## 3 Method
### Analytical Hierarchy Process (AHP)  
Introduced by [PERSON] in 1980, the analytic hierarchy process (AHP) provides a mechanism for switching the criteria rating into weights [4; 42]. AHP is an effective and powerful tool for multi-criteria decision-making approaches. In fact, it is a powerful technique for solving complicated problems that may have correlations and interactions among different goals. When using in multi-criteria problems, AHP breaks down these problems into multiple levels of hierarchy. The goal or objective seats in the top level. Intermediate levels include the criteria and sub-criteria, and the lowest level can provide alternatives. AHP then develops priorities among all the criteria and sub-criteria within each level of the hierarchy [43; 44]. The basis of AHP can be both experts' judgments and predetermined measurements. Experts are interviewed, and pair-wise comparison judgments are applied to pairs of criteria. Eventually, priorities will be determined. AHP is easy to apply and helps engineers obtain the final ranking from the individual evaluations, and finally, select an optimal alternative [45]. Because of these features, AHP has been used in bridge engineering in the past decades. Generally, the AHP can be included in the following steps [46]:  
1. Constructing the pair-wise comparison judgment matrix. 2. Determining the weight of decision elements. 3. Controlling the compatibility index. The purpose of this study is to present a simple, applicable methodology for the health monitoring and prioritizing of bridges. This methodology works based on calculating the bridge condition index (BCI). For the determination of BCI, the methodology uses AHP. In cases where AHP is used for decision making, a proper hierarchy tree should be designed. This hierarchy tree has different levels depending on the type of problem under investigation. As mentioned earlier, the first level of this tree is goal or objective. In this study, the goal is to determine the BCI of the bridge. In intermediate levels, first, criteria are located. These criteria are eight indices affecting the quality of a bridge, including structural index, hydrology and climate index, safety index, bridge performance index (load impact), geotechnical and seismic index, strategic importance index, facilities index, and traffic and pavement index. Sub-criteria are set in the next level. The sub-criteria, in fact, are sub-indexes of eight indexes of the previous level. Figure 3 shows the hierarchy tree of this research. In this work, the problem is to calculate BCI. For solving this problem, the authors must provide the relative importance of all indexes and sub-indexes. The relative importance values depend on weights which are measured using the AHP method. AHP is an analytical method that allows making appropriate decisions by considering qualitative, quantitative, and mixed criteria. This process is based on a dual comparison system [47]. For this reason, a questionnaire (Appendix A) is designed and distributed among experts. The experts' group comprises several specialists and advisors involved in the maintenance and reinforcement of bridges, also, university processors with relevant expertise. In this questionnaire, firstly, experts are asked to determine the relative importance of eight indices of Figure 3. Table A1 was designed for this purpose. In each cell of Table A1, experts assigned a value between 0 and 10 based on their technical experience and expertise. In fact, this table is a dual comparison between all indices. In this table, if a row index outweighs a column index, experts assigned a value between 1 and 10. If the column index outweighs the row index, a value between 0 and 1 was assigned by experts. Of course, the value of 1 was used at the diameter of the table. Table 6 shows the final results. In fact, the numbers  
Figure 3: Hierarchy tree in this study. in Table 6 are the average of experts' viewpoints.