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19 August 2021

A Comparative Evaluation of Multi-Criteria Analysis Methods for Sustainable Transport

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Faculty of Civil Engineering and Environmental Sciences, Bialystok University of Technology, Wiejska St. 45A, 15-351 Bialystok, Poland
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Energies2021, 14(16), 5100;https://doi.org/10.3390/en14165100
This article belongs to the Special Issue Planning and Management of Sustainable Transport
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Abstract

The article pertains to the utilization of the application potential of MCDM/MCDA (Multi-Criteria Decision Making/Multi-Criteria Decision Analysis) methods in decision-making problems in the field of transport in light of sustainable development. The article consists of a theoretical and an empirical part. As part of the literature studies, a review was carried out on the latest applications of MCDM/MCDA methods for decision-making problems in the field of transport. In the empirical part, a multi-criteria analysis of the placement selection for a strip of expressway located in north-eastern Poland was carried out. For this purpose, a hybrid approach was used, consisting of three selected MCDM/MCDA methods: DEMATEL, REMBRANDT, and VIKOR. The ranking was compared with the results achieved in the EIA report of the investment and the results were obtained by using a different set of MCDM/MCDA methods that were proposed in the first part of the research, i.e., AHP, Fuzzy AHP, TOPSIS, and PROMETHEE. The performed multi-criteria analyses allowed for an eventual multi-dimensional evaluation of the most popular MCDM/MCDA methods currently applied in the field of transport.

1. Introduction

Transport is an important branch of the economy and science, in which the decisions made are often multi-criteria in character. The choice of the investment location, route for road infrastructure, and public transport development scenario are just some of the decision-making problems in the field of transport [1] that require considering multiple environmental, economic, and social factors according to the idea of sustainable transport. The concept of sustainable transport appeared almost parallel with the definition of sustainable development in the Report of the World Commission on Environment and Development: Our Common Future [2]. In the early 1990s, Daly [3] and Pearce [4] defined sustainable transport as transport with non-declining capital, in which the capital includes human capital, monetary capital, and natural capital. Multi-criteria decision-making support in the area of sustainable transport is significant due to the multitude of aspects that should be considered.
Multi-criteria decision-making support in the area of sustainable transport is significant due to the multitude of aspects that should be considered.
There is, after all, a clear relationship between the level of development of transport systems and the area’s economic development. Transport performs many functions in the economy: it is an essential instrument for the exchange of goods and services, it determines the distribution of investments, and it is also an important factor in the location of settlements. Transport also affects the development of other branches of the economy and is an essential factor in GDP growth. Sustainable development requires considering environmental issues in economic decisions. As a component of the economy significantly influencing the environment, transport requires paying particular attention to environmental issues. The social function of transport is also worth emphasizing. Efficient transport satisfies society’s communication needs and shapes the spatial availability of the necessary functions [5].
Among the main features of transport infrastructure, one should include: a long period of its implementation and operation; high capital demands with a long return-on-investment period; immobility; and the possibility for various external influences to exist (especially in the context of the natural environment) [5]. Due to the functions of transport in the modern world and its features, the decision-making process in this field is an important and responsible task that often requires multi-criteria analyses.
The main goal of this work is to perform a comparative analysis of the results obtained while applying various MCDM/MCDA methods to a selected decision-making problem in the field of transport. The specific objectives of the study pertain to:
  • updating the review of the current applications of the MCDM/MCDA methods to the selected decision-making problems in the field of transport, along with indication of the latest trends;
  • carrying out a multi-criteria analysis of design variants using a hybrid approach that includes the DEMATEL, REMBRANDT, and VIKOR methods;
  • carrying out a comparative analysis of the results obtained with previous tests, which used a combination of the AHP, Fuzzy AHP, TOPSIS, and PROMETHEE methods; and
  • an assessment of the methods applied in both studies in the context of their advantages, disadvantages, and limitations in solving contemporary problems in the field of transport.
The research questions the authors try to answer are as follows: (1) whether the assessment of road construction investment options differs with the use of several multi-criteria methods and (2) which of the MDCA methods are most helpful in assessing this type of decision problem.
Therefore, this paper is devoted to the study of the applicability potential of selected MCDM/MCDA methods in the field of transport. In the beginning, a review of the literature on the latest applications of the selected methods in various decision-making processes was performed. Then, computational examples were developed through a case study on routing an expressway section in north-eastern Poland. Finally, based on multi-criteria and comparative analyses, the selected methods that have been used most commonly in the field of transport were assessed in detail. They were used to select the variant of the expressway section in north-eastern Poland and compare the result of the analysis with the choice made in the analyzed environmental impact report.
In the available literature on the subject, you can find many items devoted to the analysis of the application potential of MCDM/MCDA methods in various areas of life and science (see, e.g., [6,7,8,9]). However, this work focuses only on decision-making problems in the field of transport: the most popular research topics have been identified and, on the basis of several dozen previous scientific papers, the most popular methods from the MCDM/MCDA family have been identified. In addition, a proprietary hybrid approach was proposed, supporting multi-criteria decision support in environmental impact assessments of transport investments.

