Interval-valued hesitant preference relations and their applications to group decision making

We introduce a new type of fuzzy preference structure, called interval-valued hesitant preference relations, to describe uncertain evaluation information in group decision making (GDM) processes. Moreover, it allows decision makers to offer all possible interval values that are not accounted for in current preference structure types when one compares two alternatives. We generalize the concept of hesitant fuzzy set (HFS) to that of interval-valued hesitant fuzzy set (IVHFS) in which the membership degrees of an element to a given set are not exactly defined, but denoted by several possible interval values. We give systematic aggregation operators to aggregate interval-valued hesitant fuzzy information. In addition, we develop an approach to GDM based on interval-valued hesitant preference relations in order to consider the differences of opinions between individual decision makers. Numerical examples are provided to illustrate the proposed approach.