The application of variable fuzzy sets theory in coastal waterway selection

Variable fuzzy set theory (VFS) has evolved into a valuable method to solve multi-criteria decision making problems under fuzzy environments. This paper is concerned with the exposition of VFS theory and its application on coastal waterway selection. First, basic conceptions of VFS theory are described including relative difference function and relative membership function with interval values. Then a variable fuzzy optimization model is presented to get ranking order of all alternatives based on VFS. Finally, an example of coastal waterway selection for Yangshan Port (Phase I) is given, and the ranking order of all alternative is deduced by VFS theory, considering the uncertainty in port authority, shipowner and society. The results show that the evaluation process is reasonable, steady and easy to use in practice, which would be widely applied in port and waterway engineering.