## 5 Fuzzy Expert System  
Expert systems leverage knowledge and inference techniques to address complex problems that typically require human expertise. These systems offer several advantages, including rapid response, enhanced reliability, cost reduction and flexibility [26].  
Numerous studies have explored the application of expert systems in examining different forms of deterioration. For instance, [PERSON] [27] proposed an expert  
Figure 2: Symptoms and types of chemical deteriorations.  
system that utilizes a non-phase if-then algorithm to assess the types of deterioration in reinforced concrete structures. [PERSON] et al. [28] put forward an expert system designed to facilitate the maintenance of reinforced concrete bridges in Greece, acknowledging the inherent uncertainty and ambiguity in the information and decision-making process. In a similar vein, [PERSON] and [PERSON] [29] developed a fuzzy model specifically tailored for ranking the condition of concrete bridge decks.  
In this research, the expert system employed is built upon the principles of fuzzy logic. Unlike traditional binary logic, which categorizes propositions as either true or false, fuzzy logic operates on a spectrum of values, allowing for more nuanced and continuous evaluation [30]. The foundations of fuzzy logic were laid by [PERSON] [31], who introduced the concept in his influential 1965 paper titled \"Fuzzy Sets.\" Fuzzy theory encompasses various approaches that utilize fundamental concepts of fuzzy sets and membership functions. According to [PERSON] [31], membership functions are used to determine the degree to which an element belongs to a set. Unlike crisp sets, where membership is strictly binary, membership degrees in fuzzy sets range between zero and one, allowing for partial membership (Equation (1)). A membership degree of zero indicates that an element does not belong to the set, while a degree of one denotes complete membership. The introduction of fuzzy theory has provided a novel means of expressing and handling uncertainties [32].  
\[\begin{split}\text{m}_{\text{A}}(x):x\in[0,1]\ \ \text{ where :}\\ \mu_{\text{A}}(x)=1\ \ \text{ if }x\text{ is totally in A;}\\ 0<\mu_{\text{A}}(x)<1\ \ \text{ if }x\text{ is partly in A;}\\ \mu_{\text{A}}(x)=0\ \ \text{ if }x\text{ is not in A.}\end{split} \tag{1}\]  
Fuzzy logic employs linguistic terms to represent variables, with each linguistic variable being a fuzzy variable that incorporates uncertainty. Input and output fuzzy variables can be expressed using conditional terms (Equation (2)). For instance, consider the conditional term \"If the room temperature is higher, then the cooler will work at a higher speed.\" In this example, the words \"temperature\" and \"speed\" are linguistic variables, while \"higher\" and \"more\" are fuzzy values that encompass uncertainty.  
\[\text{If }(x\text{ is }\text{ A})\ \text{ Then }(y\text{ is B}) \tag{2}\]  
The fuzzy inference system (FIS) relies on if-then rules to establish relationships between input and output variables. It serves as a simulated model for scenarios involving uncertain input and output data, as classical methods are unable to account for such uncertainty. In this study, the Mamdani method, the most commonly used technique for FIS development, is employed. Unlike the Sugeno method, the Mamdani method can handle input and output uncertainty, enabling a more intuitive and systematic simulation of expert knowledge [31].  
The proposed fuzzy expert system is developed and is implemented in four steps, as follows.