This study presented a comprehensive multi-attribute decision-making framework founded on bipolar complex intuitionistic fuzzy numbers (BCIFNs) to enhance decision reliability under conditions of uncertainty and dual (positive-negative) evaluation. First, new operational laws were formulated for BCIFNs, providing a rigorous mathematical foundation for developing two aggregation mechanisms: the bipolar complex intuitionistic fuzzy weighted average (BCIFWA) and the bipolar complex intuitionistic fuzzy weighted geometric (BCIFWG) operators. These operators were systematically derived to ensure logical consistency, robustness, and suitability for handling uncertain, imprecise, and bipolar information. Building on these operators, a structured multi-attribute decision-making methodology was proposed to evaluate alternatives across multiple conflicting attributes. The approach was applied to a real-world case study on waste-to-energy (WtE) and circular economy solutions, focusing on identifying the most sustainable strategy for integrated waste management. Six WtE alternatives were assessed across environmental, economic, and social dimensions. The analysis revealed that incineration with energy recovery emerged as the most effective solution, offering a balance of high energy recovery, substantial waste volume reduction, and technological reliability. A comparative analysis with existing fuzzy decision-making methods highlighted the superior ranking stability and adaptability of the proposed BCIFWA and BCIFWG operators, particularly in complex evaluation scenarios with bipolar uncertainty. The results demonstrated the framework's flexibility, scalability, and enhanced decision precision, contributing to both the theoretical development of fuzzy multi-attribute decision-making and the practical advancement of sustainable waste management and circular economy strategies.