS
In the fuzzy TOPSIS [30] method, a fuzzy decision matrix D with dimensions m × n is initially constructed.The elements of this matrix are TFNs x ij = a ij , b ij , c ij , d ij , which are normalized according to the Formulas ( 29) and (30) for the benefit and cost criteria, respectively: The values p ij obtained in this way are elements of the new normalized fuzzy decision matrix P [60].
In the next step, the weighted normalized fuzzy decision matrix V elements are calculated according to the Formula (31): Then, the fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) are calculated according to the Formulas ( 32) and (33), and the distances of alternatives from FPIS and FNIS using Formulas (34) and (35): where d v ( x, y) is the distance measure calculated according to the vertex method (36): The final value of the i-th alternative is calculated as the closeness coefficient, according to the Formula (37) [61]:

Fuzzy SAW
The fuzzy SAW method [31] is somewhat similar to fuzzy TOPSIS, because also in fuzzy SAW a fuzzy decision matrix D with dimensions m × n is initially constructed.As in fuzzy TOPSIS, the elements of the matrix D are TFNs x ij = a ij , b ij , c ij , d ij , which are normalized according to Formulas ( 29) and ( 30) for benefit and cost criteria, respectively, creating a new normalized fuzzy decision matrix P = p ij .
In the next step, the criteria weights w j = w j1 , w j2 , w j3 , w j4 should be defuzzified using the bisector method, according to the Formula (38): Finally, we have to calculate the total fuzzy score based on the normalized values of p ij and defuzzified weights w j , according to the Formula (39): The result obtained in this way must finally be defuzzified using the bisector method presented in the Formula (38).

