In this article, we shall introduce picture fuzzy bidirectional projection method and some fundamental theories of picture fuzzy information. First of all, we briefly review the definition of picture fuzzy sets (PFS) and introduce the score function, accuracy function and operational laws of PFS. In addition, to fuse overall picture fuzzy evaluation information, we introduce two aggregation operators of PFS including PFWA and PFWG operators. Furthermore, the picture fuzzy bidirectional

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... n method for multiple attribute group decision making (MAGDM) is established and all computing steps are simply depicted. In our presented model, it's more accuracy and effective for considering the conflicting attributes. Finally, a numerical example for safety assessment of construction project has been given to illustrate this new model and some comparisons between bidirectional projection method with picture fuzzy numbers (PFNs) and PFWA, PFWG aggregation operators are also conducted to further illustrate advantages of the new method. INDEX TERMS Multiple attribute group decision making (MAGDM), picture fuzzy sets (PFSS), bidirectional projection method, picture fuzzy weighted average (PFWA) operator, picture fuzzy weighted geometric (PFWG) operators, construction project. 166138 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ VOLUME 7, 2019