Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of intuitionistic uncertain linguistic variables, some new intuitionistic uncertain linguistic Heronian mean operators, such as intuitionistic uncertain linguistic arithmetic Heronian mean (IULAHM) operator, intuitionistic uncertain linguistic weighted arithmetic Heronian mean (IULWAHM) operator, intuitionistic uncertain linguistic geometric Heronian mean (IULGHM) operator, and intuitionistic uncertain linguistic weighted geometric Heronian mean (IULWGHM) operator, are proposed. Furthermore, we have studied some desired properties of these operators and discussed some special cases with respect to the different parameter values in these operators. Moreover, with respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic uncertain linguistic variables, some approaches based on the developed operators are proposed. Finally, an illustrative example has been given to show the steps of the developed methods and to discuss the influences of different parameters on the decision-making results.