We study the properties and relations of fuzzy pseudo-filters of pseudo-BCK algebras. After we discuss the equivalent conditions of fuzzy normal pseudo-filter of pseudo-BCK algebra (pP), we propose fuzzy implicative pseudo-filter and its relation with fuzzy Boolean filter of (bounded) pseudo-BCK algebras (pP). Then two open problems: “In pseudo-BCK algebra or bounded pseudo-BCK algebra, Is the ...

The notion of positive implicative vague ideals in BCKalgebras is introduced. A relation between a vague ideal and a positive implicative vague ideal is discussed. Characterizations of a positive implicative vague ideal are considered. 2010 AMS Classification: 06F35, 03G25, 03E72

The study of BCK-algebras was initiated by Iséki [7] as a generalization of the concept of set-theoretic difference and propositional calculus. Iséki posed an interesting problem; whether the class of BCK-algebras is a variety. In connection with this problem Komori introduced in [9] a notion of BCC-algebra which is a generalization of a BCK-algebra and proved that the class of all BCC-algebras...

In this note, we study the lattice structure on the class of all weak hyper K-ideals of a hyper K-algebra. We first introduce the notion of (left,right) scalar in a hyper K-algebra which help us to characterize the weak hyper K-ideals generated by a subset. In the sequel, using the notion of a closure operator, we study the lattice of all weak hyper K-ideals of ahyper K-algebra, and we prove a ...

In this paper rst we dene the notions of positive implicativehyper MV -ideals of types 1,2,3 and 4 in hyper MV -algebras and we investigatethe relationship between of them . Then by some examples we show that thesenotions are not equivalent. Finally we give some relations between these notionsand the notions of (weak) hyper MV -ideals and (weak) hyper MV -deductivesystems of hyper MV -algebras.

in this paper rst we dene the notions of positive implicativehyper mv -ideals of types 1,2,3 and 4 in hyper mv -algebras and we investigatethe relationship between of them . then by some examples we show that thesenotions are not equivalent. finally we give some relations between these notionsand the notions of (weak) hyper mv -ideals and (weak) hyper mv -deductivesystems of hyper mv -algebras.