A New Approach of Generalized Interval-Valued Neutrosophic Rough Set and Its Application in Medical Diagnosis

This study introduces a framework of Generalized Interval-Valued Neutrosophic Rough Sets (GIVNRSs) to improve the modeling of uncertainty, indeterminacy, and incompleteness in complex data. The framework extends classical rough set theory by incorporating interval-valued neutrosophic elements, providing a richer representation of imprecise information. We establish the fundamental operations of GIVNRSs and explore their theoretical properties in comparison with existing neutrosophic and rough set models. To enhance approximation flexibility, we propose two novel operatorsring sum and ring productwithin the GIVNRS structure. The practical utility of the model is demonstrated through decision-making applications, highlighting its potential to address real-world problems characterized by vagueness and incomplete data.