TODIM method with unknown weights under t-arbicular fuzzy environment for optimal gate security system selection

This study introduces the t-arbicular fuzzy (t-AF) set, an extension of the t-spherical fuzzy set, to enhance decision-making in complex environments. The research focuses on the theoretical foundation of the t-AF set, encompassing the development of algebraic operations and comparison rules. In addition, we propose novel aggregation operators (AOs), including the t-AF weighted average (t-AFWA) and t-AF weighted geometric (t-AFWG) operators. Key properties such as idempotency, monotonicity, and boundedness of these operators are thoroughly examined. Furthermore, distance measures are formulated alongside their essential characteristics and special cases. To address multi-criteria group decision-making (MCGDM) problems under t-AF environment with unknown weight information, the tomada de decisao interativa multicriterio (TODIM) method is integrated with the criteria importance through an intercriteria correlation (CRITIC) approach. Finally, the proposed methodologies are validated through a case study on selecting the optimal gate security system, demonstrating their effectiveness and applicability in real-world scenarios.