Multicriteria decision-making method based on a cosine similarity measure between trapezoidal fuzzy numbers

The degree of similarity or dissimilarity between the objects under study plays an important role. In vector space, especially, the cosine similarity measure is often used in information retrieval, citation analysis, and automatic classification. However, it scarcely deals with trapezoidal fuzzy information and multicriteria decision-making problems. For this purpose, a cosine similarity measure between trapezoidal fuzzy numbers is proposed based on an extension of the cosine similarity between fuzzy sets and is applied to fuzzy multicriteria decision-making problems under the conditions that the criteria weights and the evaluated values in the decision matrix are expressed by the form of trapezoidal fuzzy numbers. Through the expected weight and the weighted cosine similarity measure between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. The proposed method is simple and effective. Finally, an illustrative example demonstrates the implementation process of the technique.