Extended Heronian Mean Based on Hesitant Fuzzy Linguistic Information for Multiple Attribute Group Decision-Making

This paper investigates the hesitant fuzzy linguistic multiple attribute group decision-making (MAGDM) problem with the heterogeneous relationship among the attribute variables that cannot be solved by most existing decision-making methods. To address this problem, a new operator is introduced based on partitioning attribute variables into different sets according to their interrelationship. This operator is called the extended Heronian mean (EHM) operator. To obtain each expert's comprehensive values of the alternatives in the hesitant fuzzy linguistic MAGDM problem, we investigate the EHM operator under a hesitant fuzzy linguistic environment and propose the hesitant fuzzy linguistic EHM operator and the hesitant fuzzy linguistic linear support degree weighted EHM operator. In addition, the axiom definition of a linguistic type similarity measure of hesitant fuzzy linguistic term sets is proposed. The weight of the experts can be determined based on this type similarity measure. Finally, a practical case is presented to demonstrate the steps of our method, and a comparison analysis illustrates its feasibility and effectiveness.