Interval-Valued Picture Fuzzy Soft Rough Sets: A New Hybrid Framework for Robust Multi-Criteria Group Decision-Making

This paper introduces a novel hybrid framework called Interval-Valued Picture Fuzzy Soft Rough Sets (IVPFSRS) designed to address complex uncertainty in multi-criteria group decision-making (MCGDM) problems. The model achieves a synergistic integration of three powerful mathematical theories: interval-valued picture fuzzy sets (IVPFS) for representing nuanced, interval-valued degrees of membership, neutrality, and non-membership; soft sets for parameterized problem formulation; and rough sets for handling data granularity and approximation under incompleteness. We formally define the IVPFSRS framework, investigate its fundamental properties and algebraic operations, and develop a comprehensive MCGDM algorithm with explicit weight incorporation to address the critical role of criterion importance. The effectiveness and robustness of the proposed approach are demonstrated through a detailed illustrative example of administrative position selection and a systematic comparative analysis with existing models. Results show that the IVPFSRS framework provides a more powerful, flexible, and logically coherent tool for robust decision making in highly uncertain and information-deficient environments. The proposed framework complements recent advancements in cloud-rough integration for large group decision making while offering unique advantages in parameterized three-way uncertainty representation and structured multi-criteria evaluation.