In the process of decision-making , uncertain information is always challenging to deal with. T-spherical fuzzy set (TSFS) operates vagueness of data by analysing three independent functions, namely membership, non-membership, and abstinence function. The TSFS provides us robust scheme with parameter to handle the countless opportunities. Hence, this set proves its superiority over the existing picture fuzzy set (PFS) and spherical fuzzy set (SFS). Now a day, decision-makers usually assign impartial values throughout the assessment. This manuscript demonstrates some new operational laws by fusing the neutral characteristics of the degrees of membership and using the probability sum (PS) function. Meanwhile, we determine several aggregation operators (AOs) including weighted averaging neutral, ordered weighed neutral, and hybrid averaging neutral AOs to aggregate the data under T-spherical fuzzy (TSF) environment. As it came to the notice that weighted neutral averaging aggregation operators of the Pythagorean fuzzy set (PyFS), single-valued neutrosophic fuzzy set (SVNFS), and -rung orthopair fuzzy set ( -ROFS) have some restrictions during the decision-making problems. So, to overcome this, we introduce a new multi-attribute group decision-making method (MAGDM) based on proposed AOs. Lastly, we provide various numerical instances to explain the method and exhibit its supremacy. Furthermore, a comparative analysis is conducted to compare the potential of proposed AOs with some other existing methods.