Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making

Intuitionistic fuzzy information aggregation plays an important part in intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we investigate the multiple attribute decision making (MADM) problems with intuitionistic fuzzy numbers. Then, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, and Einstein exponentiation, and further develop some new Einstein hybrid aggregation operators, such as the intuitionistic fuzzy Einstein hybrid averaging (IFEHA) operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) operator, which extend the hybrid averaging (HA) operator and the hybrid geometric (HG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. Then, we apply the intuitionistic fuzzy Einstein hybrid averaging (IFEHA) operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) operator to deal with multiple attribute decision making under intuitionistic fuzzy environments. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.