## 3 Method
### Proposed Semi-Supervised Explainable BRBES Framework
** In this step, the input data corresponding to the three antecedent attributes of the rule base--interior space, solar illumination, and interior inhabitance--are transformed into their respective referential values. For interior space, the utility values for low (L), medium (M), and high (H) are set to 10, 85, and 200, respectively. For solar illumination, the L, M, and H values are 0, 0.50, and 1; and for occupancy, they are 0.10, 0.55, and 1, respectively. These utility values are initially set based on the opinions of two energy experts and two civil engineers. To illustrate our proposed framework, an apartment in Skelleftea, Sweden, is considered as a case study. This apartment has an interior space of 142 square meters and is heated with electrical technique. The goal is to predict its hourly energy consumption for 11:00 AM on a Saturday in July. The input values are converted into referential values. For interior space, M = \((200-142)/(200-85)\) = 0.51, H = \((1-0.51)\) = 0.49, and L = 0. For solar illumination, H = 1, M = \((1-1)\) = 0, and L = 0. For occupancy, L = 1, M = 0, and H = 0. **Rule Activation Weight Calculation. ** In this step, the activation weight for each of the twenty-seven rules in the rule base is calculated. The activation weight is influenced by the input values corresponding to the three antecedent attributes. To determine the activation weight (ranging from 0 to 1) of each rule, we take into account factors such as the rule's matching degree, rule weight, the total number of antecedent attributes, and the weight assigned to each antecedent attribute [47]. The mathematical formulations for calculating the matching degree and activation weight of each rule are provided in Equations (A1) and (A2) in Appendix A, respectively. The activation weights of the rules are presented in the last column of Table 5, where Rule No. 12 exhibits the highest activation weight of 0.51 for the given example. **Belief Degree Update. ** Uncertainty arising from ignorance may result in the unavailability of input data for one or more antecedent attributes. To address this issue, the BRBES updates the initial belief degrees of the referential values for its consequent attribute, as outlined in Equation (A3) of Appendix A[46]. In this manner, the BRBES effectively manages uncertainty due to ignorance. **ER-based Inference. ** In this step, we utilize an analytical ER approach to aggregate all twenty-seven rules of the BRBES [64; 65]. The final aggregated belief degree for each of the three referential values of the consequent attribute is calculated using the analytical ER equations, as presented in Equations (A4) and (A5) of Appendix A. The resulting aggregated belief degrees for the referential values H, M, and L of the consequent attribute are 0, 0.73, and 0.27, respectively. Subsequently, the crisp value of energy consumption is determined from these three aggregated belief degrees of the consequent attribute. **Prediction of Consumed Energy. ** The three aggregated belief degrees of the consequent attribute in the BRBES are converted into a single numerical crisp value. Table 6 outlines the calculation procedure for this crisp value, which quantifies energy consumption in kWh. In addition to the belief degrees, the apartment's heating method--either district or electric--is incorporated into the calculation. As noted by [66], electric heating typically results in higher energy consumption compared to district heating. Based on the values presented in Table 6, the final crisp value of energy consumption for the example under consideration is 1.41 kWh, which closely approximates the actual measured consumption of 1.38 kWh. However, as a knowledge-driven approach, the BRBES tends to exhibit lower accuracy compared to machine learning and deep learning models [67]. Therefore, to enhance the accuracy of the BRBES, we focus on integrating learning-based AI techniques with the framework. **Learning AI. ** To improve accuracy of initial BRBES, we conducted its learning with labeled training data.