(α,β)-区间值模糊子环  

(α,β)-Interval-Valued Fuzzy Subring

作　　者：任咏红[1] 孙煜超 闫玉华 REN Yong-hong;SUN Yu-chao;YAN Yu-hua(School of mathematics,Liaoning Normal University,Dalian 116029,China;Fushun Exper Twental Primary School,Fushum 113008,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029 [2]抚顺市实验小学,辽宁抚顺113008

出　　处：《模糊系统与数学》2024年第1期54-64,共11页Fuzzy Systems and Mathematics

基　　金：辽宁省教育厅科学研究一般项目(LJ2019005)。

摘　　要：基于区间值模糊点和区间值模糊集邻属关系,给出了(α,β)-区间值模糊子环的定义.分别研究了当α,β∈{∈,q,∈∨q,E∧q},时的(α,β)-区间值模糊子环,其中有意义的3种分别是(∈,∈)(∈,∈∨q)和(∈∧q,∈)-区间值模糊子环.证明了环R上的一个区间值模糊子集分别为这3种区间值模糊子环的充要条件是其对应的区间值水平截集为环R的三值模糊子环.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(α,β)-区间值模糊子环理论.Based on the neighborhood relations between interval-valued fuzzy point and interval-valued fuzzy set,(α,β)-interval-valued fuzzy subrings are defined.(α,β)-interval-valued fuzzy subrings with α,β∈{∈,q,∈∨q,E∧q}are studied respectively,and the three meaningful ones are(∈,∈)(∈,∈∨q)and(∈∧q,∈)-interval-valued fuzzy sub-rings.It is proved that the necessary and sufficient condition for an interval-valued fuzzy subset over a ring to be an in-terval-valued fuzzy subring is that the coresponding interval-valued level cut set is a three-valued fuzzy subring.Therefore,a kind of new(α,β)-interval-valued fuzzy subring theory based on the neighborhood relations between in-terval-valued fuzzy point and interval-valued fuzzy set is established.

关 键 词：区间值模糊点 区间值模糊子环 三值模糊子环 区间值水平截集 

分 类 号：O159[理学—数学]