Multi-criteria group decision-making methods based on new intuitionistic fuzzy Einstein hybrid weighted aggregation operators

Intuitionistic fuzzy sets (IFSs) are a very efficient tool to depict uncertain or fuzzy information. In the course of decision making with IFSs, intuitionistic fuzzy aggregation operators play a very important role which has received more and more attention in recent years. This paper proposes a family of intuitionistic fuzzy Einstein hybrid weighted operators, including the intuitionistic fuzzy Einstein hybrid weighted averaging operator, the intuitionistic fuzzy Einstein hybrid weighted geometric operator, the quasi-intuitionistic fuzzy Einstein hybrid weighted averaging operator, and the quasi-intuitionistic fuzzy Einstein hybrid weighted geometric operator. All these newly developed operators not only can weight both the intuitionistic fuzzy arguments and their ordered positions simultaneously but also have some desirable properties, such as idempotency, boundedness, and monotonicity. Based on these proposed operators, two algorithms are given to solve multi-criteria single-person decision making and multi-criteria group decision making with intuitionistic fuzzy information, respectively. Two numerical examples are provided to illustrate the practicality and validity of the proposed methods and aggregation operators.