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

摘要

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.