# Knowledge-Based Fuzzy Expert System to the Condition Assessment of Historic Road Bridges
## 2 Materials and Methods
### Proposed Model to Historic Road Bridge Condition Rating
The \(CR\) is obtained by dividing the consistency index (CI) by the random consistency index (RCI) proposed by [PERSON] [50]. The CI is obtained by calculating \(\lambda_{max}\). [PERSON] [50] defines the consistency index of the matrix \([A]\) as:  
\[\text{CI}=\frac{\lambda_{max}-n}{n-1} \tag{30}\]  
Step 10. Defining Historic Road Bridge Condition Assessment Index (HRBCAI). The obtained weights are multiplied by the defuzzified values of the component ratings in order to obtain the final rating of the historic road bridge, i.e., to calculate Historic Road Bridge Condition Index (HRBCI) as follows:  
\[\text{IPSPCM}=R_{SP}*w_{SP}+R_{SB}*w_{SB}+R_{EQ}*w_{EQ} \tag{31}\]  
where \(R_{SP}\), \(R_{SB}\), and \(R_{EQ}\) are ratings of bridge components calculated by defuzzification, and \(w_{SP}\), \(w_{SB}\), and \(w_{EQ}\) are relative importance of components. The model of assessing the condition of historic road bridges serves to solve poorly structured tasks at the strategic level of historic road bridges reconstruction planning. The result of the model is the Historic Road Bridge Condition Assessment Index (HRBCAI), which will also be a criterion in the future study needed to rank historic road bridges according to the priority for the reconstruction activity. This index is based on the Bridge Condition Index (BCI) defined by [5] in his dissertation. The BCI index was used to assess the condition of concrete modern bridges. However, the methodology for obtaining the HRBCI has been improved from that outlined for obtaining the BCI, which will be discussed later. Bridges, as key components of the road, degrade over time due to traffic congestion, environmental impact, fatigue, etc. Historic road bridges in the area of SDC \"suffer\" loads that are not foreseen in the design process. Therefore, it is necessary to approach a thorough review and analyze their condition. To ensure continued safety and stability of bridges, periodic field inspections involving visual assessment, non-destructive or partially destructive testing should be performed. Field inspections could decide on the selection of necessary activities such as repairs, renovations, reinforcements, or, if necessary, removal of the bridge, all concerning their condition at the time of the inspection. Bridge managers are required to draw up plans for financing such activities. The development of such plans requires a rational and sustainable approach to organizing and implementing activities related to the planning, design, construction, maintenance, reconstruction, and replacement of bridges. To make a valid decision on all these activities, a sustainable and logical way of assessing the condition of bridges is needed. Assessing the condition of a bridge is very important for any bridge management system. They are based on data that represent the subjective judgment and opinion of a bridge expert. Therefore, the procedure as fuzzy logic can be useful to address vagueness and uncertain judgment. The flow diagram of the condition assessment model of historic road bridges is presented in Figure 1:0 The realization of the model begins with the formation of the expert group consisting of a bridge expert and five experts from other areas of structural engineering. Exclusively visual assessment is used to assess the condition of these bridges. Assessment starts from the elements of bridges (arches, front walls, abutments, pillars, fences, curtains,... ) which are given crisp values of the assessment grade. Before assigning grades to elements, fuzzy sets of grades and structural importance as well as their membership functions are defined. More specifically, estimates of bridges and structural importance are fuzzified. The ratings of the elements are assigned by the bridge expert, and based on his assessment, the other five experts from other areas of structural engineering define the structural importance using determined fuzzy sets.