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In this study, we consider a new aspect of belief function or Dempster-Shafer theory to define a belief set and cosine similarity measure between two belief sets under uncertainty. For this purpose, firstly, the concept of belief sets will be represented as a triple vector space that is characterized by truth-belief degree, uncertainty-belief degree; and falsity-belief degree. Then, the cosine similarity measure between two belief sets is proposed to determine the degree of similarity between them. This measure is directly defined upon the framework of Dempster-Shafer theory without switching by other theories. Finally, an application of a new method in the decision-making process is provided in the medical diagnosis, when values were presented on the structure of belief set. Furthermore, a numerical example of the medical diagnosis is presented to show the effectiveness and flexibility of the proposed method.

Developed cosine similarity measure on belief function theory: An application in medical diagnosis