Abstract
The paper proposes the concepts of an interval neutrosophic linguistic set (INLS) and an interval neutrosophic linguistic number (INLN) as a further generalization of the concepts of an intuitionistic linguistic set (ILS) and an intuitionistic linguistic fuzzy number (ILFN). Then, we introduce basic operational rules of INLNs and define the score function, accuracy function, and certainty function of an INLN. Furthermore, we propose an interval neutrosophic linguistic weighted arithmetic average (INLWAA) operator and an interval neutrosophic linguistic weighted geometric average (INLWGA) operator and investigate their properties, and then establish a decision-making method based on the INLWAA and INLWGA operators to handle multiple attribute decision-making problems with interval neutrosophic linguistic information. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.