摘要
基于模糊划分和公理化模糊集合的定义,研究公理化模糊集合的特征和分类.定义公理化模糊集合的2种规范形式:模交模糊集范式和模并模糊集范式,并证明带Zadeh算子、强否定算子的公理化模糊集合的规范形式存在定理.在此基础之上,给出带Zadeh算子、强否定算子的公理化模糊集合隶属函数的特征定理,依据特征定理给出公理化模糊集合的一种分类方式,最后分析在此分类下的类之间的关系.
Based on the definition of fuzzy partition and axiomatic fuzzy set, we study the characteristics and classification of the axiomatic fuzzy set and define two standard forms, modular intersection fuzzy set paradigm and modular union fuzzy set paradigm. We also prove theorems for existences of the normal form for axiomatic fuzzy sets with Zadeh operators and strongly negative operators. Based on this, we give the feature theorem for the axiomatic fuzzy set's membership functions with Zadeh operators and strong negative operators, and then we give a classification method of axiomatic fuzzy sets based on the feature theorem. Finally, the relationship between these classes is analyzed.
作者
张波
潘小东
谢健祥
ZHANG Bo;PAN Xiaodong;XIE Jianxiang(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,Sichuan)
出处
《四川师范大学学报（自然科学版）》
CAS
2023年第1期37-43,共7页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(61673320、61976130)
四川省应用基础研究计划项目(2020YJ0270)*。
关键词
模糊隶属空间
公理化模糊集合
隶属函数
规范形式
分类
fuzzy membership space
axiomatic fuzzy set
membership function
normal form
classification