2. Literature Review Materials and Methods

We considered a total of 52 scientific articles [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59] in which MCDM/MCDA methods were applied to decision-making problems in the field of transport in 2020 and 2021 worldwide (Previous publications from 2000–2019 were analyzed in the first part of the paper: Broniewicz, E., Ogrodnik, K., 2020. Multi-criteria analysis of transport infrastructure projects, Transportation Research Part D: Transport and Environment 83, 102351, https://doi.org/10.1016/j.trd.2020.102351, accessed on 15 May 2021). Articles indexed in Scopus and Web of Science were considered, with the leading search criteria being the following keywords: MCDM, MCDA, and transport. Appendix A presents the types of MCDM/MCDA methods used, the research problem, and the temporal and territorial delimitation of the research. As in the previous study [1], six areas of activity related to transport infrastructure were identified: quality and safety of public transport, scenarios for the development of public transport systems, choice of investment location, road, air, rail and sea transport, and electric vehicles, among other areas of activity. It can be observed that between 2020 and 2021, AHP, TOPSIS, PROMETHEE, Fuzzy AHP, and DEA are still the most popular methods of multi-criteria decision making. There are also multiple new, hitherto unobserved multi-criteria decision-making methods such as CODAS, COMET, CRITIC, EDAS, MARCOS, PIPRECIA, and MEW PROMETHEE II, among others (see Appendix A).
Data on multi-criteria decision-making methods were summarized to obtain a database from 2000 to 2021 (Appendix B). Figure 1 shows the methods that have been used in at least two studies over the past 20 years.
Figure 1. The most popular MCDM/MCDA methods used in the field of transport between 2000 and 2021. Source: author’s work.
Based on the data in Figure 1, it can be observed that—in the last 20 years—the most frequently used MCDM/MCDA methods in the field of transport were the AHP, TOPSIS, and PROMETHEE methods. It should be emphasized that these exact methods were used in previous studies [1]. In the second part, a decision was made to use the selected methods included in the following items of the carried out review. The hybrid approach proposed in this article is the result of the literature review. In the case study, alternative methods were used to those from the first part of the study [1], which were also at the forefront of the MCDM/MCDA method ranking. A hybrid approach was again used including the following methods:
  • DEMATEL; the method placed fifth in the ranking. This method makes it possible to perform dependency analyses at the level of decision factors, making it possible to conduct a multi-criteria analysis in a new dimension.
  • VIKOR; the method was placed, along with other methods, in the seventh position, selected as an alternative to the TOPSIS method from the first research part.
  • REMBRANDT; although this method was placed in a distant nineth place, it is one of the few methods enabling the weighting of decision factors. It was selected as an alternative to the AHP and Fuzzy AHP methods from the first part of the study.

3. Research Methods

Figure 2 shows the hybrid approach proposed in the article and the scope of multi-criteria and comparative analyses.
Figure 2. The basis for the proposed hybrid approach. Source: author’s work.

