FUZZY (POSITIVE, WEAK) IMPLICATIVE HYPER BCK-IDEALS

Abstract

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