# Knowledge-Based Fuzzy Expert System to the Condition Assessment of Historic Road Bridges
## 3 Results
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Fuzzy Set** & **Linguistic Value** & **Description** \\ \hline (20, 30, 40) & Bad & The bridge is in poor condition, several cracks of medium width along the elements, vegetation and seepage are very well visible. \\ \hline (30, 40, 50) & Medium & Multiple cracks of medium to minimum width, vegetation and seepage in medium intensity on the element. \\ \hline (40, 50, 60) & Slightly bad & Parts of the elements (blocks) contain several cracks of medium to minimum width. Mild vegetation and seepage can be seen. \\ \hline (50, 60, 70) & Medium & Element blocks contain multiple cracks of minimum width. Slight vegetation and seepage is present. \\ \hline (60, 70, 80) & Good & Element blocks contain multiple cracks of minimum width. Slight vegetation and seepage is present. \\ \hline (70, 80, 90) & Quite good & The bridge is in a pretty good condition, there are almost no cracks, the vegetation and seepage is of very low. \\ \hline (80, 90, 100) & Very good & There are almost no cracks, vegetation and seepage on the bridge, the colour of the material is a little darker. \\ \hline (90, 100, 100) & Excellent & The bridge is in excellent condition. There is no damage, all elements are in excellent condition, no vegetation and seepage. The colour of the material is in excellent condition. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c} \hline \hline
**Fuzzy Set** & **Linguistic Value** \\ \hline (0, 0, 0,25) & Extreme bad \\ \hline (0, 0.25, 0.5) & Very bad \\ \hline (0.25, 0.5, 0.75) & Bad \\ \hline (0.5, 0.75, 1) & Medium good \\ \hline (0.75, 1, 1) & Good \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fuzzy sets of structural importance of elements with linguistic values. Figure 2: Membership functions of fuzzy sets of elements ratings. Figure 4: Bridge on the river Jaruga nearby Mračaj in Imotski field (figures in order from above left: bridge from east side, bridge from west side, abutment wing, pier, access road, fence). Figure 3: Membership functions of fuzzy sets of elements structural importance. Evaluations of the elements for the bridge components and their structural importance are given below. First, it is started with the component superstructure, which contains 4 elements: arch 1, arch 2, spandrel walls 1, and spandrel walls 2. In Table 4, crisp values of the elements ratings of the superstructure are given, and fuzzy sets to which these values belong are singled out. Fuzzy sets represent fuzzy ratings of elements and each set gets its fuzzy structural importance expressed as the average value of all fuzzy structural importance given by the experts. Additionally, each fuzzy set of element rating values is a description of the condition of the elements at the time of the expert visual assessment. According to the given crisp values of ratings, it can be noticed that two or three conditions are singled out for each element. After rating the elements of the superstructure, and determining their fuzzy values and the average values of fuzzy structural importance of the elements, the total number of combinations of elements in all possible conditions with given structural importance to calculate the final rating of the component is defined. Each component has a different number of combinations, so the algorithm is only applicable to combinations of superstructure elements. What the algorithm will look like depends on the number of elements and their conditions that are singled out based on the rating. The input data a1, a2, b1, b2, b3, c1, c2, d1, and d2 represent the conditions of the elements, so the data a1 and a2 are the conditions for the element arch 1, b1, b2, and b3 are the conditions for the element arch 2, c1