Interval-valued Hesitant Fuzzy Sets Research Articles

Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making MADM problems with hesitant interval-valued fuzzy information. We first introduce some operations on hesitant fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and propose the hesitant interval-valued fuzzy sets. Then, we further develop some new Einstein aggregation operators with hesitant interval-valued fuzzy information, such as the hesitant interval-valued fuzzy Einstein weighted average HIVFEWA operator, hesitant interval-valued fuzzy Einstein weighted geometric HIVFEWG operator, hesitant interval-valued fuzzy Einstein ordered weighted average HIVFEOWA operator, hesitant interval-valued fuzzy Einstein ordered weighted geometric HIVFEOWG operator, induced hesitant interval-valued fuzzy Einstein ordered weighted averaging I-HIVFEOWA operator and induced hesitant interval-valued fuzzy Einstein ordered weighted geometric I-HIVFEOWG operator. Then, we apply the induced hesitant interval-valued fuzzy Einstein ordered weighted averaging I-HIVFEOWA operator and induced hesitant interval-valued fuzzy Einstein ordered weighted geometric I-HIVFEOWG operator to deal with multiple attribute decision making under the hesitant interval-valued fuzzy environments. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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.