Intuitionistic Fuzzy Linguistic Numbers Geometric Aggregation Operators and Their Application to Group Decision Making

Intuitionistic fuzzy linguistic numbers (IFLNs) are an extension of the linguistic variables and the intuitionistic fuzzy sets, which are proposed by Wang and Li (Wang J.Q., Li J.J. (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Science & Technology Information (33), 8-9.). In this paper, we introduced some operational laws of IFLNs, and proposed the comparison method for IFLNs, firstly. Then, we developed an intuitionistic fuzzy linguistic numbers weighted geometric average (ILNWGA) operator, an intuitionistic fuzzy linguistic numbers ordered weighted geometric (ILNOWG) operator, and an intuitionistic fuzzy linguistic numbers hybrid geometric (ILNHG) operator which generalizes both the ILNWGA operator and the ILNOWG operator, and explored some desirable properties of these operators, such as commutativity, monotonicity, idempotency, and etc. Furthermore, we proposed a new method for the multiple attribute group decision making with intuitionistic fuzzy linguistic information based on these operators .Finally, we gave an illustrative example to verify the proposed method.