Spherical uncertain linguistic Hamacher aggregation operators and their application on achieving consistent opinion fusion in group decision making

The aim of this research is to establish a new type of aggregation operator based on Hamacher operational law of spherical uncertain linguistic numbers (SULNs).

First, the authors define spherical uncertain linguistic sets and develop some operational laws of SULNs. Furthermore, the authors extended these operational laws to the aggregation operator and developed spherical uncertain linguistic Hamacher averaging and geometric aggregation operators.

The authors were limited in achieving a consistent opinion on the fusion in group decision-making problem with the SULN information.

In order to give an application of the introduced operators, the authors first constrict a system of multi-attribute decision-making algorithm.