## 3 Results
### Fuzzy Protforms and Fuzzy Rules  
In this section, we describe the linguistic protoforms which define temporal restrictions from the raw audio prediction in order to provide a coherent recognition of daily audio \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Trainable** & **Learning** & **Millions of Instructions** & **Evaluation** \\  & **Parameters** & **Time** & **(MI)** & **Time** \\ \hline Model CNN & 1.7 M & 96 min & 230.4 \(\times\) 10\({}^{3}\) MI & 2.53 s \\ + MFCC & & & & \\ Model CNN & 23.3 M & 207 min & 496.8 \(\times\) 10\({}^{3}\) MI & 2.81 s \\ + LM & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Trainable parameters, learning time, millions of instructions (MI), and evaluation time. \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Accuracy** & **Precision** & **Recall** & **F1-Score** \\ \hline Scene 1 & 0.95 & 0.97 & 0.95 & 0.96 \\ Scene 2 & 0.99 & 0.99 & 0.98 & 0.98 \\ Scene 3 & 0.97 & 0.98 & 0.97 & 0.98 \\ Scene 4 & 0.96 & 0.97 & 0.96 & 0.96 \\ Scene 5 & 0.91 & 0.93 & 0.91 & 0.92 \\ Scene 6 & 0.92 & 0.92 & 0.90 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Classification metrics from real-time case study evaluation for each scene. events. The FTWs and fuzzy quantifiers were defined with membership functions defined by TS and TL functions (listed in Abbreviations). In Tables 6 and 7, we describe the membership functions for quantifiers and FTWs, together with the protoforms for each audio event, which define the temporal restrictions for normality. The impact of filtering the raw audio events from the recognition model was evaluated for the real-time scenarios (offline evaluation was not possible due to not providing a stream of daily events). Beyond the encouraging results described in the previous section, in these scenes, we identified the recognition of scarce audio events which are not related to the correct occurrence of events. In Figure 6, we demonstrate the ground truth and raw audio events predicted in a timeline for the four scenes, including the detection of false-positive events. In Table 8, we describe the false positives and negatives computed from the time interval detection of home events using (i) raw processing and (ii) fuzzy temporal restrictions. Computing the false positives and negatives of time intervals has been described as a relevant metric for detecting events in activity recognition regardless of their duration [10]. The evaluation of these audio events in temporal windows using protoforms, which determine a minimal restriction for recognition, has enabled filtering the most spurious occurrences, as well as defining a degree of adherence between 0 and 1 to the protoform. The use of fuzzy temporal restrictions provides an encouraging method, reducing false positives from the raw audio recognition from 24 occurrences to 2 occurrences while including only 2 false negatives. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Description in Natural Language** & **Type** & \(\mathbf{\mu_{T}}\) \\ \hline _some_ & \(Q_{k}\) & \(TR(s_{i}^{l})\) [0.25, 1] \\ _most_ & \(Q_{k}\) & \(TR(s_{i}^{l})\) [0.5, 1] \\ _for a short time_ & \(T_{j}\) & \(TS(\Delta t_{i})\) [\(-6\) s, \(-3\) s, \(3\) s, \(6\) s] \\ _for a while_ & \(T_{j}\) & \(TS(\Delta t_{i})\) [\(-12\) s, \(-6\) s, \(6\) s, \(12\) s] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Membership functions for FTWs and quantifiers defined for the protoform \(V_{r}\)\(T_{j}\)\(Q_{k}\).