## 5 Application of Our Proposed Approach
### Case Study-1: Demand Data for Transformer Tanks
#### 5.1.3 Development of Level Prediction Model
\tag{17}\]  
where, \(i_{1}\), \(i_{2}\), \(i_{3}\), \(i_{4}\), \(o_{1}\) are the variables related to the level, growth rate, seasonality, actual demand and predicted level, respectively. The triangular fuzzy numbers for the input variables i.e., the demand (\(D_{T}\)), level (\(L_{T}\)), growth rate (\(b_{T}\)), seasonal parameter (\(SN_{T}\)), and the output variables i.e., the predicted level (\(L_{Tpred}\)) are given in Table 3 by characterizing the definition as well as the properties presented in the work of [PERSON] and [PERSON] (2018). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable Name** & **Fuzzy Numbers** & **Variable Name** & **Fuzzy Numbers** \\ \hline \multirow{8}{*}{Level, \(L_{T}\)} & E. Low = (13, 14, 15; 1) & E. Low = (0.8, 0.82, 0.84; 1) \\  & V. Low = (14.75, 16, 17; 1) & V. Low = (0.837, 0.86, 0.88; 1) \\  & Low= (16.75, 18, 19; 1) & Low = (0.875,0.9, 0.92; 1) \\  & Avg= (18.75, 20, 21; 1) & Seasonal parameter (\(SN_{T}\)) & Avg = (0.9175, 0.94, 0.96; 1) \\  & High= (20.75, 22, 23; 1) & High = (0.9575, 0.98,1; 1) \\  & V. High = (22.75, 24, 25; 1) & V. High = (0.9975, 1.2, 1.4; 1) \\  & E. High = (24.75, 26, 27; 1) & E. High = (1.375, 1.6, 1.8; 1) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fuzzy numbers for the input and output variables. However, to demonstrate this fuzzification process through mathematical interpretation [42; 57; 68], the membership functions for the input and output variables are worked out by using Equation (7). Figure 15(a)-e as provided in Appendix A illustrate all the developed membership functions in the MATLAB platform. However, for fuzzification and/or articulation of the membership functions, the associated values of the coefficients of the entire input and output variables are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**Linguistic Variables**} & \multirow{2}{*}{**Type**} & \multicolumn{3}{c}{**Coefficient**} \\ \cline{3-5}  & & & **C1** & **C2** & **C3** \\ \hline \multirow{5}{*}{\(L_{T}\)} & E. Low & Triangular & 13 & 14 & 15 \\  & V. Low & Triangular & 14.75 & 16 & 17 \\  & Low & Triangular & 16.75 & 18 & 19 \\  & Avg & Triangular & 18.75 & 20 & 21 \\  & High & Triangular & 20.75 & 22 & 23 \\  & V. High & Triangular & 22.75 & 24 & 25 \\  & E. High & Triangular & 24.75 & 26 & 27 \\ \hline \multirow{5}{*}{\(b_{T}\)} & E. Low & Triangular & 0.1 & 0.15 & 0.2 \\  & V. Low & Triangular & 0.175 & 0.25 & 0.3 \\  & Low & Triangular & 0.275 & 0.35 & 0.4 \\  & Avg & Triangular & 0.375 & 0.45 & 0.5 \\  & High & Triangular & 0.475 & 0.55 & 0.6 \\  & V. High & Triangular & 0.575 & 0.65 & 0.7 \\  & E. High & Triangular & 0.675 & 0.75 & 0.8 \\ \hline \multirow{5}{*}{\(SN_{T}\)} & E. Low & Triangular & 0.8 & 0.82 & 0.84 \\  & V. Low & Triangular & 0.837 & 0.86 & 0.88 \\  & Low & Triangular & 0.875 & 0.9 & 0.92 \\  & Avg & Triangular & 0.9175 & 0.94 & 0.96 \\  & High & Triangular & 0.9575 & 0.98 & 1 \\  & V. High & Triangular & 0.9975 & 1.2 & 1.4 \\  & E. High & Triangular & 1.375 & 1.6 & 1.8 \\ \hline \multirow{5}{*}{\(D_{T}\)} & E. Low & Triangular & 13 & 14 & 15 \\  & V. Low & Triangular & 14.75 & 16 & 17 \\  & Low & Triangular & 16.75 & 18 & 19 \\  & Avg & Triangular & 18.75 & 20 & 21 \\  & High & Triangular & 20.75 & 22 & 23 \\  & V. High & Triangular & 22.75 & 24 & 25 \\  & E. High & Triangular & 24.75 & 26 & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Coefficients of membership functions for variables.