剩余格中的Fuzzy(P)滤子

Fuzzy(P) filters in residuated lattices

在剩余格中引入了Fuzzy(P)滤子的概念,得到A是Fuzzy(P)滤子的充要条件是当λ∈[0,1]且Aλ≠时,Aλ是(P)滤子;在正则剩余格中引入了素Fuzzy(P)滤子的概念,证明了正则剩余格中的Fuzzy(P)滤子A是素Fuzzy(P)滤子的充要条件为a、b∈L,A(a b)=A(a)∨A(b)等结论.

The concept of Fuzzy（P） filter in a residuated lattice is introduced, it is proved that A is a Fuzzy （P） filter if and only if Aλ is a （P） filter whenever λ∈ [ 0, 1 ] and Aλ ≠ Ф. Moreover, the concept of prime Fuzzy （P） filter in a regular residuated lattice is proposed and it is proved that the Fuzzy （P） filter A in a regular residuated lattice is a prime Fuzzy （P） filter if and only if ↓A a, b ∈ L, A（a＋b）= A（a） ∨ A（b）.