Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which the attributes are dependent and the attribute values take the forms of intuitionistic linguistic numbers and intuitionistic uncertain linguistic numbers, this paper investigates two novel MAGDM methods based on Maclaurin symmetric mean (MSM) aggregation operators. First, the Maclaurin symmetric mean is extended to intuitionistic linguistic environment and two new aggregation operators are developed for aggregating the intuitionistic linguistic information, such as the intuitionistic linguistic Maclaurin symmetric mean (ILMSM) operator and the weighted intuitionistic linguistic Maclaurin symmetric mean (WILMSM) operator. Then, some desirable properties and special cases of these operators are discussed in detail. Furthermore, this paper also develops two new Maclaurin symmetric mean operators for aggregating the intuitionistic uncertain linguistic information, including the intuitionistic uncertain linguistic Maclaurin symmetric mean (IULMSM) operator and the weighted intuitionistic uncertain linguistic Maclaurin symmetric mean (WIULMSM) operator. Based on the WILMSM and WIULMSM operators, two approaches to MAGDM are proposed under intuitionistic linguistic environment and intuitionistic uncertain linguistic environment, respectively. Finally, two practical examples of investment alternative evaluation are given to illustrate the applications of the proposed methods.