Extensions of power aggregation operators for decision making based on complex picture fuzzy knowledge

This article puts forward an innovative notion of complex picture fuzzy set (CPFS) which is particularly an extension and a generalization of picture fuzzy sets (PFSs) by the addition of phase term in the description of PFSs. The uniqueness of CPFS lies in the capability to manage the uncertainty and periodicity, simultaneously, due to the presence of phase term which broadens the range of CPFS from a real plane to the complex plane of unit disk. We describe and verify the fundamental operations and properties of CPFSs. We introduce the aggregation operators, namely; complex picture fuzzy power averaging and complex picture fuzzy power geometric operators in CPFSs environment, based on weighted and ordered weighted averaging and geometric operators. We construct multi-criteria decision making (MCDM) problem, using these operators and describe a numerical example to illustrate the validity and competence of this article. Finally, we discuss the advantages of this generalized concept of aggregation technique and analyze a comparative study to demonstrate the superiority and consistency of our model.

Automated summary

This article introduces the innovative concept of complex picture fuzzy set (CPFS) which can handle uncertainty and periodicity simultaneously. By adding a phase term, CPFS extends its range from the real plane to the complex plane, broadening its capabilities. The fundamental operations and properties of CPFS are described and validated, and the effectiveness of CPFS is demonstrated through the construction of multi-criteria decision making problems.