## 2 Literature Review
There are six steps to formulating AHP methods [32; 33; 34]:  
First step: problem identification and set up of evaluation standards;  
Second step: setting up the AHP hierarchy;  
Third step: creating matrices for pairwise comparison of the criteria;  
Fourth step: comparison matrices' normalizing;  
Fifth step: calculation of the priority vectors;  
Sixth step: calculation of consistency ratio (CR). Following the abovementioned steps for the pairwise comparison of the criteria, their rankings from each comparison are averaged out and normalized to obtain the relative weight of the criteria, as per Equation (1). \[\text{W}=[(\prod_{i=1,n}\text{R}_{i})^{1/n}]/(\sum_{i=1,n}\left(\prod_{i=1,n} \text{R}_{i}\right)^{1/n}] \tag{1}\]  
where  
R = ranking for each pair of factors;  
n = number of pairs of factors. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Methods** & **References** & **Description** & **Key Features** & **Comments** \\ \hline Analytic network process & [PERSON] and [PERSON] (2018) [23], [PERSON] et al. (2018) [24] & Extension of AHP that models complex decision structures with interdependencies and feedback loops & Incorporates dependence and feedback relationships, super matrix representation & Requires expert knowledge in structuring and modeling the decision problem \\  & [PERSON] and [PERSON] (2018) [23], [PERSON] (2018) [24] & Extension of AHP that incorporates the concept of Pythagorean fuzzy sets and combines fuzzy logic and the AHP & Pythagorean fuzzy subset & Requires expertise in fuzzy logic and fuzzy set theory \\  & & &  
The pairwise comparison was performed for each goal based on one criterion at a time. The rankings from multiple comparisons of goals were combined, similar to criteria, to obtain their weights. The resulting weight of each goal is the dot product of its weight, calculated for each criterion, and the weight of the specific criterion. As the weights (as explained above) are calculated using multiple independent comparisons, there is a chance of inconsistency in the rankings. To consider that issue, the consistency ratio (CR) and consistency index (CI) are calculated for the matrix resulting from multiple comparison at each stage. CR is a measure of variation within the data, derived from the eigen vector of the ranking matrix, while CI is a relative ratio for the CR with the standard randomness index given by [PERSON] (2005) [35]. These values can be determined using Equations (2) and (3). \[\text{CR}=(\lambda-\text{n})/(\text{n}-1) \tag{2}\]  
\[\text{CI}=\text{CR}/\text{RI} \tag{3}\]  
where  
\(\lambda=\text{maximum value of eigen vector for the ranking matrix;}\)  
n = size of the matrix;  
RI = random consistency index, given by [35]. The rankings of criteria and goals are normally taken using the perception or opinion of respondents to a survey [36]. In AHP, a complicated problem requiring decision making is divided into smaller, more manageable components, and each component is assessed in relation to the others. According to their relative importance, the criteria and options are compared pairwise in the conventional AHP. This research proposes a new proportion-based approach for calculating ratings for each event and crash severity. It is a newly developed variant of AHP that evaluates the components using percentage scores of the requirements that each alternative meets, rather than using ratio scales. PBAHP's capability to consider the comparative relevance/occurrence of each element causing traffic crashes is one of its primary features. PBAHP assesses each factor's significance using percentage scores, enabling a more precise evaluation of the elements that contribute to serious collisions. Furthermore, PBAHP is a straightforward approach that is simple to comprehend and use. It is expected that the current methodology can be adopted in a variety of fields for the application of AHP, wherein the available data are extracted from an experiment or field.