A robust multi-criteria supplier evaluation in supply chain management using interval-valued bipolar q-fractional...

Supplier evaluation in supply chain management involves uncertainty, conflicting expert opinions, and criteria with both positive and negative aspects. Traditional fuzzy models cannot simultaneously handle interval uncertainty, bipolar reasoning, and fractional control. To address this limitation, we propose the interval-valued bipolar q-fractional fuzzy set model, which integrates bipolar fuzzy sets (to capture positive and negative membership degrees), interval-valued fuzzy sets (to handle expert imprecision), and q-fractional fuzzy sets (to flexibly control the balance between membership and non-membership degrees). We define the fundamental operations of the model and examine their algebraic properties. Two aggregation operators-the interval-valued bipolar q-fractional fuzzy weighted averaging operator and the interval-valued bipolar q-fractional fuzzy weighted geometric operator-are developed to aggregate such information while preserving idempotency, monotonicity, and boundedness. A systematic ranking procedure applied to a supplier evaluation problem demonstrates the model's effectiveness in handling conflicting, interval-based assessments. Comparative and sensitivity analyses further reveal that the proposed model provides stable rankings and reliably identifies the best alternative across different parameter settings, confirming its robustness and practical applicability in multi-criteria decision-making for supply chain management.