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Triangular Atanassov's intuitionistic fuzzy number (TAIFN) has better ability to model fuzzy ill-defined quantity. The information aggregation of TAIFNs is of great importance in multi-attribute group decision-making (MAGDM). In this paper, some arithmetic aggregation operators for TAIFNs are defined, with the triangular Atanassov's intuitionistic fuzzy weighted average (TAIFWA) operator, ordered weighted average (TAIFOWA) operator and hybrid weighted average (TAIFHWA) operator included. Then we further investigate the Atanassov's triangular intuitionistic fuzzy generalized ordered weighted average (TAIFGOWA) operator and generalized hybrid weighted average (TAIFGHWA) operator. Some desirable and useful properties of these operators, such as idempotence, monotonicity and boundedness, are also discussed. For the MAGDM with TAIFNs and incomplete attribute weight information, a multi-objective programming model is constructed by minimizing total deviation between all alternatives and fuzzy positive ideal solution, which is transformed into a linear goal programming. Consequently, the attribute weights are objectively derived. Thereby, an innovated MAGDM method is proposed on the basis of the TAIFWA and TAIFGHWA operators. Finally, a green supplier selection example is provided to illuminate the practicability of the proposed method in this paper. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]