Interval valued q-rung orthopair fuzzy sets and their properties

Yager [1] introduced the concept of q-rung orthopair fuzzy sets (q-ROFSs) in which the sum of the qth exponent of the support for membership and the qth exponent of the support against membership is bounded by one. Thus, the q-ROFSs are an important way to express uncertain information in broader space, and they are superior to the intuitionistic fuzzy sets (IFSs) and the Pythagorean fuzzy sets (PFSs). However, in dealing with many real life situations, it is not appropriate for experts to precisely quantify their judgements with a crisp number due to insufficiency in available information. In such situation it is advisable for decision makers to provide their judgements by the subset of the closed interval [0, 1]. The notion of interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) is presented in this paper, which allows decision makers to provide their satisfying degrees and non-satisfying degrees to a given set of alternatives by an interval value. Some of its important operations such as: negation, union and intersection are also given. Based on these operations, the aggregation of IVq-ROFSs is also studied.