A Novel Approach for the Assessment of Logistics Performance Index of EU Countries

1 Introduction

In modern business conditions, a competitive and efficient logistics system has become imperative in the development and creation of advantages on the regional, and especially on the global market. An adequate level of competitiveness in logistics performance has a positive effect on both the business results of an individual company and the overall logistics efficiency of the country in which the company operates. The developed countries of the world are aware of the positive trend of development and investment in logistics, and through a large number of strategies and policies, they strive to improve this area as much as possible. High-quality logistics performance has a positive impact on the volume of international trade. On the other hand, countries with poor logistics infrastructure, as well as low-quality logistics service, can represent an obstacle in the international supply chain. As a result, such countries are often, to a greater or lesser extent, excluded from certain international flows, and thus, their economic and financial growth and development stagnate. For this very reason, it is crucial for countries to constantly monitor, measure, and compare their logistics performance with the logistics performance of other countries in order to find solutions for their own growth and progress in the field of logistics, supply chain (Kouchaki Tajani et al., 2022; Sahoo & Goswami, 2024), and logistics services (Adabavzeh & Nikbakht, 2022). For the adoption of any action plan or policy, such as infrastructure investments or changes in national regulations and laws, an in-depth assessment of the country’s logistics performance is necessary, resulting in a clear and comprehensive set of parameters that evaluate the quality of logistics performance. To achieve a more efficient logistics system, particular attention should be paid to the logistics performance index (LPI), which facilitates the identification of the state in the field of logistics in all countries in the world. The LPI is a set of qualitative and quantitative indicators that help build a country’s logistics profile. It is calculated by the WB and is an indicator of the quality of the country’s logistics environment. The LPI results can be used to compare countries, but also at the level of research within one country, making it a comprehensive international tool for comparison, measuring logistics performance, and achieving facilitation in international transport cooperation.

Due to many advantages of fuzzy set theory (Kabgani, 2023) and the wider application of fuzzy Multiple-Criteria Decision Making (MCDM) methods (Barati & Fanati Rashidi, 2022; Wang et al., 2023) in this article, a novel F-ROV algorithm was developed for the evaluation of potential solutions and, in this specific case, for ranking the LPI of EU countries.

1. The subject of the research in this article is the analysis of the state of logistics in countries of the European Union from the aspect of LPI scores. The focus and main analysis are based on the 2023 results, which are available in the World Bank reports.

2. The aims of the research are the development and application of a subjective–objective MCDM model for determining the values of weighting criterion coefficients, and the evaluation of EU countries based on LPI scores. In the article, three methods for determining the weights of the criteria were applied: Entropy, Criteria Importance Through Intercriteria Correlation (CRITIC), and Method based on the Removal Effects of Criteria (MEREC). According to the classification, these methods belong to objective methods to define the weights of criteria, while F-ROV is a method of a subjective nature in this article because it is based on a certain evaluation of the decision maker.

3. One of the most important problems of LPI evaluation is the equal treatment of influential factors, which can lead to insufficiently precise rankings. At the core, solving this problem is one of the main motivations for creating such a model in this article.

4. Special emphasis is on the importance of sensitivity analysis. The results obtained can help in understanding and improving logistics performance, which can ultimately lead to improvements in international trade and cooperation between countries.

In addition to the introductory considerations, the article consists of the following sections. Section 2 shows the importance of measuring and monitoring the LPI, and the application of different MCDM approaches for their ranking. Section 3 includes a detailed description of the F-ROV algorithm with an emphasis on the normalization procedure. Also, it is emphasized that three objective methods were used to determine factor weights and that they were converted into TFN. Section 4 presents the results, which include a detailed description of the application of the novel fuzzy approach. In Section 5, verification tests are performed, including testing the influence of the change in factor weights, analysis with other approaches, changing the size of a decision matrix, and calculating the correlation of the ranks of alternative solutions. Finally, concluding considerations are given with a clear direction for improving the LPI assessment methodology.