3.1. DEMATEL Method (Decision-Making Trial and Evaluation Laboratory)

The DEMATEL method was developed in the second half of the 1970s in Switzerland. Generally, it allows for the analysis of cause-and-effect relationships at the level of decision factors. The algorithm of the classic DEMATEL method is relatively simple, as is the case with the AHP method, and is based on comparing factors in pairs using a point scale. The basic assumptions of the method’s algorithm are characterized below [60] (pp. 64–65) [61] (pp. 125–129) [62] (pp. 67–68) [7] (pp. 63–65). The first step in the DEMATEL method is to develop a matrix of direct relations. This matrix is created using a point scale. The classical scale (by Fontel and Gabus, the authors of the method) consists of the following five levels: 0 meaning no direct influence; 1 meaning low impact; 2 meaning medium impact; 3 meaning high impact; and 4 meaning very high impact. There are also other scales. An increased interest in fuzzy scales is observed (see, e.g., [63]). The assessment of the direct interrelationships between the elements is made in pairs (by a single decision-maker or a group of decision-makers). The effect of these comparisons is the so-called matrix of direct relations M. A matrix of direct relations is a square matrix in which the elements on the main diagonal are equal to 0.
In contrast, the other matrix elements show direct relations between the factors within a given pair. The next step in the DEMATEL method is the normalization of elements in the developed matrix of direct relations. The normalization procedure in the DEMATEL method consists of dividing the elements in the matrix of direct relations by the highest value of its row or column sums, thus creating a normalized matrix of direct relations M’. Then, the following formula creates a matrix of integral relations:
N = M′(I − M′)−1
where N is the matrix of total relations, M′ is the normalized matrix of direct relations, and I is the unit matrix (the dimension that relates to the dimension of the direct relation matrix).
The elements of the n matrix represent both direct and indirect relations between decision factors. The final stage in the DEMATEL method is the calculation of two key indicators, the so-called significance index and relation index. Based on their values, the final cause-and-effect diagram is created, illustrating both the activity of the decision factors and their nature in the created cause–effect chain. The factors with positive values of the relation index are causal, i.e., they have the most significant impact on the remaining elements in the data set under consideration. Conversely, factors with negative values of the dependency index affect the created cause–effect chain.
It is worth adding that the DEMATEL and AHP methods have common features including similar initial matrices, namely the matrix of comparisons and matrix of direct relations. Both matrices are square with the constant form of a diagonal (in the AHP comparison matrix, it is 1; in the DEMATEL matrix, the values on the main diagonal are 0). Both methods also utilize point scales [61]. Examples of approaches to linking the classic Saaty scale with the Fontel and Gabus scale (both classic and its modification) are presented in Table 1.
Table 1. An example of how to combine the scales used in the family of AHP and DEMATEL methods.
Despite the possibility of transforming the initial comparison matrix within the AHP method onto the matrix of direct relations within the DEMATEL method, it should be noted that the procedure of comparing elements in the classic DEMATEL variant concerns the mutual relationships between factors, not the estimation of their importance. Therefore, a multi-criteria analysis using the classic DEMATEL method should be performed regardless of the pairwise comparison procedure present in the AHP method. As part of this article, a cause-and-effect chain of decision-making factors has been developed. It should be emphasized that this is the only multi-criteria analysis developed as part of the research, not related to the level of variants. The REMBRANDT method, an alternative to the AHP method, was used to estimate the weight of decision factors.

3.2. REMBRANDT Method

The REMBRANDT method (Ratio Estimation in Magnitudes or deciBells to Rate Alternatives which are Non-DominaTed) was developed in the Netherlands to respond to the selected solutions used in the AHP method that have been subject to criticism. Among the debatable elements of the algorithm of the AHP method, the authors Forman [66] and Moghtadernejad et al. [67] indicated, among others, that the independence of the examined elements, the measurable subjectivity within pairwise comparisons, or the difficulty in accounting for uncertainties related to judgments. Although the REMBRANDT method, similarly to the AHP method, enables the weighting of decision factors, there are significant technical differences between the methods [68,69,70]:
  • in the REMBRANDT method, a logarithmic scale is used instead of a Saaty scale;
  • a logarithmic method of least squares is used to derive scale vectors; and
  • the geometric mean aggregation is used for the generalized evaluation of variants.
A comparison of the scales used in the AHP and REMBRANDT methods and the grades definition is presented in Table 2.
Table 2. The classic Saaty scale and the scale used in the REMBRANDT method.
The first step in the REMBRANDT method is the comparing of pairs of elements at a given decision stage using a numerical scale. The grades are then converted into values on a geometric scale. The conversion is done according to the following formula [69]:
rij = exp(γδij)
where γ is the ln 2 and δij is the figure from the scale.
In the second stage, a geometric mean for each row is calculated and then normalized to give the weight vector [68,69,71].
It should be emphasized that in this study, to be able to conduct a full-scale comparative analysis, the ratings from the initial comparison matrix in the AHP method were transformed into ratings that are in accordance with the REMBRANDT scale.

