自动化学报2017，Vol.43Issue(7)：1114-1141,28.DOI:10.16383/j.aas.2017.c160638
关于二型模糊集合的一些基本问题
Some Fundamental Issues on Type-2 Fuzzy Sets
摘要
Abstract
New and revised definitions such as unit fuzzy sets,type-2 fuzzy sets (T2 FSs) and their restriction at a point are introduced by the method of set theory to make them easily understandable.All the definitions are uniform and formal,and able to represent type-2 fuzzy sets conveniently.An embedded unit fuzzy set is defined to describe general T2 FSs and the representations of discrete and partially connected T2 FSs are given as well.Based on the universes of discourse,primary membership grade,and membership function,type-2 fuzzy sets are divided into four classes:discrete,partially connected,connected,and compounded.Connected T2 FSs are further classified into two types:single connected and multi-connected.The partition method for closure of support (CoS) is used to represent the primary membership grades and interval type-2 fuzzy sets.A method of second/third partition for CoS is proposed to represent single connected/multi connected T2 FS,respectively after CoS is divided twice and three times;the upper and lower membership functions,and the restriction of the secondary membership function have same analytic expressions,respectively.Finally,the connections among the restriction of T2 FS at a point,primary membership function,CoS,embedded type-1 fuzzy set are discussed.关键词
二型模糊集合/主隶属度/支集的闭包/单位模糊集合/嵌入单位模糊集合/二型模糊集合在一点的限制Key words
Type-2 fuzzy sets (T2 FS)/primary membership grade/closure of support (CoS)/unit fuzzy set/embedded unit fuzzy set/restriction of type-2 fuzzy set at a point引用本文复制引用
王飞跃,莫红..关于二型模糊集合的一些基本问题[J].自动化学报,2017,43(7):1114-1141,28.基金项目
国家自然科学基金(61533019,71232006,61233001,61074093,61473048)资助 Supported by National Natural Science Foundation of China(61533019,71232006,61233001,61074093,61473048)100190 （61533019,71232006,61233001,61074093,61473048）
2.国防科学技术大学军事计算实验与平行系统技术研究中心 （）
长沙410073 （）
3.长沙理工大学电气与信息工程学院 长沙410114 （）
