Some Maclaurin symmetric mean aggregation operators based on two-dimensional uncertain linguistic information and their application to decision making

Abstract

The Maclaurin symmetric mean (MSM) operator has the characteristic of capturing the interrelationship among the multi-input arguments. The two-dimensional uncertain linguistic variables (2DULVs) add a subjective evaluation on the reliability of the evaluation results given by decision makers, so they can better express fuzzy information, and the improved operational laws of 2DULVs can avoid omitting information and make the operations more accurate. In order to fully take the advantages of the MSM operator and the improved operational laws of the 2DULVs, in this paper, we extend the MSM operator to the environment of 2DULVs, and two new aggregated operators are proposed, including the MSM operator for 2DULVs (2DULMSM) and the weighted MSM operator for 2DULVs (W2DULMSM). Simultaneously, we discuss some desirable properties and special cases with respect to different parameter values in these operators. Further, based on W2DULMSM operator, an approach to multiple-attribute group decision-making problems with 2DULVs is developed. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods.