Einstein Exponential Operational Laws Based on Fractional Orthotriple Fuzzy Sets and Their Applications in Decision Making Problems

The fractional orthotriple fuzzy set (FOFS) model is a recently created extension of fuzzy sets (FS) for coping with ambiguity in DM. The purpose of this study is to define new exponential and Einstein exponential operational (EO) laws for fractional orthotriple fuzzy sets and the aggregation procedures that accompany them. We present the operational laws for exponential and Einstein exponential FOFSs which have crisp numbers as base values and fractional orthotriple fuzzy numbers as exponents (weights). The proposed operations' qualities and characteristics are then explored. Based on the defined operation laws regulations, various new FOFS aggregation operators, named as fractional orthotriple fuzzy weighted exponential averaging (FOFWEA), fractional orthotriple fuzzy ordered weighted exponential averaging (FOFOWEA), fractional orthotriple fuzzy hybrid weighted averaging (FOFHWEA), fractional orthotriple fuzzy Einstein weighted exponential averaging (FOFEWEA), fractional orthotriple fuzzy Einstein ordered weighted exponential averaging (FOFEOWEA), and fractional orthotriple fuzzy Einstein hybrid weighted exponential averaging (FOFEHWEA) operators are presented. A decision-making algorithm based on the newly defined aggregation operators is proposed and applied to a multicriteria group decision-making (MCGDM) problem related to bank security. Finally, we compare our proposed method with other existing methods.