New Operators for Aggregating Intuitionistic Fuzzy Information With Their Application in Decision Making

Aggregation of intuitionistic fuzzy information is a hot topic in Atanassov’s intuitionistic fuzzy set theory, which has attracted much interest from researchers in recent years. In this paper, a series of new aggregation operators and weighted averaging operators are proposed for aggregating intuitionistic fuzzy information. First, some basic laws for operations on intuitionistic fuzzy values are presented together with their properties. Then, we propose intuitionistic fuzzy weighted arithmetic averaging operator and intuitionistic fuzzy weighted geometric averaging operator to aggregate intuitionistic fuzzy information. Inspired by the idea of ordered weighted averaging and hybrid weighted averaging, we further develop intuitionistic fuzzy ordered weighted arithmetic averaging operator, intuitionistic fuzzy ordered weighted geometric averaging operator, intuitionistic fuzzy hybrid weighted arithmetic averaging (IFHWAA) operator, and intuitionistic fuzzy hybrid weighted geometric averaging (IFHWGA) operator. It is proved that all proposed weighted averaging operators have the properties of idempotency, boundary, monotonicity, and commutativity. Finally, we propose new methods based on IFHWAA and IFHWGA operators, respectively, to solve multi-attribute group decision making under intuitionistic fuzzy environment. Some examples are applied to illustrate the performance of the proposed methods. The experimental results show the effectiveness and advantages of the developed method by comparing with the other methods.