A novel distance between single valued neutrosophic sets and its application in pattern recognition

Among the most classic measures in single valued neutrosophic sets ( SVNS ) theory, the distance is an important tool to compare and calculate degree of difference between SVNS . Although there exist some types of distance for single valued neutrosophic sets, most of them lack of strictly axiomatic definition and exist counter-intuitive cases. In this paper, a novel distance between single valued neutrosophic sets based on matrix norm is given. Then we proved that the new distance satisfies the axiomatic definition of the metric. Finally, the distance is applicated to pattern recognition and medical diagnoses.