The Evaluation based on Distance from Average Solution (EDAS) method, as a compensatory approach, was introduced in 2015 by Keshavarz Ghorabaee et al. [3]. This method is particularly applicable when multiple criteria exist, especially in the presence of conflicting criteria. Based on the distance of each alternative from the average solution, the best alternative is selected. Moreover, EDAS demonstrates high compatibility with the complexities of decision-making processes. For this reason, in 2023, a modified EDAS method was adapted for MCDM in the field of robotic agriculture. By managing the unique challenges of robotic agriculture, such as dynamic environmental conditions and diverse decision criteria, the modified EDAS method provides practical solutions for improving operational efficiency and productivity [4].

According to the EDAS literature, in 2021, the EDAS method was used to evaluate the admission of COVID-19 patients to intensive care units. This study facilitated rational decision-making in the selective admission of COVID-19 patients during ICU bed shortages [5]. In another study, a conventional fuzzy EDAS approach was employed to evaluate energy alternatives in Turkey by considering MCDM aspects. The objective was to provide insights into the most suitable renewable energy options for Turkey, taking into account factors such as environmental impacts, economic feasibility, and technological readiness [6].

The VIKOR method was developed to solve discrete decision-making problems involving conflicting and incommensurable criteria. This method emphasizes selecting from a set of alternatives and achieving a compromise solution for problems with conflicting criteria. In a study conducted in 2024, the authors applied the VIKOR approach to evaluate and select the most appropriate smart vehicle transportation system by considering multiple criteria in decision-making processes. The study highlighted the importance of multiple criteria in decision-making, particularly in complex systems such as intelligent transportation systems [7]. Based on existing literature, another study carefully compared the VIKOR and TOPSIS methods under different conditions by examining their characteristics, advantages, and disadvantages. The results indicated that the VIKOR method performed significantly better than the TOPSIS method [8].

In another article, appropriate dispute resolution methods for airport projects were investigated by considering multiple criteria, with an emphasis on the fuzzy VIKOR method. The findings demonstrated that the fuzzy VIKOR approach can be effectively used to prioritize dispute resolution methods for airport projects [9].

Taxonomy analysis is widely used in various classification contexts. A specific type, numerical taxonomy, focuses on the quantitative evaluation of similarities and proximities among the studied units and classifies elements into taxonomic groups. In a study conducted in 2022, a new decision support system based on the taxonomy method was proposed to assist in recommending and selecting MCDM methods. The taxonomy introduced in this study was presented as an effective tool for categorizing existing concepts and methods under different conditions in multi-criteria decision analysis [10].

In another study, an improved numerical taxonomy method was combined with the Analytic Network Process (ANP), a hybrid model, and a mathematical dispersion model to select suitable locations based on passive defense considerations. As a result, sensitive centers were classified into three categories: public facilities, undesirable facilities, and critical facilities [11]. Due to certain shortcomings associated with the taxonomy method, Faraji and his colleagues proposed a modified taxonomy model in which the criteria were no longer considered equal, significantly improving the method's accuracy. In addition, the positive and negative nature of the criteria was taken into account in this new approach, leading to more reliable results [12].

One of the critical stages in the MCDM process is identifying appropriate criteria for comparing different alternatives. To select suitable criteria, previous research articles published in this field were utilized. This section reviews the literature of several studies conducted in the area of MCDM and other decision analysis methods related to green vehicles.

The first study analyzed different types of sustainable vehicles within a sustainable road transportation system. In this research, the economic, environmental, and technical impacts of each vehicle type were evaluated and compared [13]. In this context, another study aimed to identify barriers to the widespread adoption of electric vehicles. The results indicated that consumer perceptions play a significant role in the adoption of electric vehicles, and several barriers exist, including trust in technology, access to charging infrastructure, high initial costs, and concerns related to vehicle performance and economics [14].

Another study examined the economic and environmental impacts associated with conventional, hybrid, and electric vehicles, employing various analytical methods to assess the advantages and limitations of each vehicle type [15]. A further study analyzed consumer attitudes toward purchasing electric vehicles, focusing on technological threats and trust in vehicles. The criteria used in this research included initial purchase cost, charging infrastructure, environmental aspects, and technical performance characteristics [16].