3.3. VIKOR Method

The VIKOR method (Serb. VIsekrzterijumska Optimizacija i Kompromisno Resenje) was developed in the 1990s and then disseminated thanks to the work of Opricovic and Tzeng [72], in which a comparative analysis of the VIKOR and TOPSIS methods (the latter being characterized by similar assumptions) was performed [70]. Similar to TOPSIS, the VIKOR method enables assessing decision alternatives based on their position to defined reference points [62]. The VIKOR method algorithm assumes the following calculation steps [70,72,73,74]. In the first stage, the best and worst grades are determined against the given criteria; these are so-called ideal and anti-ideal points. Then, for individual decision variants, the sum of the weighted, normalized distances from the ideal solution (metric S) and the maximum distance of the weighted, normalized assessment (metric R) are calculated. The lower the value of these metrics, the better. In the next step, the value of the comprehensive indicator is determined (metric Q) according to the following formula [72,73]:
Q i = v   S i − S + S − − S + + ( 1 − v )   R i − R + R − − R +
where v is the weight of the strategy of “the majority of criteria”, Si is the S metric (the sum of the weighted, normalized distances of the i-variant from the ideal solution), and Ri is the R metric, the maximum weighted, normalized rating distance.
Three ranking lists constitute the results of the above calculations: variant evaluations in light of S, R, and Q metrics. The lower the values of these metrics, the higher the position in the rankings is awarded to a given variant. The final stage consists of comparing the rankings obtained in terms of an acceptable advantage and acceptable decision stability. Importantly, rankings in the VIKOR method can be carried out with different values of criteria weights, which enables the analysis of the impact of the weights of these criteria on the proposed compromise solution.

4. Case Study

This article once again takes advantage of the data from the report on the environmental impact of a project comprising the construction of an expressway and the construction of a national road in north-eastern Poland. The data was made available by the General Directorate for National Roads and Motorways, Bialystok Branch [75]. Detailed information on the decision-making factors and variants can be found in this article [1].
The planned project involves the construction of an expressway on the Choroszcz-Ploski section and a national road on the section between the towns of Kudrycze and Grabówka, together with the construction of the necessary technical infrastructure. The planned investment is essential for the economic development of this region of Poland. Additionally, it will contribute to improving the quality and safety of road traffic. This road belongs to the international transport corridor network. Six location variants were adopted for the analysis, including two variants of the expressway and three variants of the national road connected to it. The road route variants differ in the location and number of engineering structures [75]. The characteristics of the analyzed variants are presented in Table 3.
Table 3. Variants’ characteristics.

4.1. Decomposing a Decision-Making Problem

As part of this multi-criteria analysis, six different variants of the road route and 13 decision-making factors reflecting the impact of this investment on the environment and society at large were considered. The criteria for the evaluation of variants are each time individually selected depending on the nature and subject of the analysis. The decision criteria in this case study were adopted from the environmental impact report [75]. The hierarchical structure of the decision problem under consideration is shown in Figure 3.
Figure 3. Hierarchical structure tree. Source: author’s work based on [75].

