Abstract
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.
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