In another article, the energy, environmental, and economic performance of electric vehicles was evaluated through empirical assessment. Various criteria were used to measure energy performance, including energy consumption, greenhouse gas emissions, and financial costs associated with electric vehicles [17]. In a case study, pollutant emissions and energy requirements related to electric vehicles were assessed, considering criteria such as energy consumption, charging infrastructure, and vehicle performance [18].

Another study aimed to examine the adoption of electric vehicles and the impact of local policy instruments. The findings showed that local policy tools can significantly influence the increased adoption of electric vehicles by society by providing facilitators that support consumer decision-making [19].

In another study, the energy consumption and greenhouse gas emissions of a hydrogen fuel cell electric vehicle were compared with those of a conventional gasoline-powered vehicle. Criteria such as purchase cost, fuel efficiency, and fuel availability were used to assess energy consumption and emissions across both energy production and vehicle usage phases [20]. Another article applied both the Analytic Hierarchy Process (AHP) and a matrix-based MCDM approach. This integrated framework enabled the evaluation and selection of electric vehicles based on various criteria, including performance, cost, energy consumption, and environmental impact [21].

Another study examined the market acceptability of electric vehicles by simultaneously considering economic, technical, environmental, and social factors to facilitate effective decision-making regarding the development of this technology [14]. In [22], a study employing a multi-criteria approach simultaneously considered stochastic and fuzzy uncertainties in selecting electric vehicles with high social acceptance, using criteria such as price, fuel efficiency, and environmental impacts.

The results obtained from these studies and the selected articles are summarized in Table 1. It should be noted that, for the purpose of advancing the present research, all criteria are considered independent of one another, such that no overlap exists among them Numerous studies to date have addressed issues related to green vehicles and MCDM methods separately, considering various criteria. By reviewing the existing literature summarized in Table 1, the most effective and frequently cited criteria were selected based on expert opinions. These criteria include vehicle reliability, public acceptance and societal attitudes toward the vehicle, accessibility to charging networks and fuel supply stations, safety, technical and performance limitations of the vehicle, environmental sustainability, fuel efficiency, the time required for charging or refueling, maintenance and repair costs, and the vehicle purchase price. These criteria have been employed for the evaluation and decision-making process concerning green vehicles. Based on the steps conducted in the present study, the operational framework illustrated in Fig 1. has been developed for decision-making on green vehicles using the IDA–VIKOR–Taxonomy (IDAVIKORONOMY) method. This framework can serve as a comprehensive guideline for implementing and conducting similar research in other locations or at different points in time.

•Part One •A complete study and review of the types of green vehicles •Selection and finalization of criteria

•Collection of vehicle data and formation of decision matrix Studying •and Partcriteria Two weight vector phase

•Study of types of multi-criteria decision-making methods •Design of the Idavicornomic decision-making method

• Applying the Idavicornomics technique and calculating the

In this section, the steps of the Taxonomy algorithm are examined.

First, the alternatives and the different criteria involved in the decision-making problem must be clearly defined. For this purpose, it is assumed that the decision-making problem consists of m alternatives (A₁ to Am), which are evaluated by decision-makers based on n criteria (C₁ to Cn).

After forming the decision matrix, the mean and standard deviation of the data related to each criterion in the decision matrix are calculated using Eqs. (1) and (2):

r̅ = ∑ rij , j = 1, . . . , n, (1)

Sj = ∑(rij − r ̅j) , j = 1, … , n, (2)

In the third step, it is necessary to form a standard matrix using Eq. (3).

rij − r ̅j

zij = . (4)

sj In the fourth step, the composite distance between the options must be determined. For this purpose, using the standard matrix, the distance of each option to the other options is calculated through the Euclidean equation, which is obtained through Eq. (4).

In the fifth step, it is necessary to determine the minimum distance of each row of the matrix and then obtain the average distance of the options and their standard deviation. For this purpose, Eqs. (5)-(7) are used. o ̅ = ∑ Oi , (5)

SO = ∑(Oi − O ̅) , (6)

O = o ̅ ± 2SO. (7)

This operation is performed to homogenize the options. As a result, if an option does not fall within a certain distance, it is heterogeneous, and this step must be repeated after its removal.

