As discussed in the introduction, it is important for AHP to solve road safety issues for sustainable traffic safety; thus, we applied the Analytic Hierarchy Process (AHP) for the assessment of nominated driver behavior criteria affecting road safety. The primary step of the methodology was to construct a hierarchy structure for the driver behavior criteria and sub-criteria. A driver behavior questionnaire survey was used as a tool to collect driver behavior data from three driver evaluator groups. Furthermore, the procedure involved to construct the pairwise comparison matrix (PCM) of criteria and scale the matrix based on relative scale measurement. After the measurement of the eigenvector of the criterion, the consistency ratio was computed. The next step was to calculate the composite priority (overall weights in the entire hierarchy). The last step was to rank the alternatives for each level and detect the agreement level among the evaluator groups. Finally, the overall rank for each criterion for all evaluator groups was highlighted by implementing the geometric mean technique.
2.1. Sample Characteristics
The AHP questionnaire survey was designed to enumerate the driver behavior factors associated with road safety. The questionnaire was used as a tool in a personal interview with three car driver groups in Budapest city, Hungary. The first driver group (Group A) contained foreign divers having a Hungarian driver license with considerable driving experience. It was noted that significant regional differences exist, reflecting perhaps the individualities related to the mentality and history of each region; these differences should play an important role in planning safety campaigns and policies [
39]. Foreign drivers in Hungary were observed to have a specific behavior such as failing to yield to the person on your right, which is a cause of accidents. A driver’s license can be issued to foreign citizens in Hungary who have stayed for 6 months in Hungary before the issuance of the driver’s license. The second group (Group B) involved experienced drivers with high driving experience. It was observed in a study that increasing driving experience and exposure to traffic increases the level of driving skills with less traffic violations and accidents [
40]. The third group (Group C) included young drivers with less driving experience. Young people are overrepresented in traffic crashes, with most of the drivers being young men [
41,
42,
43]. The study was illustrated for 35 randomly selected participants for each group. These participants were sought to provide linguistic judgement data based on the AHP questionnaire.
The questionnaire survey was based on two parts: The first part aimed to collect demographic data about the participants and results were tabulated in
Table 2. The results showed the mean and standard deviation (SD) values of each observed characteristics. We used digits (1, 0) for statistical evaluation purpose to describe some characteristics such as gender and driver occupation. Moreover, the important noticeable results are that group A contained foreign drivers which have a mean value of 1 for gender which means that they are all males. Also, group B contained experienced drivers which have a mean value of 1 for driver occupation which means that they all have jobs. The importance of selected groups for analysis has been discussed in the above paragraph. The second part aimed to explore and study the driver behavior criteria for road safety as discussed in the results and discussion section.
2.2. Pairwise Comparison (PC)
The experts estimated the relative measurement between the criteria and the alternatives using pairwise comparison (PC) proposed by Saaty in 1977 [
44]. The questionnaire survey was arranged according to the PCM-s, and binary comparisons were performed from decision options for examined criteria. In creating a binary comparison matrix, each element weight was compared with another element in the structure using Saaty’s eigenvector method. The principal eigenvector of the matrix exhibited the maximum eigenvalue of six which is the biggest matrix in the hierarchical structure as presented in
Table 3. It is obvious that this can be extended to any size-consistent PCM. Thus, the principal eigenvector of consistent PCM-s can be easily calculated [
45] and characterizes the matrix elements perfectly. However, in AHP, the evaluators most likely do not evaluate PCM-s consistently by the provided Saaty-scale (
Table 4), a judgment from the scale is a ratio indicating how many times the dominant factor is more important than the dominated one.
For experiential PCM-s: reciprocity is indeed fulfilled for every PCM,
where
provided. However, the consistency is most likely not fulfilled for empirical matrices. The consistency criterion:
Participants were asked to indicate how often they committed each of the examined driver behavior factors based on a Saaty scale as shown in
Table 4.
