Decision-making model under complex picture fuzzy Hamacher aggregation operators

The paper aims are to propose a new concept called as complex picture fuzzy set (CPFS), as an extension of complex intuitionistic fuzzy set (CIFS). The addition of a neutral membership degree to the definition of CIFS makes CPFS a generalized form of CIFS. The uniqueness of this new theory lies in the capability to attain the wider range with the help of degree of neutral membership, non-membership, and membership. The range of values of membership degrees is broaden to the unit disk in a complex plane. We define elementary operations and properties of CPFSs and explore the MCDM issues with the help of CPFSs, based on Hamacher operations and some aggregation methods. Then, we introduce some operators to aggregate the CPF data, namely complex picture fuzzy Hamacher weighted averaging, ordered weighted averaging, hybrid averaging and complex picture fuzzy Hamacher weighted geometric, ordered weighted geometric and hybrid geometric operators, benefited from the basic Hamacher operations, and averaging, geometric aggregation techniques. We also construct MCDM problem using these operators and perform a calculation for the selection of best ERP system, to demonstrate the authenticity and efficiency of this manuscript. Moreover, we study a comparison to validate the consistency and superiority of our techniques.