Modeling Dual-Uncertainty In Sustainable Supplier Selection Using Bipolar Complex Pythagorean Fuzzy Sets

Abstract

Managing sustainability in modern supply chains requires decision-making tools that can accommodate conflicting criteria, uncertain data, and evaluations that involve both positive and negative impacts. To address these challenges, this study develops a new decision-making framework based on bipolar complex Pythagorean fuzzy sets (BCPFSs). The model integrates bipolarity, complex-valued membership degrees, and Pythagorean structures to capture the nuanced interplay of economic, environmental, and social considerations. On this foundation, two aggregation operators—the bipolar complex Pythagorean fuzzy weighted averaging (BCPFWA) and weighted geometric (BCPFWG) operators—are introduced to synthesize multidimensional information while preserving uncertainty and dual evaluations. The applicability of the framework is demonstrated through a case study on green supply chain management (GSCM). Six supplier strategies, ranging from cost-oriented to fully balanced sustainability-focused approaches, are assessed against eight attributes including cost efficiency, product quality, carbon emissions, waste management, technological integration, and social responsibility. The analysis reveals that the balanced sustainability supplier emerges as the most effective choice, consistently ranked highest by both operators. Comparative results with conventional fuzzy aggregation approaches show that the proposed operators provide richer, more stable, and more interpretable rankings, especially when trade-offs between cost and sustainability are present. This research contributes to both theory and practice: it extends the scope of fuzzy decision-making by unifying multiple existing models as special cases, and it offers a practical toolset for organizations seeking resilient and environmentally responsible supply chain solutions. The findings demonstrate that BCPF-based aggregation can enhance strategic decision-making in contexts where sustainability and uncertainty are inseparably linked.