Multi-attribute group decision-making based on Bonferroni mean operators for picture hesitant fuzzy numbers

The picture hesitant fuzzy sets are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets and the hesitant fuzzy sets. Their eminent characteristic is that the sum of the supremum of the membership degree, the abstinence degree, and the non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we propose the picture hesitant fuzzy Bonferroni mean operator, picture hesitant fuzzy weighted Bonferroni mean operator, picture hesitant fuzzy geometric Bonferroni mean operator, and picture hesitant fuzzy weighted geometric Bonferroni mean operator to deal with the decision information, and some important properties of these are proved. Further, based on these operators, we presented a new method to deal with the multi-attribute group decision-making problems. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing these with other existing methods.