<p>The challenges in decision-making in the selection of combined heat and power (CHP) system are usually typified by conflicting criteria, inaccurate information, and the presence of both positive and negative assessments. The current decision-making models that rely on fuzzy sets (FSs), bipolar fuzzy sets (BFSs), fuzzy rough sets (FRSs) and their variants can only address some of these aspects separately, but they cannot jointly represent bipolarity and rough boundary uncertainty in a single framework. Fruther, up till now, no Schweizer-Sklar aggregation operators (AOs) have been formulated in the framework of bipolar fuzzy rough sets (BFRSs), and no multi-criteria decision-making (MCDM) method has been built using Schweizer-Sklar operators in a BFRSs. These critical research challenges are addressed in this manuscript by developing an MCDM model based on Schweizer-Sklar operators in the framework of a BFRS. The primary contribution of this research is the construction of Schweizer-Sklar operators in bipolar fuzzy rough (BFR) information to combine the data and then apply these operators in the construction of the MCDM approach. The proposed methodology can systematically incorporate Schweizer-Sklar operators, which gives it unprecedented power to address the intricate uncertainties of CHP system selection criteria. The importance of this research can be explained by the detailed examination of CHP system selection for industrial energy requirements, which is a field that is highly uncertain and has rather vague decision criteria. The proposed approach provides not only a more accurate mathematical solution but also creates a new paradigm for solving the multi-criteria problem in various disciplines. The research also shows that it can alter decision-making approaches by a great extent when compared with certain prevailing theories as it offers a more detailed and mathematically rigorous method of handling uncertainty and complexity.</p>