Anamika Verma, Rajesh Dangwal
Reliability assessment under generalized intuitionistic fuzzy uncertainty has become increasingly important due to its capability to represent incomplete and imprecise information encountered in practical engineering systems. However, many existing reliability measures do not adequately incorporate the combined effects of membership, non-membership, and hesitation degrees into a unified reliability framework. To overcome this limitation, this study introduces a Generalized Intuitionistic Fuzzy Reliability Index (GIFRI) that integrates these three uncertainty measures through an exponential hesitation penalty function. The developed reliability index satisfies important mathematical properties, including boundedness, monotonicity, normalization, and ranking preservation, which are established through theoretical proofs. In addition, the proposed GIFRI is integrated with the Universal Generating Function (UGF) to evaluate the reliability of multi-state systems under generalized intuitionistic fuzzy environments. An illustrative numerical example is presented to illustrate the computational steps, where generalized intuitionistic fuzzy information is transformed into normalized reliability weights and subsequently incorporated into the UGF framework for system reliability evaluation MATLAB-based computational verification and sensitivity analysis confirm the correctness, consistency, and computational effectiveness of the proposed methodology The results indicate that the developed GIFRI–UGF framework provides a mathematically consistent and practical approach for reliability assessment of generalized intuitionistic fuzzy multi-state systems and offers a useful foundation for future extensions to more complex reliability models.