Affiliations: [a]
College of Mathematics and Software Science, Sichuan Normal University, Chengdu, P.R. China | [b]
School of Business, Sichuan Normal University, Chengdu, P.R. China
Correspondence:
[*]
Corresponding author. Zengxian Li, College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, P.R. China. E-mail: lzx_cd2017@163.com.
Abstract: In this paper, we extend the Hamming distance, the Hausdorff distance with Pythagorean fuzzy sets (PFSs) to define the generalized Pythagorean fuzzy normalized Hamming distance, the generalized Pythagorean fuzzy normalized Hausdorff distance and the generalized hybrid Pythagorean fuzzy normalized distance. According to the relation between distance and similarity measure, we can obtain similarity measure. Furthermore, we study the Pythagorean fuzzy weighted distance and similarity measures. On the basis of the set-theoretic approach, the matching function, the notion of complement and the continuous functions, we extend other similarity measures. In the end, we utilize an applicable example to prove the proposed methods.
Keywords: Hamming distance, Hausdorff distance, Pythagorean fuzzy sets, hybrid Pythagorean fuzzy normalized distance, the set-theoretic approach, the matching function, the notion of complement, the continuous functions
