(α,β)-区间值模糊子格

(α,β)-interval-valued fuzzy sublattices

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.