An optimization-based approach with minimum preference loss to fuse incomplete linguistic distributions in group decision making

The linguistic distribution is becoming a popular tool to model linguistic expressions in group decision making. Due to the knowledge limitation, it is difficult for decision makers to provide complete linguistic distribution information and partial ignorance exists in practical group decision making problems. Meanwhile, in group decision making it is hoped to find a group opinion whose distribution information is complete and the preference loss between this group opinion and individual opinions is the minimum. To tackle these issues, this paper introduces the concept of incomplete linguistic distributions and proposes a new model called the minimum preference loss model (MPLM), aiming at minimizing the preference loss between the group opinion and individual opinions in the group decision making with incomplete linguistic distributions. Finally, a numerical example is provided to demonstrate our model.