ULHHM operator and its application to group decision making with uncertain linguistic preference information

In this paper, we study multiple attribute group decision making problem with uncertain linguistic information, in which the attribute weights and expert weights take the form of real numbers, and the preference values take the form of uncertain linguistic variables. Some aggregation operator are proposed such as uncertain linguistic weighted harmonic mean (ULWHM) operator, uncertain linguistic ordered weighted harmonic mean (ULOWHM) operator and uncertain linguistic hybrid harmonic mean (ULHHM) operator. We have proved both ULWHM and ULOWHM operators are the special case of the ULHHM operator. The ULHHM operator generalizes both the ULWHM and ULOWHM operators, and reflects the importance degrees of both the given arguments and their ordered positions. An approach to multiple attribute group decision making (MAGDM) with uncertain linguistic information is developed based on the ULWHM and the ULHHM operators. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.