Multiple attribute group decision making based on IVHFPBMs and a new ranking method for interval-valued hesitant fuzzy information

• A new ranking method for interval-valued hesitant fuzzy sets is presented.
• We develop the interval-valued hesitant fuzzy power Bonferroni means.
• The properties of the new proposed aggregation operators are investigated.
• New approaches to multiple attributes decision making are investigated.

The interval-valued hesitant fuzzy set is a significant tool to express the uncertain information. In this paper, we define the interval-valued hesitant fuzzy 2nd-order central polymerization degree (IVHFCP2) function and the interval-valued hesitant fuzzy 2nd-order dispersive central polymerization degree (IVHFDCP2) function to further compare different interval-valued hesitant fuzzy sets. To capture much more information for the multiple attribute group decision making, we combine the Bonferroni mean with the power average operator to accommodate to interval-valued hesitant fuzzy environments and develop the interval-valued hesitant fuzzy power Bonferroni mean (IVHFPBM) and the interval-valued hesitant fuzzy weighted power Bonferroni mean (IVHFWPBM). We investigate the desirable properties of the new interval-valued hesitant fuzzy aggregation operators and discuss their special cases in detail. Finally, the new aggregation operators are applied to interval-valued hesitant fuzzy multiple attribute group decision making and a numerical example is given to illustrate the effectiveness of the presented approaches.