FUZZY (POSITIVE, WEAK) IMPLICATIVE HYPER BCK-IDEALS

Abstract

In this note first we define the notions of fuzzy positive implicative hyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems which characterize the above notions according to the level subsets. Also we obtain the relationships among these notions, fuzzy (strong, weak, reflexive) hyper BCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7 and 8. Then, we define the notions of fuzzy (weak) implicative hyper BCK- ideals and we obtain some related results. Finally, by considering the product of two hyper BCK-algebras we give some theorems which show that how the projections of a fuzzy (positive implicative, implicative) hyper BCK-ideal is again a fuzzy (positive implicative, implicative) hyper BCK-ideal.