## 3 Method
### Proposed Semi-Supervised Explainable BRBES Framework
These float values range from 10.00 (minimum interior space) to 200.00 (maximum interior space), with an interval of 0.20, excluding the values of weakly augmented dataset \(fa_{uu}\). Thus, in terms of attribute noise, these values with decimal point address the \"missing or do not know values\" of the antecedent attribute \"interior space\". These floating-point values of the interior space are combined with specific values of solar illumination and interior inhabitance to constitute a new set of antecedent attributes. Against this set of antecedent attributes, we employ a weakly semi-supervised BRBES to predict the value of consequent attribute 'energy consumption' (Figure 1j). Thus, with these predictive values, we assign pseudo-labels, \(pl_{s}\), to the strongly augmented unlabeled dataset. We mathematically show this process in Equation (6):  
\[pl_{s}=BRBES_{wss}(fa_{su},dl_{u},io_{u}) \tag{6}\]  
\[where \begin{cases}fa_{su}=10.00+0.20k,&\text{where k}\in\mathbb{Z},\,0\leq \text{k}\leq 950,fa_{su}\
eq fa_{uu}\\ 0\leq dl_{u}\leq 1&\text{Table 2}\\ 0\leq io_{u}\leq 1&\text{Tables 3 and 4}\end{cases} \]  
Here, \(fa_{su}\) is the strongly augmented unlabeled float values for interior space, and \(\mathbb{Z}\) is the set of integers. In the next step, we evaluate the impact of this strongly augmented pseudo-labeled dataset to reduce the class noise of \(wp\). **Semi-supervised BRBES. ** In this step, we append this strongly augmented pseudo-labeled dataset to the initial labeled and weakly augmented pseudo-labeled dataset. Thus, we formulate an extended dataset to cover maximum possible instances of antecedent attributes to predict energy consumption. Then, we employ the JOPS to optimize the weakly semi-supervised BRBES with this extended dataset (Figure 1k). After this optimization, if the accuracy increases or remains same, the weakly semi-supervised BRBES will transition to a semi-supervised BRBES (Figure 11). Otherwise, we consider that the strong augmentation is noisy and go back to Equation (6) to refine the design of strong augmentation. We mathematically show this transition from weakly semi-supervised to semi-supervised BRBES in Equation (7):  
\[BRBES_{\text{uss}}= \begin{cases}BRBES_{semi-supervised}&\text{if (InfoNCE}_{\text{loss}}(\text{S})\geq\text{InfoNCE}_{\text{loss}}(\text{W})) \\ \text{Equation (6)}&\text{otherwise}\end{cases}  \tag{7}\]  
\[\text{where} \begin{cases}S=JOPS(BRBES_{\text{uss}}(il+wp+sp))\\ W=JOPS(BRBES_{\text{uss}}(il+wp))\end{cases} \]  
Here, \(il\) is the initial labeled training data, \(wp\) is the weakly augmented pseudo-labeled data, and \(sp\) is the strongly augmented pseudo-labeled data. We show the step-by-step transition from initial BRBES to semi-supervised BRBES in Figure 4. Using this semi-supervised BRBES, we predict heating method based crisp value of energy consumption with improved accuracy (Figure 1m), as shown in Equation (8):  
\[ec=BRBES_{semi-supervised}(aa+hm) \tag{8}\]  
Here, \(ec\) is the crisp value of predictive energy consumption in kWh, \(aa\) is the set of three antecedent attributes of the rule base of the BRBES, and \(hm\) is the heating method of the apartment. **Explanation**. To make the predictive energy consumption trustworthy, we provide explanation in support of this predictive output to the user through a user interface (Figure 1n). We provide this explanation in nontechnical human language to enable any layperson to understand it. The rule with the maximum activation weight, which is rule 12 (Table 5) in our present example at hand, serves as the foundation for this explanation. The following is our pattern to provide explanation:  
\"Solar illumination is [e1] in a [e2] [e3], leading to [e4] likelihood for inhabitants to remain inside on a [e5] [e3].