Rough cubic intuitionistic fuzzy soft relation framework for risk identification and hospital selection in breast cancer treatment.

Conventional fuzzy or rough set models struggle to capture the ambiguity, hesitancy, and partial information that are frequently present in healthcare decision-making. To address this challenge, we propose a novel rough cubic intuitionistic fuzzy soft relational framework that combines interval-valued membership, intuitionistic non-membership, and soft binary relations within a harmonious rough set paradigm. The model captures multi-dimensional uncertainty by representing membership, non-membership, hesitation, and boundary approximations simultaneously. To this end, we use soft binary relations, defined by foresets and aftersets, to approximate an internal cubic intuitionistic fuzzy set. Initially, two pairs of rough approximation operators for an internal cubic intuitionistic fuzzy set, concerning foresets and aftersets, and their different algebraic features are examined. Furthermore, a variety of similarity relations between internal cubic intuitionistic fuzzy sets related to soft binary relations are discussed. We develop a decision-making scheme utilizing two algorithms with methodical procedural steps to demonstrate the effectiveness of the proposed framework. A comprehensive real-world breast cancer risk identification and hospital selection case study demonstrates the model's effectiveness, achieving higher diagnostic reliability than classical fuzzy, intuitionistic fuzzy, and rough set approaches. A detailed comparative analysis with specific prevailing techniques reveals that the presented strategy achieves higher decision accuracy and reduced boundary ambiguity across multiple evaluation metrics.