(α,β)-区间值模糊子格  

(α,β)-interval-valued fuzzy sublattices

作　　者：任咏红[1] 孙煜超 闫玉华 REN Yonghong;SUN Yuchao;YAN Yuhua(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2022年第4期433-440,共8页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学技术研究项目(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)-区间值模糊子格的定义.分别研究了当α,β∈{∈,q,∈∨q,∈∧q}时的(α,β)-区间值模糊子格,其中,有意义的3种分别是(∈,∈)-区间值模糊子格、(∈,∈∨q)-区间值模糊子格和(∈∧q,∈)-区间值模糊子格.证明了格L上的一个区间值模糊子集分别为这3种区间值模糊子格的充要条件是其对应的区间值水平截集为格L的三值模糊子格.Based on the neighborhood relations between the interval-valued fuzzy point and the interval-valued fuzzy set,the(α,β)-interval-valued fuzzy sublattices were defined.The(α,β)-interval-valued fuzzy sublattices were studied when α,β∈{∈,q,∈∨q,∈∧q}respectively,and the meaningful ones are the(∈,∈),(∈,∈∨q)and(∈∧q,∈)-interval-valued fuzzy sublattices.It was proved that an interval-valued fuzzy subset on lattice L is the three kinds of interval-valued fuzzy sublattices respectively if and only if its corresponding interval-valued horizontal cut set is the three-valued fuzzy sublattice of lattice L.

关 键 词：区间值模糊点 区间值模糊子格 三值模糊子格 

分 类 号：O159[理学—数学]