4.2. Numerical Example

The results of the basic calculations performed using each of the selected methods are presented below: DEMATEL and then REMBRANDT, used to estimate the factor weights, which were later used with the VIKOR method.
The first stage concerned the analysis of dependencies at the level of decision factors. First, the decision criteria were compared in pairs using the classic DEMATEL scale, obtaining the matrix of direct relations M (Table 4). Then, the grades were normalized (Table 5) and the matrix of total N relations was determined (Table 6), which allowed for the ranking of factors under consideration in the form of a cause-and-effect chain (Table 7 and Figure 4).
Table 4. The matrix of direct relations for decision factors M (DEMATEL method).
Table 5. Normalized matrix of direct relations M (DEMATEL method).
Table 6. Matrix of total relations (direct and indirect) N with row and column sums (DEMATEL method).
Table 7. The value of the position indicator and relation indicator (DEMATEL method).
Figure 4. Cause-and-effect diagram. Source: author’s work.
It should be emphasized that the classic DEMATEL method enables the analysis of dependencies (direct and indirect) between decision factors. This should not be identified directly with the weights of these factors. Therefore, a multi-criteria analysis using DEMATEL helps rank the factors in terms of their mutual relations to identify those that have the most significant impact on the others. In the case of the analyzed data set, the causal factors, i.e., the ones that have the most significant impact on the others, are: factors related to the location of NATURA 2000 areas pertaining to the planned investment (C1, C2, and C5), as well as linear factors, i.e., length sections with a high degree of pollution risk (C9) and the length of the intersection of the complex of soils 2 and 2z (C11). Conversely, the following factors were classified as the resultant of the impact of the above-mentioned criteria: the number of herpetofauna locations in the test buffer (C8); the impact on snail habitats (C6); the impact on the habitats of insects (C7); the number of vascular plant species destroyed (C3); the number of fungi (lichens) species destroyed (C4); and the number of buildings exposed to excessive noise (C13). Two factors remained neutral (C10 and C12), which may indicate their different nature. The classic DEMATEL method facilitates ordering at the level of decision factors and their analysis regarding their mutual interactions. Therefore, it can be an instrument supporting the selection of factors at the stage of the decomposition of the decision-making problem.
Alternatively, the REMBRANDT method was used to estimate the weights of the criteria. It should be noted that the matrix of comparisons in the REMBRANDT method Based on the primary comparison matrix of the AHP method (Table 8), which was used in the first part of the study [1], it was developed (Table 9). Then, according to Formula 2, the matrix elements were transformed into values on the geometric scale. The decision factor weights were estimated using the geometric mean and additive normalization (Table 10).
Table 8. Matrix of comparisons, criteria weights, and consistency assessment estimated using the classical AHP method.
Table 9. Decision factor comparison matrix (REMBRANDT method).
Table 10. Transformed comparison matrix of decision factors: the geometric mean of the rows and weights of decision factors (REMBRANDT method).
The final stage focuses on developing a ranking of the considered decision variants in light of the defined criteria. For this purpose, the VIKOR method was used. In addition to the weights calculated by the REMBRANDT method, sets of weights estimated by the AHP and Fuzzy AHP methods were also used, finally obtaining three rankings (Table 11 and Table 12).
Table 11. Initial data (VIKOR method).
Table 12. The values of S, R, and Q metrics together with a ranking and verification of conditions.

4.3. Comparative Analysis

Figure 5 presents individual decision factors’ weights estimated using the following methods: AHP, Fuzzy AHP [1], and REMBRANDT. It should be emphasized that the starting point for the calculations was the AHP comparison matrix evaluations, which were then transformed according to the algorithm of the other two methods.
Figure 5. Decision factor weights calculated using the AHP, Fuzzy AHP, and REMBRANDT methods. Source: author’s work.
Comparing the sets of weights estimated with the AHP, Fuzzy AHP, and REMBRANDT methods, it can be noticed that there are specific differences; however, the order of the factors in terms of their importance has not changed. It should be added, though, that the differences between the weights obtained with the AHP method and the weights estimated with the Fuzzy AHP method are much lower than the differences between the sets of AHP and REMBRANDT scales. Therefore, it can be concluded that the modifications proposed in the REMBRANDT method (mainly the form of the scale and the logarithmic method of least squares that is used to estimate the weight vector) have a greater overall impact on the final vector of the weights than the case with a transformation of a classic Saaty scale into a fuzzy triangular scale has (see also [68]).
The assessment of the impact that a change in the value of factor weights has on the final ranking of decision variants serves as yet another important element of the comparative analysis. Table 13 presents the final rankings of alternatives developed using the three MCDM/MCDA methods: TOPSIS, PROMETHEE, and VIKOR. Additionally, the ranking of variants developed as part of the environmental impact report for the investment in question was given as a reference point. A detailed description of the obtained rankings in terms of content is presented in [1].
Table 13. Ranking of decision variants: summary list.
A change in the weighting of decision factors did not affect the final ranking of the variants. For both the TOPSIS and PROMETHEE methods, even after changing the set of weights, the final order did not change. Similar observations apply to the multi-criteria analysis performed using the VIKOR method. It should be emphasized that the final rankings of the decision variants presented in Table 13 are almost identical. However, in the case of receiving different rankings, it is recommended to use, for example, the rank similarity coefficient in decision-making problems (see [76]).
Significantly, the obtained rankings of the decision alternatives differ in regards to the first position. In the case of the method used in the report and the PROMETHEE method, which represents the family of methods based on the height difference, W3 arrived in the first place. However, among the methods based on reference points, identical rankings were obtained, with W2 in the first place. In the case of the rankings obtained using the TOPSIS method, the differences between the first and second place were negligible (e.g., with the use of weights calculated by using the classic AHP and the final index of W2 = 0.777 and W3 = 0.772). In contrast, in the rankings prepared using the VIKOR method, the difference between the first two places was higher and W2 met both the condition of “acceptable advantage” and “acceptable stability”.
It should be emphasized that the comparative analysis of the distance methods VIKOR and TOPSIS (especially in the context of the algorithms used) was the subject of previous research; see, e.g., [72,77].