2.3. The AHP Approach
The analytic hierarchy process (AHP) is a mathematical device in multi-criteria decision making which designs the decision factors in a hierarchic problem structure [
46]. AHP was widely used to make efficient and effective decisions for decision-making problems for multiple fields like civil engineering, transport engineering and industrial engineering [
47,
48,
49,
50]. The AHP method helps the analyst not only to identify the key factors, but also to determine the allocation of resources and consider different tangible and non-tangible preferences. By using AHP, decisions can be made using weights based on subjective pairwise relative comparisons through multilevel hierarchical structures. AHP is a systematic and comprehensive method to solve multi-criteria decision problems and avoid inconsistencies in the decision-making process. The use of the application is illustrated below.
Despite the empirical matrices filled by the evaluators are generally not consistent, in the eigenvector method the calculation of the eigenvector coordinates is the same as for consistent matrices. Because of this, Saaty invented the consistency check in AHP that ensures that all matrices meet the consistency criterion of acceptable inconsistency.
where CI is the Consistency Index and
is the maximum eigenvalue of the PCM, while, m represents the number of rows in the matrix. However, CR can be determined by the following equation:
where RI is the average CI value of randomly generated PCM of the same size (
Table 5).
In the AHP method, the acceptable value of Consistency Ratio (CR) is CR < 0.1.
In the first level of the structured hierarchical model, the elements of were filled by the different evaluator groups in order to compare among C1, C2 and C3.
The evaluators filled total matrices in such a way: four (3
3) matrices (one (3 × 3) matrix in level 1 + 2 (3 × 3) matrices in level 2 + one (3 × 3) matrix in level 3) as shown in
Table 6, one (2
2) matrix in level 2 as shown in
Table 7, and one (6
6) matrix in level 3 as shown in
Table 8.
The constructed PC of the m × m matrix A corresponding to the eigenvalue of A is the set of all eigenvectors of A corresponding to .
If
is a consistent square matrix, then the equivalent equation in standard form will be
The eigenvectors make up the null space of
. When we know the maximum eigenvalue
of the consistent matrix
, the eigenvector could be found
For aggregating the evaluators’ answers, the most popular aggregation procedure for the geometric mean was employed [
51]. If “
h” evaluators take part in the procedure, an aggregated matrix is to be created as:
where
denotes entries, in the same position (
), of PCM-s, filled in by the
-th evaluators.
Afterwards, the right-side eigenvector is to be computed by Equation (7) for the aggregated matrices, and final weight scores are gained by multiplying the eigenvector coordinates with the respective coordinates from the previous level of the hierarchy.
Sensitivity analysis enables in understanding the effects of changes in the main criteria on the sub-criteria ranking and helps the decision maker to check the stability of results throughout the process.
2.4. Kendall’s Agreement Test
The need of ranking the factors is very familiar in management, engineering, education, medicine, finance, and politics, in which cases new products, new positions, new elections public or private services are ranked by the public, experts and decision makers [
52,
53,
54]. However, the natural question is how much the given rankings are in concordance with different groups. To answer this question, the well-known measure, Kendall’s coefficient of concordance (W), was proposed by Kendall and Smith in 1939 [
55]. W is a normalization of the statistic of the Friedman test, which is considered as a non-parametric statistic technique and can be used for a set of criteria to highlight the agreement level among different raters [
56]. For the current study, the authors used Kendall’s W technique to highlight the agreement degree (the concordant degree) between the different driver groups for each level in the hierarchal structure. Kendall’s concordance degree (W) ranges from 0 (no agreement) to 1 (complete agreement), however, the values’ interpretations between 0 and 1 are presented in
Table 9.
The calculation process starts by aggregating the ranking of the factor i throw the following equation:
where
is the aggregated ranking of the factor
i,
is the rank given to factor
i by the evaluator group
j, and
n is the number of rater groups rating
m factors.
Then, calculating
, which is the mean of the
values.
where
K is the sum-of-squares statistic deviations over the row sums of ranking
.
Following that, Kendall’s “W” statistic is between (0 and 1), and it can be obtained from the following equation:
After implementing the equation, the outcome will estimate the concordance degree among the different rater groups.