On fuzzy ΛbΛb sets and fuzzy ΛbΛb continuity

We introduce a new class of fuzzy open sets called fuzzy ΛbΛb sets which includes the class of fuzzy γγ-open sets due to Hanafy [Hanafy IM. Fuzzy γγ-open sets and fuzzy γγ-continuity. J Fuzzy Math 1999;7:419–30]. We also define a weaker form of fuzzy ΛbΛb sets termed as fuzzy locally ΛbΛb sets. By means of these new sets, we present the notions of fuzzy ΛbΛb continuity and fuzzy locally ΛbΛb continuity which are weaker than fuzzy γγ-continuity due to Hanafy [Hanafy IM. Fuzzy γγ-open sets and fuzzy γγ-continuity. J Fuzzy Math 1999;7:419–30] and furthermore we investigate the relationships between these new types of continuity and some others.