In this step, it is necessary to calculate the distance of each option from the ideal option. For this, Eq. (8) can be used.

Cio = ∑(zij − zoj)2 , i = 1, . . . , m, (8)

√j=1

Zoj represents the best option under the j-th criterion in the standard matrix, depending on whether the criterion is positive or negative. In addition, it is necessary to obtain the mean and standard deviation of the obtained Cio. 7. In the last step, it is necessary to first obtain the maximum possible distance through Eq. (9), and finally, to obtain the taxonomic rank, Eq. (10) can be used [24].

CO = C ̅̅io ̅̅ + 2SCio , i = 1, . . . , m, (9)

Cio

Fi = , (10)

CO

(∑ wj = 1). (11)

The steps of the VIKOR algorithm are discussed below.

I. As in the first step of the taxonomy method, it is necessary to form a decision matrix.

II. In addition to the decision matrix, it is also necessary to form a weight vector matrix. According to Eq.

(11), wj represents the weight of the jth criterion. It should also be noted that the sum of all weights must be equal to 1.

III. In this step, it is necessary to determine the best and worst options for each criterion according to the decision matrix. As a result, for each positive criterion, we will have:

fj∗ = maxfij

{ − i , i = 1, . . . , m , j = 1, . . . , n, (12)

fj = minfij

and for each negative criterion, we will have:

fj∗ = minfij

{ − i , i = 1, . . . , m , j = 1, . . . , n, (13)

fj = maxfij

IV. In this step, the utility value (Si) and the regret value (Ri) will be determined according to Eqs. (14) and (15). (fj − fij)

Si = ∑ wj ∗ − , i = 1, … , m, (14)

(fj − fj )

(fj∗ − fij)

Ri = max [wj ∗ − ] , i = 1, . . . , m , j = 1, . . . , n, (15)

j (fj − fj )

V. In the fifth step, it is necessary to calculate the VIKOR index using Eq. (16).

(Si − S∗) (Ri − R∗)

Qi = v[ − ∗ ] + (1 − v)[ − ∗ ], (16)

(S − S ) (R − R ) Subject to

S∗ = minSi , S− = maxSi , R∗ = minRi , R− = maxRi,

i i i i

VI. During this step, the results obtained from S, R, and Q are sorted in ascending order. Option a1, which has the lowest value in the list Q, is selected, and option a2 is considered as the second-best option after a1 in the list Q. Option a will be selected as the best option if it satisfies the following two conditions:

I. Q(a2) – Q(a1)≥DQ.

II. Option a1 is the best option in both S and R lists.

In the first condition, m is the number of options, and we will have:

DQ = . (17)

m − 1 If one of the two aforementioned conditions is not satisfied, the procedure will be carried out as follows:

I. If only the second condition is not satisfied, a1 and a2 will be selected as the best alternatives.

II. If the first condition is not satisfied, a set of alternatives corresponding to the maximum value will be selected as the most preferable alternatives, such that they satisfy the following equation [24].

Q(az) − Q(a1) < DQ. (18)

The EDAS algorithm is as follows.

I. As in the taxonomy and VIKOR methods, it is necessary to create a decision matrix. In addition to the decision matrix, it is necessary to form a weight vector matrix such that wj represents the weight of the j-th criterion.

II. To obtain the average solution, we act according to Eq. (19).

∑m i=1 rij

AVj = , j = 1, . . . , n. (19)

III. After calculating the mean solution, it is necessary to calculate the values of the positive distance from the mean and the negative distance from the mean. For this purpose, if the criterion is of the positive type, Eqs. (20) and (21) can be used.

max (0, (rij − AVj))

PDAij = , i = 1, … , m , j = 1, … , n, (20)

AVj max(0, (AVj − rij))

NDAij = , i = 1, . . . , m , j = 1, . . . , n, (21)

AVj If the criterion is negative, Eqs. (22) and (23) can be used.

max (0, (AVj − rij))

PDAij = , i = 1, … , m , j = 1, … , n, (22)

AVj max(0, (rij − AVj))

NDAij = , i = 1, . . . , m , j = 1, . . . , n, (23)

AVj 4. As mentioned in the first step, in the EDAS method, the weights of different criteria are not the same; therefore, in this step, it is necessary to consider the weight of each criterion. For this purpose, Eqs. (24). and (25) are used.

