Novel operations of weighted hesitant fuzzy sets and their group decision making application

Weighted hesitant fuzzy set (WHFS) is an extension of hesitant fuzzy set (HFS), in which the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. In this paper, we redefine the union and intersection operations of weighted hesitant fuzzy elements (WHFEs), investigate their operation properties, and propose the variance function of the weighted hesitant fuzzy element (WHFE) to compare WHFEs. Furthermore, we develop two aggregation operators such as weighted hesitant fuzzy ordered weighted averaging (WHFOWA) and weighted hesitant fuzzy ordered weighted geometric (WHFOWG) operators to aggregate weighted hesitant fuzzy information, and present multiple-attribute group decision making algorithm under weighted hesitant fuzzy environment. Finally, four numerical examples are used to illustrate the effectiveness of our proposed aggregation operators.