2 Literature Review

In this section, we present a review of previous research related to the logistics performance of countries, their monitoring and measurement, as well as their importance and impact on the economy. In addition, the importance of the application of methods and models of multi-criteria decision-making in the evaluation of alternatives, i.e., the ranking of the results of the logistics performance quality of countries, was pointed out. Logistics includes a large number of processes, activities, functions, as well as participants, which must be coordinated in a way that allows all parties participating in the implementation of logistics services to fulfill their requirements. According to that many various models have been created and used for optimization logistics problems, to increase efficiency in any stage of the supply chain or logistics network, solve internal activities in logistics companies in literature etc. (Baharisaravi & Hasan Zadeh, 2020; Dabić-Miletić & Raković, 2023; Saeedi et al., 2023; Stević et al., 2023; Stanimirović et al., 2023; Pajić & Andrejić, 2023). The conditions prevailing in the global market require companies to constantly improve in order to maintain their competitive position. In order for companies to be able to work on improving their performance, it is necessary to monitor and record the results of the processes, activities, and functions they implement. In addition to individual performance indicators for each company, the results at the level of the country in which the company operates are also extremely important.

The LPIs of countries can be found in the data calculated and published by the WB since 2007. World Bank data on LPI values represent the most comprehensive international tool for measuring and comparing logistics performance (Aytekin et al., 2023; Üre et al. 2023). Measuring logistics performance and understanding its indicators are more important today than ever before in the context of major changes in the global market that have occurred since 2018, mainly due to the COVID-19 pandemic, which has caused major disruptions in the receipt and shipment of goods. In order for countries to be able to cope adequately with new changes in the market, it is necessary to understand, measure, and monitor logistics performance, both their own and the logistics performance of countries in the region and throughout the world (Arvis et al., 2023). Poor logistics performance is an obstacle to trade and foreign direct investment and, therefore, an obstacle to economic growth and development. To develop a logistics competitive advantage, governments must assess the current logistics system at the country level and identify which subsystems need to be optimized, developed, created, or completely eliminated through policies and initiatives (Jhawar et al., 2017). Adequate analysis of logistics performance can help countries improve the efficiency of freight transport, and help identify those countries that can be helpful in overcoming their own obstacles and shortcomings through cooperation (Ojala & Çelebi, 2015).

As already pointed out, to achieve high-quality logistics performance, it is necessary to constantly monitor and measure it. Measurement and evaluation of logistics performance is successfully implemented using various methods and integrated models of multicriteria decision-making (MCDM). Thus, for example, in their research, Isik et al. (2020) apply SV and MABAC methods within an integrated MCDM model for the analysis and evaluation of logistics performance in 11 selected countries of Central and Eastern Europe. The fact that the ranking results obtained by applying the model are the same as the ranking results of the World Bank suggests that the applied model is consistent and reliable to use. Biswas and Anand (2020) compare the LPI results of BRICS countries (Brazil, Russia, India, China, South Africa) and G7 countries (Canada, France, Germany, Italy, Japan, United Kingdom and USA) using an integrated PSI and PIV model. Based on the research results, the authors came to the conclusion that the developed G7 countries are more competitive than the BRICS countries in terms of quality of logistics performance. The new methodology for measuring the logistics performance of OECD countries (The Organization for Economic Cooperation and Development) involves the integration of CRITIC, SAW, and Peters’ fuzzy regression method, and was applied in the article by Çakır (2016) and is proved to be a suitable alternative approach in assessing logistics performance of the countries. Yildirim and Mercangoz (2020) also considered the assessment of the LPI results of OECD countries in their research. Ulutaş and Karaköy (2021) integrate the grey SWARA and grey MOORA methods in evaluating the logistics performance of countries in transition. Infrastructure was determined as the most important criterion, and the best-ranked country in transition was Serbia. Özceylan et al. (2016) analyzed and assessed logistics performance in the provinces of Turkey using the AHP-TOPSIS and ANP-TOPSIS models, in which a total of 16 geographic and economic indicators were observed. The authors came to the conclusion that the methodology used provides the possibility of analyzing the impact that the observed indicators have on the quality of the country’s logistics performance, as well as the possibility of creating a map of the country’s logistics performance using a GIS system. In the research by Mercangoz et al. (2020), the authors try to eliminate the uncertainty that inevitably occurs due to the nature of problems that require multi-criteria decision-making. In this sense, they use grey system theory in combination with multi-criteria decision-making methods, i.e., form an integrated grey numbers-COPRAS (COmplex Proportional Assessment) model, and conclude that it can be effectively used to assess the LPI scores of countries.

