# Knowledge-Based Fuzzy Expert System to the Condition Assessment of Historic Road Bridges
## 3 Results
In Figures 2 and 3 the listed membership functions are shown, where the abscissa axis contains membership functions for fuzzy sets of ratings and structural importance, respectively, and the ordinate axis shows the degree of membership, i.e., the membership of the assigned rating and structural importance, respectively, to each set. The entire calculation for obtaining the component rating was made with the help of _Matlab_. As the procedure for obtaining the rating of each component, and finally the rating of the bridge, is very comprehensive, the detailed calculation for all bridges is not given, but only the final ratings are presented. Hereby, the whole model calculation is presented on the bridge at river Jaruga near Mracaj in Imotski filed, labeled B10. In the group of photographs in Figure 4, the bridge at the river Jaruga near Mracaj in Imotski filed is shown, where damage to the bridge can be easily observed, such as dense vegetation and seepage, cracks in the bridge elements, landslides and falling off parts of the elements. In Figure 5 the elements of the assessment bridge are marked, provided that the group of spandrel walls 2 is not visible because it is on the other (east) side of the bridge. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Superstructure**} & \multicolumn{2}{c}{**Substructure**} & \multicolumn{2}{c}{**Equipment**} \\ \hline
**Bridge** & **Name of the Bridge** & **Arches** & **Spandrel Walls** & **Piers** & **Abutments** & **Fence, Lightening, Payement and Drainage** \\ \hline B1 & Jovica bridge & 4 & 2 & 3 & 2 & 3 \\ \hline B2 & Bridge over the river Matica & 6 & 2 & 5 & 2 & 2 \\ \hline B3 & Bridge in Rastoke & 4 & 2 & 3 & 2 & 3 \\ \hline B4 & Bridge Brvina on the river Vrljika & 4 & 2 & 3 & 2 & 3 \\ \hline B5 & Bridge on Bublin on the river Vrljika & 6 & 2 & 5 & 2 & 3 \\ \hline B6 & Zmijaváki bridge on the river Vrljika & 6 & 2 & 5 & 2 & 3 \\ \hline B7 & Bridge on the stream & 4 & 2 & 3 & 2 & 3 \\ \hline B8 & Bridge Sumet over the channel Jaruga & 3 & 2 & 2 & 2 & 3 \\ \hline B9 & Bridge Jasenovac on the river Jaruga & 3 & 2 & 2 & 2 & 3 \\ \hline B10 & Bridge on the river Jaruga nearby & 2 & 2 & 1 & 2 & 3 \\ \hline B11 & Bridge at the quarry “Lavécvić” & 3 & 2 & 2 & 2 & 4 \\ \hline B12 & Zmrováki bridge & 4 & 2 & 3 & 2 & 4 \\ \hline B13 & Bridge over the river Jadro & 5 & 2 & 4 & 2 & 4 \\ \hline B14 & Bridge at the entrance to the factory & 3 & 2 & 2 & 2 & 3 \\ \hline B15 & Rera/Vetmin bridge & 6 & 2 & 5 & 2 & 3 \\ \hline B16 & Bridge on the river Grab & 5 & 2 & 4 & 2 & 4 \\ \hline B17 & Bridge on the river Kosinac & 12 & 2 & 11 & 2 & 3 \\ \hline B18 & Bridge Blato on the river Cetina & 0 & 0 & 4 & 2 & 4 \\ \hline B19 & Pavác bridge & 7 & 2 & 6 & 2 & 4 \\ \hline B20 & Bridge on Panj & 8 & 2 & 6 & 2 & 4 \\ \hline B21 & Baleki bridge & 3 & 2 & 2 & 2 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Historic road bridges with a total number of elements per component. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Fuzzy Set** & **Linguistic** & **Description** \\
**Value** & & \\ \hline (0, 0, 10) & Extreme bad & The bridge is in extremely poor condition. Parts of the element are eroded or fallen off, cracks of maximum width along the entire element, abundant vegetation and seepage. \\ \hline (0, 10, 20) & Very bad & Cracks of maximum width can be seen on the elements of the bridge, parts of the elements (blocks) are damaged or partially fallen off. Dense vegetation and seepage. \\ \hline (10, 20, 30) & Quite bad & The elements of the bridge contain cracks of maximum to medium width, as well as parts of the elements (blocks). Vegetation and percolation are of considerable intensity. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fuzzy sets of element ratings with linguistic values and description.