## 2 Literature Review
Meanwhile, [PERSON] and [PERSON] in 2007 [4] adapted the Microsoft Excel solver tool for solving the mathematical interpretation of the Holt-Winters method where the initial values were determined by minimizing the forecasting errors. An analytical approach is also proposed by [PERSON], [PERSON] and [PERSON] [31] to quantify and optimize the initial values of the time-series components. Moreover, [PERSON] in 2010 [36] also used the forecast error as an objective function and solved the mathematical interpretation of the Holt-Winters approach (through MS solver) by optimizing the initial values. In addition, while forecasting the short-term electricity demand through the Holt-Winters approach, [PERSON] [37] considers the averages of the early observations as the initial smoothed values of the components. [PERSON] and [PERSON] [38] also take the mean of historical data as the initial values of time-series components. [PERSON] and [PERSON] [39] consider the average of the first day's historical data of their test week as an initial level and the average of the first two days' historical data as the initial growth rate. The initial seasonal components are calculated by averaging the yearly historical data. Meanwhile, [PERSON] et al. [40] average the historical data to estimate the initial values of the time-series components. In order to forecast, the multiplicative HW method needs to undergo an intricate recursive procedure for updating its level, growth rate and seasonal index. The exactitude or appropriateness of this recursion process largely depends on the initial values and the patterns of the historical data [18; 27]. Nevertheless, with the availability of various estimation processes for the initial values as presented earlier, the recent research works consider the stationary means in initiating the recursion process. However, incorporation of initial values in the stationary form is anticipated to affect forecasting accuracy in an adverse way. On the other hand, the computational difficulty of dynamically quantifying and updating the values of level (\(L_{T}\)) by modifying the conventional multiplicative Holt-Winters (CMHW) approach poses a greater challenge. In these situations, an intuitional intervention within a mathematical technique known as a collaborative approach might lead to better performance [3; 41; 42]. In this context, fuzzy logic-based prediction models could aid in quantifying the levels and improving the overall forecasting performance. Nowadays, the fuzzy logic based model is widely applied in various fields of engineering and applied science [43; 44; 45; 46; 47; 48; 49]. For instance, to enhance the wastewater treatment process effectiveness by controlling the volume of dissolved oxygen in the reactor, [PERSON] et al. [50] proposed an archetype of a fuzzy logic-based controller. This proposed predictive controller exhibits a satisfactory performance, usage of the conventional sludge model, and least square technique to define the rules and the parameters, respectively. Besides, the researchers have also found a way to employ the fuzzy logic in their proposed model for enhancing system stability and performance by means of fault detection [51; 52]. Separately, by considering the need of developing an appropriate schedule for satisfying a customer's electricity demand, [PERSON], [PERSON] and [PERSON] [53] proposed a fuzzy inference system (FIS)-based approach to predict the short-term electricity load. In developing their intended fuzzy logic-based model, the authors have followed four successive steps i.e., fuzzification, development of fuzzy knowledge base, construction of the fuzzy inference engine and de-fuzzification of the outputs. Besides, the researchers have also considered five different input parameters, their corresponding membership functions and 37 different fuzzy IF-THEN rules in developing the Mamdani inference system. Thus, they were successful in reducing the mean absolute percent error (_MAPE_) by 5% in comparison to the traditional statistical forecasting approaches.