5. Discussion and Conclusions

The performed multi-criteria analyses allowed to verify the choice of the course of the selected investment made as part of the report [75] and which made it possible to evaluate the usefulness of the selected MCDM/MCDA methods in the field of transport. Based on the performed calculations as well as the comparative analyses of the obtained results and their interpretations, Table 14 presents the evaluation of the MCDM/MCDA methods applied, their advantages/opportunities, and disadvantages/limitations, including the fields of application in the transport domain. It should be noted that, due to the growing popularity of MCDM/MCDA methods, they have already been studied in terms of their advantages and disadvantages (see, e.g., [8,78,79,80,81]). However, in the framework of this paper, the observations formulated by the authors concern the application of these methods in decision-making problems in the area of transport. Of course, despite such a narrower approach, selected comments on the usefulness of the selected methods can be considered universal.
Table 14. Assessment of the most popular MCDM/MCDA methods used so far in the field of transport with their SWOT analysis and examples of applications.
Based on the literature studies and the conducted analyses, the following conclusions can be drawn:
  • Multi-criteria decision support in the field of transport is invariably based mainly on the methods from the AHP, PROMETHEE, and TOPSIS family. This is primarily due to their universal nature, transparent and proven algorithms, and the available software to facilitate the performance of multi-dimensional analyses. However, each year, new methods not yet observed in the field of transport emerge, such as CODAS, COMET, CRITIC, EDAS, MARCOS, PIPRECIA, or MEW.
  • In any multi-criteria analysis, the weighting of decision-making factors serves as a crucial stage, especially in investments in the field of transport, which are usually characterized by large dimensions and thus a large scale of potential impacts. Therefore, it seems appropriate to use methods that enable pairwise comparisons of factors as part of the expert research stage (AHP, Fuzzy AHP, or REMBRANDT).
  • The DEMATEL method can serve as a support tool at the stage of selecting and analyzing decision factors. To increase objectivity, the analysis of dependencies can be successfully performed as part of expert interviews.
  • When ranking decision alternatives, the number of multi-criteria methods available is significant. Concerning decision-making problems in the field of transport, especially in a situation where the considered alternatives are similar, it is recommended to use at least two methods.
Due to the dynamic development of MCDM/MCDA methods, the development of multi-criteria analyses in the field of transport with the use of other methods, especially the “youngest” methods which have so far been characterized by single implementations of the study, should be indicated among the future directions of development. Furthermore, it would be interesting to compare their usefulness with classic methods well known in theory and practice that dominate the developed application overview.

Author Contributions

Conceptualization, K.O. and E.B.; methodology, K.O.; writing, E.B. and K.O. Both authors have read and agreed to the published version of the manuscript.

