# Utilising Neutrosophic Logic in the Design of a Smart Air-Conditioning System
## 4 Proposed System Design and Simulation
### Neutrosophication  
The proposed framework replaces fuzzy logic statements as predecessors and consequents of the \"IF-THEN\" commands with neutrosophic logic expressions. By transforming brittle inputs using the three membership functions of neutrosophic logic, i.e., truth, falsehood, and indeterminacy, one can create the neutrosophic knowledge base. Inference rules, which support the system's computation capabilities, are one of the core ideas behind the [PERSON] method [39]. These guidelines may be influenced by previous information, observations, and expert insight. Two concepts--the if-then statements and the linguistic variables--make up each inference rule. The ability to make any automated choice as well as the interactions of the input and output are taken into consideration when creating the proposed work.  
In this study, the number of rules depends on the potential membership functions of inputs such as the outdoor temperature, humidity, the number of people inside, the type of activity being performed, and the time of day. However, outputs are things such as temperature, fan speed, and compressor speed. For truth, twenty-three rules are required, but indeterminacy and falsehood require nine rules each, as demonstrated in Tables 2-4. The neutrosophication is the last phase, when we can obtain the precise value of each output. The most popular defuzzification technique we employed in this study is the centre of area approach (COA), and we also acknowledged the centroid technique. With the help of this method, one may locate the fuzzy set's centre and obtain the related crisp value.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Unputs**} & \multicolumn{5}{c}{**Outputs**} \\ \hline
**OTE** & **H** & **T-O** & **T-A** & **TOD** & **Temp.** & **CS** & **FS** \\ \hline Low & Dry & Less & More & Morning & High & Slow & Medium \\ Low & Normal & Medium & More & Morning & Low & Slow & High \\ Very high & Sticky & More & More & Morning & Low & Fast & Low \\ Very high & Sticky & More & Medium & Afternoon & Low & Fast & Low \\ \hline \hline \end{tabular}
\end{table}
Table 2: Rules for truth membership of neutrosophic logic represented as (T-O, T-A).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Variables in the Proposed System**} & \multicolumn{5}{c}{**Membership Functions**} \\ \hline \multicolumn{2}{c}{**TFNs (Triangular Fuzzy Numbers)**} \\ \hline I-1 & Outside temperature (I-Input) & Low & Moderate & High & Very high \\ Range: [0–100\%] & [0–30] & [30–60] & [30–60] & [50–80] & [75–100] & [75–100] \\ \hline I-2 & Humidity & Dry & Normal & Sticky & \\ Range: [0–100\%] & [0–50] & [50–70] & [50–70] & [70–100] & - \\ \hline I-3 & Occupants & Low & Medium & High & \\ Range: [0–8] & [0–4] & [3–6] & [6–8] & [6–8] & - \\ \hline I-4 & Activity & Less & Medium & More & \\ Range: [0–100\%] & [0–40] & [40–75] & [75–100] & [75–100] & - \\ \hline I-5 & TOD & Morning & Afternoon & Night & \\ Range: [0–24 h] & [0–11:30] & [11–17] & [1–17] & [17–18] & [17–24] & - \\ \hline OT-1 (OT-Output) & Temperature & Low & Medium & High & \\ Range: [18–30 °C] & [18–22] & [18–22] & [22–27] & [22–27] & [27–30] & - \\ \hline OT-2 & Compressor Speed & Low & Medium & High & \\ Range: [0–100\%] & [0–40] & [38–70] & [65–100] & - \\ \hline OT-3 & Fan Speed & Off & Minimum & Average & Maximum \\ Range: [0–100\%] & [0–10] & [10–40] & [10–40] & [40–70] & [68–100] & [68–100] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Variable classifications and their membership functions.