Abstract: Considering the different importance of different elements in hesitant triangular fuzzy elements as membership, the concepts of weighted hesitant triangular fuzzy elements and weighted hesitant triangular fuzzy sets are proposed, the group decision problem with decision value as weighted hesitant triangular fuzzy element is studied. Firstly, the formula of weighted hesitant triangular fuzzy distance is given. Secondly, in order to facilitate calculation and do not change the importance of triangular fuzzy numbers as membership, a method of adding elements to weighted hesitant triangular fuzzy elements is proposed. Finally, a group decision-making method based on weighted hesitant triangular fuzzy distance measurement is proposed and applied to group decision-making under the weighted hesitant triangular fuzzy environment. Numerical examples show that the weighted hesitant triangular fuzzy distance metric has rationality and feasibility in group decision making. 

Key words: hesitant triangular fuzzy set, weighted hesitant triangular fuzzy set, weighted hesitant triangular fuzzy element, distance measure, group decision-making