Abstract
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 projection 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.
Highlights
The concept of intuitionistic fuzzy sets(IFSs) was proposed by Atanassov [1], which generalized the theory of fuzzy set [2]
There are many different works related to applications of picture fuzzy sets (PFS) in MADM or multiple attribute group decision making (MAGDM) problems based on different methods and models
The final purpose is to demonstrate the application, practicality and effectiveness of the proposed MAGDM method using a case study about safety assessment of construction project and some comparisons between bidirectional projection method with picture fuzzy numbers (PFNs) and picture fuzzy weighted average (PFWA), picture fuzzy weighted geometric (PFWG) aggregation operators, picture fuzzy projection method, picture fuzzy cross-entropy method and cosine similarity measure for picture fuzzy sets are conducted to further illustrate advantages of the new method
Summary
The concept of intuitionistic fuzzy sets(IFSs) was proposed by Atanassov [1], which generalized the theory of fuzzy set [2]. There are many different works related to applications of PFSs in MADM or MAGDM problems based on different methods and models With this motivation, based on the traditional bidirectional project method [32], [33], this paper extended the bidirectional project method to handle the MADM problem under the picture fuzzy environment. The second lies in introducing several picture fuzzy aggregation operators based on a convex combination of PFNs. The third is to establish the bidirectional projection method for MAGDM problems considering both PFSs and ideal alternative matrix. The final purpose is to demonstrate the application, practicality and effectiveness of the proposed MAGDM method using a case study about safety assessment of construction project and some comparisons between bidirectional projection method with PFNs and PFWA, PFWG aggregation operators, picture fuzzy projection method, picture fuzzy cross-entropy method and cosine similarity measure for picture fuzzy sets are conducted to further illustrate advantages of the new method.
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