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Due to the increasing complexity and uncertainty in green supplier selection, there would be some hesitations for decision makers (DMs) to provide evaluation information of suppliers. Hesitant fuzzy set is a suitable tool to model such hesitations. This paper develops a hesitant fuzzy Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) for multi-criteria group decision-making and applies to green supplier selection. First, a new hesitancy index of hesitant fuzzy element (HFE) is defined. Then, a generalized hesitant fuzzy Hausdorff distance is proposed considering the individual deviation of membership values and the hesitancy index simultaneously. A combined hesitant fuzzy entropy is presented integrating the defined fuzziness entropy and hesitancy entropy of HFEs. Subsequently, a linear programming model is established to derive DMs’ weights objectively. To determine the criteria weights for each DM, a nonlinear programming model is built through minimizing the relative entropy. The PROMETHEE is employed to obtain individual ranking of alternatives for each DM. To obtain the collective ranking of alternatives, a multi-objective assignment model is constructed and transformed into a single-objective assignment model for resolution. Thereby, a hesitant fuzzy PROMETHEE method is presented. A green supplier selection example is demonstrated to validate the proposed method.

This paper develops a new method for group decision making with hesitant fuzzy preference relations (HFPRs) considering the multiplicative consistency and consensus simultaneously. A consistency index of HFPR is introduced and the acceptable consistent HFPR is defined. For improving the unacceptable consistent HFPR, a mathematical program is constructed to derive an acceptable consistent HFPR. Thus, an algorithm for checking and improving consistency of HFPR is proposed. A consensus index for the group is defined to measure the agreement among decision makers (DMs). To improve the consistency and consensus simultaneously, a new goal program is established to obtain a group of HFPRs with acceptable consistency and consensus. Subsequently, an interval-valued hesitant fuzzy group decision matrix (IVHFGDM) is elicited from the individual HFPRs. A positive ideal matrix, a left negative ideal matrix, and a right negative matrix are derived from the IVHFGDM. According to the relative closeness degrees, DMs’ weights are determined objectively. Afterward, the individual HFPRs are integrated into a normalized collective HFPR. It is proven that the normalized collective HFPR is acceptable consistent if all individual HFPRs are acceptable consistent. The final ranking is generated by the collective overall values of alternatives. Some examples of fuzzy decision-making applications are provided to validate effectiveness of the method.