A novel framework for handling uncertainty: Intuitionistic fuzzy rough soft sets

Intuitionistic fuzzy sets extend traditional fuzzy sets by incorporating degrees of membership, non-membership, and indeterminacy, making them particularly useful in contexts where uncertainty and hesitancy are prevalent. Rough soft sets combine rough sets' approximation capabilities with soft sets' flexible, parameterized approach to managing uncertainty. This study introduces Intuitionistic Fuzzy Rough Soft (IFRS) sets, integrating these advantages to create a robust framework for handling uncertainty, vagueness, and ambiguity in complex decision-making environments. The paper meticulously defines operations, operators, and measures between IFRS sets, establishing their characteristic properties through rigorous mathematical demonstrations. An innovative algorithm is proposed to address multi-criteria decision-making problems within this framework. The algorithm's effectiveness is thoroughly evaluated through comparisons with state-of-the-art algorithms using reputable datasets in medical consultation, agricultural land evaluation, educational support, and sensitivity analysis experiments. The results demonstrate the proposed algorithm's superior performance and robustness in complex decision-making scenarios, highlighting its potential as a valuable practical tool. • Defining a new concept, intuitionistic fuzzy rough soft sets, combining the advantages of intuitionistic fuzzy sets, rough sets, and soft sets to handle uncertainty, vagueness, and ambiguity effectively. • Determining operations, operators, and measures between intuitionistic fuzzy rough soft sets, establishing their characteristics through rigorous mathematical demonstrations. • Proposing a novel multi-criteria decision-making algorithm based on the well-defined intuitionistic fuzzy rough soft framework. • Proving the considerations and effectiveness of the proposed algorithm through comparisons with state-of-the-art algorithms using reputable datasets in medical consultation, agricultural land evaluation, and educational support, along with sensitivity analysis experiments.