Complex Pythagorean uncertain linguistic group decision-making model based on Heronian mean aggregation operator considering uncertainty, interaction and interrelationship

Abstract

To effectively solve the mixed problem of considering the uncertainty of individuals and groups, the interaction between membership degree (MD) and non-membership (ND), and the interrelationship between attribute variables in complicated multiple attribute group decision-making (MAGDM) problems, in this paper, a concept of complex Pythagorean uncertain linguistic (CPUL) set (CPULS) is introduced, the interaction operational laws (IOLs) of CPUL variables (CPULVs) are defined. The CPUL interaction weighted averaging and geometric operators are presented. A new concept of CPUL rough number (CPULRN) is further constructed. The CPUL rough interaction weighted averaging and geometric aggregation operators (AOs) are extended. The ordering rules of any two CPULRNs are defined. The CPUL rough interaction Heronian mean (HM) (CPULRIHM) operator and its weighted form are advanced, related properties and special cases are explored. An MAGDM model based on CPUL rough interaction weighted HM (CPULRIWHM) operator is built. Lastly, we conduct a case study of location selection problem for logistics town project to show the applicability of the proposed methodology. The sensitivity and methods comparison are analyzed to verify the effectively and superiority.