The study by Yu and Hsiao (2016) presented an alternative Meta-DEA–AR approach intended to assess the efficiency of the logistics performance index of certain countries, which also takes into account differences in the level of income of these countries. The results of the study indicate that the final ranking of the LPI results of the countries obtained by the proposed alternative model is largely comparable to the results of the World Bank ranking. Mešić et al. (2022) apply an integrated CRITIC-MARCOS MCDM model to evaluate the LPI results of the Western Balkan countries. Rezaei et al. (2018) evaluated the importance of each of the six criteria used in the calculation of the final LPI scores, using the BWM (Best Worst Method). They came to the conclusion that although weights have only a slight influence on ranking due to the correlation between LPI indicators, they can influence the formation of different policy priorities in the calculation of LPI values. In the study by Çalık et al. (2022), a large number of MCDM methods were integrated: AHP (Analytic Hierarchy Process), FAHP (Fuzzy AHP), PFAHP (Pythagorean fuzzy AHP), TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), VIKOR (Višekriterijumska Optimizacija i Kompromisno Rešenje, in Serbian), CODAS (Combinative Distance-based Assessment), and BCM (Base Criterion Method), with the aim of pointing out the importance of precise determination of criterion weights, and that changes in criterion weight values significantly affect the final evaluation results. Ulutaş and Karaköy (2019) obtained the weighting coefficient values by integrating the subjective method – SWARA, and the objective method – CRITIC, while they used the PIV method to evaluate EU countries. In that way, they tried to balance the differences in the final ranking of the alternatives that occur in relation to the different values of the weighting coefficients of the criteria. The research by Stević et al. (2022) is another research in which the integrated CRITIC-MARCOS model confirmed the significant influence of the values of the weighting coefficients of criteria on the final ranking of solutions. Namely, in the research, the Balkan countries were evaluated, and then, 36 new scenarios were formed as part of the sensitivity analysis with changed values of the weighting coefficients of the criteria. The results obtained showed that the final ranking of the solutions changed depending on the extent of the change in the values of individual criteria.

Regarding the review analysis of many different studies related to evaluation countries according to LPI score, it can be concluded that no universal model can help decision-makers make precise decisions involving influencing factors from the economic system. It should be emphasized that a novel approach related to the extension of the ROV method with TFN, which facilitates the precise evaluation of a larger set of alternative solutions, has been developed as the solution to solve research gaps.

3 Methods

The flow diagram of research and development is shown in Figure 1. Research flow has been divided into four main stages that are represented separately. The first stage consists of four activities, while the second and third have three. The last stage has five steps and two substeps for sensitivity analysis.

Figure 1

Diagram flow of developed methodology.

In the first stage, recognizing the need for performing such research, we have processed the World Bank report for the 2023 year. After that, we selected 27 countries of the EU for mutual comparison regarding LPI and processed their LPI score. The second stage represented the development of the MCDM model for the assessment of EU countries according to the LPI score. Three steps are to form the MCDM model, developing an algorithm for the fuzzy ROV method, and transform data from the World Bank report into TFN. In the next phase, the first criteria weights were obtained using three objective MCDM methods, and after that converted to TFN to apply the developed F-ROV method in a precise way. The last represents performing verification tests.

