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• Propose a hybrid IVIF framework to evaluate the EMW disposal modes. • Develop an innovative IVIF-GBWM to derive the global criteria weights. • Fuse IVIF regret theory and MABAC to evaluate alternatives. This article attempts to develop a hybrid heterogeneous framework to evaluate the disposal modes for emergency medical waste (EMW) by fusing GBWM (group best-worst method), RT (regret theory), and MABAC (multi-attributive border approximation area comparison). This hybrid framework tries to address three key challenges: (i) determining criteria weights, (ii) computing the regret-rejoice evaluation matrix, and (iii) identifying the optimal alternative. To address the first challenge, this paper innovates an innovative interval-valued intuitionistic fuzzy (IVIF) GBWM, which considers multiplicatively consistent IVIF preference relation, to efficiently determine global criteria weights (GCWs). For the second challenge, RT is incorporated to compute the regret-rejoice evaluation matrix using experts' heterogeneous evaluations which consist of intervals, triangular fuzzy numbers, hesitant fuzzy linguistic term sets and IVIF values. Regarding the third challenge, MABAC is applied to sort alternatives based on the obtained regret-rejoice evaluation matrix. Afterwards, the validity of the hybrid framework is verified by an illustrative example, and its advantages are demonstrated with some worthy sensitivity and comparative analyses. Some innovations of the proposed framework are highlighted below: (i) The IVIF GBWM streamlines calculation load, since it derives GCWs by solving the group weight assignment model only once; (ii) The introduction of RT into MABAC assists decision-makers in mitigating regret psychology, enhancing the quality of decision outcomes; (iii) The proposed framework's practicality is enhanced by leveraging heterogeneous evaluations which capture the inherent complexities of actual decision-making problems. [ABSTRACT FROM AUTHOR]

T-Spherical fuzzy sets provide a robust framework for handling uncertainty in real-world decision-making. This paper addresses the construction of T-Spherical fuzzy Heronian mean averaging aggregation operators using novel Hamacher operations. The study mathematically verifies the properties of these operators and develops new distance measures such as Hamming, Euclidean and Jaccard for quantifying dissimilarity between T-Spherical fuzzy numbers. Furthermore, the TOPSIS method is implemented using the proposed operators and distance measures to solve a practical decision-making problem in selecting the best transportation firm for medical waste disposal. A sensitivity analysis is made to assesses the efficacy of the proposed operators, while a comparison study with existing methods is exhibited to establish their efficiency. • Novel Hamacher operational laws for T-spherical fuzzy (T-SF) numbers. • New distance measures: Hamming, Euclidean, Jaccard and T-SF Heronian mean averaging operators. • TOPSIS method using proposed operators and distance measures. • Effective handling of complexities and uncertainties. • Example: selecting best transportation firm. [ABSTRACT FROM AUTHOR]