An approach to multiple attributes decision making with hesitant interval-valued fuzzy information and its application

In this paper, we investigate the multiple attribute decision making (MADM) problems with hesitant interval-valued fuzzy information. We first introduce some operations on the hesitant interval-valued fuzzy sets. Then, we further develop some new Einstein aggregation operators based on the Choquet integral with hesitant interval-valued fuzzy information, such as the hesitant interval-valued fuzzy Einstein correlated averaging (HIVFECA) operator and hesitant interval-valued fuzzy Einstein correlated geometric (HIVFECG) operator. Then, we apply the hesitant interval-valued fuzzy Einstein correlated averaging (HIVFECA) operator and hesitant interval-valued fuzzy Einstein correlated geometric (HIVFECG) operator to deal with multiple attribute decision making under the hesitant interval-valued fuzzy environments. Finally, an illustrative example for evaluating the quality of physical education class in universal institutions is given to verify the developed approach.