4 Results

To evaluate the LPI, the latest report of the World Bank report has been used, and its ratings for all EU countries are presented in Table 1. Although it is already a well-known fact, it should be noted that the LPI is evaluated based on six criteria (Hadžikadunić et al., 2023): customs (C₁), infrastructure (C₂), ease of arranging shipments (C₃), quality of logistics services (C₄), tracking and tracing of consignments (C₅), and timeliness, i.e., delivery of shipments within scheduled time (C₆).

It should be emphasized that for the purpose of determining the weighting coefficients of the six factors on the basis of which the LPI ranking was performed, three methods were applied. CRITIC, MEREC, and Entropy, and the results given in Table 2 were obtained.

Using equation (1), the fuzzy weights of the criteria are obtained, and then, they are used in the F-ROV method, obtaining the following values:

After that, it is necessary to form a fuzzy initial matrix, which is shown in Table 3. The LPI score from the World Bank report was converted using a linguistic scale with 9 variations that are transformed into TFN. Linguistic scale is as follows: Extremely poor (EP) – (1, 1, 1); Very poor (VP) – (1, 1, 3); Poor (P) – (1, 3, 3); Medium poor (MP) – (3, 3, 5); Medium (M) – (3, 5, 5); Medium good (MG) – (5, 5, 7), Good (G) – (5, 7, 7), Very good (VG) – (7, 7, 9); Extremely good (EG) – (7, 9, 9).

EU countries have an LPI score interval of 2.7–4.3 (because the lowest score from the World Bank report is 2.7, and the highest is 4.3), and when we take into account a scale of nine levels, we get intervals of 0.2. The initial matrix for the F-ROV method is defined by transforming the values of Table 1 as follows: LPI score values 2.7–2.8 = (1, 1, 1); 2.9–3.0 = (1, 1, 3); 3.1–3.2 = (1, 3, 3); 3.3–3.4 = (3, 3, 5); 3.5–3.6 = (3, 5, 5); 3.7–3.8 = (5, 5, 7), 3.9–4.0 = (5, 7, 7), 4.1–4.2 = (7, 7, 9) and 4.3 = (7, 9, 9).

The normalized F-ROV matrix (Table 4) is obtained by applying equations (2)–(7), and all criteria are modeled with the desired maximum value.

In the normalized matrix, the values ℜ j and ℝ j are first calculated, and for C1, they are ℜ 1 = ( 7 , 7 , 9 ) and ℝ 1 = ( 1 , 1 , 1 ) in order to calculate the values κ i j , and ς j : κ 11 = ( 4 , 4 , 6 ) = ( 5 − 1 , 5 − 1 , 7 − 1 ) , ς 1 = ( 6 , 6 , 8 ) = ( 7 − 1 , 7 − 1 , 9 − 1 ) . Then, the final normalized fuzzy values are obtained by applying the expression: ϑ 11 = ( 1.50 , 1.67 , 2.00 ) = 1 + 4 8 , 1 + 4 6 , 1 + 6 6 .

It should be noted that for equal values in the initial fuzzy decision matrix, it is not mandatory to have equal values in a normalized fuzzy matrix. The example for this case is alternative A25 according to the C1 and C4 criteria. This depends from ℜ j and ℝ j values which are for A25 as follows: ℜ 1 = ( 7 , 7 , 9 ) , ℜ 4 = ( 7 , 7 , 9 ) , and ℝ 1 = ( 1 , 1 , 1 ) , ℝ 4 = ( 1 , 3 , 3 ) .

κ 25 ( 1 ) = ( 2 , 2 , 4 ) = ( 3 − 1 , 3 − 1 , 5 − 1 ) , ς 1 = ( 6 , 6 , 8 ) = ( 7 − 1 , 7 − 1 , 9 − 1 ) . Then, the final normalized fuzzy values are obtained by applying the expression: ϑ 25 ( 1 ) = ( 1.25 , 1.33 , 1.67 ) = 1 + 2 8 , 1 + 2 6 , 1 + 4 6 .

