LAUSR

Linguistic intuitionistic fuzzy number (LIFN) is characterized by the degrees of membership and non-membership which take the form of linguistic variables, so it can more easily describe the vague and imprecise information existing in the real decision-making problems. Density weighted averaging operator considers the density preference of information distribution, so it can produce the more reasonable decision results. In this paper, some arithmetic aggregation operators are combined with density weighted averaging operator under the linguistic intuitionistic fuzzy environment and some linguistic intuitionistic fuzzy density aggregation operators are proposed. Firstly, the related theories of LIFN have been reviewed briefly, and the method of calculating density weighted vector and the clustering method are presented. Then, some linguistic intuitionistic fuzzy density aggregation operators, such as linguistic intuitionistic fuzzy density weighted averaging operator, linguistic intuitionistic fuzzy density ordered weighted averaging operator, and linguistic intuitionistic fuzzy density hybrid weighted averaging (LIFDHWA) operator are proposed, and some properties are discussed. Moreover, a new group decision-making method based on LIFDHWA operator is proposed. Finally, an illustrative example is used to demonstrate the validity of the proposed method.