# Knowledge-Based Fuzzy Expert System to the Condition Assessment of Historic Road Bridges
## 3 Results  
To rank historic road bridges according to the priority for reconstruction activity, it is necessary to determine the condition of the bridges at the time of inspection, which examines the mechanical stability and resistance, but also safety for vehicles and pedestrians. The condition of the bridge can be assessed by visual inspection or in-situ testing which can be destructive or non-destructive. For this research, i.e., to assess the condition of historic road bridges, the only visual expert assessment was conducted. First, the scope of the test had to be defined. So, the assessment started from the elements to obtain the rating of the bridge components, and then the overall rating of each bridge, which is also the result of the proposed model (HRBCAI). Each bridge is subdivided into three components: superstructure, substructure, and equipment. How many elements each component has depends on the bridge. However, as these are massive stone bridges, they are characterized by arched construction, so the elements were observed for the superstructure: arches and spandrel walls, for the substructure: piers and abutments, and for equipment: pavement, fence, drainage, and lighting. In Table 1 the total number of elements of each component is given. The spandrel walls are observed in groups. The bridge expert gave the ratings to the elements based on a visual inspection. Structural importance was then assigned by five construction experts based on element ratings. Although these are very experienced experts with rich knowledge and expertise, their opinions (assessments and structural importance) can sometimes be subjective and thus give uncertain and inaccurate estimates. Therefore, as a solution to such a problem, fuzzy logic is imposed, which has been discussed more in the previous subchapter. The beginning of any fuzzy logic starts with defining fuzzy sets. Thus, the experts agreed to take values of ratings from 0 to 100 for the evaluation of the element and distribute their vagueness in 11 sets, to achieve the most accurate evaluation of the component, and finally to obtain a precise rating of the bridge. To each set, a membership function is assigned. The same is done for structural importance which is divided into 5 sets, from 0 to 1. Each defined fuzzy set has linguistic value. The ratings of the elements were assigned a crisp value to single out the fuzzy sets to which that rating belongs. Each singled out the fuzzy set was assigned fuzzy structural importance. Five experts assigned importance to elements using defined fuzzy sets of structural importance. The average value of the experts' assigned structural importance is used for further calculation. In Tables 2 and 3, sets with linguistic values of ratings and structural importance are shown, respectively. Figures 2 and 3 show the assigned membership functions for fuzzy sets of element ratings and structural importance, respectively. The experts opted for a triangular membership function to describe the sets for ratings and the importance of the elements. The experts found the triangular membership function more useful because of the narrow peak of the absolute membership, unlike the trapezoidal membership function where the peak (absolute membership) is presented through the interval. The bridge Blato on the river Cetina has no arches and front walls, but its superstructure is composed of longitudinal and transverse girders and a deck. It is a similar situation with the Bridge on the river Grab, which contains arches and spandrel walls, and a deck, while the Bridge at the entrance to the \"Majdan\" factory, cross beams, and a deck. Furthermore, the defined fuzzy numbers and their belonging linguistic values for the structural importance of elements are given in Table 3. Experts decided to define them in the range from 0 to 1. As already mentioned, since triangular fuzzy sets are defined, each set is assigned a triangular membership function for grades and structural importance.