κ 25 ( 4 ) = ( 0 , 0 , 4 ) = ( 3 − 3 , 3 − 3 , 5 − 1 ) , ς 1 = ( 6 , 6 , 8 ) = ( 7 − 1 , 7 − 1 , 9 − 1 ) . Then, the final normalized fuzzy values are obtained by applying the expression: ϑ 25 ( 4 ) = ( 1.00 , 1.00 , 2.00 ) = 1 + 0 8 , 1 + 0 4 , 1 + 4 4 .

The formation of the weighted normalized F-ROV matrix is performed using equation (9), and the values are given in Table 5.

By completing the F-ROV algorithm, the final results presented in Table 6 are obtained. It is important to emphasize that equations (11) and (12) are not applied in this case since all criteria are benefit.

By completing the calculation procedure of the F-ROV method, which is shown in detail above, the final results are obtained. In general, compared to the World Bank report, there is some conformity, but there is no situation where several countries share the same position, which is the contribution of the research. Finland, Germany, Denmark, The Netherlands, and Belgium represent the top five countries among the 27 observed within the EU network. In comparison to World Bank report results, Finland kept the first position while applying the F-ROV method Germany, Denmark, and the Netherlands are not in the same position; then, Germany is in the second place, Denmark in third, and the Netherlands in fourth, while in WB report all are in the second position (considering only EU countries). Also, Belgium, Austria, and Sweden are in third position in the WB report, while in the MCDM model, they are in the fifth, sixth, and seventh positions, respectively.

5 Verification Tests

5.1 Sensitivity Analysis

In a large number of studies (Švadlenka et al., 2023; Wiȩckowski & Sałabun, 2023), it has been proven that changing the initial values of input parameters plays an important role in the final ranking of alternative solutions. Consequently, in this section, 60 scenarios were created that define new values of input indicators. This specifically means that the reduced values of all six parameters are in the range of 5–95%, depending on the scenario. The values of the first factor were modeled in S1–S10, the second in S11–S20, and so on until the last factor in S51–S60. The newly defined values of the input parameters are shown in Figure 2. This practically means that the first criterion in S10 has been reduced by 95%, and its value is only (0.008, 0.010, 0.011) compared to its initial value (0.153, 0.198, 0.215). The values of other parameters increase proportionally.

Figure 2

Newly defined factor weights.

In accordance with the previously defined new values of the input indicators, it is necessary to reapply the F-ROV method in all 60 scenarios in order to obtain new rankings of the EU countries on the basis of the LPI assessment. As expected, the results are sensitive to changes in the initial values of the criteria, which is particularly expressed by a large set of potential solutions, as shown in Figure 3.

Figure 3

The influence of changing the initial criterion values on the ranking of alternative solutions.

As can be noticed, there is a large number of scenarios (55) in which there is a change in the ranking of the alternatives, at least to the smallest possible extent. In only five scenarios, there is no change in ranks (S1, S11, S31, S32, and S33) since the smallest value reductions (5–25%) occur in them. It is important to emphasize that there are countries that do not change their original ranking in any scenario, which confirms that the weights of the criteria in their ranking do not play any role, namely A8, A14, A15, A22, and A26, which are in ninth, 16th, 17th, 18th, and eighth places, respectively. When it comes to the best-ranked EU countries, depending on the decrease in the importance of the criteria, there are changes in the ranks. Finland maintains the first position in a total of 56 scenarios, which is about 93%. The only negative impact on its ranking is the ease of arranging shipments as the third criterion. By drastically reducing the value of this criterion, Denmark takes the first position, because according to this criterion, it has the lowest score, and if the importance of this criterion is reduced to a minimum, the importance of this country, i.e., the rank, is increasing. In general, regardless of any changes in factor values, it can be found that Finland, Denmark, and Germany are at the top of the list.

