Application of Hamacher Aggregation Operators in the Selection of the Cite for Pilot Health Project based on Complex T-spherical Fuzzy Information

Abstract

The framework of complex T-spherical fuzzy set (CTSFS) deals with unclear and imprecise information with the help of membership degree (MD), abstinence degree (AD), nonmembership degree (NMD), and refusal degree (RD). Due to this characteristic, the CTSFSs can be applied to any phenomenon having the involvement of human opinions. This article aims to familiarize some Hamacher aggregation operators (HAOs) grounded on CTSFSs. To do so, we define some Hamacher operational laws in the environment of CTSFS by using Hamacher t-norm (HTNM) and Hamacher t-conorm (HTCNM). A few numbers of AOs are developed with the help of defined operational laws based on HTNM and HTCNM including the complex T-spherical fuzzy (CTSF), Hamacher weighted averaging (HWA) (CTSFHWA), CTSF Hamacher ordered weighted averaging (CTSFHOWA) operator, CTSF Hamacher hybrid weighted averaging (CTSFHHWA) operator, CTSF Hamacher weighted geometric (CTSFHWG) operator, CTSF Hamacher ordered weighted geometric (CTSFHOWG) operator, and CTSF Hamacher hybrid weighted geometric (CTSFHHWG) operator. Some interesting properties of developed HAOs are investigated and then these HAOs are applied to the multi-attribute decision making (MADM) problem. For the significance of these HAOs, the results obtained from these HAOs are compared with existing aggregation operators (AOs).