Results
In accordance with the presented research procedure, a set of alternatives and a set of criteria were first defined, and then a preference model and an alternative performance model were constructed.Table 4 presents the preference model, including the directions of preferences, weights of criteria, and for the NEAT F-PROMETHEE method, this model additionally takes into account the preference functions and thresholds.Table 5 shows the performance model developed on the basis of individual vehicle parameters.These parameters are detailed in Appendix A (Table A1).It should be noted that in the case of vehicles with a minimum price lower than PLN 225,000, the C9-Price criterion takes into account the possibility of obtaining the maximum surcharge in the 'My electrician' program.The surcharge is PLN 27,000 and the minimum vehicle price included in Table 5 and Appendix A is reduced accordingly.
In the next step, the decision problem defined by the preference model and the performance model was solved.As a result of using each of the three fuzzy MCDA methods, three solutions were obtained in the form of rankings presented in Table 6.
The analysis of the rankings obtained shows that regardless of the MCDA method used, the best vehicle was awarded to A11-Volkswagen ID.3 Pro S, the second was A14-Nissan LEAF e+, the third was A10-Volkswagen ID.3 Pro, and the last was A3-Smart EQ forfour.Therefore, for the adopted weights of criteria, it is a relatively stable sequence, and it is not affected even by additional parameters included in the preference model of the NEAT F-PROMETHEE method.As for the similarity between the individual rankings, it was tested based on the correlation analysis.The Kendall's tau coefficient, recommended in the case of similarity studies [62], was used here.The correlation values between the rankings are presented in Table 7.The values of the Kendall's tau coefficient indicate that the results obtained with the use of individual rankings are very similar.The greatest similarity exists between the fuzzy TOPSIS and fuzzy SAW rankings, which results directly from the fact that both of these methods belong to the group of methods based on utility theory and have many common elements, e.g., the normalization procedure.On the other hand, NEAT F-PROMETHEE belongs to the group of outranking based methods, which means that the ranking generated by it differs slightly more.Interestingly, despite some differences in the rankings of the fuzzy TOPSIS and fuzzy SAW methods, these rankings are equally different from the NEAT F-PROMETHEE II ranking.Scatterplots are included in Figure 2 to better illustrate the differences between the individual rankings.The analysis of Figure 2 shows that in the case of the fuzzy TOPSIS and fuzzy SAW rankings, the differences are only between the ranks of the alternatives A7-A9 and A4-A6.The comparison of the fuzzy TOPSIS and NEAT F-PROMETHEE rankings shows differences in positions 4 to 11.On the other hand, the comparison of the fuzzy SAW and NEAT F-PROMETHEE rankings shows differences in positions 5 to 13.
Another study, which was robustness analysis, concerned a situation where the preference model to be used by a decision-maker is unknown.In this case, the stochastic simulations were aimed at checking the rankings obtained for individual methods in the case of pseudo-random values of the preference model.show the rank acceptability indices for the fuzzy TOPSIS, fuzzy SAW and NEAT F-PROMETHEE methods, respectively.In particular, Table 10 contains the rank acceptability indices obtained for NEAT F-PROMETHEE when only the criteria weights were random, and in the case of Table 11, the weights, preference functions and thresholds were random (see Formulas (9)-( 15)).
better illustrate the differences between the individual rankings.The analysis of Figure 2 shows that in the case of the fuzzy TOPSIS and fuzzy SAW rankings, the differences are only between the ranks of the alternatives A7-A9 and A4-A6.The comparison of the fuzzy TOPSIS and NEAT F-PROMETHEE rankings shows differences in positions 4 to 11.On the other hand, the comparison of the fuzzy SAW and NEAT F-PROMETHEE rankings shows differences in positions 5 to 13.Another study, which was robustness analysis, concerned a situation where the preference model to be used by a decision-maker is unknown.In this case, the stochastic simulations were aimed at checking the rankings obtained for individual methods in the case of pseudo-random values of the preference model.Tables 8-11 show the rank acceptability indices for the fuzzy TOPSIS, fuzzy SAW and NEAT F-PROMETHEE methods, respectively.In particular, Table 10 contains the rank acceptability indices obtained for NEAT F-PROMETHEE when only the criteria weights were random, and in the case of Table 11, the weights, preference functions and thresholds were random (see Formulas (9)-( 15)).Comparing the collective results of stochastic simulations to the rankings presented in Table 6, it should be stated that generally speaking, rank acceptability indices confirm the order of alternatives in the rankings.Both in the simulation results and in the rankings, the leading positions are taken by the following alternatives: A11, A14, A10, and A9.On the other hand, the last positions are usually taken by the A3 and A6 alternatives.Some differences between the rankings and the rank acceptability indices can be seen in the case of, for example, A1 and A2 alternatives, which ranked relatively high in the rankings, but the results of the stochastic simulation indicate that these alternatives are not so good.
The analysis of Tables 8 and 9 shows a high similarity of the simulation results carried out with the use of the fuzzy TOPSIS and fuzzy SAW methods.Taking into account that the assumed simulation error may be 1%, it can be seen that some results are very similar.In particular, it can be seen in the example of alternatives with the highest acceptability values for the highest (A11, A14, A10, A9, and A13) and lowest (A3, A6, A1, and A4) ranks.The similarities are also visible when comparing Tables 10 and 11, presenting the results of simulations carried out with the use of the NEAT F-PROMETHEE method.In this case, you can see that the highest ranks are the most acceptable for alternatives A11, A14, A9, and A10.In contrast, the worst ranks are the most acceptable for the alternatives A3, A1, A6 and A2.Although they are similar groups of alternatives as in the case of the fuzzy TOPSIS and fuzzy SAW methods, the differences for A9, A10, A1 and A6 are significant.These observations are confirmed by the graphical analysis of the simulation results, presented in Figure 3 (for the fuzzy TOPSIS and fuzzy SAW methods) and Figure 4 (for the NEAT F-PROMETHEE method).

Managerial and Political Implications
As mentioned in the Introduction, the basic problem with BEVs in Poland is the Polish energy mix, which is mostly based on coal.As a result, the basic advantages of BEVs, related to the reduction of GHG, lose their importance [63].However, the situation should improve significantly soon, as the Polish energy policy assumes a significant in-

Managerial and Political Implications
As mentioned in the Introduction, the basic problem with BEVs in Poland is the Polish energy mix, which is mostly based on coal.As a result, the basic advantages of BEVs, related to the reduction of GHG, lose their importance [63].However, the situation should improve significantly soon, as the Polish energy policy assumes a significant in-

