Route Selection of the Arctic Northwest Passage Based on Hesitant Fuzzy Decision Field Theory

The hesitant fuzzy set (HFS) is widely applied in actual multi-attribute group decision-making (MAGDM) problems. It can depict experts' hesitant evaluation information with the membership degree consisting of several possible values. Most existing methods based on HFSs only focus on the final integrated information by different kinds of aggregation operators but fail to provide detailed comparisons between alternatives. They are essentially result-oriented static decision-making methods, based on which, the decision-making results may be inconsistent with reality. However, there is no process-oriented research on hesitant fuzzy information. The decision field theory (DFT) is a dynamic decision-making method and can better simulate the uncertain decision-making process. Thus, this paper integrates the HFS into the DFT and proposes a new decision-making method named as hesitant fuzzy decision field theory (HFDFT) to fill this vacancy. First, we define the hesitant fuzzy momentary preference function and other parameters in HFDFT. After that, for the MAGDM problems with incompletely known attribute weight information, the programming model is used to determine the weights of attributes. Then, the group decision-making method based on HFDFT is presented. Moreover, we apply the proposed HFDFT method to a case about route selection of the Arctic Northwest Passage. Two traditional methods based on the score function and the correlation coefficient, respectively, are further implemented for comparisons to illustrate the validity of the proposed HFDFT method.