正则剩余格的模糊超⊙-理想

Fuzzy ultra ⊙-ideals in regular residuated lattices

引入正则剩余格的模糊超⊙-理想概念并考察其性质,获得了模糊超⊙-理想的几个等价刻画。在正则剩余格L的全体模糊超⊙-理想集F U(L)上定义了格运算∨,∧和逆序对合对应■,证明了当L满足条件(P)时,(F U(L),∨,∧,■,0L,1L)构成一个De Morgan代数。在F U(L)上定义了一个伴随对(■,→),证明了当L满足条件(P)时,(F U(L),■,■,→,0L,1L)也构成一个剩余格。

Firstly, the notion of fuzzy ultra ⊙-ideal is introduced and its properties are investigated in regular residuated lattices, and some equivalent characterizations of fuzzy ultra ⊙-ideals are obtained. Secondly, the lattice operations ∨,∧ and the order-reversing involution on the set （L） of all fuzzy ultra Q-ideals in a regular residuated lattice L are defined. It is proved that （ FH （L）,∨,∧ , ,0L ,1L） formes a De Morgan algebra ifL satisfies the condition （P）. Fi- nally, the adjoint pair （ , ） on （L） is defined. It is also proved that （FH （L） , , , ,0L, 1L ） formes a residu- ated lattice if L satisfies the condition （P）.