拓展模糊集之间的若干等价变换

On the equivalent mapping between extensions of fuzzy set theory

系统研究了模糊知识处理技术发展引起的各种模糊集拓展理论及其等价变换问题。首先给出了模糊集理论的各种拓展,如直觉模糊集、L 模糊集与L 直觉模糊集、区间值模糊集与区间值直觉模糊、Vague集等的定义与描述。重点研究了直觉模糊集到一般模糊集的变换,直觉模糊集与Vague集的等价关系,证明了利用D K算子可实现L 直觉模糊集到L 模糊集,区间值直觉模糊集到L 模糊集,区间值直觉模糊集到直觉模糊集,直觉模糊集到区间值直觉模糊集的等价变换。最后,给出了各种模糊集理论拓展形式之间联系的图示。

The extensions of fuzzy set teory emerging with the development of fuzzy techniques in knowledge processing and their equivalent mapping problems are systemically investigated. First, the definitions and descriptions of extensions of fuzzy sets, such as Intuitionistic fuzzy Sets, L-fuzzy sets and L-IFS, interval-valued fuzzy sets and IVIFS and Vague sets, etc., are presented. Then a discussion is made with the emphasis on the mapping of an IFS to a fuzzy set and the equivalence relation of IFS to Vague sets, and an equivalent mapping of L-IFSs to L-fuzzy sets, IVIFSs to L-fuzzy sets, IVFSs to IFSs, and IFSs to IVIFSs is proved by using the D-K's operators. Finally, the links between extensions of fuzzy sets are illustrated with a plot.