Decision-Making under Uncertainty with Bipolar Complex n,m-Rung Orthopair Fuzzy Sets: A Water Crisis Application

Abstract

Decision-making in complex and uncertain environments often involves handling multidimensional, conflicting, and partially contradictory information. While existing fuzzy frameworks—such as bipolar, n,m-rung orthopair, and complex fuzzy sets—address specific aspects of uncertainty, none fully capture bipolarity, complex-valued membership, and flexible n,m-rung
representation simultaneously. To address this gap, this study introduces the bipolar complex n,m-rung orthopair fuzzy set (BCn,m-ROFS), a unified framework capable of representing positive and negative evaluations alongside complex-valued uncertainties with adjustable n and m parameters. Within this framework, two novel aggregation operators—BCn,m-ROF weighted averaging (BCn,m-ROFWA) and weighted geometric (BCn,m-ROFWG)—are developed to integrate multi-dimensional attribute information efficiently, while maintaining discriminative power and computational feasibility. The proposed approach is applied to multi-attribute decision-making problems, illustrating its capability to rank alternatives consistently and interpretably under varying conditions. Comparative analyses with traditional fuzzy models demonstrate that BCn,m-ROFS-based operators offer superior stability, ranking discrimination, and adaptability in uncertain decision environments. Sensitivity studies further confirm the robustness of the approach, highlighting practical considerations for extreme parameter settings. Overall, the BCn,m-ROFS framework provides a flexible, theoretically grounded, and computationally practical methodology for decision support, enabling more informed and balanced choices in scenarios characterized by complex, bipolar, and uncertain information.