Bipolar complex q-rung orthopair fuzzy aggregation operators for enhanced decision-making in uncertain environments

TL;DR

This paper introduces a new fuzzy framework for better decision-making in uncertain situations by combining multiple fuzzy logic techniques.

Contribution

The novel BCq-ROFS framework unifies bipolarity, complex fuzzy structures, and q-rung orthopair fuzzy logic for enhanced decision-making.

Findings

BCq-ROFS-based operators provide more stable and interpretable rankings in decision-making.

The framework demonstrates robustness and scalability in sustainable livestock farming applications.

Abstract

Effective decision-making in uncertain and complex environments requires managing multidimensional, conflicting, and partially contradictory information. Existing fuzzy extensions—such as bipolar, q-rung orthopair, and complex fuzzy sets—address only parts of this uncertainty: bipolar sets handle positive and negative evaluations, q-rung orthopair sets allow flexible weighting of membership and nonmembership, and complex fuzzy sets capture phase-dependent or oscillatory information. However, none of these frameworks alone can simultaneously manage all these aspects. To overcome these challenges, this study introduces a bipolar complex q-rung orthopair fuzzy set (BCq-ROFS), which integrates bipolarity, complex membership structures, and q-rung orthopair fuzzy logic into a unified framework. Two aggregation mechanisms—BCq-ROF weighted averaging (BCq-ROFWA) and BCq-ROF weighted geometric (BCq-ROFWG) operators—are developed to effectively combine bipolar and complex fuzzy data across multiple attributes while maintaining a manageable computational cost. The framework applies to a multi-attribute decision-making problem in sustainable livestock farming, a domain characterized by conflicting objectives, resource limitations, and environmental–economic trade-offs. Results reveal that BCq-ROFS-based operators provide more stable, interpretable, and discriminative rankings than traditional fuzzy approaches. Comparative and sensitivity analyses confirm the robustness and scalability of the method, demonstrating improvements in decision accuracy and practical relevance.

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