## 5 Fuzzy Expert System
### Step 1. Fuzzification of Inputs and Outputs  
In this step, the inputs of the system are 21 symptoms of chemical deteriorations (Table 1) and the outputs are 10 types of chemical deteriorations (Table 2), for each of which a range of linguistic changes is defined. In the design of this system, the set of linguistic changes A is used for the symptoms of deteriorations 1 to 11 and all ten types of chemical deterioration, and the set of deteriorations B is used for the symptoms of deteriorations 12 to 21.  
\[\text{A}=\{\text{Low, Moderate, High}\};\ \text{B}=\{\text{No, Yes}\} \tag{3}\]  
A continuous numerical range from 0 to 100 is considered for the symptoms and types of chemical deterioration that are inputs and outputs of the program, with 100 as the maximum value and 0 as the minimum value of the symptom of deterioration.  
A membership function is considered for each range of linguistic changes. The membership functions considered for the symptoms of deteriorations are triangular (Figures 3 and 4), and the Gaussian membership function is selected for the types of chemical deteriorations (Figure 5).  
\begin{table}
\begin{tabular}{c c c} \hline
**Symptoms of Chemical Deteriorations** & **Symbol** & **Associated Fuzzy Set** \\ \hline Concrete strength reduction & DS & [Low, Medium, High] \\ Concrete durability reduction & Du & [Low, Moderate, High] \\ Aggregate pop-outs & PA & [No, Maybe, Yes] \\ Concrete disintegration & Di & [No, Maybe, Yes] \\ Increase in chloride ion concentration & IC & [Low, Moderate, High] \\ Concrete spalling & Sp & [No, Maybe, Yes] \\ Concrete porosity/permeability & IP & [Low, Moderate, High] \\ Interfacial transition zone (ITZ) strength reduction & ST & [Low, Moderate, High] \\ Increase in salt/ion concentration & Sa & [Low, Moderate, High] \\ Increase in sulfate ion concentration & So & [Low, Moderate, High] \\ Irregular cracks & Cr & [Low, Moderate, High] \\ Map cracking & TC & [No, Yes] \\ Alkali-silica gel leakage & JS & [No, Yes] \\ Alkali–carbonate gel leakage & JC & [No, Yes] \\ Efflorescence & Ef & [No, Yes] \\ Steel rust production (corrosion) & CS & [No, Yes] \\ Increase in cement Na\({}_{2}\)O equivalent alkali percentage & AS & [No, Yes] \\ Existence of potentially active aggregate for ASR & SG & [No, Yes] \\ Existence of potentially active aggregate for ACR & CG & [No, Yes] \\ Appearance of the purple region after spraying & Fn & [No, Yes] \\ phenolphthalein (concrete carbonation) & & \\ Structural deformations & Df & [No, Yes] \\ \hline \end{tabular}
\end{table}
Table 1: Fuzzy symptoms of chemical deteriorations.  
\begin{table}
\begin{tabular}{c c c} \hline
**Types of Chemical Deteriorations** & **Symbol** & **Associated Fuzzy Set** \\ \hline Cation exchange reaction–formation of soluble calcium salt & CCA & [Low, Moderate, High] \\ Cation exchange reaction–formation of insoluble and & & \\ non-expandable salt & CIS & [Low, Moderate, High] \\ Cation exchange reaction–chemical attack by magnesium salt & CMg & [Low, Moderate, High] \\ Concrete disintegration from products of expansive & EAS & [No, Maybe, Yes] \\ reactions-sulfate attack due to ingress of external sulfate ion & IAS & [No, Maybe, Yes] \\ Concrete disintegration from products of expansive reactions—ASR & ASR & [No, Maybe, Yes] \\ Concrete disintegration from products of expansive reactions—ACR & ACR & [No, Maybe, Yes] \\ Concrete disintegration from products of expansive & & \\ reactions–hydration of magnesium oxide and crystalline & HMC & [Low, Moderate, High] \\ calcium oxide & & \\ Reinforced concrete corrosion due to chloride ion diffusion & CCI & [Low, Moderate, High] \\ \hline Reinforced concrete corrosion due to carbonation & CSC & [Low, Moderate, High] \\ \hline \end{tabular}
\end{table}
Table 2: Fuzzy types of chemical deteriorations.