(untitled) (Contemporary Mathematics, 2025)
Introducing Bipolar T-Spherical Fuzzy Hypersoft Set as a hybrid extension of the bipolar fuzzy set and the T-spherical fuzzy set is a notable advancement in the fuzzy set theory. To address situations involving numerous sub-attributes, the Hypersoft set is presented as an additional generalization of the soft set. The theory of Bipolar T-Spherical Fuzzy Hypersoft Sets (BTSFHSS) with related score and accuracy functions are developed in this study to handle situations involving decision-making in a bipolar fuzzy environment with intricate attribute structures. In order to connect BTSFHSS to the fundamental algebraic structures of existing fuzzy set theories, fundamental algebraic properties and elementary theorems are established. There are many air filters that have some benefits and drawbacks compared to one another. The efficiency of air filters in lowering industrial air pollution is investigated as a real-world application. The best filter is then chosen from a range of options using a Multi-Attribute Decision-Making (MADM) technique.