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,∈Vq,∈ Λq},时的(α,β)-区间值模糊子环,其中有意义的3种分别是(∈,∈)、(∈,∈ V q)和(∈Λq,∈)-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.
(α,β)-Interval-Valued Fuzzy Subring
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,∈ V q,∈ Λ q}are studied respectively,and the three meaningful ones are(∈,∈),(∈,∈ V q)and(∈ Λq,∈)-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 corresponding 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.
Interval-valued fuzzy pointInterval-valued fuzzy subringThree-valued fuzzy subringInterval-valued level cut set
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