Three Classes Of L-fuzzy Filters Of EQ-algebras And Their Relations

In order to develop logic Algebra and solve some problems in logic proof,the concept of EQ-algebra was put forward by Novák.EQ-algebra is a kind of special algebraic structure which contains three basic binary operations(∧,(?),～)and one maximal element 1.Filter plays an important role in all kinds of logic algebras.In this paper,the filter theory on EQ-algebra was studied and the following results are obtained.Firstly,the concepts of L-fuzzy positive implicative prefilter and L-fuzzy implicative prefilter,and L-fuzzy fantastic prefilter,and three examples of L-fuzzy prefilter were given.The relations between these three classes of L-fuzzy prefilter and prefilter were obtained by using λ-cut sets.The properties,equivalent characterizations and extension theorems of of L-fuzzy positive implicative prefilter were studied.Moreover,obtained the conclusion that L-fuzzy implicative prefilter is L-fuzzy positive implicative prefilter and so on.Secondly,the concept of(α,β]-fuzzy prefilter were proposed,and three kinds of(α,β]-fuzzy prefilter were introduced:(α,β]-fuzzy positive implicative prefilter,(α,β]-fuzzy implicative prefilter and(α,β]-fuzzy fantastic prefilter.Similarly,the properties and equivalent characterizations of the three kinds of(α,β]-fuzzy prefilters were studi-ed,the relations between these classes(α,β]-fuzzy prefilters and corresponding prefilt-ers were obtained.And there are conclusions that(α,β]-fuzzy implicative prefilter is(α,β]-fuzzy prefilter,and(α,β]-fuzzy implicative prefilter is(α,β]-fuzzy positive im-plicative prefilter.