关于模糊集合的公理化定义  

On the Axiomatic Definition of Fuzzy Sets

作　　者：潘小东[1] PAN Xiao-dong(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《数学的实践与认识》2022年第3期189-199,共11页Mathematics in Practice and Theory

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)。

摘　　要：基于对模糊现象的本质及其特征的深入分析,提出了关于模糊现象本质的新认识,建立了隶属度的公理系统,在此基础之上,定义了模糊划分的概念,并基于模糊划分给出了模糊集合的公理化定义.本文基于模糊隶属空间所建立的公理化模糊集合能够为从“全局”或“整体”上处理模糊信息提供一种有效的数学模型.Based on the in-depth analysis of the nature and characteristics of fuzzy phenomena,this paper puts forward a new understanding of the nature of fuzzy phenomena and establishes an axiomatic system governing membership degrees.On this basis,the concept of fuzzy partition is introduced and the axiomatic definition of fuzzy sets is given.In this paper,the axiomatic fuzzy sets establishing on fuzzy membership space can provide an effective mathematical model for processing fuzzy information from the "global" or "whole" point of view.

关 键 词：模糊现象 公理化 模糊隶属空间 模糊划分 公理化模糊集合 

分 类 号：O159[理学—数学]