A Hybrid Picture Fuzzy Similarity Measure and Improved VIKOR Method

Picture fuzzy set (PFS) can intuitively express the answers of “yes”, “neutral”, “no” and “reject”, which have strong advantages in solving uncertain information. The similarity measure is an effective tool to determine the relationship between two picture fuzzy sets (PFSs). In this paper, we propose a hybrid picture fuzzy (PF) similarity measure which combines the Hamming distance and the transformed tetrahedral centroid distance and verifies that it satisfies the four properties of the similarity measure. The proposed and existing picture fuzzy similarity measures are compared and investigated through numerical examples and some applications of pattern recognition. The results show that the proposed similarity measure not only produces no unreasonable results, but also overcomes the shortcomings of the existing similarity measures. Furthermore, we investigate an improved VIKOR method based on the proposed similarity measure of PFS. Finally, through an example, several multi-attribute decision-making (MADM) methods are compared and analyzed to illustrate the effectiveness and practicability of the improved VIKOR method.