Funding

The study was carried out as part of study number WZ/WB-IIL/6/2019 and WZ/WB-IIŚ/1/2020 at the Bialystok University of Technology and was financed by a subvention provided by the Minister of Science and Higher Education.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table
Table A1. Compilation of the literature review on multi-criteria methods applied in transport-related projects in 2020–2021.
Table A1. Compilation of the literature review on multi-criteria methods applied in transport-related projects in 2020–2021.
Author (Year of Publication)LocationMCDM/MCDA Methods UsedThe Main Subject of the Research
Safety and Quality of Public Transport
Vavrek and Bečica (2020) [6]Czech RepublicCV-TOPISISEvaluation of transport companies
Blagojević et al. (2020) [7]Bosnia and HerzegovinaFuzzy PIPRECIA and Entropy methodSafety evaluation of railway traffic
Damidavičius et al. (2020) [8]LithuaniaCOPRAS, TOPSIS, ARAS, and EDASAssessment of urban transport systems and their potential in terms of sustainable mobility
Zehmed and Jawab (2020) [9]Fez, MoroccoFuzzy SERVPERF and DEA Quality of urban bus transport service
Kumar and Anbanandam (2020) [10]IndiaFuzzy Best–Worst method (FBWM)Assessment of social sustainability indicators in the freight transport industry
Kumar and Anbanandam (2020A) [11]IndiaIntuitionistic fuzzy AHP (IF-AHP) and IF-VICORAssessment of environmental sustainability indicators in the freight transport industry
Pamucar et al. (2020) [12]Istanbul (Turkey)Fuzzy Full Consistency Method-Dombi–Bonferroni (fuzzy FUCOM-D’Bonferroni)Assessment of transport demand management measures
Kumar et al. (2020B) [13]IndiaAHP, DEA, VICOR, and MPIAssessment of the performance of public road transportation systems
Blagojević et al. (2021) [14]Bosnia and HerzegovinaFuzzy FUCOM, fuzzy PIPRECIA, and fuzzy MARCOSEvaluation of safety degree at railway crossings
Karim and Jawab (2020) [15]MoroccoDEA and fuzzy SERVPERFAssessment of the quality of urban bus transport
Scenarios for the Development of Public Transport Systems
Kizielewicz and Dobryakova (2020) [16]PolandCOMET (Characteristic Objects METhod)The assessment of model electric scooters in cities
D’Orso et al. (2020) [17]SpainAHPThe optimal allocation of economic resources for identifying the actions in the transport sector
Ogrodnik (2020) [18]PolandPROMETHEESustainable solutions for public transport and infrastructure
Hamurcu and Eren (2020) [19]Kırıkkale, TurkeyTOPSISPrioritizing alternative public transportation projects
Kim et al. (2020) [20]KoreaFAHPStrategies for efficient use of Trans-Siberian Railway for multimodal transport
Görçün (2021) [21]Istanbul, TurkeyCRITIC (CRiteria Importance Through Intercriteria Correlation) and EDAS (Evaluation based on Distance from Average Solution)Evaluation of the selection of urban rail vehicles
Choice of Investment Location
Palczewski and Sałabun (2019) [22]PolandPROMETHEE IILocation of the airport
Akin and Kara (2020) [23]Istanbul, TurkeyAdditive value (AV) modelLocation of intercity bus terminal
Ortega et al. (2020) [24]Ecuador, CuencaFuzzy AHPLocation of park-and-ride facility
Broniewicz and Ogrodnik (2020) [1]PolandAHP, Fuzzy AHP, TOPSIS, and PROMETHEELocation of the expressway section
Tadic et al. (2020) [25]Western Balkans regionAHP and CODASDry port terminal location selection
Aljohani and Thompson (2020) [26]Inner Melbourne, AustraliaTOPSISLocation of freight consolidation facility
Sukmanee et al. (2020) [27]ThailandAnalytic Network Process (ANP) and Design Structure Matrix (DSM)Location of dry port
Zagorskas and Turskis (2020) [28]Kaunas, LithuaniaMEW, EDAS, ARAS, and SWARALocation of new pedestrian bridges
Aksoy and Gursoy (2020) [29]TurkeyAHP and ELECTRELocations of logistic villages
Muravev et al. (2020) [30]ChinaDEMATEL–MAIRCALocation optimization of international logistics centers
Ayub and Balogun (2021) [31]Bandar Seri Iskandar MalaysiaAHPOptimal bus-stop locations
Road, Air, Railway, and Sea Transport
Li et al. (2020) [32]ChinaBest–Worst method (BWM)Customers’ preferences for the main attributes that define the transport service
Shishegaran et al. (2020) [33]Tehran, IranTOPSISSustainability evaluation of scenarios transport network condition
Stokic et al. (2020) [34]Belgrade, SerbiaHybrid DANP–TOPSISSelection of the most suitable vehicle
Stoilova et al. (2020) [35]Trans-European Transport Network (TEN-T)SIMUSEvaluation of railway network performance
Tolga and Durak (2020) [36]Istanbul, TurkeyFuzzy COPRASEvaluation of innovation projects in the air cargo sector
Lameira et al. (2020) [37]the AmazonAHP, DEMATEL, and ELECTREEvaluation and selection of the best river train in the Amazon region
Electric Vehicles
Shekhovtsov et al. (2020) [38]PolandVICOR and TOPSIS Evaluation of electric bicycles
Kaya et al. (2020) [39]IstanbulVIKOR and PROMETHEELocation of electric vehicle charging stations
Wilken et al. (2020) [40]GermanyPROMETHEEComparison of electric vehicles with internal combustion engine vehicles
Cheng and Wei (2020) [41]Beijing, ChinaAHP and DEALocation selection of bike-sharing parking points
Other
Solecka et al. (2020) [42]Krakow, PolandCompensation-Conjunctive method (CC)Adaptation of interchanges to the needs of people with reduced mobility
Dang and Yeo (2020) [43]VietnamFuzzy TOPSISSynchronization in developing transport infrastructures, such as between transport systems and dry port networks
Zapolskytė et al. (2020) [44]Vilnius, LithuaniaAHP, COPRAS, TOPSIS, and SAW Assessment of the level of development of infrastructure and transport services
Zagorskas and Turskis (2020) [45]Vilnius, LithuaniaAdditive Ratio ASsessment with Fuzzy (ARAS-F)Ranking the priorities for development and the renewal of bicycle pathway segments
Galinska (2019) [46]PolandPromethee IISelection of logistics operator
Pamucar et al. (2020) [47]RomaniaBWM and MARCOSPrioritizing the alternatives of the hydrogen bus development
Liachovičius et al. (2020) [48]LithuaniaSAW, COPRAS, TOPSIS, EDAS, and PROMETHEEBusiness valuation of road freight transport companies
Ur Rehman and Ali (2021) [49]China Pakistan Economic Corridor (CPEC)Fuzzy-TOPSISIdentification of China’s most optimal route for crude oil import
Kaska and Tolga (2021) [50]TurkeyTOPSISSelection of software for a maritime organization
Koohathongsumrit and Meethom (2021) [51]ThailandAHP, DEA, and TOPSISRoute selection in multimodal supply chains
Aghamohagheghi et al. (2001) [52]IranInterval-valued pythagorean fuzzy set (IVPFS)Assessment of sustainable transport projects
Ðalić et al. (2021) [53]Bosnia and HerzegovinaModel based on the integration of fuzzy PIPRECIA, FUCOM, and MARCOSSet of business strategies of the transport company
Risk Analysis
Cunha et al. (2021) [54]Brazilian airportsMCDA-CAnalysis of risks related to airport runway maintenance
Erdoğan and Kaya (2020) [55]Istanbul, TurkeyFuzzy rule-based system FRBS and particle swarm optimization PSOEvaluation of risks and failures of public transport systems
Bakioglu and Atahan (2021) [56]TurkeyAHP, PF-TOPSIS, and PF-VIKORRisk prioritization in self-driving vehicles

