Through the integration of matrix theory with sets of intuitionistic fuzzy hypersoft variables, the Matrix-based Intuitionistic Fuzzy Hypersoft Decision Framework (MIFHDF) is presented in this research. The MIFHDF is designed to improve decision-making systems that face many qualities. As a result of the incorporation of innovative ideas and approaches, the framework provides a comprehensive solution for the management of unclear decision-making processes. MIFHDF is a sophisticated approach that leverages matrix operations to analyze and evaluate complex decision scenarios. subsequently does this by extending standard intuitionistic fuzzy sets from hypersoft sets and fuzzy sets. In order to put an emphasis on the practical usability and effectiveness of matrix-based methodologies in addressing real-world decision issues, the theoretical foundation of the framework has been rigorously constructed. Based on the employment of intuitionistic fuzzy hypersoft sets and matrix theory, MIFHDF offers decision-makers a strategy that is both structured and systematic, allowing them to navigate complex choice landscapes that contain numerous qualities. The one-of-a-kind insights and analytical methodologies that are presented in this study pave the way for future advancements in the field of decision-making systems, particularly in circumstances that are characterized by ambiguity and a wide variety of criteria.

Keywords :

Matrix theory; Intuitionistic fuzzy hypersoft sets; Decision-making systems; Multiple attributes; Matrix-based framework; Real-world applications.