Additionally, we have performed a sensitivity analysis with averaging criteria weights using the Bonferroni operator (Radovanović et al., 2023; Tešić et al., 2023).

As can be seen in Table 7 there is no change (absolute values of difference between the original values obtained here) in the ranks of countries, but slight changes have been made in the final values for all countries. The difference between the original values and those obtained here are presented as absolute values, respectively: 0.034, 0.038, 0.026, 0.021, 0.034, 0.031, 0.035, 0.033, 0.029, 0.016, 0.025, 0.029, 0.013, 0.021, 0.026, 0.025, 0.020, 0.028, 0.036, 0.040, 0.028, 0.022, 0.020, 0.025, 0.028, 0.033, 0.039.

Table 7

Results obtained by the F-ROV method and Bonferroni operator for w _j

	T i +			Crisp value	EU country	Sorting
A1	1.417	1.781	2.449	1.831	Austria	6
A2	1.458	1.792	2.498	1.854	Belgium	5
A3	0.956	1.198	1.654	1.233	Bulgaria	23
A4	0.988	1.203	1.718	1.253	Czech Republic	22
A5	1.512	1.835	2.573	1.904	Denmark	3
A6	1.195	1.458	2.099	1.521	Estonia	13
A7	1.537	1.892	2.613	1.953	Finland	1
A8	1.375	1.612	2.363	1.697	France	9
A9	1.243	1.549	2.162	1.600	Greece	10
A10	0.954	1.131	1.650	1.188	Croatia	26
A11	1.169	1.455	2.017	1.501	Ireland	15
A12	1.253	1.501	2.152	1.568	Italy	11
A13	0.921	1.134	1.519	1.163	Cyprus	27
A14	1.125	1.408	1.928	1.448	Latvia	16
A15	0.999	1.364	1.707	1.361	Lithuania	17
A16	1.123	1.586	1.924	1.565	Luxembourg	12
A17	0.958	1.184	1.595	1.215	Hungary	25
A18	1.063	1.196	1.772	1.270	Malta	20
A19	1.463	1.792	2.507	1.856	Netherlands	4
A20	1.501	1.842	2.583	1.909	Germany	2
A21	1.169	1.458	2.017	1.503	Poland	14
A22	0.963	1.364	1.635	1.342	Portugal	18
A23	0.992	1.177	1.664	1.227	Romania	24
A24	1.005	1.198	1.720	1.253	Slovakia	21
A25	1.046	1.202	1.770	1.271	Slovenia	19
A26	1.370	1.680	2.386	1.746	Spain	8
A27	1.465	1.744	2.511	1.825	Sweden	7

5.2 Comparison with Other Approaches

In this section of the article, as recommended by a large number of researchers (Biswas et al., 2023; Ranjan et al., 2023), a comparison analysis with other methods is performed in fuzzy form. F-MARCOS, F-SAW, and F-WASPAS are applied to verify the results obtained, which is shown in Figure 4.

Figure 4

Comparison with other approaches.

The results obtained with the F-ROV method provide excellent results, which is confirmed in this comparison analysis with three other MCDM methods in fuzzy form. This statement is manifested through the change of only six ranks out of a total of 27, which is negligible because it is a change of only one or two positions. Those are the alternatives: A1 (F-MARCOS and F-SAW,), A3 (F-MARCOS, F-SAW, and F-WASPAS), A4 (F-MARCOS, F-SAW, and F-WASPAS), A18 (F-MARCOS, F-SAW, and F-WASPAS), A25 (F-MARCOS, F-SAW, and F-WASPAS) and A27 (F-MARCOS and F-SAW). It is also necessary to state that the top five countries do not change their position.

5.3 Matrix Resizing

In these studies that involve a large set of potential solutions for evaluation, the stability of the proposed model is often tested with a reduction in the size of the initial matrix. A total of 25 were formed, whereby the weakest component or alternative was eliminated and the procedure was repeated. Figure 5 shows the results of the EU countries based on the LPI assessment when reducing the size of the initial fuzzy matrix.

Figure 5

Influence of matrix size change on values and ranks.

In general, a conclusion can be drawn about the variability of the developed F-ROV method, since it is necessary to emphasize that there are changes in the final results when the size of the matrix is changed. In particular, most alternative solutions do not change position, but, e.g., Germany and Denmark change their positions in some sets, while Finland is always ranked best. For example, Germany is in second place in the original set, while in some sets (S11, S16–S24), it is in third position. A similar situation exists with Denmark, which changed its position in the same sets, but Denmark grew from third to second places. Other changes refer to the rise or fall of some alternatives for a single position, which may be negligible in relation to the total number of countries representing alternative solutions.

5.4 Calculation of Correlation

Since there are changes in the ranks when the values of input factors change, and in the comparative analysis, the correlation of the ranks with the SCC (Božanić et al., 2023) and WS (Więckowski et al., 2023) coefficients was tested, which is shown in Figures 6 and 7, respectively.

Figure 6

Correlation in sensitivity analysis.

Figure 7

Correlation in comparative analysis.

Previously, we have stated that there is variability in the ranks of alternatives when the weights of input indicators are changed. Taking this into account, it is necessary to determine to what extent there is a correlation compared to the initial solution. Both calculated coefficients show an extremely high degree of correlation since the average values are almost identical, SCC = 0.994 and WS = 0.993, while the minimum correlations are the following: SCC = 0.974 and WS = 0.946. Such coefficients show an almost complete correlation.

The correlation of the initial results and the comparative analysis show an almost complete correlation on average. The complete correlation is as follows: F-ROV with F-MARCOS and F-SAW: SCC = 0.993, WS = 0.999, F-ROV with F-WASPAS: SCC = 0.991 and WS = 1. The lowest SCC is with F-WASPAS due to the changes for alternatives A4 and A17 for two positions.

6 Conclusion

To create an original fuzzy ROV algorithm, data from the latest World Bank report published in 2023 for EU countries and their LPI scores according to six influential factors were used. The last report underwent certain changes in the aspect of methodology, since domestic performance was eliminated, which is a novelty. One of the most important problems of LPI evaluation is the equal treatment of influential factors, which can lead to insufficiently precise rankings. The greatest contribution of this article can be seen through the creation of a unique F-ROV approach to evaluate the logistics performance index of EU countries. From the social aspect, the contribution is manifested by indicating the need to define a methodology for treating the six factors on the basis of which the LPI is assessed and the World Bank report is formed. It is necessary to implement different weights that can be changed in real time and depending on different reports. The results show consistency with the current report when it comes to the top three countries, while other analyses show that there is a variation in the ranks and a deviation from the initial rank. The contribution of this research and the implementation of the defined model is reflected in a comparison with the World Bank report in which many countries share the same position, which is not the case in this article. Due to the applied model, precise rankings are defined for each country, and there is no division of the same position. Apart from contributing to determining criteria weights from the current aspect of the WB report, one of the limitations is not including experts from EU territory to assess criteria because it is a very difficult task. The second limitation has been related to considering only one year of LPI score.

Future research is related to the estimation of LPI by applying one of the MCDM models in different forms, such as integration with plithogenic numbers (Martin et al., 2022), pentagonal neutrosophic numbers (Mohanta & Toragay, 2023), neutrosophic trapezoidal numbers (Bhat, 2023), single-valued neutrosophic sets (Qiu et al., 2023), and single-valued neutrosophic uncertain linguistic variables (Ahmed Mohammed Zubair, 2023) for different regions and areas. Additionally, it is proposed to introduce the weights of LPI evaluation criteria, and this should be achieved through extensive research that would involve surveying all experts who evaluate LPI and apply some of the averaging operators to determine the final weights.