Abstract
In a picture fuzzy environment, almost all multiple attribute decision-making (MADM) methods have been discussed a type of problem in which there is no relationship among the attributes. Although the relationship among the attributes should be considered in the actual applications, so we need to pay attention to that important issue. This article applied graph theory to the picture fuzzy set (PFS) and obtained a new method, MADM, to solve complicated problems under a picture fuzzy environment. The developed method can capture the relationship among the attributes that cannot be handled well by any existing methods. This study introduces union, intersection, sum, Cartesian product, the composition of picture fuzzy graphs (PFGs), and their important properties. Finally, by considering the importance of relationships among attributes in the determination process, two algorithms, based on PFG, have developed to solve complicated problems using picture fuzzy information. Also, two numerical examples have introduced to explain how to deal with the MADM problem under picture fuzzy environment.