Free Double Hierarchy Hesitant Fuzzy Linguistic Term Sets: An application on ranking alternatives in GDM

Hesitant fuzzy linguistic term sets have been an active field of research in recent times. Notwithstanding its usefulness to capture the human way of reasoning using linguistic expressions involving different levels of precision, in some situations they do not depict enough details. In this paper, we present a new kind of linguistic term sets, called free double hierarchy linguistic term sets, and their corresponding free double hierarchy hesitant fuzzy linguistic elements, in order to describe the complexity of linguistic expressions used by the decision makers in a more accurate and precise way. Furthermore, an order and a distance between free double hierarchy hesitant fuzzy linguistic elements are introduced to present an approach based on the TOPSIS method to rank alternatives with free double hierarchy hesitant fuzzy linguistic information by taking into consideration the opinions of a group of decision makers. A case study based on tourism management in Barcelona is also provided to illustrate the usefulness of the presented approach.