Affiliations: [a] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
| [b] School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
Correspondence:
[*]
Corresponding author. Zengtai Gong, College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. Tel.: +86 09317971430; E-mails: gongzt@nwnu.edu.cn and zt-gong@163.com.
Note: [1] This work was supported by the National Natural Science Foundation of China (Grant No. 61763044).
Abstract: Intuitionistic fuzzy transform is an approximate method based on the intuitionistic fuzzy partition. To begin with, a novel definition of intuitionistic fuzzy partition is given, and the properties of triangular intuitionistic fuzzy partition are also given. Secondly, the method of intuitionistic fuzzy transform is introduced, which transforms a continuous function into two gravity vectors according to the membership and non-membership functions that based on intuitionistic fuzzy partition. Some fundamental properties of intuitionistic fuzzy partition are surveyed. Thirdly, the method of inverse intuitionistic fuzzy transform is established by using the previous gravity vectors corresponding to the intuitionistic fuzzy partition. The results show that the approximate function of the original one can be rebuilt by the membership and non-membership functions respectively. even a hybrid approximate function can be rebuilt by both the membership and non-membership functions. Finally, some elementary properties of the inverse intuitionistic fuzzy transform are studied and the method is illustrated by a specific example.
