Road capacity utilization is causally connected with an appropriate level of efficiency and an optimal level of traffic safety. Therefore, in this paper, it is considered the issue of maximum utilization of road capacity through the maximization of the input parameter AADT (Annual Average Daily Traffic), and the minimization of output parameters related to the categories of traffic accidents. It was defined six main road sections, which were evaluated based on seven technooperational criteria using an integrated Multicriteria decisionmaking (MCDM) model. The data refer to buses as a vehicle category. The Improved Fuzzy StepWise Weight Assessment Ratio Analysis (IMF SWARA) method was chosen to determine the weights of criteria, while the road sections were ranked using the Evaluation based on distance from average solution (EDAS). In addition, in one of the stages of applying the model when it comes to AADT, the Bonferroni operator (BFO) is used. The results show that the highest level of safety refers to a main road section with the following characteristics: average AADT, minimal deviation from the speed limit, an ascent of 7% and the lowest number of traffic accidents by all categories. In the paper, it was performed a multiphase sensitivity analysis in order to identify possible differences in results when determining new circumstances.
Risk assessment in road transportation is mainly based on strategic risk assessment. Strategic risk refers to longterm decisions made by institutions that control traffic safety in the areas analyzed. The main focus of researchers is usually related to the causes and consequences of road traffic accidents and the reliability of appropriate infrastructure to reduce risk [1]. The efficiency of a traffic system is also associated with the prediction of traffic flows (AADT), and thus the overruns regarding the daily, weekly, monthly, quarterly and annual prediction. By introducing exogenous factors and dummy variables in the prediction, ensembles with different review periods were created [2]. At the same time, the conducted research on the modeling of road, socioeconomic and land characteristics on AADT, using the method of least squares and geographically weighted regression on ten spatially distributed districts, shows that road density, land use and AADT on the nearest nonlocal road have a significant impact on the AADT of the local road [3]. Additionally, traffic monitoring programs can be adapted for the needs of developing spatial models. The output of these models can be used to assess the impact of land use on active travel rates and, as an input, to assess exposure to the negative effects of traffic safety [4].
By researching the attitudes of a sample of 331 bus drivers over a period of six months, it was shown that the external environment and company management, according to the structural equation, reveal the risky behavior of bus drivers directly and indirectly [5]. Such indicators can provide an empirical basis for road traffic safety interventions. Also, based on a survey of 107 bus drivers in Iran, it was developed a logistic regression model indicating a number of factors (driving older buses, inexperienced drivers, smokers and night drivers) with a higher probability of being involved in traffic accidents [6]. Based on limited research on a driving simulator about the impact of stopping a school bus in relation to surrounding drivers, it was determined a different traffic law awareness status, traffic volume status and initial location status of the bus. The results showed that after the promotion of laws and regulations, the speed of driving is significantly lower, and the number of people complying with the regulations has increased, which positively affects the potential risk [7].
Based on research on traffic infrastructure elements for buses, it was determined that the risk of a traffic accident near bus stops is higher because bus stops are near intersections and side roads, where an accident is more likely to occur, and not because of the design of the elements of traffic infrastructure [8].
The aim of this paper is to create an adequate integrated IMF SWARAEDAS model based on the Bonferroni operator for the ranking of road infrastructure sections for buses as a category of vehicles. This kind of model has just been presented for the first time in the literature, which gives special importance and novelty to this paper as well.
After the introduction, the paper is created through the following sections. Section 2 provides the algorithms of the IMF SWARA method, the EDAS method and the Bonferroni operator which was used to average the AADT for a period of five years. Section 3 presents the definition of input data, their averaging, the formation of an initial decision matrix, and the application of the defined MCDM model in order to obtain results that are also given in this section of the paper. In Section 4, verification was performed by applying the following tests: simulation of new criterion weights through 70 scenarios, testing the influence of matrix size and comparative analysis with other five MCDM methods. The paper ends with concluding considerations and guidelines for the continuation of the research.