SPi = ∑ PDAij. wj, i = 1, . . . , m, (24)

SNi = ∑ NDAi. wj, i = 1, . . . , m, (25)

IV. In the fifth step, it is necessary to standardize and normalize the values obtained in the fourth step, which is done through Eqs. (26). and (27).

SPi

NSPi = max(SP) , i = 1, … , m, (26)

SNi

NSNi = max(SN ) , i = 1, … , m, (27)

V. In the final step, the final score of the options can be calculated and ranked using the following equation.

The final option is obtained through Eq. (28).

ASi = (NSPi + NSNi), i = 1, … , m, (28)

The option with the highest ASi is the one with the highest utility [24].

First, as in the first step of the methods mentioned, it is necessary to clearly identify the various options and criteria in decision-making. Each of these criteria can be positive or negative, which needs to be identified at this stage.

According to Table 2, the decision matrix consists of six alternatives and ten criteria. The first criterion is vehicle reliability; the second criterion is public acceptance and societal perception of the vehicle; the third criterion is accessibility to charging networks and fuel supply stations; the fourth criterion is safety; the fifth criterion refers to the vehicle's technical and performance limitations; the sixth criterion is environmental sustainability; the seventh criterion is fuel efficiency; the eighth criterion is the time required for charging or refueling; the ninth criterion represents maintenance and repair costs; and the tenth criterion is the vehicle purchase price.

In order to evaluate green vehicles in Iran, due to the lack of reliable and comprehensive data, a combination of desk research, public surveys, and expert opinions was employed. Technical characteristics of vehicles, such as environmental performance, reliability, charging time, fuel efficiency, and similar attributes, were extracted from reputable international sources, including the Alternative Fuels Data Center, under the supervision of the United States Department of Energy, as well as official vehicle technical manuals. To assess public acceptance, a questionnaire was designed and distributed among experts, academics, and other respondents, and the survey results were analyzed using specified weighting coefficients. It should be noted that the vehicle purchase price corresponds to the average factory-gate price of vehicles in the year 2022.

In this step, after forming the decision-making matrix, it is necessary to calculate the mean and standard deviation of the data related to the criteria in the decision-making matrix in accordance with Eqs. (29) and (30)

r̅ = ∑ rij , j = 1, . . . , n, (29)

Sj = ∑(rij − r ̅j) , j = 1, … , n. (30)

The mean and standard deviation of each option are in Table 3.

In the third step, it is necessary to form a standard (normalized) matrix. Each criterion in the decision-making matrix has different scales and units of measurement; therefore, it is necessary to eliminate the units and scales in this step, which is done using Eq. (31).

rij − r ̅j

zij = , (31)

sj

In the fourth step, the composite distance between the options must be determined. For this purpose, using the standard matrix, the distance of each option to the others is calculated through the Euclidean equation Eq. (32).

Cab = ∑(zaj − zbj) . (32)

√j=1

According to Eq. (33), a and b are two options to be evaluated. The distance of each option to itself is equal to zero, and the distance of option a to option b is equal to the distance of option b to option a. Therefore, the composite distance matrix of the options is as shown in Table 5, whose main diagonal is equal to zero.

In this step, it is necessary to determine the minimum distance of each row of the matrix. Then, the average distance of the options and their standard deviation should be calculated. For this purpose, Eqs. (33)-(35) are used.

o ̅ = ∑ Oi, (33) SO = ∑(Oi − O ̅) , (34)

O = o ̅ ± 2SO, (35)

A heterogeneous option is an option that does not fall within the above limit. Therefore, if an option is heterogeneous, we eliminate it and reform the decision matrix with the remaining options.

In addition to the decision matrix, it is also necessary to form a weight vector matrix. According to Table 8, wj represents the weight of the jth criterion. It should also be noted that the sum of all weights must be equal to 1.

In this step, it is also necessary to obtain the average solution. For this, Eq. (36) is used. The result is shown in Table 9.

