基于区间值模糊点和区间值模糊集邻属关系的区间值模糊子群  

The Interval-valued Fuzzy Subgroup Based on the Neighborhood Relation between Interval-valued Fuzzy Point and Interval-valued Fuzzy Set

作　　者：袁学海[1,2] 李洪兴[2] 宋晶晶[3] 

机构地区：[1]大连理工大学盘锦校区基础教学部,辽宁盘锦124221 [2]大连理工大学控制科学与工程学院,辽宁大连116024 [3]大连理工大学数学科学学院,辽宁大连116024

出　　处：《模糊系统与数学》2014年第1期1-8,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(90818025;61074044)

摘　　要：利用区间值模糊集的区间值水平截集的概念,给出了区间值模糊点与区间值模糊集邻属关系的定义,将这种邻属关系应用到区间值模糊代数的研究中,从而给出了(α,β)-区间值模糊子群的定义。通过研究16种(α,β)-区间值模糊子群,指出有意义的是(∈,∈)((∈,∈∨q),(∈∧q,∈))-区间值模糊子群。证明了群G的一个区间值模糊子集A为(∈,∈)((∈,∈∨q)或(∈∧q,∈))-区间值模糊子群的充要条件是对所有的λ=[a1,a2]≤[0.5,0.5],[0.5,0.5]<μ=[b1,b2],其区间值水平截集Aλ和Aμ(Aλ或Aμ)为G的三值模糊子群。从而建立了基于区间值模糊点和区间值模糊集邻属关系的新的区间值模糊子群理论。By use of the concept of interval-valued level cut set on interval-valued fuzzy set, the neighborhood relations between the interval-valued fuzzy point and the interval-valued fuzzy set are presented. By applying these neighborhood relations, the （α,β）-interval-valued fuzzy subgroups are defined. It is pointed that the significant ones in 16 kinds of （α,β）-interval-valued fuzzy subgroups are the （E,E）（∈,∈Vq）, and （∈∧q,E）-interval-valued fuzzy subgroups. It is proved that an interval- valued fuzzy subgroup A over a group G is a （E, E）-interval-valued fuzzy subgroup （∈,∈Vq）- interval-valued fuzzy subgroup, or （∈∧q ）-interval-valued fuzzy subgroup） if and only if the interval- valued level cut set Aa is a three-valued fuzzy subgroup for any ）,= [a1 ,a2]≤[0. 5,0. 5] and ）,λ= [a1 ,a2] [0. 5,0. 5] （or for any ,;t=[a1,a2][0.5,0. 5] or ）.=[a1,a2]〉[0. 5,0.5], respectively）. Therefore, we established a kind of new interval-valued fuzzy subgroup theory based on the neighborhood relation between interval-valued fuzzy point and interval-valued fuzzy set.

关 键 词：区间值模糊子集 区间值模糊点 区间值模糊集的水平截集 区间值模糊子群 三值模糊子群 

分 类 号：O159[理学—数学]