Further in the paper, it is presented the applied methodology which consists of IMF SWARA, EDAS and Bonferroni operator, the steps of which are given in detail.
Vrtagić et al. [9] developed the Improved fuzzy SWARA method and it includes the following steps [10]:
Step 1: Defining all the criteria used for decisionmaking, and sorting them in descending order.
Step 2: Using the previously determined ranking, it is identified a relatively smaller importance of a criterion (criterion Cj) in relation to the previous one (Cj−1). This relation, i.e. comparative importance of an average value, is denoted by $\overline{S_j}$. An appropriate TFN scale that facilitates accurate and highquality determining the importance of criteria by IMF SWARA is given in Table 1.
Linguistic Variable  Abbreviation  TFN Scale  
Absolutely less significant  ALS  1  1  1 
Dominantly less significant  DLS  1/2  2/3  1 
Much less significant  MLS  2/5  1/2  2/3 
Really less significant  RLS  1/3  2/5  1/2 
Less significant  LS  2/7  1/3  2/5 
Moderately less significant  MDLS  1/4  2/7  1/3 
Weakly less significant  WLS  2/9  1/4  2/7 
Equally significant  ES  0  0  0 
Step 3: Determination of the fuzzy coefficient $\overline{k_j}$ (1):
Comparative importance of the average value is denoted by $\overline{s_j}$.
Step 4: Determination of the calculated weights $\overline{q_j}(2)$:
$\overline{k_j}$ is a fuzzy coefficient from the previous step.
Step 5: Calculation of the fuzzy weight coefficients by applying Eq. (3):
where, $w_j$ represents the fuzzy relative weight of the criteria $j$, and $m$ represents the total number of criteria.
The Bonferroni and PerezArellano et al. operator [11], [12] was applied in this case in order to calculate the average value of AADT for a period of five years.
where, $e$ is a number of years of the AADT, and $p, q \geq 0$, is a group of positive numbers.
This method was created in 2015 [13]. When solving problems using the EDAS method, the following steps are applied:
Step 1. Defining an initial table in which the characteristics of alternatives according to criteria are presented in a classic way.
Step 2. Calculation of the average value of all criteria:
$x_{i j}$ denotes the value of $i$ alternative in relation to $j$ criteria.
Step 3. Calculation of the positive distance from the average value (PDA) and the negative distance from the average value (NDA), according to the types of criteria:
if B:
In case the criterion is C:
if B:
In case the criterion is C:
Step 4. Determining the weighted value of the sum of PDA and NDA for each alternative:
$w_j$ is the value of criterion importance.
Step 5. Normalizing SP and SN values for all alternatives:
Step 6. Calculation of the average estimate for all alternatives:
Step 7. Ranking the alternatives according to descending assessment values (AS).
This section shows the results of applying the previously developed model with the analysis of influential parameters, characteristics of main road sections (Table 2), as well as the setting of a multicriteria model, the results of determining criterion weights and the ranking of considered sections.
Road sections  Section code  Section length km  Ascent/descent at 1000 m in %  Speed limit (km/h)  Speed deviation from the speed limit  
A1  VrhoviŠešlije I  MI103  14.073  5.00%  80  3.000 
A2  VrhoviŠešlije II  MI103  14.073  1.92%  80  4.000 
A3  RudankaDoboj  MI105  7.405  0.017%  60  1.000 
A4  ŠepakKarakaj 3  MI115  20.95  +1.00%  80  0.100 
A5  Donje CapardeKarakaj 1  MI110  15.35  +3.00%  80  0.100 
A6  Border (RS/FBIH)Donje Caparede  MI110  3.14  +7.00%  80  0.100 
Based on the analysis carried out on six sections of main roads in Bosnia and Herzegovina, Table 2 provides the values of speed limits, as well as deviations from the speed limits for buses. Different lengths of sections combined with values of longitudinal gradients (ascent/descent) were taken by random sampling in empirically obtaining values of deviations from speed limits.
