ß-FUZZY FILTERS OF STONE ALMOST DISTRIBUTIVE LATTICES

In this paper, we studied on ss-fuzzy filters of Stone almost distributive lattices. An isomorphism between the lattice of ss-fuzzy filters of a Stone ADL A onto the lattice of fuzzy ideals of the set of all boosters of A is established. The fact that any ss-fuzzy filter of A is an e-fuzzy filter of A is proved. We discuss on some properties of prime ss-fuzzy filters and some topological concepts on the collection of prime ss-fuzzy filters of a Stone ADL. Further we show that the collection T = {X-ss(lambda) : lambda is a fuzzy ideal of A} is a topology on FSpec(ss)(A) where X-ss(lambda) = {mu epsilon FSpec(ss)(A) : lambda not subset of mu}.