Wei-Ching Chuang

Symbolic interval data analysis (SIDA) has been successfully applied in a wide range of fields, including finance, engineering, and environmental science, making it a valuable tool for many researchers for the incorporation of uncertainty and imprecision in data, which are often present in real-world scenarios. This paper proposed the interval improved fuzzy partitions fuzzy C-means (IIFPFCM) clustering algorithm from the viewpoint of fast convergence that independently combined with Euclidean distance and city block distance. The two proposed methods both had a faster convergence speed than the traditional interval fuzzy c-means (IFCM) clustering method in SIDA. Moreover, there was a problem regarding large and small group division for symbolic interval data. The proposed methods also had better performance results than the traditional interval fuzzy c-means clustering method in this problem. In addition, the traditional IFCM clustering method will be affected by outliers. This paper also proposed the IIFPFCM algorithm to deal with outliers from the perspective of interval distance measurement. From experimental comparative analysis, the proposed IIFPFCM clustering algorithm with the city block distance measure was found to be suitable for dealing with SIDA with outliers. Finally, nine symbolic interval datasets were assessed in the experimental results. The statistical results of convergence and efficiency on performance revealed that the proposed algorithm has better results.

Diffraction gratings were successfully fabricated by molding process, incorporated with the holographic technique. The high aspect ratio could be easily obtained. The polymer diffraction gratings produced by the metal mold showed the excellent diffraction effect.