In this paper, it is defined a set of seven criteria, which are marked as follows: C1  ascent/descent at 1000 m in %, C2  deviation from the speed limit, C3  AADT, C4  traffic accidents with fatalities (TAF), C5  TA with seriously injured (TAS. inj.), C6  TA with slightly injured (TAS. inj.) and C7 – TA with material damage (TAMD).
Figure 1 shows the AADT for a period of five years. The last available data relating to the interval 20132017 were used. The average values of AADT using the Bonferroni operator are shown, too.
By analyzing the third criterion C3, the average values of AADT in the fiveyear period are approximate and do not exceed the value of 6500 [veh/day], which is not the case on the section RudankaDoboj, where there is a significant deviation of AADT from the values on other sections.
The available data for traffic accidents, taking into account all categories, are in the interval from 2015 to 2019 and are shown in Figure 2. For their averaging, the geometric mean was applied and that value was further included in the MCDM model.
In Figure 2, showing the number of accidents from 2015 to 2019, the highest number of traffic accidents is with material damage, and the lowest with fatalities, so finding the arithmetic mean of the number of accidents on given sections cannot be taken subjectively. That is why the given values are classified according to the severity of consequences and according to the years of observation.
Based on defining a list of criteria according to their importance, determining comparative values using the scale mentioned above, and applying Eqns. (1)(3), it was obtained the weight values of the criteria, shown in Table 3.
Sj  Kj  qj  wj  DF  
C4 


 1.000  1.000  1.000  1.000  1.000  1.000  0.218  0.228  0.240  0.228  
C5  1/4  2/7  1/3  1.250  1.286  1.333  0.750  0.778  0.800  0.164  0.177  0.192  0.177  
C2  0  0  0  1.000  1.000  1.000  0.750  0.778  0.800  0.164  0.177  0.192  0.177  
C3  2/9  1/4  2/7  1.222  1.250  1.286  0.583  0.622  0.655  0.127  0.142  0.157  0.142  
C1  2/9  1/4  2/7  1.222  1.250  1.286  0.454  0.498  0.536  0.099  0.113  0.129  0.113  
C6  2/9  1/4  2/7  1.222  1.250  1.286  0.353  0.398  0.438  0.077  0.091  0.105  0.091  
C7  2/9  1/4  2/7  1.222  1.250  1.286  0.274  0.319  0.359  0.060  0.073  0.086  0.073  
SUM  4.164  4.392  4.587 
As can be concluded from the obtained results, the greatest importance is given to TAs with fatalities, which is expected considering the set goal related to determining the level of safety of the considered sections. The second and third criterion according to importance refer to C5 – TASer. inj. and C2  deviation from the permissible speed limit, which have equal values. The least significant criterion in the given circumstances is C7 – TAMD. The obtained weights are further implemented in the continuation of the MCDM model.
Based on the previously collected and processed data, it was formed an initial decision matrix (Table 4), which for the first two criteria represents the quantified values of decisionmakers' assessment, and the other criteria represent the average values based on the previous explanation.
C1  C2  C3  C4  C5  C6  C7  
A1  7  3  4484.25  0.8  2.6  3.8  9.6 
A2  3  4  4484.25  0.8  2.6  3.8  9.6 
A3  1  1  13293.31  1.4  5  14.6  49.8 
A4  2  0.1  6148.48  1.4  5.8  19.4  53.4 
A5  4  0.1  3503.25  0.8  3.2  6.4  21.2 
A6  5  0.1  4053.14  0.00  0.4  1  2 
MIN  MIN  MAX  MIN  MIN  MIN  MIN 
Applying the methodology of the EDAS method, i.e. Eqns. (5)(12), taking into account the weighting procedure with the weights obtained by applying the IMF SWARA method, the final results are shown in Table 5.
