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Multi-attribute decision making (MADM) is a hot research area in fuzzy mathematics and to deal with that, the averaging and geometric aggregation operators (AOs) are the widely used tools. The aim of this manuscript is to propose the notion of averaging and geometric AOs in the environment of T-spherical fuzzy sets (TSFSs). TSFS enables the selection of grades of memberships from considerably a larger domain and hence overcome the drawbacks of the existing fuzzy frameworks. In this paper, we develop some novel operations for TSFSs including algebraic sum, product etc. Based on new operations some averaging AOs including T-spherical fuzzy weighted averaging (TSFWA) and T-spherical fuzzy weighted geometric (TSFWG) operators are developed. The monotonicity, idempotency and boundedness of the defined operators are investigated, and their fitness is validated using induction method. With the help of an illustrative example, the problem of policy decision making using a MADM algorithm is solved. The new proposed work and the existing literature is compared numerically and the advantages of the TSFWA and TSFWG operators are investigated over existing work.