Power partitioned Heronian mean operators for q-rung orthopair uncertain linguistic sets with their application to multiattribute group decision making

In this paper, a new tool, called q-rung orthopair uncertain linguistic numbers (q-ROULNs), is developed and a new multiattribute group decision making (MAGDM) method for q-ROULNs is proposed. First, the concept of q-rung orthopair uncertain linguistic sets (q-ROULSs) is introduced, and some operational laws, expected function, accuracy function, and distance measure of q-ROULSs are defined. Further, to effectively aggregate q-ROULNs, we take advantage of partitioned Heronian mean operator and power average operator and propose the q-rung orthopair uncertain linguistic power partitioned Heronian mean operator and its weighted form. The proposed operators not only deal with this situations where attributes are divided into several parts and attributes in the same part are interrelated each other, whereas attributes in different parts have no relationship, but also reduce the negative influence of unreasonable attribute values provided by decision makers on final results. Some desirable properties and special cases of the proposed operators are also investigated. Finally, a MAGDM method based on the proposed operators is developed and a numerical instance as well as comparative analysis is conducted to illustrate the effectiveness and advantages of the proposed method.