A Novel Similarity Measure Based on the Centre of Nine-point Circle of the Isosceles Triangular Fuzzy Numbers and Their Applications

A new similarity/distance measure based on the centre of nine-point circle of the isosceles triangular fuzzy numbers is recommend in this paper. Extend the similarity/distance measure based on centroid, orthocenter, circumcenter, incenter and nine-point circle center of the isosceles triangles. It is proved that this general similarity/distance measure conforms to the properties of distance. Subsequently, some examples are presented to justify the superiority and validity of the proposed similarity/distance measure between IFSs based on the center of nine-point circle, which demonstrate that this measure overcomes the disadvantage of the existing similarity measures. The application of the proposed similarity measure to deal with pattern recognition problems is described, and the results are correlated with those reported in some prevailing studies. In addition, a clustering technique to classify objects based on the proposed similarity measure is discussed. Through a detailed comparative analysis of some existing measures, it is concluded that some of the existing measures fail to discriminate the results obtained under different circumstances, such as zero division or counter intuitive cases; in contrast, the proposed similarity measure successfully overcomes this weakness.