fuzzy (positive, weak) implicative hyper bck-ideals

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the notions of fuzzy (weak) implicative hyper bckidealsand we obtain some related results. finally, by considering the productof two hyper bck-algebras we give some theorems which show that how theprojections of a fuzzy (positive implicative, implicative) hyper bck-ideal isagain a fuzzy (positive implicative, implicative) hyper bck-ideal.