Applications of T-spherical fuzzy aczel-alsina power muirhead mean operators in identifying the most effective water purification process for commercial purpose.

One of the key areas of research in ambiguous and inconsistent problems with decision-making is T-spherical multiple-attribute decision making (TP-FMADM). The TP-F number (TP-FN), which is an extension of the fuzzy number, an intuitionistic fuzzy number, and other fuzzy structures, may deal with problems involving a significant amount of incorrect, incomplete, and inconsistent data. Being an extension of various fuzzy structures, the TP-F sets (TP-FSs) provide decision-makers greater freedom to voice their actual opinions and offer a broader range of acceptable membership grades.