Cosine Similarity Measure Based Multi-attribute Decision-making with Trapezoidal Fuzzy Neutrosophic Numbers

The objective of the study is to present cosine similarity measure based multi-attribute decision making under neutrosophic environment. The assesments of alternatives over the attributes are expressed with trapezoidal fuzzy neutrosophic numbers in which the three independent components namely, truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F) are expressed by trapezoidal fuzzy numbers. Cosine similarity measure between two trapezoidal fuzzy neutrosophic numbers and its properties are introduced. Expected value of trapezoidal fuzzy neutrosophic number is defined to determine the attribute weight. With these attribute weights, weighted cosine similarity measure between relative positive ideal alternative and each alternative is determined to find out the best alternative in multi-attribute
decision-making problem. Finally, a numerical example is provided to illustrate the proposed approach.