RETRACTED: Multi-attribute decision-making method based on complex T-spherical fuzzy frank prioritized aggregation operators

Abstract

This article aims to introduce new aggregation operators (AOs) by assigning the positive real values known as priority degree among the strict priority levels. To Develop the complex T-spherical fuzzy (TSF) frank prioritized (CTSFFP) AOs, using the frank t-norm (FTN) and frank t-conorm (FTCN) operational laws, also explain sum, product, and power operations under complex TSF information. The TSF set framework has a superior structure for uncertain data handling than an existing intuitionistic fuzzy set (FS), Pythagorean FS (PyFS), q-rung orthopair FS (q-ROFS), picture FS (PFS), and spherical FS (SFS). Because the structure of the TSF set has the most generalized form of IFS, PyFS, q-ROFS, PFS, and SFS, it provides greater freedom to decision experts for handling information where these discussed sets fail to aggregate ambiguous details. Utilizing the idea of priority degree, proposed new AOs called CTSFFP weighted averaging (CTSFFPWA), CTSFFP ordered weighted averaging (CTSFFPOWA), CTSFFP hybrid weighted averaging (CTSFFPHWA), CTSFFP weighted geometric (CTSFFPWG), CTSFFP ordered weighted geometric (CTSFFPOWG), CTSFFP hybrid weighted geometric (CTSFFPHWG) operators. Some desirable properties of AOs, such as idempotency, monotonicity, and boundedness, are also discussed. To show the importance of proposed AOs, the real-life problem of multi-attribute decision-making (MADM) is solved with the help of developed CTSFFPWA and CTSFFPWG operators. To enhance the proposed AOs' superiority, compare the diagnosed theory with existing AOs and give conclusions.

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