Multiple attribute group decision-making method based on linguistic neutrosophic numbers

Abstract

Existing intuitionistic linguistic variables can describe the linguistic information of boththe truth/membership and falsity/non-membership degrees, but it cannot represent the indeterminateand inconsistent linguistic information. To deal with the issue, this paper originally proposesthe concept of a linguistic neutrosophic number (LNN), which is characterized independently bythe truth, indeterminacy, and falsity linguistic variables. Then, we define the basic operational lawsof LNNs and the score and accuracy functions of LNN for comparing LNNs. Next, we developan LNN-weighted arithmetic averaging (LNNWAA) operator and an LNN-weighted geometricaveraging (LNNWGA) operator to aggregate LNN information and investigate their properties.Further, a multiple attribute group decision-making method based on the proposed LNNWAAor LNNWGA operator is established under LNN environment. Finally, an illustrative exampleabout selecting problems of investment alternatives is presented to demonstrate the application andeffectiveness of the developed approach.