SPI  NSI  NSPI  NSNI  ASi  Rank  
A1  0.054  0.346  0.098  0.067  0.083  5 
A2  0.074  0.371  0.136  0.000  0.068  6 
A3  0.304  0.234  0.555  0.368  0.462  3 
A4  0.220  0.278  0.401  0.251  0.326  4 
A5  0.186  0.069  0.339  0.813  0.576  2 
A6  0.548  0.087  1.000  0.765  0.883  1 
The values obtained using the IMF SWARAEDAS model rank the Border (RS/FBIH)Donje Caparede section with the highest, and the VrhoviŠešlije II section, with a descent of 1.92%, with the lowest potential risk, according to the criteria specified. The section with the highest AADT value is rated with an average rank, according to the specified methodology of the ranking model.
This section consists of verification tests. First, a simulation of criterion weights was carried out through 70 scenarios (Figure 3) in order to determine possible deviations from the originally obtained results, while taking into account new circumstances related to the importance of input indicators.
The simulation through 70 scenarios was performed by reducing the weights of each criterion in a range of 595%, while the values of the other criteria were proportionally increased depending on each scenario individually. Based on these values, 70 models were reproduced again, and their results are presented in Figure 4.
In Figure 4, it can be seen that in certain scenarios there is a change in the ranking of particular road sections, with the fact that the best ranked section does not change the first position regardless of the importance of the criteria, which implies that it has the best performance by far. A1 changes its position in scenarios S12S15, while it keeps its original position in others. The situation with A2 is interesting since it is mostly in the last place, but in S19 and S20 it reaches the second position, which means that the second criterion, deviation from the speed limit, plays an important role, more precisely, when its value is reduced to a minimum, A2 improves its ranking. This is logical, given that A2 has the worst value according to the second criterion. Other alternatives change their rank in certain scenarios, but not too much. The next verification test involves analyzing the impact of the initial matrix size, the results of which are shown in Figure 5. This test implies that in each scenario the worst alternative is eliminated and the model is reproduced again.
On the left side of Figure 5, the values of the alternatives are shown, and on the right, the ranks for each new model, which consists of one alternative less compared to the previous model. The only change that occurs in this analysis is in the second scenario, when the total number of alternatives is reduced to four. Then A3 takes the fourth instead of the third position, i.e. exchange the position with A4.
In the last test, it was performed a comparative analysis with MARCOS [14], CRADIS [15], [16], WASPAS [17], ARAS [18], SAW [19].
The comparative analysis (Figure 6) shows that there are certain deviations in the ranks, but which are generally highly correlated with the original model.
The paper analyzes the risk assessment for the movement of buses on the given road sections, which are included as potential alternatives. By applying MCDM, it was analyzed seven criteria, and each of them influenced the potential definition of reference values. Section A6 was assessed as the riskiest section, and section A2 as the least risky for bus movement, according to predefined criteria.
It is shown that the section RudankaDoboj, regardless of AADT, does not represent the best nor the worst ranked section from the aspect of traffic risk, according to the mentioned criteria for bus movement. By sensitivity analysis, testing was carried out through 70 scenarios. By applying different sensitivity analyses through simulated criterion weights, it was determined that the ranking would be variable, in terms of certain sections for the movement of BUSes.
In guidelines for further research, it is especially necessary to note that with an increase in the number of sections, it can be determined potential groups of risky sections for the movement of buses, which is especially important for reducing traffic risk in public mass movement of passengers.
“Conceptualization, Ž.S. and M.S.; methodology, Ž.S.; validation, M.S., E.S. and B.B.; formal analysis, M.S.; investigation, B.B.; data curation, Ž.S.; writing—original draft preparation and M.S, Ž.S.; writing—review and editing, M.S. and E.S; supervision, E.S.; project administration, B.B.. All authors have read and agreed to the published version of the manuscript.”
The data supporting our research results are included within the article or supplementary material.
The authors declare no conflict of interest.