证明了坡代数(X,+,*)上所有模糊子坡代数构成的集合(SI[0,1](X,+,*),≤),所有模糊理想构成的集合(Id[0,1](X,+,*),≤),所有模糊滤子构成的集合(F il[0,1](X,+,*),≤)都是([0,1]X,≤)的子完备格,所有模糊等价关系构成的集合(Equ[0,1](X,+,*),≤),所有模糊同余关系构成的集合(Con[0,1](X,+,*),≤)都是([0,1]X×X,≤)的子完备格。给出了(SI[0,1](X,+,*),≤)、(Id[0,1](X,+,*),≤)、(F il[0,1](X,+,*),≤)以及(Equ[0,1](X,+,*),≤)中任意一族元素的下确界和上确界的构造。
This paper proves that (SI(X,+,*),≤)(the set of all fuzzy subinclines of(X,+,*)),(Id(X,+,*),≤)(the set of all fuzzy ideals of(X,+,*)) and(Fil(X,+,*),≤)(the set of all fuzzy filters of(X,+,*)) are all sub-complete lattices of(X,≤)(the set of all fuzzy subsets on X),(Equ(X,+,*),≤) (the set of all fuzzy equivalence relations on(X,+,*)) and(Con(X,+,*),≤) (the set of all fuzzy congruence relations on(X,+,*)) are both sub-complete lattices of(X×X,≤) (the set of all fuzzy subsets on X×X).Structures of the infimum and the supremum of a class of elements in (SI(X,+,*),≤),(Id(X,+,*),≤),(Fil(X,+,*),≤) and(Equ(X,+,*),≤) are also given out respectively.