Implementation of Cumulative Belief Degree Approach to Group Decision-Making Problems Under Hesitancy

In multi-criteria group decision-making problems (GDM), decision-makers (DMs) may have hesitancy in their evaluations on assigning linguistic terms. Recently, the use of the Hesitant Fuzzy Linguistic Terms (HFLTs) has increased rapidly due to the flexibility it provides to DMs for representing the hesitancy in their evaluation. Using HFLTs, DMs can assign more than one linguistic term in their evaluations. There are a lot of studies in the literature for solving GDM problems with HFLTs. However, when HFLTs and other evaluation formats such as direct value assignment, classical fuzzy sets, linguistic terms, etc. are used in the same problem, the methods in the literature are limited. The Cumulative Belief Degree (CBD) approach, based on fuzzy linguistic terms and belief structure, is a solution method applied in many complex multi-criteria GDM problems under different assessment methods. In this study, a multi-criteria GDM problem in which the evaluations are provided with different evaluation formats including HFLTs is considered. A method based on the CBD approach has been developed. Specifically, the transformation formula for converting HFLTs to CBDs is proposed. The proposed method has been applied to a sales manager selection problem in the literature. The method has been shown to be convenient for GDM problems with HFLTs.