Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine

Similarity measure is an important tool in pattern recognition and fault diagnosis. This paper proposes two cotangent similarity measures for single-valued neutrosophic sets (SVNSs) based on cotangent function. Then, the weighted cotangent similarity measures are introduced by considering the importance of each element. Moreover, by the comparison between the cotangent similaritymeasures of SVNSs and existing cosine similaritymeasure of SVNSs, the developed cotangent similarity measures demonstrate their advantages and rationality and in some cases can overcome some disadvantages of the cosine similarity measure defined in vector space. Finally, the cotangent similarity measures are applied to the fault diagnosis of steam turbine. The proposed fault diagnosis method demonstrates its effectiveness and rationality by the comparative analysis with the cosine similarity measure in the fault diagnosis of steam turbine.