This article introduces new aggregation operators (AOs) for multi-attribute decision-making (MADM) problems, focusing on complex T-spherical fuzzy (TSF) sets. The proposed operators, including the CTSFFPWA, CTSFFPOWA, CTSFFPHWA, CTSFFPWG, CTSFFPOWG, and CTSFFPHWG, are based on Frank t-norm (FTN) and Frank t-conorm (FTCN) operations. These operators handle periodic and two-dimensional data more effectively than existing methods, as they incorporate phase terms. The article also discusses the properties of these AOs, such as idempotency, monotonicity, and boundedness. A numerical example is provided to demonstrate the application of the proposed operators in selecting the best solar system among four options, considering attributes like power output, temperature, and size. The results are compared with existing AOs, showing the优越性 of the proposed methods in handling complex TSF information. The article concludes by highlighting the significance of the proposed CTSFFPWA and CTSFFPWG operators in MADM and their ability to handle ambiguous and periodic data.This article introduces new aggregation operators (AOs) for multi-attribute decision-making (MADM) problems, focusing on complex T-spherical fuzzy (TSF) sets. The proposed operators, including the CTSFFPWA, CTSFFPOWA, CTSFFPHWA, CTSFFPWG, CTSFFPOWG, and CTSFFPHWG, are based on Frank t-norm (FTN) and Frank t-conorm (FTCN) operations. These operators handle periodic and two-dimensional data more effectively than existing methods, as they incorporate phase terms. The article also discusses the properties of these AOs, such as idempotency, monotonicity, and boundedness. A numerical example is provided to demonstrate the application of the proposed operators in selecting the best solar system among four options, considering attributes like power output, temperature, and size. The results are compared with existing AOs, showing the优越性 of the proposed methods in handling complex TSF information. The article concludes by highlighting the significance of the proposed CTSFFPWA and CTSFFPWG operators in MADM and their ability to handle ambiguous and periodic data.