Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses

Objective: In pattern recognition and medical diagnosis, similariymeasure is an important mathematical tool. To overcome some disadvantages of existing cosine similarity measures of simplified neutrosophic sets (SNSs) in vector space, this paper proposed improved cosine similarity measures of SNSs based on cosine function, including single valued neutrosophic cosine similarity measures and interval neutrosophic cosine similarity measures. Then, weighted cosine similarity measures of SNSs were introduced by taking into account the importance of each element. Further, a medical diagnosis method using the improved cosine similarity measures was proposed to solve medical diagnosis problems with simplified neutrosophic information. Materials and methods: The improved cosine similarity measures between SNSs were introduced based on cosine function. Then, we compared the improved cosine similarity measures of SNSs with existing cosine similarity measures of SNSs by numerical examples to demonstrate their effectiveness and rationality for overcoming some shortcomings of existing cosine similarity measures of SNSs in some cases. In the medical diagnosis method, we can find a proper diagnosis by the cosine similarity measures between the symptoms and considered diseases which are represented by SNSs. Then, the medical diagnosis method based on the improved cosine similarity measures was applied to two medical diagnosis problems to show the applications and effectiveness of the proposed method. Results: Two numerical examples all demonstrated that the improved cosine similarity measures of SNSs based on the cosine function can overcome the shortcomings of the existing cosine similarity measures between two vectors in some cases. By two medical diagnoses problems, the medical diagnoses using various similarity measures of SNSs indicated the identical diagnosis results and demonstrated the effectiveness and rationality of the diagnosis method proposed in this paper. Conclusions: The improved cosine measures of SNSs based on cosine function can overcome some drawbacks of existing cosine similarity measures of SNSs in vector space, and then their diagnosis method is very suitable for handling the medical diagnosis problems with simplified neutrosophic information and demonstrates the effectiveness and rationality of medical diagnoses. (C) 2014 Elsevier B.V. All rights reserved.