Appendix B

Table
Table A2. Summary of the methods’ application in selected areas associated with transport infrastructure in 2000–2021.
Table A2. Summary of the methods’ application in selected areas associated with transport infrastructure in 2000–2021.
MethodSafety snd Quality of Public TransportScenarios for the Development of the Public Transport SystemChoice of Investment LocationRoad, Air, Rail, and Sea TransportElectric VehiclesOtherTotal
AHP76561631
ANOVA1000001
ANP0110024
ARAS-F1020014
AV0010001
BWM0002013
CC0000011
CFA0010001
CODAS0010001
COMET0100001
COPRAS2000024
COPRAS-G0100001
COSIMA0001001
CRITIC0100001
CV-TOPSIS1000001
DANP0002002
De Borda0001001
DEA3000126
Delphi2010014
DEMATEL1212129
DSM0010001
EDAS1010013
ELECTRE III/IV0312006
Entropy2000002
FARE1000001
FSWARA0001001
Fuzzy AHP32220211
Fuzzy ANP0010001
Fuzzy BWM1001002
Fuzzy COPRAS0001001
Fuzzy Delphi0010001
Fuzzy DEMATEL0000011
fuzzy FUCOM-D’Bonferroni1000012
Fuzzy GRA1100002
Fuzzy MARCOS1000001
Fuzzy MULTIMOORA0001001
Fuzzy particle swarm Optimisation PSO0000011
Fuzzy PIPRECIA2000013
Fuzzy SERVPERF2000002
Fuzzy TOPSIS1100136
Fuzzy VIKOR1110014
GAHP1001002
GRA1000001
Hybrid DANP-TOPSIS0001001
Interval AHP1100002
IVPFS0000011
MABAC0001001
MACBETH0010001
MARCOS0000022
MAUT0100001
MCDA-C0000011
MEW0010001
Modified rough AHP0001001
Modified VIKOR0001001
MPI1000001
MULTIMOORA0000011
PROMETHEE11213210
Promethee II0010012
REMBRANDT0001023
ROC0100001
SAW0001034
SMARTER0000011
Stochastic TOPSIS1000001
SWARA-G0110002
TOPSIS23341619
VIKOR2001205
WASPAS0010001

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