Complex T-Spherical Fuzzy Frank Aggregation Operators and Their Application to Decision Making

Abstract

Complex fuzzy (CF) sets (CFSs) play an important role in modeling two-dimensional information challenges. Researchers exploring decision-making systems have recently become interested in CFS extensions. The complex T-spherical fuzzy (CT-SF) set (CT-SFS) is a recent extension of the CFSs. The present study aims to devise the Frank operational laws for the CT-SF environment and to verify their required properties. Subsequently, some CT-SF Frank aggregation operators are explored, such as CT-SF Frank weighted averaging (CT-SFFWA) operator, CT-SF Frank weighted geometric (CT-SFFWG) operator, CT-SF Frank ordered weighted averaging (CT-SFFOWA) operator, and CT-SF Frank ordered weighted geometric (CT-SFFOWG) operator, CT-SF Frank hybrid averaging (CT-SFFHA) operator, CT-SF Frank hybrid geometric (CT-SFFHG) operator, and their peculiar cases are examined. Based on the devised operators, a novel multi-criteria group decision-making (MCGDM) methodology is investigated to tackle MCGDM problems under the CT-SF environment. Lastly, the practicality and effectiveness of the presented methodology are conducted by parameter analysis and comparative exploration.

Keywords

• Frank T-norms
• complex T-spherical fuzzy set
• aggregation operators
• MCGDM