∑m i=1 rij

AVj = , j = 1, . . . , n, (36)

After calculating the mean solution, it is necessary to calculate the values of the positive distance from the mean and the negative distance from the mean. For this purpose, if the criterion is positive, Eqs. (37) and (38) can be used max (0, (rij − AVj))

PDAij = , i = 1, … , m , j = 1, … , n, (39)

AVj max(0, (AVj − rij))

NDAij = , i = 1, . . . , m , j = 1, . . . , n. (38)

AVj If the criterion is negative, Eqs. (39) and (40) are used.

max (0, (AVj − rij))

PDAij = , i = 1, … , m , j = 1, … , n, (39)

AVj max(0, (rij − AVj))

NDAij = , i = 1, . . . , m , j = 1, . . . , n. (40)

AVj The results obtained from the above relationships are shown in Tables 10 and 11.

In this step, using the criteria weight vector and Eqs. (41) and (42), the values of SPi and SNi are calculated, and using Eq. (43), the values of SPi and SNi are relatively normalized, and Si is obtained

SPi = ∑ PDAij. wj, i = 1, . . . , m, (41)

SNi = ∑ NDAi. wj, i = 1, … , m, (42)

SPi − SP ∗ SNi − SN ∗

Si = − + − , (43)

SP − SP ∗ SN − SN ∗ In the above equations, we have:

SP∗ = maxSPi , SN− = minSNi,

In addition, the values of RPi and RNi are calculated using Eqs. (44) and (45) and normalized using Eq. (46). The results obtained from the following equations are given in Table 12.

RPi = Max(PDAij. wj), i = 1, … , m, (44)

RNi = MAX( NDAij. wj), i = 1, … , m, (45) RPi − RP ∗ RNi − RN ∗ Ri = − + − , (46) RP − RP ∗ RN − RN ∗ In the above equations, we have:

RP∗ = maxRPi , RN− = minRNi,

In this step, the Idavicoronomi index is calculated through Eq. (47).

(Si − S∗) (Ri − R∗) Qi = v[ − ∗ ] + (1 − v)[ − ∗ ], (47) (S − S ) (R − R ) Subject to;

S∗ = minSi , S− = maxSi , R∗ = minRi , R− = maxRi,

i i i i

During this step, the results obtained from S, R, and Q are sorted in ascending order. Option a1, which has the highest value in the list Q, is selected, and option a2 is considered as the second-best option after a1 in the list Q. Option a will be selected as the best option if it satisfies the following two conditions:

I. Q(a2) – Q(a1)≥DQ II. Option a is the best option in both lists S and R. In the first condition, m is the number of options, and we have:

DQ = , (48) m − 1

If one of the two above conditions is not met, then the following procedure will be followed:

I. If only the second condition is not met, a and b will be selected as the best options.

II. If the first condition is not met, a set of options will be selected as the most desirable options for the maximum value that meets the condition.

Q(az) − Q(a1) < DQ,. (49)

Based on the results obtained from the output of the EDA–VIKOR–Taxonomy (EDAVIKORONOMY) method for ν=0.4, as reported in Table 13, the acceptability conditions of this method are examined. Given that there are six alternatives, the value of DQ is 0.2. Therefore, the difference between the Qi values of the two alternatives with the highest Qi scores must be greater than 0.2. Since PHEVs and hybrid electric vehicles (HEVs) have the highest EDAVIKORONOMY index values, respectively, and the difference between their index values is 0.637, the first condition is satisfied. According to the second condition, the Ri and Si values for PHEVs are the highest; therefore, it can be concluded that PHEVs are selected as the most preferable alternative. It is while, in the VIKORONOMY and taxonomy methods, hybrid vehicles were selected as the top alternatives; however, in the EDAS method, similar to the EDAVIKORONOMY method, plug-in hybrid vehicles are selected as the best option.

To examine and analyze the results of the Idavicornomy ranking and the results obtained from this method, the Taxonomy and VIKOR MCDM methods were used alone. In the VIKOR method, plug-in hybrid vehicles (PHEV) were selected as the most desirable option, while in the Taxonomy method, hybrid vehicles (HEV) were ranked first and plug-in hybrid vehicles (PHEV) were ranked second with a very small difference; therefore, it can be claimed that the results obtained from the Idavicornomy MCDM method can be confirmed and cited.