Managerial and Political Implications
As mentioned in the Introduction, the basic problem with BEVs in Poland is the Polish energy mix, which is mostly based on coal.As a result, the basic advantages of BEVs, related to the reduction of GHG, lose their importance [63].However, the situation should improve significantly soon, as the Polish energy policy assumes a significant increase in the share of 'green' energy in the energy mix in the coming years [64].Therefore, the dynamic increase in the share of electric vehicles in the domestic vehicle fleet, assumed by the Polish government, may have positive effects on the emission policy.The subsidy programs aimed at encouraging individual and institutional users to purchase electric vehicles will be of great importance for the implementation of the goals in the field of electric vehicle market development in Poland.The 2020 programs ('Green car', 'Hummingbird' and 'e-Van') were very unsuccessful as only 344 applications were submitted in total for the three programs [65].Meanwhile, during the first 4 months of the 'My electrician' program launched in 2021, over 1000 applications for co-financing for purchases by individual users have already been submitted, and the call for applications for subsidies for enterprises has not yet started [66].The 'Green car' and 'My electrician' programs are similar in terms of the number of subsidies, but the main difference between them is the maximum vehicle price limit.This limit was increased almost twice, from PLN 125,000 to PLN 225,000.As a result, in the new 'My electrician' program, it is possible to co-finance the purchase of over 40 different BEVs models, while under the previous 'Green car' program, funding was available only for 8 BEVs models [67].So, it should be noted that attractive BEV incentive programs can be effective, but a lot depends on the design of these programs.It is worth adding that the system of support for the electric vehicle market proposed by the government should cover the entire area of electromobility and should also provide subsidies for the charging infrastructure.This infrastructure is a key factor contributing to accelerating the decarbonization of the transport sector in Poland.Therefore, it is planned to launch a support program for the construction of charging points in the near future.Under this program, it is planned to co-finance the construction of about 15,000 charging points [68].Considering that, in August 2021, there were 3178 charging points (1631 charging stations) in Poland [22], this program may ensure a significant development of infrastructure for EVs.In addition, as part of the 'My electricity' program in 2022, it will be possible to obtain a subsidy for private EVs charging points.Combined with the recently introduced legal changes facilitating the installation of private chargers in multi-family buildings, this is another step towards the popularization of EVs in Poland.Another important element in the development of electromobility is the 'Green public transport' program, which allows for co-financing of 80% of the purchase costs of electric buses and trolleybuses, as well as 90% of the purchase costs of hydrogen-powered buses [69].Moreover, the Act on Electromobility [70] adopted the requirements for the modernization of the vehicle fleet in state administration and local government units.In particular, the act obliges state administration bodies to gradually develop the BEVs fleet so that in 2025 they constitute at least 50% of the fleet used.Similarly, local government units were obliged to have a vehicle fleet, which in 2025 will consist of BEVs in at least 30%.These and other programs related to Poland's energy and emission policy [71] should contribute to the achievement of the assumed GHG emission reduction targets and the development of sustainable transport.
The policy implications cited above provide some managerial insights.Firstly, both the Polish market of EVs and charging stations, will develop dynamically in the coming years, which indicates the legitimacy of investments in related businesses, such as EV sharing and charging stations.Secondly, subsidy programs can be used and are used in the marketing efforts of vehicle manufacturers and dealers by showing the price minus the potential surcharge.Thirdly, manufacturers and retailers of home charging stations can operate in a similar way.Moreover, these two elements can be combined by offering consumers a more comprehensive offer in the form of vehicles with home charging stations and a promise of help in obtaining financing from both programs.Lastly, vehicle manufacturers can and should adapt their market offer to the co-financing programs available in Poland, proposing vehicles with technical and price parameters that guarantee that the investment will be covered by government subsidies.

