Cosine Measures of Linguistic Neutrosophic Numbers and Their Application in Multiple Attribute Group Decision-Making

The linguistic neutrosophic numbers (LNNs) can express the truth, indeterminacy, and falsity degrees independently by three linguistic variables. Hence, they are an effective tool for describing indeterminate linguistic information under linguistic decision-making environments. Similarity measures are usual tools in decision-making problems. However, existing cosine similarity measures have been applied in decision-making problems, but they cannot deal with linguistic information under linguistic decision-making environments. To deal with the issue, we propose two cosine similarity measures based on distance and the included angle cosine of two vectors between LNNs. Then, we establish a multiple attribute group decision-making (MAGDM) method based on the cosine similarity measures under an LNN environment. Finally, a practical example about the decision-making problems of investment alternatives is presented to demonstrate the effective applications of the proposed MAGDM method under an LNN environment.