On fuzzy Kb sets and fuzzy Kb continuity

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