Conclusions
The obtained results made it possible to convincingly answer the research questions posed in the Introduction.As for the question related to the indication of the optimal BEV, the Volkswagen ID.3 Pro S, which has become a new leader in the A-C segments, is currently perhaps the best choice when buying a BEV on the Polish market.In earlier studies, which used other methods and other decision models [10,19], Nissan LEAF e+ dominated, followed by the Peugeot e-208 and Hyundai IONIQ Electric vehicles (depending on the method and decision model).As for the vehicles produced by Volkswagen, in the A-C segments they were electric versions of cars with combustion engine, such as e-Golf, achieving average results compared to other electric vehicles in their segment.Meanwhile, Volkswagen ID.3 Pro S has successfully replaced its predecessors.It should be noted, however, that Nissan LEAF e+ is also a very good vehicle, and its price is much more attractive, which may be of major importance on the Polish market.
As for the second research question, regarding the differences in the results obtained with the use of various fuzzy MCDA methods, it should be stated that the differences are not large.Obviously, the more different the algorithms of individual methods are, the more visible the differences in the obtained results will be.Nevertheless, the extensive analysis of the results obtained with the fuzzy TOPSIS, fuzzy SAW and NEAT F-PROMETHEE methods indicate that the correct construction of the decision model allows us to obtain similar results for various MCDA methods, even in the case of uncertain and imprecise data and partially undefined preference model.
One research limitation is the fact that only BEVs from the A-C segments were included in the study, excluding cars belonging to higher segments.Among others, Tesla Model 3 belonging to the D segment, as well as Tesla Model S (segment F) and Hyundai KONA Electric (segment JB) were omitted, which took leading positions in the research on markets other than Polish [42,43].However, the inclusion of the indicated vehicles would also require the inclusion of many other cars currently available on the Polish market.Another limitation is related to the dynamic changes on the EVs market, mainly in terms of price changes, as well as the introduction of new vehicles to the market.As a result, comparative studies become outdated to some extent each year.
In connection with the presented conclusions, an interesting direction for further research seems to be the development and broadening of the approaches to uncertainty used in the MCDA methods under study.The combination of the fuzzy and stochastic approaches may in the long run lead to the development of new decision-making methods similar to the stochastic multicriteria acceptability analysis (SMAA) method [72] or other SMAA-based methods [73,74].These methods can deal with various types of uncertainty and provide valuable recommendations despite the lack of data.

Figure 1 .
Figure 1.The applied research procedure.

Figure 1 .
Figure 1.The applied research procedure.

Figure 2 .
Figure 2. Scatterplots between: (a) the fuzzy TOPSIS and fuzzy SAW rankings; (b) the fuzzy TOPSIS and NEAT F-PRO-METHEE II rankings; (c) the fuzzy SAW and NEAT F-PROMETHEE II rankings.

Figure 2 .
Figure 2. Scatterplots between: (a) the fuzzy TOPSIS and fuzzy SAW rankings; (b) the fuzzy TOPSIS and NEAT F-PROMETHEE II rankings; (c) the fuzzy SAW and NEAT F-PROMETHEE II rankings.

Figure 3 .
Figure 3. Graphs of rank acceptability indices obtained using: (a) the fuzzy TOPSIS and (b) fuzzy SAW methods.

Figure 4 .
Figure 4. Graphs of rank acceptability indices obtained using the NEAT F-PROMETHEE method for: (a) random weights and (b) random weights, function preferences and thresholds.

Figure 3 .Figure 3 .
Figure 3. Graphs of rank acceptability indices obtained using: (a) the fuzzy TOPSIS and (b) fuzzy SAW methods.

Figure 4 .
Figure 4. Graphs of rank acceptability indices obtained using the NEAT F-PROMETHEE method for: (a) random weights and (b) random weights, function preferences and thresholds.

Figure 4 .
Figure 4. Graphs of rank acceptability indices obtained using the NEAT F-PROMETHEE method for: (a) random weights and (b) random weights, function preferences and thresholds.

Table 1 .
The latest examples of MCDA methods applications in sustainable transport decision-making problems.

Table 2 .
Criteria used in the assessment of BEVs.

Table 3 .
Linguistic scale used for the criteria weights.

Table 4 .
Preference model for the considered problem of EVs assessment.

Table 5 .
Performance model of the considered EVs.

Table 6 .
Rankings of alternatives obtained by individual MCDA methods.

Table 7 .
Correlations between rankings of individual MCDA methods.

Table 9 .
Rank acceptability indices (%) obtained using the Fuzzy SAW method.

Table 10 .
Rank acceptability indices (%) obtained using the NEAT F-PROMETHEE II method for random values of criteria weights.

Table 11 .
Rank acceptability indices (%) obtained using the NEAT F-PROMETHEE II method for random weights, preference functions and thresholds.